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Building New Course Structures

6 Teaching Undergraduate History: A Problem-Based Approach

Robert K. Poch and Eskender Yousuf

problem solving, historical thinking skills, learning assessment

Introduction

Among the challenges that faculty encounter is facilitating active engagement with their discipline within classrooms of diverse undergraduate students (Calder, 2006; Rendon, 2009). We face this challenge regularly when teaching history. Within a mostly lecture-based format, it is easy to deny students opportunities to engage the discipline as historians.

While we concentrate primarily on the discipline of history, this approach can be applied within other disciplines where the aim is to provide diverse undergraduate students with the opportunity to “do” the work of those disciplines and find personal connection within them.  Historians discover and use primary source documents, confront vexing contextual and interpretational problems, experience the diverse perspectives of peers, and so too can students. For many faculty, the temptation in undergraduate survey courses is to place full emphasis on content coverage and to ignore or minimize development of discipline-based skills (Calder, 2006; Sipress and Voelker, 2009). This produces poor results if our instructional goals include providing a more genuine experience with our discipline, developing analytic skills, and engaging students meaningfully (Weimer 2002). When students are passive recipients of disciplinary information with no apparent connection to themselves, they withdraw intellectually and emotionally (Freire 1970; Langer 1997).

However, it is possible for highly diverse students to experience the dynamic nature of disciplines such as history by “doing” – that is, by actively developing the skills and engaging the processes and problems involved in being a practitioner of the discipline (Sipress and Voelker, 2009; Weimer, 2002). This can happen in large and small classes and also in survey courses. We want students to encounter history as historians. We also want them to experience the excitement of historical discovery and personal meaning-making that first drew us into the work. In doing so, students also learn and retain substantive course content.

We focus below on a “problem-based” approach to teaching and learning history where students are active disciplinary practitioners engaged in addressing problem topics of relevance and connection to their diverse lives. In doing so, the following questions are addressed:

  • What are some of the core elements of historical inquiry? What do skilled historians actually do?
  • What actions encourage students from different cultural and disciplinary backgrounds to engage the core elements of historical inquiry as practitioners?
  • How can course pedagogy, assignments, and assessments become consistent with what skilled historians do and foster student engagement?
  • How can the results of these efforts be assessed? What are some of the assessment results from using a problem-based approach to learning history?

While we concentrate primarily on the discipline of history, this approach can be applied within other disciplines where the aim is to provide diverse undergraduate students with the opportunity to “do” the work of those disciplines and find personal connection within them (Gurung, Chick, and Haynie, 2009).

Identifying and Using Core Elements of Historical Inquiry

In creating learning environments where students become historians, it is necessary to consider what it is that historians do and what skills are necessary to be practitioners of the discipline. In a macro sense, many historians describe their work as problem solving guided by active questioning (Elton, 1967; Fischer, 1970; Marius and Page, 2005; Nevins, 1963). That is, questions are posed; sources and facts are collected, critically read, contextualized, and organized; and, an interpretation of the past is formed while recognizing that the complexities of history defy easy explanations (Ayers, 2006; Commager, 1965; Wineburg, 1991, 1999). Whenever possible, historians utilize primary sources to form their own interpretations rather than relying mostly on the interpretations of other historians.

Historians are regularly challenged to analyze, contextualize, and interpret the past from incomplete disparate sources. Such actions require a series of more discrete skills including the critical evaluation, interpretation, and communication of evidence; the detection of bias; and careful consideration of historical causation (Ayers, 2005; Barzun and Graff, 1977; Bloch, 1953; Carr, 1961; Commager, 1965; Elton, 1967; Evans, 1999; Fischer, 1970; Lerner, 1997; Nevins, 1963; Wood, 2008). These skills are expressed concisely as the “5Cs” of historical thinking: “change over time, causality, context, complexity, and contingency” (Andrews and Burke, 2007, 1).

Through using the 5Cs, students become increasingly aware of how much can change over time – such as political systems, landscapes, and social values – while, simultaneously, acknowledging retention of strong elements of the past such as holidays and the rituals surrounding them. Further, once developed through classroom engagement with historical sources, the elements of causality, context, complexity, and contingency enable students to identify and appreciate the incomplete nature of historical records and the intricate, simultaneous, and broad scale human interactions and competing interests in history (Ayers, 2006; Nevins, 1963; Wood, 2008). The awareness of complexity causes professional historians and students to probe more deeply into explanations of causality and to reject simplistic reasoning.

To have students engage history problems in a manner that is relevant and meaningful, it is necessary to also think carefully about how to invite students and their interests into the process of historical inquiry. While engineering, mathematics, physics and accounting are experienced as real, relevant, and practical, history is not experienced that way. Students often encounter it as an abstruse, fact-laden, memorization-based, irrelevant, impersonal discipline. We must, therefore, address how to engage students in being practitioners of historical inquiry and interpretation. These are some of the key components of the real work of historians and the historical reasoning used to create interpretations of the past. In working with undergraduate students – some of whom just graduated from high school – the 5Cs are a useful, understandable, and easy to remember toolset for engaging historical inquiry. With these parts of the work of historians and historical thinking in mind, it is possible to design classroom experiences that bring students into the dynamic nature of this work and its associated challenges. Students can then experience the discipline of history more fully and also learn how to create their own historical meaning from available sources (Sipress and Voelker, 2009). These components of historical thinking help to form the “history problems” that we utilize in our U.S. history classroom and which we describe further below.

However, to have students engage history problems in a manner that is relevant and meaningful, it is necessary to also think carefully about how to invite students and their interests into the process of historical inquiry. While engineering, mathematics, physics and accounting are experienced as real, relevant, and practical, history is not experienced that way. Students often encounter it as an abstruse, fact-laden, memorization-based, irrelevant, impersonal discipline. We must, therefore, address how to engage students in being practitioners of historical inquiry and interpretation.

Engaging Students in Core Elements of Historical Inquiry as Practitioners

The invitation to participate in our class, “America’s Past and Present: Multicultural Perspectives,” is underscored by bringing students into direct interaction with historical thinking skills, primary source materials that are reflective of multiple cultures on the American landscape, and with complex historical issues and problems that invite students to interpret history with their own voices rather than having a textbook or the instructor be the sole interpretive voices. We want students to gain more elegant and inclusive views of history that expose the complex dynamics between people over time and which stimulate curiosity about how life was experienced and interpreted by different diverse populations. This is enabled in part by the diversity of our students. The multiple complexities of persons in the past are reflected in our students. As observed by Lee, Poch, Shaw, and Williams (2012),

“…we have observed our institution’s student population become increasingly diverse in terms of racial and ethnic demographics. Historically, generalized categories of racial and ethnic identity have become more diffuse and complex. We are also more mindful of the often less visible forms of difference that are present in any learning environment, such as socioeconomic status, sexual orientation, religion, disability, and many others”

As students engage each other in class and discover how their classmates form different historical interpretations based in part on their different lived experiences, it stimulates and reinforces an understanding of the different perspectives and lived experiences of persons throughout history.

To better ensure the relevance of the history problems to diverse student interests, students are asked on the first day of the course what part of U.S. history between the Civil War and present time is of greatest interest to them. While some students do not know how to answer such a question at first, many others have some notion of their interests. Examples of these student responses from spring semester 2015 are as follows:

  • World War II
  • U.S. Civil Rights movements (including the role of youth in such movements)
  • Vietnam War
  • The Great Depression
  • 9/11 and its effect on the world
  • Other countries and perceptions of the U.S.
  • Native Americans and Tribes
  • Civil War & differing economies

When we, as instructors, are responsive to such interests, students more fully engage with the topics and are willing to invest the energy to do the challenging work of historical meaning-making using disciplinary thinking skills. These interests are invaluable in making the course ours – that is, a shared experience of historical investigation that reflects mutual interests rather than those of the instructor alone. It is a powerful opportunity to communicate to students at the beginning of the course that the instructors are engaged co-investigators of historical topics that the students suggest and that student interests are of great value. We use student historical interests to create substantive class discussion questions, short reading and writing assignments, and further engagement with historical thinking skills through lengthier history problems that come later in the semester. While assembling sources related to the interests, we spend the first three to four weeks of the course introducing and practicing the 5Cs of historical thinking. Initial reading and writing assignments selected before the course starts enable students to begin the process of understanding, recognizing, and using context, causality, complexity, change and continuity over time, and contingency. These historical thinking skills are then used to explore more deeply and intentionally the historical topics that students suggest. In doing so, student interests become integrated and useful parts of the course experience.

Students also tell us that they want to explore historical themes and issues that are not commonly approached in historical texts or rooted in fact memorization. For example, one student expressed in a topical interest survey that she wanted “…to learn the truth about history. The real original text. I want to find it and research it. Interest in causality and what caused all the events in history to happen? WHYYY! The reason things went down the way they did!” Students express that they want to explore the meaning and use of racism, the rise of feminism, and the perspectives of other nations whose histories intersect with those of the United States. They want to do so in a way that engages history through interesting questions full of encounters with ordinary people who experienced the past in powerful but mostly unknown ways. When we, as instructors, are responsive to such interests, students more fully engage with the topics and are willing to invest the energy to do the challenging work of historical meaning-making using disciplinary thinking skills.

Making Pedagogy, Assignments, and Assessments Consistent with what Historians Actually Do

Engaging students as historians takes careful thought and planning. Core elements of course design are important parts of this work. The course curriculum must provide space for the development of student evaluative and interpretive skills. This often comes with winnowing some course content as traditionally delivered through lengthy lectures (Calder, 2006). The process of winnowing involved using part of a summer break to critically review course materials to identify where unnecessary content was located that cluttered class time and reduced the capacity to develop student historical thinking skills. For example, a discussion of Civil War medicine and pro- and anti-U.S. imperialist arguments were removed given that they were peripheral to more important course themes. Further, those subjects tended to lead to more lecturing rather than active discussion. Rendon (1993) observed that “…many culturally diverse students do not learn best through lecture. Instead, we should focus on collaborative learning and dialogue that promote critical thinking, interpretation and diversity of opinion” (10).

Students can mine rich primary sources of the period as guided by research questions collaboratively developed by students and the instructor. Lectures are balanced with skill-building by doing – actively engaging students in learning how to develop researchable questions, engaging primary and secondary texts with critical lenses, forming interpretations from available evidence, and presenting results. Further, significant thought must be invested in designing course assignments and resources that enable skill development to occur and be assessed. Assessments must be constructed to evaluate student work in a manner consistent with skill development expectations. Class time invested in developing the foundational skills used within the discipline is necessary given that “…history teachers cannot simply present students with documents, tell them what to do, and then expect magical gains in the development of students’ historical sense. Much more elaborate and carefully thought out ‘scaffolding’ is needed to realize the potential of this approach” (Calder et al., 2002, 59).

This approach has significant student developmental implications. It may involve moving students and the course structure away from a dualistic form of learning history where questions are framed in terms of right and wrong response outcomes and there is strong dependency upon the instructor. Instead, there will be movement toward a course design wherein students are met with formulating questions within a course-related area of personal historical interest that has interpretive complexities associated within it (Donald, 2002, 3; Evans et al, 2010).

For example, rather than presenting students with a course design that asks them to identify within an exam three major outcomes of Reconstruction after the U.S. Civil War from lecture notes, students can experience the real problems of Reconstruction in depth by reading conflicting newspaper accounts in the North and the South regarding the political enfranchisement of African American men and the political balances of power that were at play (Langer, 1989). Rather than searching secondary and tertiary sources (such as many textbooks and lectures) alone for such information, students can mine rich primary sources of the period as guided by research questions collaboratively developed by students and the instructor. One research question that was developed in this manner focused on the tactics that some southern states utilized to stymie the voting capacity of black males following passage of the Fifteenth Amendment. In response, students were able to find and analyze different literacy tests for voting (the class even tried taking some of the tests which produced a high failure rate) and also details on the administration of poll taxes.

Such collaboration and student interpretive responsibilities can lead to movement from what psychologist Ellen Langer refers to as “mindlessness” wherein students are stuck with rote memorization and the search for the “right” answer rather than experiencing the rich contexts and possibilities that exist as part of the act of discovering and making meaning within disciplines (Langer, 1997). Langer notes that, “In math, teaching for understanding involves teaching students to think about what a problem means and to look for multiple solutions. Studies have confirmed that science is better taught through hands-on research and discovery than through memorization alone. In English, teaching for understanding means emphasizing the process of writing and exploring literature rather than memorizing grammar rules and doing drills. Understanding is encouraged in history by turning students into junior historians” (Langer, 1997, 71, 72). It is in that spirit that we developed history problems.

History Problems

 “As an interpretive historian using the primary source readings that are provided in this problem, how do you define Jim Crow?” This question, which seems deceptively simple at first, quickly exposes the complexities of Jim Crow as a comprehensive system within American society that touched every aspect of life. Each history problem is comprised of three essential parts: an introduction to the problem with concise contextual information; open-ended problem questions designed to provide students with interpretive space to utilize their voice and perspectives (rather than the instructor’s voice or that of the textbook); and a set of primary source materials that reflect diverse authors and views. Students are given three history problems throughout the semester and they have approximately four weeks to complete them given the complexity of the readings. Although there is no required page length for the problem responses, students often write seven pages or more for each problem. The history problems used during the Spring 2015 semester were based on student interests expressed at the beginning of the semester and involved the following topics: “The challenges of Jim Crow and the dynamics found within it;” “’Equal protection under the law:’ The challenges of separate but equal – The struggle for Brown v. Board of Education ;” and, “September 11, 2001.”

The history problem questions provide students with the ability to create responses based on their own interpretation of the material. The questions replicate real challenges and problems for historians that are consistent with the 5Cs of historical thinking that we use in class. Some questions expose students to the complexities of powerful systems of racial oppression such as Jim Crow. Other questions focus on establishing context or examining change over time. For example, in the problem examining Jim Crow, students were asked the following: “As an interpretive historian using the primary source readings that are provided in this problem, how do you define Jim Crow?” This question, which seems deceptively simple at first, quickly exposes the complexities of Jim Crow as a comprehensive system within American society that touched every aspect of life.

To assist in developing a definition of Jim Crow, the history problem packet includes a variety of primary sources that include memoirs, excerpts from scholarly books and novels, and a 1949 travel guide for African American motorists. Within this particular problem packet, the sources included pieces from W.E.B. Dubois’ The Souls of Black Folk (1903); Ralph Ellison’s Invisible Man (1952); John Hope Franklin’s autobiography, Mirror to America (2005); Howard Thurman’s The Luminous Darkness: A Personal Interpretation of the Anatomy of Segregation and the Ground of Hope (1965); Richard Wright’s Uncle Tom’s Children (1940); and, The Negro Motorist Green Book (1949). The Green Book was published to provide African American travelers with “…information that will keep him from running into difficulties, embarrassments and to make his trips more enjoyable” (1). These sources provided different views of and experiences with Jim Crow and, unlike a textbook, did not provide the definition and interpretation of Jim Crow for the students. Instead, the students worked with the different texts, situated them contextually in their particular time and place and with consideration of who wrote them, and gradually developed their own definition of Jim Crow. Further, the sources spanned a number of decades so that some consideration could be given to change over time in addition to complexity. The sources worked well in providing multiple perspectives of how Jim Crow, as a system, affected different parts of life and also a sense of the varieties of materials that historians use.

The same history problem also asked students to consider how the sources in the packet related to any prior readings we had used in the course (such as Frederick Douglass’ 1865 speech, “What the Black Man Wants”), so that students could further analyze and gain familiarity with context, change over time, complexity, contingency, and causality. Douglass’ speech was useful not only as an earlier expression of the challenges and contradictions that Jim Crow created within a nation that professed freedom and democracy, but also served as a source to explore the challenging concept of contingency. By expressing how black men wanted political participation through receipt of the right to vote and full recognition for their intellectual capacity to be informed contributors to democracy, Douglass’ speech highlighted contingencies necessary for breaking explicit bonds of enslavement and more diffuse societal systems of oppression. These varied course and problem-based primary sources enabled students to make complex connections between forms of evidence and further solidified historical thinking skills as expressed within the 5Cs. Providing approximately four weeks to work with each history problem gave plenty of in-class time to further discuss the sources, the context of the sources, and to practice the skills necessary to utilize them effectively.

Assessing the Results of Using a Problem-Based Approach to Learning History

We utilized several forms of assessment to evaluate the problem-based approach to learning history: 1) the evaluation of student written responses to history problems, 2) individual interviews with students, and, 3) an independently conducted end-of-semester student survey. In each assessment approach, it was important that student voices were prominent and listened to attentively (Patton, 1980). Each of these assessment forms is discussed below.

Written responses to history problems

Student written responses to the four history problems were evaluated carefully for progressive use of the elements of historical thinking. Each of the papers went through two evaluative reviews – one by the course teaching assistant and the other by the primary instructor. The papers were scored on a standard A-F grading scale and were preceded by smaller writing assignments that practiced discrete elements of five identified historical thinking skills. For example, the Frederick Douglass speech, “What the Black Man Wants,” was used early in the semester in part so students could practice establishing and expressing context and recognizing some elements of contingency. This was done with multiple other pieces of short reading and writing exercises that involved the voices and writing of diverse speakers and authors. With this practice experience in place, students could move with greater confidence in addressing contextual issues in the first history problem and those that followed. The papers were also useful in assessing student command or struggle with certain components of historical thinking. We discovered in multiple early papers that students did not fully understand the idea of contingency and, in response, were able to spend more time discussing and practicing it in class.

Toward the end of the semester as students worked with perhaps the most challenging history problem involving the September 11, 2001 attacks, we could detect that students were engaging in far more sophisticated historical reasoning and explicit use of historical thinking skills. For example, one student, a freshman, having studied the presence and role of the United States in the Middle East since the early twentieth-century (using maps, documents, interviews, reports, and political cartoons provided in the fourth history problem), constructed a complex contextual background in her written response to one set of the problem questions (“Using information from our class sessions and the materials provided within this problem packet, describe the relationships that existed and some of the events that occurred between the United States and the ‘Middle East’ region prior to 9/11. With these sources in mind, what are some of the possible motives for the 9/11 attack?”). She responded in part in her introduction,

The events of September 11th, 2001 came as a shock to millions of American citizens; however, a complex history of rocky foreign relations combined with the struggles regarding religion and government in the ‘Middle East’ suggest that the attack was only one part of several interconnected issues. As we examine the context of the events surrounding the 9/11 attacks, the complexity of the United States’ position in world affairs, the major causes leading up to the attack, and contingency of other nations’ histories on our own, we can begin to analyze the affect that each of these has had on the aftermath of 9/11 over time… [the] ten to fifteen years before the attacks on the Twin Towers… show a deeply complex relationship between different nations. While the Saudi Arabian government aided the United States [in the Gulf War by providing a U.S. military staging ground along the border with Kuwait] there were other entities such as Iraq that were pitted against the United States, resulting in conflict between the nations in that area regarding involvement of the United States. To add to this complexity is the idea of a theocracy and questions on how to rule a nation when military forces within those nations do not share the political philosophy or religious beliefs of those nations.

In this brief excerpt which was supported by lengthier supporting text and examples, we could easily detect the use of historical thinking skills (some of which were explicitly mentioned), including greater recognition of the deep complexities that long preceded the events of 9/11.

The written responses to the history problem questions were returned to the students with evaluative comments that served, in part, to prepare students for individual meetings with the course instructor and the graduate research assistant. With highly diverse students from different nations, it was important to provide different opportunities for the students to express how they approached the problems that extended beyond their written responses.

Individual meetings with students about the history problems

Individual student interviews were conducted on two of the problem set essays (history problems one and three). Each student was given the opportunity to schedule a conversation with us to discuss their responses and to further sharpen their historical thinking skills based on the 5Cs. During these meetings, the students could gain additional points (but no subtraction of points) by further clarifying their written responses and the processes that they used to construct them. The meeting questions were provided to each student in advance and included: Where did you encounter the greatest challenges in responding to this history problem? How did you approach the challenges? What do you believe you learned through engaging in this history problem? An opening question was designed to further probe each student’s writing by asking: “We found some engaging interpretations within your paper [if this was truthful] and also some places where we would like to know more. Can you further describe [this was customized for each student paper]….” The questions presented opportunities for students to further explain their own interpretations and how they approached the problems over time. Through the questions, students reflected on and expressed their own historical interpretations in a manner that replicates much of the way that historians utilize peers within their professional communities.

Within the second set of individual meetings on the third history problem, students began to express more of the 5Cs of historical thinking. During the first set of interviews regarding the “Challenges of Jim Crow and the dynamics found within it,” we met individually with twenty-three students who expressed a wide array of historical thinking skills. For example, one student, in expanding upon her interpretation of Jim Crow, remarked that developing her own definition of Jim Crow enabled her to “…go far below the surface to see the complexity of Jim Crow and its relationship to definitions of racism.” Further, the student explained that examining the use of Jim Crow-related art revealed to her the complex strategies of Jim Crow systems of oppression. Another student observed that reading primary source accounts of African Americans who lived within Jim Crow brought forth “contradictions” within the imagery and terms used within Jim Crow such as using ideas of “light” and “visibility” to describe American society while those who lived under the weight of Jim Crow described darkness, shadows, and invisibility. Within these comments, and many others, we observed students expressing different elements of historical thinking including complexity (very explicitly), as well as change over time, and causality as students considered and described the structures of Jim Crow messaging and how the messaging was delivered in different ways during specific spans of time.

Within the second set of individual meetings on the third history problem, students began to express more of the 5Cs of historical thinking. We used a slightly modified set of questions that included: Did you feel that you were able to utilize any particular historical thinking skills in this problem? Students commented more extensively and easily about historical thinking skills and demonstrated within their papers greater complexity in historical thinking. For example, one student expressed complex differences in how African American’s responded to racial oppression over time. She interpreted primary sources in the first history problem as being “defensive in nature – how persons responded or protected themselves within the Jim Crow system” whereas in the third history problem on the legal strategies that African American attorneys used to eventually prevail in the Brown v. Board of Education decision, the strategy was “more offensive in nature in that it showed black persons taking back their rights and being more confident in doing so.” This student, and others, expressed greater awareness and mastery of complexity, causality, and change over time in their interpretations of primary historical source materials.

Independently conducted end-of-semester student survey

At the request of the instructor, a grant-supported survey was developed and given to students in the history course at the very end of spring semester 2015. Among those who responded to the survey (50% of a class of 24 first-year students where this problem-based approach was fully implemented), the following are representative of their responses:

Question: What parts of the course were particularly effective for you in developing historical thinking skills and the capacity to be an effective historian? What parts were particularly ineffective?

  • “The parts of this course that were effective in developing historical thinking skills were definitely the history problems and also the 5Cs. I learned so much through the history problems that I would have never learned through a test and I will remember the information much better by writing about it in a history problem. I didn’t feel like any part was ineffective.”
  • “The history problems were effective because they allowed us to give our own opinion on the matter and we got involved instead of just mindless memorization.”
  • “I think that the most effective things that we did in class to develop my historical thinking skills were definitely the problem sets and our class discussions. Both of those two platforms pushed us to think for ourselves and contribute to a larger group discussion. I loved the problem sets because they forced me to think and form my own opinions using the historical thinking skills that we were given.”
  • “The history problems really helped me see how contemporary historians actually applied their skills to modern problems.”

Question: Do you believe that you know and can apply the essential elements of historical thinking, as a result of this course? Please explain.

  • “Yes, I have already applied it to other classes and feel very comfortable doing it.”
  • “Yes, the history problems gave us that opportunity.”
  • “I do believe that I could apply the elements of historical thinking into other classes and in my everyday life as a historian. I feel confident that I know the 5Cs of historical thinking and could use them in other situations. They were drilled into us, I won’t forget them.”
  • “Yes. I believe that using the 5Cs from the beginning of this course helped me to gain further knowledge and also to help me dig deeper into historical problems and questions.”
  • “I definitely feel that this course has aided my skills in critical analysis and historical thinking and I can see how to use these skills in different contexts and subjects besides history.”

Student survey responses found that 1) history thinking elements of the 5C’s gave them a grasp of historical thinking skills; 2) established a process whereby students could formulate their own interpretations of historical sources thereby moving from mindless memorization to mindfulness and, 3) students were able to utilize their own lived experiences and interests as historians engaged in investigating historical problems.

The use of history problems in our course stems from a twofold purpose. First, we want students to experience the discipline of history as actively engaged historians who use primary sources in addressing challenging questions of historical interpretation through use of well-defined historical thinking skills. Second, we want to facilitate personal interaction with the discipline by using sources and stories that are reflective of the diversity of our students and enabling their interpretive voices to emerge and be respected in our assessments of their learning. Through the use of history problems, unlike our past exams, we noticed the disappearance of instructor voice in student interpretations of historical source materials and an increase in deliberate use of the 5Cs of historical thinking: context, change over time, contingency, complexity, and causality. Continued exploration of the use of history problems in developing more focused development of particular historical thinking skills will occur in our future work as will the capacity to assess those skills effectively through combinations of written work and in-person conversational interactions with students.

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Acknowledgements

Facilitation and evaluation of this project was enabled by the invaluable support and guidance of Ilene Alexander, Jeff Lindgren, and J.D. Walker. We also acknowledge the work and influence of the following excellent undergraduate teaching assistants who, over the last seven years, contributed to the development, implementation, and the strengthening of the problem based approach to teaching and learning: Emily DePalma, Emily McCune, Julianna Ryburn, Jade Beauclair Sandstrom, and Chris Stewart

Innovative Learning and Teaching: Experiments Across the Disciplines Copyright © 2017 by Individual authors is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

National Academies Press: OpenBook

How People Learn: Brain, Mind, Experience, and School: Expanded Edition (2000)

Chapter: 7 effective teaching: examples in history, mathematics, and science, 7 effective teaching: examples in history, mathematics, and science.

The preceding chapter explored implications of research on learning for general issues relevant to the design of effective learning environments. We now move to a more detailed exploration of teaching and learning in three disciplines: history, mathematics, and science. We chose these three areas in order to focus on the similarities and differences of disciplines that use different methods of inquiry and analysis. A major goal of our discussion is to explore the knowledge required to teach effectively in a diversity of disciplines.

We noted in Chapter 2 that expertise in particular areas involves more than a set of general problem-solving skills; it also requires well-organized knowledge of concepts and inquiry procedures. Different disciplines are organized differently and have different approaches to inquiry. For example, the evidence needed to support a set of historical claims is different from the evidence needed to prove a mathematical conjecture, and both of these differ from the evidence needed to test a scientific theory. Discussion in Chapter 2 also differentiated between expertise in a discipline and the ability to help others learn about that discipline. To use Shulman’s (1987) language, effective teachers need pedagogical content knowledge (knowledge about how to teach in particular disciplines) rather than only knowledge of a particular subject matter.

Pedagogical content knowledge is different from knowledge of general teaching methods. Expert teachers know the structure of their disciplines, and this knowledge provides them with cognitive roadmaps that guide the assignments they give students, the assessments they use to gauge students’ progress, and the questions they ask in the give and take of classroom life. In short, their knowledge of the discipline and their knowledge of pedagogy interact. But knowledge of the discipline structure does not in itself guide the teacher. For example, expert teachers are sensitive to those aspects of the discipline that are especially hard or easy for new students to master.

This means that new teachers must develop the ability to “understand in a pedagogically reflective way; they must not only know their own way around a discipline, but must know the ‘conceptual barriers’ likely to hinder others” (McDonald and Naso, 1986:8). These conceptual barriers differ from discipline to discipline.

An emphasis on interactions between disciplinary knowledge and pedagogical knowledge directly contradicts common misconceptions about what teachers need to know in order to design effective learning environments for their students. The misconceptions are that teaching consists only of a set of general methods, that a good teacher can teach any subject, or that content knowledge alone is sufficient.

Some teachers are able to teach in ways that involve a variety of disciplines. However, their ability to do so requires more than a set of general teaching skills. Consider the case of Barb Johnson, who has been a sixth-grade teacher for 12 years at Monroe Middle School. By conventional standards Monroe is a good school. Standardized test scores are about average, class size is small, the building facilities are well maintained, the administrator is a strong instructional leader, and there is little faculty and staff turnover. However, every year parents sending their fifth-grade students from the local elementary schools to Monroe jockey to get their children assigned to Barb Johnson’s classes. What happens in her classroom that gives it the reputation of being the best of the best?

During the first week of school Barb Johnson asks her sixth graders two questions: “What questions do you have about yourself?” and “What questions do you have about the world?” The students begin enumerating their questions, “Can they be about silly, little things?” asks one student. “If they’re your questions that you really want answered, they’re neither silly nor little,” replies the teacher. After the students list their individual questions, Barb organizes the students into small groups where they share lists and search for questions they have in common. After much discussion each group comes up with a priority list of questions, rank-ordering the questions about themselves and those about the world.

Back together in a whole group session, Barb Johnson solicits the groups’ priorities and works toward consensus for the class’s combined lists of questions. These questions become the basis for guiding the curriculum in Barb’s class. One question, “Will I live to be 100 years old?” spawned educational investigations into genetics, family and oral history, actuarial science, statistics and probability, heart disease, cancer, and hypertension. The students had the opportunity to seek out information from family members, friends, experts in various fields, on-line computer services, and books, as well as from the teacher. She describes what they had to do as becoming part of a “learning community.” According to Barb Johnson, “We decide what are the most compelling intellectual issues, devise ways to investigate those issues

and start off on a learning journey. Sometimes we fall short of our goal. Sometimes we reach our goal, but most times we exceed these goals—we learn more than we initially expected” (personal communication).

At the end of an investigation, Barb Johnson works with the students to help them see how their investigations relate to conventional subject-matter areas. They create a chart on which they tally experiences in language and literacy, mathematics, science, social studies and history, music, and art. Students often are surprised at how much and how varied their learning is. Says one student, “I just thought we were having fun. I didn’t realize we were learning, too!”

Barb Johnson’s teaching is extraordinary. It requires a wide range of disciplinary knowledge because she begins with students’ questions rather than with a fixed curriculum. Because of her extensive knowledge, she can map students’ questions onto important principles of relevant disciplines. It would not work to simply arm new teachers with general strategies that mirror how she teaches and encourage them to use this approach in their classrooms. Unless they have the relevant disciplinary knowledge, the teachers and the classes would quickly become lost. At the same time, disciplinary knowledge without knowledge about how students learn (i.e., principles consistent with developmental and learning psychology) and how to lead the processes of learning (i.e., pedagogical knowledge) would not yield the kind of learning seen in Barb Johnson’s classes (Anderson and Smith, 1987).

In the remainder of this chapter, we present illustrations and discussions of exemplary teaching in history, mathematics, and science. The three examples of history, mathematics, and science are designed to convey a sense of the pedagogical knowledge and content knowledge (Shulman, 1987) that underlie expert teaching. They should help to clarify why effective teaching requires much more than a set of “general teaching skills.”

Most people have had quite similar experiences with history courses: they learned the facts and dates that the teacher and the text deemed relevant. This view of history is radically different from the way that historians see their work. Students who think that history is about facts and dates miss exciting opportunities to understand how history is a discipline that is guided by particular rules of evidence and how particular analytical skills can be relevant for understanding events in their lives (see Ravitch and Finn, 1987). Unfortunately, many teachers do not present an exciting approach to history, perhaps because they, too, were taught in the dates-facts method.

Beyond Facts

In Chapter 2 , we discussed a study of experts in the field of history and learned that they regard the available evidence as more than lists of facts (Wineburg, 1991). The study contrasted a group of gifted high school seniors with a group of working historians. Both groups were given a test of facts about the American Revolution taken from the chapter review section of a popular United States history textbook. The historians who had backgrounds in American history knew most of the items, while historians whose specialties lay elsewhere knew only a third of the test facts. Several students scored higher than some historians on the factual pretest. In addition to the test of facts, however, the historians and students were presented with a set of historical documents and asked to sort out competing claims and to formulate reasoned interpretations. The historians excelled at this task. Most students, on the other hand, were stymied. Despite the volume of historical information the students possessed, they had little sense of how to use it productively for forming interpretations of events or for reaching conclusions.

Different Views of History by Different Teachers

Different views of history affect how teachers teach history. For example, Wilson and Wineburg (1993) asked two teachers of American history to read a set of student essays on the causes of the American Revolution not as an unbiased or complete and definitive accounts of people and events, but to develop plans for the students’ “remediation or enrichment.” Teachers were provided with a set of essays on the question, “Evaluate the causes of the American Revolution,” written by eleventh-graders for a timed, 45-minute test. Consider the different types of feedback that Mr. Barnes and Ms. Kelsey gave a student paper; see Box 7.1 .

Mr. Barnes’ comments on the actual content of the essays concentrated on the factual level. Ms. Kelsey’s comments addressed broader images of the nature of the domain, without neglecting important errors of fact. Overall, Mr. Barnes saw the papers as an indication of the bell-shaped distribution of abilities; Ms. Kelsey saw them as representing the misconception that history is about memorizing a mass of information and recounting a series of facts. These two teachers had very different ideas about the nature of learning history. Those ideas affected how they taught and what they wanted their students to achieve.

Studies of Outstanding History Teachers

For expert history teachers, their knowledge of the discipline and beliefs about its structure interact with their teaching strategies. Rather than simply introduce students to sets of facts to be learned, these teachers help people to understand the problematic nature of historical interpretation and analysis and to appreciate the relevance of history for their everyday lives.

One example of outstanding history teaching comes from the classroom of Bob Bain, a public school teacher in Beechwood, Ohio. Historians, he notes, are cursed with an abundance of data—the traces of the past threaten to overwhelm them unless they find some way of separating what is important from what is peripheral. The assumptions that historians hold about significance shape how they write their histories, the data they select, and the narrative they compose, as well as the larger schemes they bring to organize and periodize the past. Often these assumptions about historical significance remain unarticulated in the classroom. This contributes to students’ beliefs that their textbooks are the history rather than a history.

Bob Bain begins his ninth-grade high school class by having all the students create a time capsule of what they think are the most important artifacts from the past. The students’ task, then, is to put down on paper why they chose the items they did. In this way, the students explicitly articulate their underlying assumptions of what constitutes historical significance. Students’ responses are pooled, and he writes them on a large poster that he hangs on the classroom wall. This poster, which Bob Bain calls “Rules for Determining Historical Significance,” becomes a lightening rod for class discussions throughout the year, undergoing revisions and elaborations as students become better able to articulate their ideas.

At first, students apply the rules rigidly and algorithmically, with little understanding that just as they made the rules, they can also change them. But as students become more practiced in plying their judgments of significance, they come to see the rules as tools for assaying the arguments of different historians, which allows them to begin to understand why historians disagree. In this instance, the students’ growing ability to understand the interpretative nature of history is aided by their teacher’s deep understanding of a fundamental principle of the discipline.

Leinhardt and Greeno (1991, 1994) spent 2 years studying a highly accomplished teacher of advanced placement history in an urban high school in Pittsburgh. The teacher, Ms. Sterling, a veteran of over 20 years, began her school year by having her students ponder the meaning of the statement, “Every true history is contemporary history.” In the first week of the semester, Sterling thrust her students into the kinds of epistemological issues that one might find in a graduate seminar: “What is history?” “How do we know the past?” “What is the difference between someone who sits down to

When the French and Indian war ended, British expected Americans to help them pay back there war debts. That would be a reasonable request if the war was fought for the colonies, but it was fought for English imperialism so you can’t blame them for not wanting to pay. The taxes were just the start of the slow turn toward rebellion another factor was when parliament decided to forbid the colonial government to make any more money, Specie became scarcer than ever, and a lot of merchants were pushed into a “two way squeeze” and faced bankruptcy. If I had the choice between being loyal, or rebelling and having something to eat, I know what my choice would be. The colonist who were really loyal never did rebel, and 1/3 support the revolution.

The main thing that turned most people was the amount of propaganda, speeches from people like Patrick Henry, and organizations like the “Association.” After the Boston Massacre and the issuing of the Intolerable acts, people were convinced there was a conspiracy in the royal government to extinguish America’s liberties. I think a lot of people also just were going with the flow, or were being pressured by the Sons of Liberty. Merchants who didn’t go along with boycotts often became the victims of mob violence. Overall though, people were sick of getting overtaxed and walked on and decided let’s do something about it.

‘write history’ and the artifacts that are produced as part of ordinary experience?” The goal of this extended exercise is to help students understand history as an evidentiary form of knowledge, not as clusters of fixed names and dates.

One might wonder about the advisability of spending 5 days “defining history” in a curriculum with so much to cover. But it is precisely Sterling’s framework of subject-matter knowledge—her overarching understanding of the discipline as a whole—that permits students entry into the advanced world of historical sense-making. By the end of the course, students moved from being passive spectators of the past to enfranchised agents who could participate in the forms of thinking, reasoning, and engagement that are the hallmark of skilled historical cognition. For example, early in the school year, Ms. Sterling asked her students a question about the Constitutional Convention and “what were men able to do.” Paul took the question literally: “Uh, I think one of the biggest things that they did, that we talked about yesterday, was the establishment of the first settlements in the Northwest

—your topic sentence is weak

—more factual detail would improve your essay

—note spelling and grammar corrections

—The greatest strength of this essay is its outstanding effort to grapple thoughtfully with the question, why did the colonists rebel? Keep thinking personally, “What if I were here?” It is a great place to start.

—To make the essay however, you need to refine your organization strategies significantly. Remember that your reader is basically ignorant, so you need to express your view as clearly as you can. Try to form your ideas from the beginning to a middle and then an end.

In the beginning, tell what side you’re on: What made the colonists rebel— money, propaganda, conformity?

In the middle, justify your view. What factors support your idea and will convince your reader?

In the end, remind your reader again about your point of view.

Go back and revise and hand this in again!

area states.” But after 2 months of educating students into a way of thinking about history, Paul began to catch on. By January his responses to questions about the fall of the cotton-based economy in the South were linked to British trade policy and colonial ventures in Asia, as well as to the failure of Southern leaders to read public opinion accurately in Great Britain. Ms. Sterling’s own understanding of history allowed her to create a classroom in which students not only mastered concepts and facts, but also used them in authentic ways to craft historical explanations.

Debating the Evidence

Elizabeth Jensen prepares her group of eleventh graders to debate the following resolution:

Resolved: The British government possesses the legitimate authority to tax the American colonies.

As her students enter the classroom they arrange their desks into three groups—on the left of the room a group of “rebels,” on the right, a group of “loyalists,” and in the front, a group of “judges.” Off to the side with a spiral notebook on her lap sits Jensen, a short woman in her late 30s with a booming voice. But today that voice is silent as her students take up the question of the legitimacy of British taxation in the American colonies.

The rebels’ first speaker, a 16-year-old girl with a Grateful Dead T-shirt and one dangling earring, takes a paper from her notebook and begins:

England says she keeps troops here for our own protection. On face value, this seems reasonable enough, but there is really no substance to their claims. First of all, who do they think they are protecting us from? The French? Quoting from our friend Mr. Bailey on page 54, ‘By the settlement in Paris in 1763, French power was thrown completely off the continent of North America.’ Clearly not the French then. Maybe they need to protect us from the Spanish? Yet the same war also subdued the Spanish, so they are no real worry either. In fact, the only threat to our order is the Indians…but…we have a decent militia of our own…. So why are they putting troops here? The only possible reason is to keep us in line. With more and more troops coming over, soon every freedom we hold dear will be stripped away. The great irony is that Britain expects us to pay for these vicious troops, these British squelchers of colonial justice.

A loyalist responds:

We moved here, we are paying less taxes than we did for two generations in England, and you complain? Let’s look at why we are being taxed— the main reason is probably because England has a debt of £140,000,000. …This sounds a little greedy, I mean what right do they have to take our money simply because they have the power over us. But did you know that over one-half of their war debt was caused by defending us in the French and Indian War…. Taxation without representation isn’t fair. Indeed, it’s tyranny. Yet virtual representation makes this whining of yours an untruth. Every British citizen, whether he had a right to vote or not, is represented in Parliament. Why does this representation not extend to America?

A rebel questions the loyalist about this:

Rebel: What benefits do we get out of paying taxes to the crown?

Loyalist: We benefit from the protection.

Rebel: (cutting in) Is that the only benefit you claim, protection?

Loyalist: Yes—and all the rights of an Englishman.

Rebel: Okay, then what about the Intolerable Acts…denying us rights of British subjects. What about the rights we are denied?

Loyalist: The Sons of Liberty tarred and feather people, pillaged homes— they were definitely deserving of some sort of punishment.

Rebel: So should all the colonies be punished for the acts of a few colonies?

For a moment, the room is a cacophony of charges and countercharges. “It’s the same as in Birmingham,” shouts a loyalist. A rebel snorts disparagingly, “Virtual representation is bull.” Thirty-two students seem to be talking at once, while the presiding judge, a wiry student with horn-rimmed glasses, bangs his gavel to no avail. The teacher, still in the corner, still with spiral notebook in lap, issues her only command of the day. “Hold still!” she thunders. Order is restored and the loyalists continue their opening argument (from Wineburg and Wilson, 1991).

Another example of Elizabeth Jensen’s teaching involves her efforts to help her high school students understand the debates between Federalists and anti-Federalists. She knows that her 15- and 16-year-olds cannot begin to grasp the complexities of the debates without first understanding that these disagreements were rooted in fundamentally different conceptions of human nature—a point glossed over in two paragraphs in her history textbook. Rather than beginning the year with a unit on European discovery and exploration, as her text dictates, she begins with a conference on the nature of man. Students in her eleventh-grade history class read excerpts from the writings of philosophers (Hume, Locke, Plato, and Aristotle), leaders of state and revolutionaries (Jefferson, Lenin, Gandhi), and tyrants (Hitler, Mussolini), presenting and advocating these views before their classmates. Six weeks later, when it is time to study the ratification of the Constitution, these now-familiar figures—Plato, Aristotle, and others—are reconvened to be courted by impassioned groups of Federalists and anti-Federalists. It is Elizabeth Jensen’s understanding of what she wants to teach and what adolescents already know that allows her to craft an activity that helps students get a feel for the domain that awaits them: decisions about rebellion, the Constitution, federalism, slavery, and the nature of a government.

These examples provide glimpses of outstanding teaching in the discipline of history. The examples do not come from “gifted teachers” who know how to teach anything: they demonstrate, instead, that expert teachers have a deep understanding of the structure and epistemologies of their disciplines, combined with knowledge of the kinds of teaching activities that will help students come to understand the discipline for themselves. As we previously noted, this point sharply contradicts one of the popular—and dangerous—myths about teaching: teaching is a generic skill and a good teacher can teach any subject. Numerous studies demonstrate that any curriculum—including a textbook—is mediated by a teacher’s understanding of the subject domain (for history, see Wineburg and Wilson, 1988; for math, see Ball, 1993; for English, see Grossman et al., 1989). The uniqueness of the content knowledge and pedagogical knowledge necessary to teach his-

tory becomes clearer as one explores outstanding teaching in other disciplines.

MATHEMATICS

As is the case in history, most people believe that they know what mathematics is about—computation. Most people are familiar with only the computational aspects of mathematics and so are likely to argue for its place in the school curriculum and for traditional methods of instructing children in computation. In contrast, mathematicians see computation as merely a tool in the real stuff of mathematics, which includes problem solving, and characterizing and understanding structure and patterns. The current debate concerning what students should learn in mathematics seems to set proponents of teaching computational skills against the advocates of fostering conceptual understanding and reflects the wide range of beliefs about what aspects of mathematics are important to know. A growing body of research provides convincing evidence that what teachers know and believe about mathematics is closely linked to their instructional decisions and actions (Brown, 1985; National Council of Teachers of Mathematics, 1989; Wilson, 1990a, b; Brophy, 1990; Thompson, 1992).

Teachers’ ideas about mathematics, mathematics teaching, and mathematics learning directly influence their notions about what to teach and how to teach it—an interdependence of beliefs and knowledge about pedagogy and subject matter (e.g., Gamoran, 1994; Stein et al., 1990). It shows that teachers’ goals for instruction are, to a large extent, a reflection of what they think is important in mathematics and how they think students best learn it. Thus, as we examine mathematics instruction, we need to pay attention to the subject-matter knowledge of teachers, their pedagogical knowledge (general and content specific), and their knowledge of children as learners of mathematics. Paying attention to these domains of knowledge also leads us to examine teachers’ goals for instruction.

If students in mathematics classes are to learn mathematics with understanding—a goal that is accepted by almost everyone in the current debate over the role of computational skills in mathematics classrooms—then it is important to examine examples of teaching for understanding and to analyze the roles of the teacher and the knowledge that underlies the teacher’s enactments of those roles. In this section, we examine three cases of mathematics instruction that are viewed as being close to the current vision of exemplary instruction and discuss the knowledge base on which the teacher is drawing, as well as the beliefs and goals which guide his or her instructional decisions.

Multiplication with Meaning

For teaching multidigit multiplication, teacher-researcher Magdelene Lampert created a series of lessons in which she taught a heterogeneous group of 28 fourth-grade students. The students ranged in computational skill from beginning to learn the single-digit multiplication facts to being able to accurately solve n-digit by n-digit multiplications. The lessons were intended to give children experiences in which the important mathematical principles of additive and multiplicative composition, associativity, commutativity, and the distributive property of multiplication over addition were all evident in the steps of the procedures used to arrive at an answer (Lampert, 1986:316). It is clear from her description of her instruction that both her deep understanding of multiplicative structures and her knowledge of a wide range of representations and problem situations related to multiplication were brought to bear as she planned and taught these lessons. It is also clear that her goals for the lessons included not only those related to students’ understanding of mathematics, but also those related to students’ development as independent, thoughtful problem solvers. Lampert (1986:339) described her role as follows:

My role was to bring students’ ideas about how to solve or analyze problems into the public forum of the classroom, to referee arguments about whether those ideas were reasonable, and to sanction students’ intuitive use of mathematical principles as legitimate. I also taught new information in the form of symbolic structures and emphasized the connection between symbols and operations on quantities, but I made it a classroom requirement that students use their own ways of deciding whether something was mathematically reasonable in doing the work. If one conceives of the teacher’s role in this way, it is difficult to separate instruction in mathematics content from building a culture of sense-making in the classroom, wherein teacher and students have a view of themselves as responsible for ascertaining the legitimacy of procedures by reference to known mathematical principles. On the part of the teacher, the principles might be known as a more formal abstract system, whereas on the part of the learners, they are known in relation to familiar experiential contexts. But what seems most important is that teachers and students together are disposed toward a particular way of viewing and doing mathematics in the classroom.

Magdelene Lampert set out to connect what students already knew about multidigit multiplication with principled conceptual knowledge. She did so in three sets of lessons. The first set used coin problems, such as “Using only two kinds of coins, make $1.00 using 19 coins,” which encouraged children to draw on their familiarity with coins and mathematical principles that coin trading requires. Another set of lessons used simple stories and drawings to illustrate the ways in which large quantities could be grouped

for easier counting. Finally, the third set of lessons used only numbers and arithmetic symbols to represent problems. Throughout the lessons, students were challenged to explain their answers and to rely on their arguments, rather than to rely on the teacher or book for verification of correctness. An example serves to highlight this approach; see Box 7.2 .

Lampert (1986:337) concludes:

…students used principled knowledge that was tied to the language of groups to explain what they were seeing. They were able to talk meaningfully about place value and order of operations to give legitimacy to procedures and to reason about their outcomes, even though they did not use technical terms to do so. I took their experimentations and arguments as evidence that they had come to see mathematics as more than a set of procedures for finding answers.

Clearly, her own deep understanding of mathematics comes into play as she teaches these lessons. It is worth noting that her goal of helping students see what is mathematically legitimate shapes the way in which she designs lessons to develop students’ understanding of two-digit multiplication.

Understanding Negative Numbers

Helping third-grade students extend their understanding of numbers from the natural numbers to the integers is a challenge undertaken by another teacher-researcher. Deborah Ball’s work provides another snapshot of teaching that draws on extensive subject content and pedagogical content knowledge. Her goals in instruction include “developing a practice that respects the integrity both of mathematics as a discipline and of children as mathematical thinkers” (Ball, 1993). That is, she not only takes into account what the important mathematical ideas are, but also how children think about the particular area of mathematics on which she is focusing. She draws on both her understanding of the integers as mathematical entities (subject-matter knowledge) and her extensive pedagogical content knowledge specifically about integers. Like Lampert, Ball’s goals go beyond the boundaries of what is typically considered mathematics and include developing a culture in which students conjecture, experiment, build arguments, and frame and solve problems—the work of mathematicians.

Deborah Ball’s description of work highlights the importance and difficulty of figuring out powerful and effective ways to represent key mathematical ideas to children (see Ball, 1993). A wealth of possible models for negative numbers exists and she reviewed a number of them—magic peanuts, money, game scoring, a frog on a number line, buildings with floors above and below ground. She decided to use the building model first and money later: she was acutely aware of the strengths and limitations of each

The teacher begins with a request for an example of a basic computation.

Jessica: There were 12 jars, and each had 4 butterflies in it.

Teacher: And if I did this multiplication and found the answer, what would I know about those

Jessica: You’d know you had that many butterflies altogether.

The teacher and students next illustrate Jessica’s story and construct a procedure for counting the butterflies.

Sally: 10.

The lesson progresses as the teacher and students construct a pictorial representation of grouping 10 sets of four butterflies and having 2 jars not in the group; they recognize that 12×4 can be thought of as 10×4 plus 2×4. Lampert then has the children explore other ways of grouping the jars, for example, into two groups of 6 jars.

The students are obviously surprised that 6×4 plus 6×4 produces the same number as 10×4 plus 2×4. For Lampert, this is important information about the students’ understanding (formative assessment—see ). It is a sign that she needs to do many more activities involving different groupings. In subsequent lessons, students are challenged with problems in which the two-digit number in the multiplication is much bigger and, ultimately, in which both numbers are quite large—28×65. Students continue to develop their understanding of the principles that govern multiplication and to invent computational procedures based on those principles. Students defend the reasonableness of their procedures by using drawings and stories. Eventually, students explore more traditional as well as alternative algorithms for two-digit multiplication, using only written symbols.

model as a way for representing the key properties of numbers, particularly those of magnitude and direction. Reading Deborah Ball’s description of her deliberations, one is struck by the complexity of selecting appropriate models for particular mathematical ideas and processes. She hoped that the positional aspects of the building model would help children recognize that negative numbers were not equivalent to zero, a common misconception. She was aware that the building model would be difficult to use for modeling subtraction of negative numbers.

Deborah Ball begins her work with the students, using the building model by labeling its floors. Students readily labeled the underground floors and accepted them as “below zero.” They then explored what happened as little paper people entered an elevator at some floor and rode to another floor. This was used to introduce the conventions of writing addition and subtraction problems involving integers 4−6=−2 and −2+5=3. Students were presented with increasingly difficult problems. For example, “How many ways are there for a person to get to the second floor?” Working with the building model allowed students to generate a number of observations. For example, one student noticed that “any number below zero plus that same number above zero equals zero” (Ball, 1993:381). However, the model failed to allow for explorations for such problems 5+(−6) and Ball was concerned that students were not developing a sense that −5 was less than −2—it was lower, but not necessarily less. Ball then used a model of money as a second representational context for exploring negative numbers, noting that it, too, has limitations.

Clearly, Deborah Ball’s knowledge of the possible representations of integers (pedagogical content knowledge) and her understanding of the important mathematical properties of integers were foundational to her planning and her instruction. Again, her goals related to developing students’ mathematical authority, and a sense of community also came into play. Like Lampert, Ball wanted her students to accept the responsibility of deciding when a solution is reasonable and likely to be correct, rather than depending on text or teacher for confirmation of correctness.

Guided Discussion

The work of Lampert and Ball highlights the role of a teacher’s knowledge of content and pedagogical content knowledge in planning and teaching mathematics lessons. It also suggests the importance of the teacher’s understanding of children as learners. The concept of cognitively guided instruction helps illustrate another important characteristic of effective mathematics instruction: that teachers not only need knowledge of a particular topic within mathematics and knowledge of how learners think about the particular topic, but also need to develop knowledge about how the indi-

vidual children in their classrooms think about the topic (Carpenter and Fennema, 1992; Carpenter et al., 1996; Fennema et al., 1996). Teachers, it is claimed, will use their knowledge to make appropriate instructional decisions to assist students to construct their mathematical knowledge. In this approach, the idea of domains of knowledge for teaching (Shulman, 1986) is extended to include teachers’ knowledge of individual learners in their classrooms.

Cognitively guided instruction is used by Annie Keith, who teaches a combination first- and second-grade class in an elementary school in Madison Wisconsin (Hiebert et al., 1997). Her instructional practices are an example of what is possible when a teacher understands children’s thinking and uses that understanding to guide her teaching. A portrait of Ms. Keith’s classroom reveals also how her knowledge of mathematics and pedagogy influence her instructional decisions.

Word problems form the basis for almost all instruction in Annie Keith’s classroom. Students spend a great deal of time discussing alternative strategies with each other, in groups, and as a whole class. The teacher often participates in these discussions but almost never demonstrates the solution to problems. Important ideas in mathematics are developed as students explore solutions to problems, rather than being a focus of instruction per se. For example, place-value concepts are developed as students use base-10 materials, such as base-10 blocks and counting frames, to solve word problems involving multidigit numbers.

Mathematics instruction in Annie Keith’s class takes place in a number of different settings. Everyday first-grade and second-grade activities, such as sharing snacks, lunch count, and attendance, regularly serve as contexts for problem-solving tasks. Mathematics lessons frequently make use of math centers in which the students do a variety of activities. On any given day, children at one center may solve word problems presented by the teacher while at another center children write word problems to present to the class later or play a math game.

She continually challenges her students to think and to try to make sense of what they are doing in math. She uses the activities as opportunities for her to learn what individual students know and understand about mathematics. As students work in groups to solve problems, she observes the various solutions and mentally makes notes about which students should present their work: she wants a variety of solutions presented so that students will have an opportunity to learn from each other. Her knowledge of the important ideas in mathematics serves as one framework for the selection process, but her understanding of how children think about the mathematical ideas they are using also affects her decisions about who should present. She might select a solution that is actually incorrect to be presented so that she can initiate a discussion of a common misconception. Or she

may select a solution that is more sophisticated than most students have used in order to provide an opportunity for students to see the benefits of such a strategy. Both the presentations of solutions and the class discussions that follow provide her with information about what her students know and what problems she should use with them next.

Annie Keith’s strong belief that children need to construct their understanding of mathematical ideas by building on what they already know guides her instructional decisions. She forms hypotheses about what her students understand and selects instructional activities based on these hypotheses. She modifies her instruction as she gathers additional information about her students and compares it with the mathematics she wants them to learn. Her instructional decisions give her clear diagnoses of individual students’ current state of understanding. Her approach is not a free-for-all without teacher guidance: rather, it is instruction that builds on students’ understandings and is carefully orchestrated by the teacher, who is aware of what is mathematically important and also what is important to the learner’s progress.

Model-Based Reasoning

Some attempts to revitalize mathematics instruction have emphasized the importance of modeling phenomena. Work on modeling can be done from kindergarten through twelth grade (K–12). Modeling involves cycles of model construction, model evaluation, and model revision. It is central to professional practice in many disciplines, such as mathematics and science, but it is largely missing from school instruction. Modeling practices are ubiquitous and diverse, ranging from the construction of physical models, such as a planetarium or a model of the human vascular system, to the development of abstract symbol systems, exemplified by the mathematics of algebra, geometry, and calculus. The ubiquity and diversity of models in these disciplines suggest that modeling can help students develop understanding about a wide range of important ideas. Modeling practices can and should be fostered at every age and grade level (Clement, 1989; Hestenes, 1992; Lehrer and Romberg, 1996a, b; Schauble et al., 1995; see Box 7.3 ).

Taking a model-based approach to a problem entails inventing (or selecting) a model, exploring the qualities of the model, and then applying the model to answer a question of interest. For example, the geometry of triangles has an internal logic and also has predictive power for phenomena ranging from optics to wayfinding (as in navigational systems) to laying floor tile. Modeling emphasizes a need for forms of mathematics that are typically underrepresented in the standard curriculum, such as spatial visualization and geometry, data structure, measurement, and uncertainty. For example, the scientific study of animal behavior, like bird foraging, is se-

Physical models, like models of solar systems or elbows, are microcosms of systems that draw heavily on children’s intuitions about resemblance to sustain the relationship between the world being modeled and the model itself. The photograph below displays a child’s model of the elbow. Note, for instance, the rubber bands that mimic the connective function of ligaments and the wooden dowels that are arranged so that their translation in the vertical plane cannot exceed 180 degrees. Though the search for function is supported by initial resemblance, what counts as resemblance typically changes as children revise their models. For example, attempts to make models exemplify elbow motion often lead to an interest in the way muscles might be arranged (from Lehrer and Schauble, 1996a, b).

verely limited unless one also has access to such mathematical concepts as variability and uncertainty. Hence, the practice of modeling introduces the further explorations of important “big ideas” in disciplines.

Increasingly, approaches to early mathematics teaching incorporate the premises that all learning involves extending understanding to new situations, that young children come to school with many ideas about mathematics, that knowledge relevant to a new setting is not always accessed spontaneously, and that learning can be enhanced by respecting and encouraging

children to try out the ideas and strategies that they bring to school-based learning in classrooms. Rather than beginning mathematics instruction by focusing solely on computational algorithms, such as addition and subtraction, students are encouraged to invent their own strategies for solving problems and to discuss why those strategies work. Teachers may also explicitly prompt students to think about aspects of their everyday life that are potentially relevant for further learning. For example, everyday experiences of walking and related ideas about position and direction can serve as a springboard for developing corresponding mathematics about the structure of large-scale space, position, and direction (Lehrer and Romberg, 1996b).

As research continues to provide good examples of instruction that help children learn important mathematics, there will be better understanding of the roles that teachers’ knowledge, beliefs, and goals play in their instructional thinking and actions. The examples we have provided here make it clear that the selection of tasks and the guidance of students’ thinking as they work through tasks is highly dependent on teachers’ knowledge of mathematics, pedagogical content knowledge, and knowledge of students in general.

Two recent examples in physics illustrate how research findings can be used to design instructional strategies that promote the sort of problem-solving behavior observed in experts. Undergraduates who had finished an introductory physics course were asked to spend a total of 10 hours, spread over several weeks, solving physics problems using a computer-based tool that constrained them to perform a conceptual analysis of the problems based on a hierarchy of principles and procedures that could be applied to solve them (Dufresne et al., 1992). This approach was motivated by research on expertise (discussed in Chapter 2 ). The reader will recall that, when asked to state an approach to solving a problem, physicists generally discuss principles and procedures. Novices, in contrast, tend to discuss specific equations that could be used to manipulate variables given in the problem (Chi et al., 1981). When compared with a group of students who solved the same problems on their own, the students who used the computer to carry out the hierarchical analyses performed noticeably better in subsequent measures of expertise. For example, in problem solving, those who performed the hierarchical analyses outperformed those who did not, whether measured in terms of overall problem-solving performance, ability to arrive at the correct answer, or ability to apply appropriate principles to solve the problems; see Figure 7.1 . Furthermore, similar differences emerged in problem categorization: students who performed the hierarchical analyses considered principles (as opposed to surface features) more often in

deciding whether or not two problems would be solved similarly; see Figure 7.2 . (See Chapter 6 for an example of the type of item used in the categorization task of Figure 7.2 .) It is also worth noting that both Figures 7.1 and 7.2 illustrate two other issues that we have discussed in this volume, namely that time on task is a major indicator for learning and that deliberate practice is an efficient way to promote expertise. In both cases, the control group made significant improvements simply as a result of practice (time on task), but the experimental group showed more improvements for the same amount of training time (deliberate practice).

Introductory physics courses have also been taught successfully with an approach for problem solving that begins with a qualitative hierarchical analysis of the problems (Leonard et al., 1996). Undergraduate engineering students were instructed to write qualitative strategies for solving problems before attempting to solve them (based on Chi et al., 1981). The strategies consisted of a coherent verbal description of how a problem could be solved and contained three components: the major principle to be applied; the justification for why the principle was applicable; and the procedures for applying the principle. That is, the what, why, and how of solving the problem were explicitly delineated; see Box 7.4 . Compared with students who took a traditional course, students in the strategy-based course performed significantly better in their ability to categorize problems according to the relevant principles that could be applied to solve them; see Figure 7.3 .

Hierarchical structures are useful strategies for helping novices both recall knowledge and solve problems. For example, physics novices who had completed and received good grades in an introductory college physics course were trained to generate a problem analysis called a theoretical problem description (Heller and Reif, 1984). The analysis consists of describing force problems in terms of concepts, principles, and heuristics. With such an approach, novices substantially improved in their ability to solve problems, even though the type of theoretical problem description used in the study was not a natural one for novices. Novices untrained in the theoretical descriptions were generally unable to generate appropriate descriptions on their own—even given fairly routine problems. Skills, such as the ability to describe a problem in detail before attempting a solution, the ability to determine what relevant information should enter the analysis of a problem, and the ability to decide which procedures can be used to generate problem descriptions and analyses, are tacitly used by experts but rarely taught explicitly in physics courses.

Another approach helps students organize knowledge by imposing a hierarchical organization on the performance of different tasks in physics (Eylon and Reif, 1984). Students who received a particular physics argument that was organized in hierarchical form performed various recall and problem-solving tasks better than subjects who received the same argument

explain the utility of problem solving method in history teaching

FIGURE 7.1 Effects of two methods of training on problem-solving, final answer, and principle understanding. SOURCE: Dufresne et al. (1992).

non-hierarchically. Similarly, students who received a hierarchical organization of problem-solving strategies performed much better than subjects who received the same strategies organized non-hierarchically. Thus, helping students to organize their knowledge is as important as the knowledge itself, since knowledge organization is likely to affect students’ intellectual performance.

These examples demonstrate the importance of deliberate practice and of having a “coach” who provides feedback for ways of optimizing performance (see Chapter 3 ). If students had simply been given problems to solve on their own (an instructional practice used in all the sciences), it is highly

explain the utility of problem solving method in history teaching

FIGURE 7.2 Effects of two methods of training on considering principles for categorizing problems. SOURCE: Dufresne et al. (1992).

unlikely that they would have spent time efficiently. Students might get stuck for minutes, or even hours, in attempting a solution to a problem and either give up or waste lots of time. In Chapter 3 , we discussed ways in which learners profit from errors and that making mistakes is not always time wasted. However, it is not efficient if a student spends most of the problem-solving time rehearsing procedures that are not optimal for promoting skilled performance, such as finding and manipulating equations to solve the problem, rather than identifying the underlying principle and procedures that apply to the problem and then constructing the specific equations needed. In deliberate practice, a student works under a tutor (human

Students enrolled in an introductory physics course were asked to write a strategy for an exam problem

A disk of mass, M=2 kg, and radius, R=0.4 m, has string wound around it and is free to rotate about an axle through its center. A block of mass, M=1 kg, is attached to the end of the string, and the system is released from rest with no slack in the string. What is the speed of the block after it has fallen a distance, d=0.5 m. Don’t forget to provide both a strategy and a solution.

 

Strategy 1: Use the conservation of energy since the only nonconservative force in the system is the tension in the rope attached to the mass M and wound around the disk (assuming there is no friction between the axle and the disk, and the mass M and the air), and the work done by the tension to the disk and the mass cancel each other out. First, set up a coordinate system so the potential energy of the system at the start can be determined. There will be no kinetic energy at the start since it starts at rest. Therefore the potential energy is all the initial energy. Now set the initial energy equal to the final energy that is made up of the kinetic energy of the disk plus the mass M and any potential energy left in the system with respect to the chosen coordinate system.

Strategy 2: I would use conservation of mechanical energy to solve this problem. The mass M has some potential energy while it is hanging there. When the block starts to accelerate downward the potential energy is transformed into rotational kinetic energy

or computer based) to rehearse appropriate practices that enhance performance. Through deliberate practice, computer-based tutoring environments have been designed that reduce the time it takes individuals to reach real-world performance criteria from 4 years to 25 hours (see Chapter 9 )!

Conceptual Change

Before students can really learn new scientific concepts, they often need to re-conceptualize deeply rooted misconceptions that interfere with the learning. As reviewed above (see Chapters 3 and 4 ), people spend considerable time and effort constructing a view of the physical world through

of the disk and kinetic energy of the falling mass. Equating the initial and final states and using the relationship between v and ω the speed of M can be found. Mechanical energy is conserved even with the nonconservative tension force because the tension force is internal to the system (pulley, mass, rope).

In trying to find the speed of the block I would try to find angular momentum kinetic energy, use gravity. I would also use rotational kinematics and moment of inertia around the center of mass for the disk.

There will be a torque about the center of mass due to the weight of the block, M. The force pulling downward is mg. The moment of inertia about the axle is 1/2 MR . The moment of inertia multiplied by the angular acceleration. By plugging these values into a kinematic expression, the angular speed can be calculated. Then, the angular speed times the radius gives you the velocity of the block.

The first two strategies display an excellent understanding of the principles, justification, and procedures that could be used to solve the problem (the what, why, and how for solving the problem). The last two strategies are largely a shopping list of physics terms or equations that were covered in the course, but the students are not able to articulate why or how they apply to the problem under consideration.

Having students write strategies (after modeling strategy writing for them and providing suitable scaffolding to ensure progress) provides an excellent formative assessment tool for monitoring whether or not students are making the appropriate links between problem contexts, and the principles and procedures that could be applied to solve them (see Leonard et al., 1996).

experiences and observations, and they may cling tenaciously to those views— however much they conflict with scientific concepts—because they help them explain phenomena and make predictions about the world (e.g., why a rock falls faster than a leaf).

One instructional strategy, termed “bridging,” has been successful in helping students overcome persistent misconceptions (Brown, 1992; Brown and Clement, 1989; Clement, 1993). The bridging strategy attempts to bridge from students’ correct beliefs (called anchoring conceptions) to their misconceptions through a series of intermediate analogous situations. Starting with the anchoring intuition that a spring exerts an upward force on the book resting on it, the student might be asked if a book resting on the

explain the utility of problem solving method in history teaching

FIGURE 7.3 Percent correct choices under strategy-based and traditional teaching conditions by problem number in a categorization, multiple-choice task. SOURCE: Leonard et al. (1996).

middle of a long, “springy” board supported at its two ends experiences an upward force from the board. The fact that the bent board looks as if it is serving the same function as the spring helps many students agree that both the spring and the board exert upward forces on the book. For a student who may not agree that the bent board exerts an upward force on the book, the instructor may ask a student to place her hand on top of a vertical spring

and push down and to place her hand on the middle of the springy board and push down. She would then be asked if she experienced an upward force that resisted her push in both cases. Through this type of dynamic probing of students’ beliefs, and by helping them come up with ways to resolve conflicting views, students can be guided into constructing a coherent view that is applicable across a wide range of contexts.

Another effective strategy for helping students overcome persistent erroneous beliefs are interactive lecture demonstrations (Sokoloff and Thornton, 1997; Thornton and Sokoloff, 1997). This strategy, which has been used very effectively in large introductory college physics classes, begins with an introduction to a demonstration that the instructor is about to perform, such as a collision between two air carts on an air track, one a stationary light cart, the other a heavy cart moving toward the stationary cart. Each cart has an electronic “force probe” connected to it which displays on a large screen and in real-time the force acting on it during the collision. The teacher first asks the students to discuss the situation with their neighbors and then record a prediction as to whether one of the carts would exert a bigger force on the other during impact or whether the carts would exert equal forces.

The vast majority of students incorrectly predict that the heavier, moving cart exerts a larger force on the lighter, stationary cart. Again, this prediction seems quite reasonable based on experience—students know that a moving Mack truck colliding with a stationary Volkswagen beetle will result in much more damage done to the Volkswagen, and this is interpreted to mean that the Mack truck must have exerted a larger force on the Volkswagen. Yet, notwithstanding the major damage to the Volkswagen, Newton’s Third Law states that two interacting bodies exert equal and opposite forces on each other.

After the students make and record their predictions, the instructor performs the demonstration, and the students see on the screen that the force probes record forces of equal magnitude but oppositely directed during the collision. Several other situations are discussed in the same way: What if the two carts had been moving toward each other at the same speed? What if the situation is reversed so that the heavy cart is stationary and the light cart is moving toward it? Students make predictions and then see the actual forces between the carts displayed as they collide. In all cases, students see that the carts exert equal and opposite forces on each other, and with the help of a discussion moderated by the instructor, the students begin to build a consistent view of Newton’s Third Law that incorporates their observations and experiences.

Consistent with the research on providing feedback (see Chapter 3 ), there is other research that suggests that students’ witnessing the force displayed in real-time as the two carts collide helps them overcome their misconceptions; delays of as little as 20–30 minutes in displaying graphic data

of an event occurring in real-time significantly inhibits the learning of the underlying concept (Brasell, 1987).

Both bridging and the interactive demonstration strategies have been shown to be effective at helping students permanently overcome misconceptions. This finding is a major breakthrough in teaching science, since so much research indicates that students often can parrot back correct answers on a test that might be erroneously interpreted as displaying the eradication of a misconception, but the same misconception often resurfaces when students are probed weeks or months later (see Mestre, 1994, for a review).

Teaching as Coaching

One of the best examples of translating research into practice is Minstrell’s (1982, 1989, 1992) work with high school physics students. Minstrell uses many research-based instructional techniques (e.g., bridging, making students’ thinking visible, facilitating students’ ability to restructure their own knowledge) to teach physics for understanding. He does this through classroom discussions in which students construct understanding by making sense of physics concepts, with Minstrell playing a coaching role. The following quote exemplifies his innovative and effective instructional strategies (Minstrell, 1989:130–131):

Students’ initial ideas about mechanics are like strands of yarn, some unconnected, some loosely interwoven. The act of instruction can be viewed as helping the students unravel individual strands of belief, label them, and then weave them into a fabric of more complete understanding. An important point is that later understanding can be constructed, to a considerable extent, from earlier beliefs. Sometimes new strands of belief are introduced, but rarely is an earlier belief pulled out and replaced. Rather than denying the relevancy of a belief, teachers might do better by helping students differentiate their present ideas from and integrate them into conceptual beliefs more like those of scientists.

Describing a lesson on force, Minstrell (1989:130–131) begins by introducing the topic in general terms:

Today we are going to try to explain some rather ordinary events that you might see any day. You will find that you already have many good ideas that will help explain those events. We will find that some of our ideas are similar to those of the scientist, but in other cases our ideas might be different. When we are finished with this unit, I expect that we will have a much clearer idea of how scientists explain those events, and I know that you will feel more comfortable about your explanations…A key idea we are going to use is the idea of force. What does the idea of force mean to you?

Many views emerge from the ensuing classroom discussion, from the typical “push or pull” to descriptions that include sophisticated terms, such as en-

ergy and momentum. At some point Minstrell guides the discussion to a specific example: he drops a rock and asks students how the event can be explained using their ideas about force. He asks students to individually formulate their ideas and to draw a diagram showing the major forces on the rock as arrows, with labels to denote the cause of each force. A lengthy discussion follows in which students present their views, views that contain many irrelevant (e.g., nuclear forces) or fictitious forces (e.g., the spin of the earth, air). In his coaching, Minstrell asks students to justify their choices by asking questions, such as “How do you know?” “How did you decide?” “Why do you believe that?”

With this approach, Minstrell has been able to identify many erroneous beliefs of students that stand in the way of conceptual understanding. One example is the belief that only active agents (e.g., people) can exert forces, that passive agents (e.g., a table) cannot. Minstrell (1992) has developed a framework that helps both to make sense of students’ reasoning and to design instructional strategies. (For a related theoretical framework for classifying and explaining student reasoning, see the discussion of “phenomenological primitives” in DiSessa, 1988, 1993.) Minstrell describes identifiable pieces of students’ knowledge as “facets,” a facet being a convenient unit of thought, a piece of knowledge, or a strategy seemingly used by the student in addressing a particular situation. Facets may relate to conceptual knowledge (e.g., passive objects do not exert force), to strategic knowledge (e.g., average velocity can be determined by adding the initial and final velocities and dividing by two), or generic reasoning (e.g., the more the X, the more the Y). Identifying students’ facets, what cues them in different contexts, and how students use them in reasoning are all helpful in devising instructional strategies.

Interactive Instruction in Large Classes

One of the obstacles to instructional innovation in large introductory science courses at the college level is the sheer number of students who are taught at one time. How does an instructor provide an active learning experience, provide feedback, accommodate different learning styles, make students’ thinking visible, and provide scaffolding and tailored instruction to meet specific student needs when facing more than 100 students at a time? Classroom communication systems can help the instructor of a large class accomplish these objectives. One such system, called Classtalk, consists of both hardware and software that allows up to four students to share an input device (e.g., a fairly inexpensive graphing calculator) to “sign on” to a classroom communication network that permits the instructor to send questions for students to work on and permits students to enter answers through their input device. Answers can then be displayed anonymously in histogram

form to the class, and a permanent record of each student’s response is recorded to help evaluate progress as well as the effectiveness of instruction.

This technology has been used successfully at the University of Massachusetts-Amherst to teach physics to a range of students, from non-science majors to engineering and science majors (Dufresne et al., 1996; Wenk et al., 1997; Mestre et al., 1997). The technology creates an interactive learning environment in the lectures: students work collaboratively on conceptual questions, and the histogram of students’ answers is used as a visual springboard for classwide discussions when students defend the reasoning they used to arrive at their answers. This technology makes students’ thinking visible and promotes critical listening, evaluation, and argumentation in the class. The teacher is a coach, providing scaffolding where needed, tailoring “mini-lectures” to clear up points of confusion, or, if things are going well, simply moderating the discussion and allowing students to figure out things and reach consensus on their own. The technology is also a natural mechanism to support formative assessment during instruction, providing both the teacher and students with feedback on how well the class is grasping the concepts under study. The approach accommodates a wider variety of learning styles than is possible by lectures and helps to foster a community of learners focused on common objectives and goals.

Science for All Children

The examples above present some effective strategies for teaching and learning science for high school and college students. We drew some general principles of learning from these examples and stressed that the findings consistently point to the strong effect of knowledge structures on learning. These studies also emphasize the importance of class discussions for developing a language for talking about scientific ideas, for making students’ thinking explicit to the teacher and to the rest of the class, and for learning to develop a line of argumentation that uses what one has learned to solve problems and explain phenomena and observations.

The question that immediately occurs is how to teach science to younger children or to students who are considered to be educationally “at risk.” One approach that has been especially useful in science teaching was developed with language-minority grade-school children: Chèche Konnen, which in Haitian Creole means search for knowledge (Rosebery et al., 1992). The approach stresses how discourse is a primary means for the search for knowledge and scientific sense-making. It also illustrates how scientific ideas are constructed. In this way it mirrors science, in the words of Nobel Laureate Sir Peter Medawar (1982:111):

Like other exploratory processes, [the scientific method] can be resolved into a dialogue between fact and fancy, the actual and the possible; between what could be true and what is in fact the case. The purpose of scientific enquiry is not to compile an inventory of factual information, nor to build up a totalitarian world picture of Natural Laws in which every event that is not compulsory is forbidden. We should think of it rather as a logically articulated structure of justifiable beliefs about a Possible World— a story which we invent and criticize and modify as we go along, so that it ends by being, as nearly as we can make it, a story about real life.

The Chèche Konnen approach to teaching began by creating “communities of scientific practice” in language-minority classrooms in a few Boston and Cambridge, MA public schools. “Curriculum” emerges in these classrooms from the students’ questions and beliefs and is shaped in ongoing interactions that include both the teacher and students. Students explore their own questions, much as we described above in Barb Johnson’s class. In addition, students design studies, collect information, analyze data and construct evidence, and they then debate the conclusions that they derive from their evidence. In effect, the students build and argue about theories; see Box 7.5 .

Students constructed scientific understandings through an iterative process of theory building, criticism, and refinement based on their own questions, hypotheses, and data analysis activities. Question posing, theorizing, and argumentation formed the structure of the students’ scientific activity. Within this structure, students explored the implications of the theories they held, examined underlying assumptions, formulated and tested hypotheses, developed evidence, negotiated conflicts in belief and evidence, argued alternative interpretations, provided warrants for conclusions, and so forth. The process as a whole provided a richer, more scientifically grounded experience than the conventional focus on textbooks or laboratory demonstrations.

The emphasis on establishing communities of scientific practice builds on the fact that robust knowledge and understandings are socially constructed through talk, activity, and interaction around meaningful problems and tools (Vygotsky, 1978). The teacher guides and supports students as they explore problems and define questions that are of interest to them. A community of practice also provides direct cognitive and social support for the efforts of the group’s individual members. Students share the responsibility for thinking and doing: they distribute their intellectual activity so that the burden of managing the whole process does not fall to any one individual. In addition, a community of practice can be a powerful context for constructing scientific meanings. In challenging one another’s thoughts and beliefs, students must be explicit about their meanings; they must negotiate conflicts in belief or evidence; and they must share and synthesize their knowledge to

The seventh- and eighth-grade students in a Haitian Creole bilingual program wanted to find the “truth” of a belief held by most of their classmates: that drinking water from the fountain on the third floor, where the junior high was located, was superior to the water from the other fountains in their school. Challenged by their teacher, the students set out to determine whether they actually preferred the water from the third floor or only thought they did.

As a first step, the students designed and took a blind taste test of the water from fountains on all three floors of the building. They found, to their surprise, that two-thirds of them chose the water from the first-floor fountain, even though they all said that they preferred drinking from the third-floor fountain. The students did not believe the data. They held firmly to their beliefs that the first-floor fountain was the worst because “all the little kids slobber in it.” (The first-floor fountain is located near the kindergarten and first grade classrooms.) Their teacher was also suspicious of the results because she had expected no differences among the three water fountains. These beliefs and suspicions motivated students to conduct a second taste test with a larger sample drawn from the rest of the junior high.

The students decided where, when, and how to run their experiment. They discussed methodological issues: How to collect the water, how to hide the identity of the sources, and, crucially, how many fountains to include. They decided to include the same three fountains as before so that they could compare results.

achieve understanding (Brown and Palincsar, 1989; Inagaki and Hatano, 1987).

What do students learn from participating in a scientific sense-making community? Individual interviews with students before and after the water taste test investigation (see Box 7.5 ), first in September and again the following June, showed how the students’ knowledge and reasoning changed. In the interviews (conducted in Haitian Creole), the students were asked to think aloud about two open-ended real-world problems—pollution in the Boston Harbor and a sudden illness in an elementary school. The researchers were interested in changes in students’ conceptual knowledge about aquatic ecosystems and in students’ uses of hypotheses, experiments, and explanations to organize their reasoning (for a complete discussion, see Rosebery et al., 1992).

They worried about bias in the voting process. What if some students voted more than once? Each student in the class volunteered to organize a piece of the experiment. About 40 students participated in the blind taste test. When they analyzed their data, they found support for their earlier results 88 percent of the junior high students they preferred water from the third-floor fountain, but 55 percent actually chose the water from the first floor (a result of 33 percent would be chance).

Faced with this evidence, the students suspicions turned to curiosity. Why was the water from the first-floor fountain preferred? How can they determine the source of the preference? They decided to analyze the school’s water along several dimensions, among them acidity, salinity, temperature and bacteria. They found that all the fountains had unacceptably high levels of bacteria. In fact, the first-floor fountain (the one most preferred) had the highest bacterial count. They also found that the water from the first-floor fountain was 20 degrees (Fahrenheit) colder than the water from fountains on the other floors. Based on their findings, they concluded that temperature was probably a deciding factor in taste preference. They hypothesized that the water was naturally cooled as it sat in the city’s underground pipes during the winter months (the study was conducted in February) and warmed as it flowed from the basement to the third floor.

Conceptual Knowledge

Not surprisingly, the students knew more about water pollution and aquatic ecosystems in June than they did in September. They were also able to use this knowledge generatively. One student explained how she would clean the water in Boston Harbor (Rosebery et al., 1992:86).

Like you look for the things, take the garbage out of the water, you put a screen to block all the paper and stuff, then you clean the water; you put chemical products in it to clean the water, and you’d take all the microscopic life out. Chlorine and alum, you put in the water. They’d gather the little stuff, the little stuff would stick to the chemical products, and they would clean the water.

Note that this explanation contains misconceptions. By confusing the cleaning of drinking water with the cleaning of sea water, the student suggests adding chemicals to take all microscopic life from the water (good for drinking water, but bad for the ecosystem of Boston Harbor). This example

illustrates the difficulties in transferring knowledge appropriately from one context to another (see Chapter 3 ). Despite these shortcomings, it is clear that this student is starting on the path to scientific thinking, leaving behind the more superficial “I’d take all the bad stuff out of the water” type of explanation. It is also clear that by making the student’s thinking visible, the teacher is in an excellent position to refine her (and perhaps the class’s) understanding.

Scientific Thinking

Striking changes appeared in students’ scientific reasoning. In September, there were three ways in which the students showed little familiarity with scientific forms of reasoning. First, the students did not understand the function of hypotheses or experiments in scientific inquiry. When asked for their ideas about what could be making the children sick, the students tended, with few exceptions, to respond with short, unelaborated, often untestable “hypotheses” that simply restated the phenomena described in the problem: “That’s a thing…. Ah, I could say a person, some person that gave them something…. Anything, like give poison to make his stomach hurt” (Rosebery et al., 1992:81).

Second, the students conceptualized evidence as information they already knew, either through personal experience or second-hand sources, rather than data produced through experimentation or observation. When asked to generate an experiment to justify an hypothesis—“How would you find out?” —they typically offered declarations: “Because the garbage is a poison for them…. The garbage made the fish die” (Rosebery et al., 1992:78).

Third, the students interpreted an elicitation for an experiment—“How would you be sure?” —as a text comprehension question for which there was a “right” answer. They frequently responded with an explanation or assertion of knowledge and consistently marked their responses as explanatory (“because”): “Because fish don’t eat garbage. They eat plants under the water” (page 78).

In the June interviews, the students showed that they had become familiar with the function of hypotheses and experiments and with reasoning within larger explanatory frameworks. Elinor had developed a model of an integrated water system in which an action or event in one part of the system had consequences for other parts (Rosebery et al., 1992:87):

You can’t leave [the bad stuff] on the ground. If you leave it on the ground, the water that, the earth has water underground, it will still spoil the water underground. Or when it rains it will just take it and, when it rains, the water runs, it will take it and leave it in the river, in where the water goes in. Those things, poison things, you aren’t supposed to leave it on the ground.

In June, the students no longer invoked anonymous agents, but put forward chains of hypotheses to explain phenomena, such as why children were getting sick (page 88):

Like, you could test what the kids ate and, like, test the water, too; it could be the water that isn’t good, that has microbes, that might have microscopic animals in it to make them sick.

The June interviews also showed that students had begun to develop a sense of the function and form of experimentation. They no longer depended on personal experience as evidence, but proposed experiments to test specific hypotheses. In response to a question about sick fish, Laure clearly understands how to find a scientific answer (page 91):

I’d put a fish in fresh water and one fish in a water full of garbage. I’d give the fresh water fish food to eat and the other one in the nasty water, I’d give it food to eat to see if the fresh water, if the one in the fresh water would die with the food I gave it, if the one in the dirty water would die with the food I gave it…. I would give them the same food to see if the things they eat in the water and the things I give them now, which will make them healthy and which wouldn’t make them healthy.

Teaching and learning in science have been influenced very directly by research studies on expertise (see Chapter 2 ). The examples discussed in this chapter focus on two areas of science teaching: physics and junior high school biology. Several of the teaching strategies illustrated ways to help students think about the general principles or “big” ideas in physics before jumping to formulas and equations. Others illustrate ways to help students engage in deliberate practice (see Chapter 3 ) and to monitor their progress.

Learning the strategies for scientific thinking have another objective: to develop thinking acumen needed to promote conceptual change. Often, the barrier to achieving insights to new solutions is rooted in a fundamental misconception about the subject matter. One strategy for helping students in physics begins with an “anchoring intuition” about a phenomenon and then gradually bridging it to related phenomena that are less intuitive to the student but involve the same physics principles. Another strategy involves the use of interactive lecture demonstrations to encourage students to make predictions, consider feedback, and then reconceptualize phenomena.

The example of Chèche Konnen demonstrates the power of a sense-making approach to science learning that builds on the knowledge that students bring with them to school from their home cultures, including their familiar discourse practices. Students learned to think, talk, and act scientifically, and their first and second languages mediated their learning in power-

ful ways. Using Haitian Creole, they designed their studies, interpreted data, and argued theories; using English, they collected data from their mainstream peers, read standards to interpret their scientific test results, reported their findings, and consulted with experts at the local water treatment facility.

Outstanding teaching requires teachers to have a deep understanding of the subject matter and its structure, as well as an equally thorough understanding of the kinds of teaching activities that help students understand the subject matter in order to be capable of asking probing questions.

Numerous studies demonstrate that the curriculum and its tools, including textbooks, need to be dissected and discussed in the larger contexts and framework of a discipline. In order to be able to provide such guidance, teachers themselves need a thorough understanding of the subject domain and the epistemology that guides the discipline (for history, see Wineburg and Wilson, 1988; for math and English, see Ball, 1993; Grossman et al., 1989; for science, see Rosebery et al., 1992).

The examples in this chapter illustrate the principles for the design of learning environments that were discussed in Chapter 6 : they are learner, knowledge, assessment, and community centered. They are learner centered in the sense that teachers build on the knowledge students bring to the learning situation. They are knowledge centered in the sense that the teachers attempt to help students develop an organized understanding of important concepts in each discipline. They are assessment centered in the sense that the teachers attempt to make students’ thinking visible so that ideas can be discussed and clarified, such as having students (1) present their arguments in debates, (2) discuss their solutions to problems at a qualitative level, and (3) make predictions about various phenomena. They are community centered in the sense that the teachers establish classroom norms that learning with understanding is valued and students feel free to explore what they do not understand.

These examples illustrate the importance of pedagogical content knowledge to guide teachers. Expert teachers have a firm understanding of their respective disciplines, knowledge of the conceptual barriers that students face in learning about the discipline, and knowledge of effective strategies for working with students. Teachers’ knowledge of their disciplines provides a cognitive roadmap to guide their assignments to students, to gauge student progress, and to support the questions students ask. The teachers focus on understanding rather than memorization and routine procedures to follow, and they engage students in activities that help students reflect on their own learning and understanding.

The interplay between content knowledge and pedagogical knowledge illustrated in this chapter contradicts a commonly held misconception about teaching—that effective teaching consists of a set of general teaching strategies that apply to all content areas. This notion is erroneous, just as is the idea that expertise in a discipline is a general set of problem-solving skills that lack a content knowledge base to support them (see Chapter 2 ).

The outcomes of new approaches to teaching as reflected in the results of summative assessments are encouraging. Studies of students’ discussions in classrooms indicate that they learn to use the tools of systematic inquiry to think historically, mathematically, and scientifically. How these kinds of teaching strategies reveal themselves on typical standardized tests is another matter. In some cases there is evidence that teaching for understanding can increase scores on standardized measures (e.g., Resnick et al., 1991); in other cases, scores on standardized tests are unaffected, but the students show sizable advantages on assessments that are sensitive to their comprehension and understanding rather than reflecting sheer memorization (e.g., Carpenter et al., 1996; Secules et al., 1997).

It is noteworthy that none of the teachers discussed in this chapter felt that he or she was finished learning. Many discussed their work as involving a lifelong and continuing struggle to understand and improve. What opportunities do teachers have to improve their practice? The next chapter explores teachers’ chances to improve and advance their knowledge in order to function as effective professionals.

First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning.

Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods—to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb.

How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system.

Topics include:

  • How learning actually changes the physical structure of the brain.
  • How existing knowledge affects what people notice and how they learn.
  • What the thought processes of experts tell us about how to teach.
  • The amazing learning potential of infants.
  • The relationship of classroom learning and everyday settings of community and workplace.
  • Learning needs and opportunities for teachers.
  • A realistic look at the role of technology in education.

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Teaching problem solving

Strategies for teaching problem solving apply across disciplines and instructional contexts. First, introduce the problem and explain how people in your discipline generally make sense of the given information. Then, explain how to apply these approaches to solve the problem.

Introducing the problem

Explaining how people in your discipline understand and interpret these types of problems can help students develop the skills they need to understand the problem (and find a solution). After introducing how you would go about solving a problem, you could then ask students to:

  • frame the problem in their own words
  • define key terms and concepts
  • determine statements that accurately represent the givens of a problem
  • identify analogous problems
  • determine what information is needed to solve the problem

Working on solutions

In the solution phase, one develops and then implements a coherent plan for solving the problem. As you help students with this phase, you might ask them to:

  • identify the general model or procedure they have in mind for solving the problem
  • set sub-goals for solving the problem
  • identify necessary operations and steps
  • draw conclusions
  • carry out necessary operations

You can help students tackle a problem effectively by asking them to:

  • systematically explain each step and its rationale
  • explain how they would approach solving the problem
  • help you solve the problem by posing questions at key points in the process
  • work together in small groups (3 to 5 students) to solve the problem and then have the solution presented to the rest of the class (either by you or by a student in the group)

In all cases, the more you get the students to articulate their own understandings of the problem and potential solutions, the more you can help them develop their expertise in approaching problems in your discipline.

Center for Teaching

Teaching problem solving.

Print Version

Tips and Techniques

Expert vs. novice problem solvers, communicate.

  • Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
  • If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
  • In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
  • When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

  • Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
  • Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
  • Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

  • Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

  • Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

explain the utility of problem solving method in history teaching

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Defining Authenticity in Historical Problem Solving

explain the utility of problem solving method in history teaching

At Sammamish High School, we've identified seven key elements of problem-based learning, an approach that drives our comprehensive curriculum. I teach tenth grade history, which puts me in a unique position to describe the key element of authentic problems.

What is an authentic problem in world history? My colleagues and I grappled with this question when we set about to design a problem-based learning (PBL) class for AP World History. We looked enviously at some of our peer disciplines such as biology which we imagined having clear problems for students to work on (they didn't, but that is another blog post).

We consulted a number of sources in research. What did the College Board say? What do the state standards say? We reached out to Walter Parker, the social studies methods instructor at the University of Washington School of Education, to help us clarify our thinking.

We arrived at two ways to think about authentic problems. One I will call the work of historians in the field, and the other was the work of historical actors at the time. We quickly felt a healthy tension between these two ideas.

Living the Decisions

The work of historians involves creating and debating the frameworks for the historical narratives our students use to interpret history. One problem that historians debate is the question of periodization, or how history should be divided chronologically in order to better understand it. We know these chunks of time -- or eras -- by the more familiar labels given them by historians: classical, medieval and modern, to name a few. These debates are highly charged because they are so important in defining what students entering the field should study. For example, should World War I be considered a turning point in world history, or is World War I really a European civil war whose significance as a global turning point diminishes with passing of each decade?

It was exciting to consider that our students would engage in such high-level and rigorous academic thinking. We could think of many meaty questions for them to explore and discuss: What was the legacy of Mongol rule? Is the modern era a time of progress? Even the question, "Is there really such a thing as world history?" However, we wondered, was it realistic to ask students to do the work of historians? Could we prepare them well enough to have these highly abstract but critical conversations? College professors spend years steeping themselves exclusively in their discipline, while our students devote one seventh of their class time to world history. My colleague and I had both engaged students in such debates during our practice, but not in an integrated systematic way.

Our approach to authentic problems came from a different perspective: that of the historical actor and decision-makers. By giving students roles based around a historical problem we could ask them, "What would you do, and why?" This, of course, is nothing new. Teachers have been creating simulations and role-plays to engage their students for generations. We wanted to build a unit or "challenge cycle" around these activities.

Ultimately, we decided that it would be difficult for students to do the work of historians if they had not done the work of historical actors. By "living" the decisions through problem-based simulations, our students would collectively be better prepared to engage in the larger questions that are debated in the discipline of history.

Challenge Cycles

What did this look like in World History? We created challenge cycles based on each of the eras into which the course was divided. Our first attempt at building a PBL challenge cycle took place when we studied the Early Modern Era (1450-1750) and focused on the theme of diplomacy. Students were assigned to empire teams based on their interests, and they played the role of foreign policy advisors. Their mission: to determine how diplomacy could help their empire maintain and expand power. The simulation component culminated in a round of treaty negotiations between empires. We found that while students were energized and came to know their roles deeply, they were not directly engaging in the conversations and debates that historians have.

After we piloted our first PBL units, we built in a day for a debrief discussion explicitly linking the challenge cycle with the authentic questions that historians address. This debrief day also allowed students to drop their simulation roles, which frequently put them in competitive or modestly adversarial relationships with one another. They were free to argue against the position their historical figure would have taken. For example, during our diplomacy challenge debrief, the Ottoman Empire could argue the position of their Spanish archrivals. We also broke down our challenge cycle into components that allowed students to deepen their understanding of their historical actors in relation to others. In our diplomacy challenge, this meant building in a diplomatic reception in which our student diplomats had to toast an empire with which they wanted to engage in trade.

Diplomats and Historians

What kind of comments have we heard from students? Their response has become more positive as we have refined our pilot units. Here is a brief sample from a survey we took on our diplomacy challenge unit:

  • "We all were sort of competing, which made us try harder."
  • "The reception was super neat."
  • "I really enjoyed knowing about my empire, therefore I wanted to learn more about that empire and master it . . . I liked the process: 1st power point, to get to know the empire. 2nd Toast. This process helped me understand the empires. ."
  • "Elaborate more on what actually happened instead of the Socratic seminar [debrief] because I would've liked to know more concrete details."
  • "Remove the reception (I think this could have been a two-week project)."

After a year of designing and testing the curriculum, we have come to understand that some problems and their components feel more authentic than others. Representatives of the early modern empires were rarely gathered together at one reception, and diplomacy is obviously conducted over a longer period of time with changing players. However, the toasts our student diplomats made at that diplomatic reception would not have been out of place at a White House state dinner (although our students' were briefer), and the skills they used in trying to woo a trading partner were just as real.

As we continue to refine this course of study, the healthy tension between the work of the historian and the work of the actor remains, as does the desire to create a curriculum where students can meaningfully engage in both.

Editor's Note: Visit " Case Study: Reinventing a Public High School with Problem-Based Learning " to stay updated on Edutopia's coverage of Sammamish High School.

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Problem-Based Learning (PBL)

What is Problem-Based Learning (PBL)? PBL is a student-centered approach to learning that involves groups of students working to solve a real-world problem, quite different from the direct teaching method of a teacher presenting facts and concepts about a specific subject to a classroom of students. Through PBL, students not only strengthen their teamwork, communication, and research skills, but they also sharpen their critical thinking and problem-solving abilities essential for life-long learning.

See also: Just-in-Time Teaching

Problem-Based Learning (PBL)

In implementing PBL, the teaching role shifts from that of the more traditional model that follows a linear, sequential pattern where the teacher presents relevant material, informs the class what needs to be done, and provides details and information for students to apply their knowledge to a given problem. With PBL, the teacher acts as a facilitator; the learning is student-driven with the aim of solving the given problem (note: the problem is established at the onset of learning opposed to being presented last in the traditional model). Also, the assignments vary in length from relatively short to an entire semester with daily instructional time structured for group work.

Pbl

By working with PBL, students will:

  • Become engaged with open-ended situations that assimilate the world of work
  • Participate in groups to pinpoint what is known/ not known and the methods of finding information to help solve the given problem.
  • Investigate a problem; through critical thinking and problem solving, brainstorm a list of unique solutions.
  • Analyze the situation to see if the real problem is framed or if there are other problems that need to be solved.

How to Begin PBL

  • Establish the learning outcomes (i.e., what is it that you want your students to really learn and to be able to do after completing the learning project).
  • Find a real-world problem that is relevant to the students; often the problems are ones that students may encounter in their own life or future career.
  • Discuss pertinent rules for working in groups to maximize learning success.
  • Practice group processes: listening, involving others, assessing their work/peers.
  • Explore different roles for students to accomplish the work that needs to be done and/or to see the problem from various perspectives depending on the problem (e.g., for a problem about pollution, different roles may be a mayor, business owner, parent, child, neighboring city government officials, etc.).
  • Determine how the project will be evaluated and assessed. Most likely, both self-assessment and peer-assessment will factor into the assignment grade.

Designing Classroom Instruction

See also: Inclusive Teaching Strategies

  • Take the curriculum and divide it into various units. Decide on the types of problems that your students will solve. These will be your objectives.
  • Determine the specific problems that most likely have several answers; consider student interest.
  • Arrange appropriate resources available to students; utilize other teaching personnel to support students where needed (e.g., media specialists to orientate students to electronic references).
  • Decide on presentation formats to communicate learning (e.g., individual paper, group PowerPoint, an online blog, etc.) and appropriate grading mechanisms (e.g., rubric).
  • Decide how to incorporate group participation (e.g., what percent, possible peer evaluation, etc.).

How to Orchestrate a PBL Activity

  • Explain Problem-Based Learning to students: its rationale, daily instruction, class expectations, grading.
  • Serve as a model and resource to the PBL process; work in-tandem through the first problem
  • Help students secure various resources when needed.
  • Supply ample class time for collaborative group work.
  • Give feedback to each group after they share via the established format; critique the solution in quality and thoroughness. Reinforce to the students that the prior thinking and reasoning process in addition to the solution are important as well.

Teacher’s Role in PBL

See also: Flipped teaching

As previously mentioned, the teacher determines a problem that is interesting, relevant, and novel for the students. It also must be multi-faceted enough to engage students in doing research and finding several solutions. The problems stem from the unit curriculum and reflect possible use in future work situations.

  • Determine a problem aligned with the course and your students. The problem needs to be demanding enough that the students most likely cannot solve it on their own. It also needs to teach them new skills. When sharing the problem with students, state it in a narrative complete with pertinent background information without excessive information. Allow the students to find out more details as they work on the problem.
  • Place students in groups, well-mixed in diversity and skill levels, to strengthen the groups. Help students work successfully. One way is to have the students take on various roles in the group process after they self-assess their strengths and weaknesses.
  • Support the students with understanding the content on a deeper level and in ways to best orchestrate the various stages of the problem-solving process.

The Role of the Students

See also: ADDIE model

The students work collaboratively on all facets of the problem to determine the best possible solution.

  • Analyze the problem and the issues it presents. Break the problem down into various parts. Continue to read, discuss, and think about the problem.
  • Construct a list of what is known about the problem. What do your fellow students know about the problem? Do they have any experiences related to the problem? Discuss the contributions expected from the team members. What are their strengths and weaknesses? Follow the rules of brainstorming (i.e., accept all answers without passing judgment) to generate possible solutions for the problem.
  • Get agreement from the team members regarding the problem statement.
  • Put the problem statement in written form.
  • Solicit feedback from the teacher.
  • Be open to changing the written statement based on any new learning that is found or feedback provided.
  • Generate a list of possible solutions. Include relevant thoughts, ideas, and educated guesses as well as causes and possible ways to solve it. Then rank the solutions and select the solution that your group is most likely to perceive as the best in terms of meeting success.
  • Include what needs to be known and done to solve the identified problems.
  • Prioritize the various action steps.
  • Consider how the steps impact the possible solutions.
  • See if the group is in agreement with the timeline; if not, decide how to reach agreement.
  • What resources are available to help (e.g., textbooks, primary/secondary sources, Internet).
  • Determine research assignments per team members.
  • Establish due dates.
  • Determine how your group will present the problem solution and also identify the audience. Usually, in PBL, each group presents their solutions via a team presentation either to the class of other students or to those who are related to the problem.
  • Both the process and the results of the learning activity need to be covered. Include the following: problem statement, questions, data gathered, data analysis, reasons for the solution(s) and/or any recommendations reflective of the data analysis.
  • A well-stated problem and conclusion.
  • The process undertaken by the group in solving the problem, the various options discussed, and the resources used.
  • Your solution’s supporting documents, guests, interviews and their purpose to be convincing to your audience.
  • In addition, be prepared for any audience comments and questions. Determine who will respond and if your team doesn’t know the answer, admit this and be open to looking into the question at a later date.
  • Reflective thinking and transfer of knowledge are important components of PBL. This helps the students be more cognizant of their own learning and teaches them how to ask appropriate questions to address problems that need to be solved. It is important to look at both the individual student and the group effort/delivery throughout the entire process. From here, you can better determine what was learned and how to improve. The students should be asked how they can apply what was learned to a different situation, to their own lives, and to other course projects.

See also: Kirkpatrick Model: Four Levels of Learning Evaluation

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I am a professor of Educational Technology. I have worked at several elite universities. I hold a PhD degree from the University of Illinois and a master's degree from Purdue University.

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Simple Guide to Problem-Solving Method of Teaching

What is Problem-Solving Method of Teaching?

You must be interested to know – What is the problem-solving method of teaching and how it works. We’ve explained its core principles, six-step process, and benefits with real-world examples.

Understand the Problem-Solving Method of Teaching

The basis of this modern teaching approach is to provide students with opportunities to face real-time challenges. It aims to help them understand how the concept behind a solution works in reality.

What is the Problem-Solving Method of Teaching?

The problem-solving method of teaching is a student-centered approach to learning that focuses on developing students’ problem-solving skills. In this method, students have to face real-world problems to solve.

They are encouraged to use their knowledge and skills to provide solutions. The teacher acts as a facilitator, providing guidance and support as needed, but ultimately the students are responsible for finding their solutions.

Must Read: How to Tell Me About Yourself in an Interview

5 Most Important Benefits of Problem-Solving Method of Teaching

The new way of teaching primarily helps students develop critical thinking skills and real-world application abilities. It also promotes independence and self-confidence in problem-solving.

The problem-solving method of teaching has several benefits. It helps students to:

#1 Enhances critical thinking

By presenting students with real-world problems to solve, the problem-solving method of teaching forces them:

– To think critically about the situation, and – To come up with their solutions.

This process helps students develop critical thinking skills essential for success in school and life.

#2 Fosters creativity

The problem-solving method of teaching encourages students to be creative in their problem-solving approach. There is often no one right answer to a problem, so students are free to come up with their unique solutions. This process helps students think creatively, an important skill in all areas of life.

#3 Encourages real-world application

The problem-solving method of teaching helps students learn how to apply their knowledge to real-world situations. By solving real-world problems, students can see:

– How their knowledge is relevant to their lives, – And, the world around them.

This helps students to become more motivated and engaged learners.

#4 Builds student confidence

When students can successfully solve problems, they gain confidence in their abilities. This confidence is essential for success in all areas of life, both academic and personal.

#5 Promotes collaborative learning

The problem-solving method of teaching often involves students working together to solve problems. This collaborative learning process helps students to develop their teamwork skills and to learn from each other.

Know 6 Steps in the Problem-Solving Method of Teaching

Also Read: Do You Know the Difference Between ChatGPT and GPT-4?

The problem-solving method of teaching typically involves the following steps:

Step 1: Identifying the problem

The first step is problem identification which students will be working on. This requires students to do the following:

– By presenting students with a real-world problem, or – By asking them to come up with their problems.

Step 2: Understanding the problem

Once students have identified the problem, they need to understand it fully. This may involve:

– Breaking the problem down into smaller parts, or – Gathering more information about the problem.

Step 3: Generating solutions

Once students understand the problem, they need to generate possible solutions. They have to do either of the following:

– By brainstorming, or – By exercising problem-solving techniques such as root cause analysis or the decision matrix.

Step 4: Evaluating solutions

Students need to evaluate the pros and cons of each solution before choosing one to implement.

Step 5: Implementing the solution

Once students have chosen a solution, they need to implement it. This may involve taking action or developing a plan.

Step 6: Evaluating the results

Once students have implemented the solution, they must evaluate the results to see if it was successful.

If the solution fails the expectations, students should re-run step 3 and generate new solutions.

Find Out Examples of the Problem-Solving Method of Teaching

Here are a few examples of how the problem-solving method of teaching applies to different subjects:

  • Math: Students face real-world problems such as budgeting for a family or designing a new product. Students would then need to use their math skills to solve the problem.
  • Science: Students perform a science experiment or research on a scientific topic to invent a solution to the problem. Students should then use their science knowledge and skills to solve the problem.
  • Social studies: Students analyze a historical event or current social issue and devise a solution. After that, students should exercise their social studies knowledge and skills to solve the problem.

How to Use Problem-Solving Methods of Teaching

Here are a few tips for using the problem-solving method of teaching effectively:

  • Choose problems that are relevant to students’ lives and interests.
  • Select those problems that are challenging but achievable.
  • Provide students with ample resources such as books, websites, or experts to solve the problem.
  • Motivate them to work collaboratively and to share their ideas.
  • Be patient and supportive. Problem-solving can be a challenging process, but it is also a rewarding one.

Also Try: 1-10 Random Number Generator

How to Choose: Let’s Draw a Comparison

The following table compares the different problem-solving methods:

MethodDescriptionProsCons
The teacher presents information to students who then complete exercises or assignments to practice the information.– Simple and easy-to-follow– Can be passive and boring for students
Students are presented with real-world problems to solve. They are encouraged to use their knowledge and skills to deliver solutions.– Promotes active learning– Can be challenging for students
Students are asked to investigate questions or problems. They are encouraged to gather evidence and come up with their conclusions.– Encourages critical thinking– Can be time-consuming

Which Method is the Most Suitable?

The most suitable way of teaching will depend on many factors such as the following:

– Subject matter, – Student’s age and ability level, and – Teacher’s preferences.

However, the problem-solving method of teaching is a valuable approach. It can be used in any subject area and with students of all ages.

Here are some additional tips for using the problem-solving method of teaching effectively:

  • Differentiate instruction. Not all students learn at the same pace or in the same way. Teachers can differentiate instruction to meet the needs of all learners by providing different levels of support and scaffolding.
  • Use formative assessment. Formative assessment helps track students’ progress and identify areas where they need additional support. Teachers can then use this information to provide students with targeted instruction.
  • Create a positive learning environment. Students need to feel safe and supported to learn effectively. Teachers can create a positive learning environment by providing students with opportunities for collaboration. They can celebrate their successes and create a classroom culture where mistakes are seen as learning opportunities.

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Some Unique Examples to Refer to Before We Conclude

Here are a few unique examples of how you incorporate the problem-solving method of teaching with different subjects:

  • English: Students analyze a grammar problem, such as a poem or a short story, and share their interpretation.
  • Art: Students can get a task to design a new product or to create a piece of art that addresses a social issue.
  • Music: Students write a song about a current event or create a new piece of music reflecting their cultural heritage.

Before You Leave

The problem-solving method of teaching is a powerful tool that can help students develop the skills they need to succeed in school and life. By creating a learning environment where students are encouraged to think critically and solve problems, teachers can help students to become lifelong learners.

Lastly, our site needs your support to remain free. Share this post on social media ( Linkedin / Twitter ) if you gained some knowledge from this tutorial.

Enjoy learning, TechBeamers.

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Article contents

John dewey and teacher education.

  • Margaret Schmidt Margaret Schmidt Arizona State University
  •  and  Randall Everett Allsup Randall Everett Allsup Teachers College Columbia University
  • https://doi.org/10.1093/acrefore/9780190264093.013.475
  • Published online: 29 July 2019

John Dewey’s writings on schooling are extensive, and characteristically wide-ranging: teachers are expected to think deeply about knowledge construction, how we think and learn, the purpose of curriculum in the life of the child, and the role of school and societal reform. He worked throughout his life to develop and refine his philosophy of experience, describing all learning as defined by the quality of interactions between the learner and the social and physical environment. According to Dewey, teachers have a responsibility to structure educational environments in ways that promote educative learning experiences, those that change the learner in such a way as to promote continued learning and growth. The capacity to reflect on and make meaning from one’s experiences facilitates this growth, particularly in increasing one’s problem-solving abilities.

While Dewey wrote little that specifically addressed the preparation of teachers, his 1904 essay, “The Relation of Theory to Practice in Education,” makes clear that he grounds his beliefs about teachers’ learning in this same philosophy of experiential learning. Dewey argued that thoughtful reflection on previous and current educational experiences is especially important in teacher preparation; teacher educators could then guide beginners to examine and test the usefulness of the beliefs formed from those experiences. Teacher educators, therefore, have a responsibility to arrange learning environments for beginning teachers to promote sequential experiences leading to increased understanding of how children learn, “how mind answers to mind.” These experiences can then help beginning teachers grow, not as classroom technicians, but as true “students of teaching.”

Dewey’s ideas remain relevant, but must also be viewed in historical context, in light of his unfailing belief in education and the scientific method as ways to promote individual responsibility and eliminate social problems. His vision of a democratic society remains a fearless amalgam of human adaptation, continuity, change, and diversity: public schools are privileged locations in a democracy for the interplay and interrogation of old and new ideas. Teacher preparation and teacher wellbeing are crucial elements; they can provide experiences to educate all children for participation in their present lives in ways that facilitate their growth as citizens able to fully participate in a democracy. Despite criticism about limitations of his work, Dewey’s ideas continue to offer much food for thought, for both research and practice in teacher education.

  • teacher preparation
  • preservice teachers
  • learning from experience
  • progressive education

Introduction

Few 20th- and 21st-century philosophers have written as prolifically as John Dewey ( 1859–1952 ), capturing ideas in wide-ranging domains such as nature, psychology, science, politics, metaphysics, ethics, and art. Like the ancients Plato and Confucius, Dewey saw philosophy and education as nearly synonymous. And like Plato and Confucius, Dewey sensed the immense power that education could play in shaping not only the individual, but more importantly, the individual in society. Dewey was exceptional in the importance he placed on education, learning, schools, and teachers.

Although practices and beliefs about the preparation of teachers have continued to evolve in the nearly 70 years since Dewey’s death, his writings are regularly referenced among teacher educators. Our intent in this article is to engage with those ideas that have continuing relevance for teacher education, drawing upon the following seminal writings on teachers and teaching: The School and Society ( 1899 ); The Child and the Curriculum ( 1902 ); How We Think ( 1933 ); Experience and Education ( 1938 ); Moral Principles in Education ( 1909 ); Democracy and Education ( 1916 ); “The Relation of Theory to Practice in Education” (1904a), and several essays. As practicing university music teacher educators, we will use examples from the world of music education that are general enough for any discipline.

To understand Dewey’s ideas about how teachers may best learn to teach, Dewey’s own starting point is first approached—that education, and indeed all learning, cannot be understood apart from experience. Next, Dewey’s description of reflective thinking, by which all learners make meaning from their experiences, is presented. Dewey’s ideas specific to teacher education follow: his understanding of the relationship between educational theory and educational practice, and the sequence of experiences he proposed for pre-service teachers. Dewey’s ideas about teaching methods and learning in laboratories are then discussed. The article concludes with reflections placing Dewey’s writings in historical context, and questions for continued research and practice in the Deweyian tradition.

Learning and Experience

All learning, Dewey ( 1938 , p. 7) believed, results from experience—not just in school, but in the individual’s life beyond school as well. Due to the “intimate and necessary relation between the processes of actual experience and education,” he wanted educators to develop deep understanding of the function of experience in learning. Dewey ( 1933 , 1938 ) defined an experience as an interaction between an individual and the environment, suggesting that all experiences—good and bad—involve doing (how the individual interacts with the environment) and undergoing (how the experience changes the individual). Dewey ( 1938 , p. 13) continually emphasized that, while all students unquestionably have “experiences” in schools, “everything depends upon the quality of the experience which is had.”

The quality of an experience can be judged in relation to two simultaneously occurring processes or principles: interaction and continuity (Dewey, 1938 ). As an individual interacts with her physical environment, she creates insights derived from her interests and curiosities (doing). A child playing the piano for the first time will soon discover gradations of high and low, loud and soft. To her delight, she will soon find out that the pedal somehow makes the sound keep going. But from the standpoint of formal education and requisites of growth, a “quality” experience requires that her discoveries become useful to her needs and her community (undergoing growth in understanding). She needs to be given a place to share and test what she has learned with others, thus affording meaningful contributions to the people around her (Dewey, 1916 , 1938 ). Quality experiences require quality interactions, and teachers are tasked with enriching and enlarging the classroom environment, “in other words, whatever conditions interact with personal needs, desires, purposes, and capacities to create the experience which is had” (Dewey, 1938 , p. 25).

The principle of continuity states that the effect of a “good” or “educative” experience is cumulative and enriching. Dewey is famously paraphrased as saying that the purpose of growth is more growth. But such an oversimplification ignores the critical role that teachers play in helping the learner make sense of what has been discovered so that further growth is not misshaped. Whether on the playground or from a history book, all teachers know that wrong lessons can be learned. For Dewey ( 1933 , 1938 ), mis-educative experiences result in insights that impede further learning, while non-educative experiences fail to connect one experience with another, leaving the learner unchanged or merely incurious. In contrast, educative experiences live on in further experiences. “Hence, the central problem of an education based upon experience is to select the kind of present experiences that live fruitfully and creatively in subsequent experiences” (Dewey, 1938 , p. 13). A teacher’s work is thus “moral,” because educators are charged with the fraught task of interfering in the incidental nature of most social learning (Dewey, 1909 ). A society trusts teachers to select experiences (via curriculum, via pedagogy) that then produce “quality” growth in “other people’s children” (Delpit, 1995 ). Likewise, according to Dewey, teachers have a moral responsibility to become familiar with their students’ home cultures and design lessons that appeal to their interests (Gay, 2010 ; Ladson-Billings, 1995 ), using conditions in the local community “as educational resources” (Dewey, 1938 , p. 23).

Dewey ( 1938 , p. 5) frequently critiqued what he and others have called “traditional education.” While we admit that the term is both imprecise and problematic, Dewey used it to refer to classrooms where teachers expected students to repeat back whatever isolated knowledge was presented to them for use in some distant future; such experiences, devoid of meaningful connections are at best noneducative, and at worst mis-educative. As music educators, the authors of this article are aware of the many dangers of isolated knowledge; for example, teaching musical notation as if its purpose were self-evident and universal (say), or teaching Western classical art music as if it were a-historical or context-free. As university teacher educators, we have too often seen beginning teachers ask children for solutions to “so-called problems” that are “simply assigned tasks ” (Dewey, 1933 , p. 233) or “activities” (Dewey, 1916 ), rather than genuine problems leading to meaningful insights. Dewey ( 1938 , p. 23, italics in the original) similarly cautioned proponents of “progressive education,” those “parents and some teachers [who seem to be] acting upon the idea of subordinating objective conditions to internal ones.” For Dewey ( 1938 , p. 63, italics in the original), the issue was not “new versus old education;” rather, his concern was “a question of what anything whatever must be to be worthy of the name education .” He believed that a middle, more pragmatic approach could help students use the interactions between their internal inclinations and the external environment to both connect present experiences with past experiences and prepare them for continued future growth. Drawing on the principles of interaction and continuity, teachers could learn “how to utilize the surroundings, physical and social, that exist so as to extract from them all that they have to contribute to building up experiences that are worthwhile” (Dewy, 1938 , p. 22; also, see Hildebrand, 2018 , for a summary of how Dewey developed these philosophical ideas over time.)

Making Meaning Through Reflective Thinking

To further develop the educative potential of experience, Dewey believed that quality of thought is the basis of all meaningful learning, both in school and in life. Dewey identifies three types of thinking: idle thought, belief, and reflection. Idle thought is “inconsequential trifling with mental pictures, random recollections . . . [and] half-developed impressions” (Dewey, 1933 , p. 114). Beliefs are ideas that “are picked up—we know not how” through “tradition, instruction, imitation . . . Even when they happen to be correct, their correctness is a matter of accident as far as the person who entertains them is concerned” (Dewey, 1933 , p. 116). In contrast, reflective thought is the “active, persistent, and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusions to which it tends” (Dewey, 1933 , p. 118). For Dewey, critical or reflective thinking is the only educational aim that can foster freedom of mind and action; he applied this principle equally to the learning and teaching of everyone involved in education, including students, pre-service teachers, and experienced teachers.

Similar to the consummatory experiences in art described by Dewey in his book Art as Experience ( 1934 ), reflective thinking has a kind of rhythm through which insights emerge. The cycle begins with “a perplexed, troubled, or confused situation,” a deviation from the expected situation, that Dewey ( 1933 , p. 200) identifies as a pre- reflective phase; the cycle concludes temporarily in a post -reflective state, a space of intellectual satisfaction—before a new puzzle or trouble reveals itself:

In between, as states of thinking, are (1) suggestions , in which the mind leaps forward to a possible solution; (2) an intellectualization of the difficulty or perplexity that has been felt (directly experienced) into a problem to be solved, a question for which the answer must be sought; (3) the use of one suggestion after another as a leading idea, or hypothesis , to initiate and guide observation and other operations in collection of factual material; (4) the mental elaboration of the idea or supposition as an idea or supposition ( reasoning , in the sense in which reasoning is a part, not the whole, of inference); and (5) testing the hypothesis by overt or imaginative action.

Reflecting mindfully about experiences “done” and “undergone” creates growth-enhancing habits , which for Dewey ( 1938 , p. 19) include emotional and intellectual dispositions, as well as “our basic sensitivities and ways of meeting and responding to all the conditions which we meet in living.” A large part of learning—and learning to teach—involves the development of productive attitudes and habits of thought. Both teachers and teacher educators must actively cultivate reflective attitudes of open-mindedness, whole-heartedness, and responsibility with their students. Open-mindedne ss, for Dewey ( 1916 , p. 182), is “accessibility of mind to any and every consideration that will throw light upon the situation that needs to be cleared up, and that will help determine the consequences of acting this way or that,” listening to all sides, and considering “the possibility of error even in the beliefs that are dearest to us” (Dewey, 1933 , p. 136). Whole-hearted involvement in finding a solution or creating meaning, a complete absorption in learning, may be cultivated by experiences that create a sense of suspense in learners, an element of story with “plot interest” (Dewey, 1933 , p. 320). Once a pre-service teacher has considered various reasonable possibilities for resolving a problem, an attitude of intellectual responsibility requires projecting and accepting the consequences of a chosen action, “mak[ing] clear what is involved in really knowing and believing a thing” (Dewey, 1916 , p. 186). Together, open-mindedness, whole-heartedness, and responsibility promote “retention of the capacity to grow” for learners of all ages, as “the reward of such intellectual hospitality” (Dewwy, 1916 , p. 182).

Dewey ( 1916 , p. 183) encouraged educators to welcome diversity of thought, to allow children and preservice teachers time to follow their ideas and make errors, and to resist seeking only “speedy, accurately measurable, correct results”:

Results (external answers or solutions) may not be hurried; processes may not be forced. They take their own time to mature. Were all instructors to realize that the quality of mental process, not the production of correct answers, is the measure of educative growth something hardly less than a revolution in teaching would be worked.

The student’s reasoning while solving a problem was far more important to Dewey than the answer itself. A good math teacher will ask students to show their work. A good art teacher will ask students about their intentions and the problems they encountered along the way. A good teacher educator will ask a preservice teacher to explain her thought process in responding to a child’s unexpected response. Dewey ( 1933 , p. 239) recommended that teachers and teacher educators regularly encourage students to conceptualize their reasoning in words, to check that educative meanings were being formed; “without this conceptualizing or intellectualizing, nothing is gained that can be carried over to the better understanding of new experiences. The deposit is what counts, educationally speaking.”

Dewey ( 1899 , p. 12) firmly believed that individuals learn from “books or the sayings of others only as they are related to [personal] experience;” he regularly criticized efforts to require children to memorize information and facts disconnected from their own lives and culture. Such strategies would lead students to repeat meaningless information in efforts to please the teacher or to avoid punishment. In contrast, an emphasis on reflection or “good habits of thinking” (Dewey, 1916 , p. 159) will motivate learners to understand the purposes for which skills and information could be applied, providing further motivation for learning by “arous[ing] curiosity, strengthen[ing] initiative, and set[ting] up desires and purposes that are sufficiently intense to carry a person over dead places in the future” (Dewey, 1938 , pp. 20–21).

For Dewey ( 1916 , p. 166), all children can be creative, no matter the age or domain: “The child of three who discovers what can be done with blocks, or of six who finds out what he can make by putting five cents and five cents together, is really a discoverer.” As learners return to their discoveries, their insights will deepen. Once the child discovers that the pedals on a piano keep the sound ringing, she is likely to explore the very mechanics of the instrument, to lift the lid and look inside. She might even ask a friend to hold down the pedal for her while she touches or plucks the steel wires. Trading places, these intrepid discoverers are likely to create a tentative theory that they bring to the teacher. The music teacher, if she is clever, will help the discoverers find new tricks and delightful problems. “There are no limits to the possibility of carrying over into the objects and events of life, meanings originally acquired by thoughtful examination, and hence no limit to the continual growth of meaning in human life” (Dewey, 1933 , p. 128).

Similarly, beginning teachers must engage in “thoughtful examination” of their educational experiences. For productive reflection, they must reframe a “difficulty or perplexity that has been felt (directly experienced) into a problem to be solved” (Dewey, 1933 , p. 200).

No hard and fast rules decide whether a meaning suggested is the right and proper meaning to follow up. The individual’s own good (or bad) judgment is the guide. There is no label on any given idea or principle which says automatically, “Use me in this situation”—as the magic cakes of Alice in Wonderland were inscribed “Eat me.” The thinker has to decide. (Dewey, 1933 , p. 215)

Unlike the beginning teacher, experienced teachers, in considering children’s conceptual learning, have a store of reflected-upon experiences from which they have learned to predict typical responses. This frees them to focus on surprises that arise in the classroom, and thus they are more likely to be able to frame and reflect on the situation and develop and test hypothetical resolutions. Beginning teachers do not yet have this bank of experiences from which to examine student learning. With so many things happening around them, much of which is surprising, preservice teachers may need guidance to identify or frame a specific problem for productive reflection.

Not Theory Versus Practice: Theory and Practice

The principles of experiential learning and reflection apply equally to teachers working with children and to teacher educators guiding preservice teachers’ learning experiences. Dewey’s important essay, “The Relation of Theory to Practice in Education,” is one of his few that specifically addresses the problems of preparing teachers to do the work of teaching. Dewey ( 1904a , p. 247) “assumes without argument” that both theory and practice are necessary components of teacher preparation; the question in his mind was the purpose of “practical work.” He criticized the apprentice model that was practiced in many programs during his time (and has continued to remain popular) because it too often focuses the apprentice on the immediate results of instructional practices, rather than on long-term growth. Dewey ( 1904a , pp. 255, 251, italics in the original) proposed instead a “laboratory view” of practice, where theory and practice “grow together out of and into the teacher’s personal experience,” and where beginners acquire “ control of the intellectual methods required for personal and independent mastery of practical skill, rather than at turning out at once masters of the craft.” This creates a challenge for teacher educators, as preservice teachers are more interested, at least initially, in “what works” and “what doesn’t” than in general “intellectual methods.” Dewey ( 1904a , p. 256) argued that an early focus on acquiring technical skills is a dangerous shortcut, helpful at the beginning stages of one’s career, but harmful in the longer term:

For immediate skill may be got at the cost of power to go on growing. The teacher who leaves the professional school with power in managing a class of children may appear to superior advantage the first day, the first week, the first month, or even the first year, as compared with some other teacher who has a much more vital command of the psychology, logic, and ethics of development. But later “progress” may with such consist only in perfecting and refining skill already possessed. Such persons seem to know how to teach, but they are not students of teaching . . . Unless a teacher is such a student, he may continue to improve in the mechanics of school management, but he can not grow as a teacher, an inspirer and director of soul-life.

Dewey ( 1904a , p. 258) suggests that teacher education classes begin with critical reflection on preservice teachers’ own “direct and personal” learning experiences, both within and outside school, as “the greatest asset” in their possession. This store of experiences provides preservice teachers with “plenty of practical material by which to illustrate and vitalize theoretical principles and laws of mental growth in the process of learning,” as well as “plenty of practical experience by which to illustrate cases of arrested development—instances of failure and maladaptation and retrogression, or even degeneration” (Dewey, 1904a , p. 258). Through guided reflection about the past experiences that most enthused and confused them when they were young learners, preservice teachers might better connect educational theory with actual practice, becoming better equipped to test out their insights in their current setting.

The principle of continuity suggests both the importance and the possibility of guiding preservice teachers to transition from a student’s perspective on schooling and learning to a teacher’s perspective on education and teaching .

Only by beginning with the values and laws contained in the [preservice teacher’s] own experience of his own mental growth, and by proceeding gradually to facts connected with other persons of whom he can know little; and by proceeding still more gradually to the attempt actually to influence the mental operations of others, can educational theory be made most effective. Only in this way can the most essential trait of the mental habit of the teacher be secured—that habit which looks upon the internal, not upon the external; which sees that the important function of the teacher is the direction of the mental movement of the student, and that the mental movement must be known before it can be directed. (Dewey, 1904a , p. 262)

By focusing preservice teachers’ attention on “how teacher and pupils react upon each other—how mind answers to mind” (Dewey, 1904a , p. 260), the function of practical experiences becomes enriching their understanding of “the knowledge of subject-matter and the principles of education” (Dewey, 1904a , p. 249). Dewey believed that practical experiences could offer a rich source from which to develop, through reflection, a broad understanding of educational psychology and curriculum development, with a goal to develop “intellectual responsibility” and become independent practitioners, not just masters of a craft of teaching.

Sequence of Experiences in the Teacher Education Program

Dewey believed the popular apprenticeship model of learning through “cadetting” or student teaching was not adequate to meet the long-term well-being of future teachers. He developed many of his ideas about teacher education in the context of the laboratory schools he helped found at the University of Chicago ( 1896–1904 ), with later refinements as professor of philosophy at Columbia University. Dewey ( 1904a ) outlined a sequence of experiences that, in conjunction with a laboratory school, could help preservice teachers integrate their theoretical studies with their teaching practices.

Dewey ( 1904a , p. 268) recommended that preservice teachers’ reflection on their own past experiences be supplemented with initial observations in a school classroom—not so much to see how teachers teach, but “to get material for psychological observation and reflection, and some conception of the educational movement of the school as a whole.” According to Dewey ( 1904a , p. 260), these early observations should be focused “to see how teacher and pupils react upon each other—how mind answers to mind. . . . What the student needs most at this stage of growth is ability to see what is going on in the minds of a group of persons who are in intellectual contact with one another.” Only then, after developing a richer understanding of the workings of the school through reflective writing and observation, could preservice teachers begin to serve as assistants for “more intimate introduction to the lives of the children and the work of the school” (Dewey, 1904a , p. 268).

When preservice teachers are ready for the next challenge, after assisting the cooperating teacher with small tasks and putting theory and practice together through observation and reflection, they may begin to select and arrange subject matter. In typical Deweyian fashion, this third stage is pragmatically considered. Dewey believed that initial curriculum-making should not include the common task of writing isolated make-believe or “practice” lesson plans. Rather, the preservice teacher should focus on one subject area across grade levels to develop “the habit of viewing the entire curriculum as a continuous growth, reflecting the growth of mind itself” (Dewey, 1904a , pp. 267–268). In this third sequence of development, the prospective teacher co-participates in lesson planning by helping the cooperating teacher find supplementary materials, creating authentic discipline-specific problems, or developing a “scheme of possible alternative subjects for lessons and studies” (Dewey, 1904a , p. 269).

Once the preservice teacher is deemed ready, she may move to the fourth stage, actual teaching. Interestingly, in this penultimate period of preparation, the prospective teacher is “given the maximum amount of liberty possible” (Dewey, 1904a , p. 269).

Students should be given to understand that they not only are permitted to act upon their own intellectual initiative, but that they are expected to do so, and their ability to take hold of situations for themselves would be a more important factor in judging them than their following any particular set method or scheme. (Dewey, 1904a , p. 269)

Dewey ( 1904a , pp. 269–270) recommended that supervisors keep observation and feedback to a minimum, thereby allowing the preservice teacher time to overcome the “shock” of being newly in charge of a classroom, and “to get enough experience to make him capable of seeing the fundamental bearing of criticism upon work done.”

At this fourth stage, only when the preservice teacher begins to feel comfortable, may the instructor or supervisor offer suggestions. But rather than criticizing specific elements of the teaching or lesson planning, the supervisor should guide “the student to judge his own work critically, to find out for himself in what respects he has succeeded and in what failed, and to find the probable reasons for both failure and success” (Dewey, 1904a , p. 270). Building on a similar process from the third stage, Dewey ( 1904a , p. 270) recommended allowing the prospective educator to “assume responsibility for the development of some one topic . . . [rather than] to teach a certain number (necessarily smaller in range) of lessons in a larger number of subjects.” This posture would afford student teachers a deeper understanding of the principles of teaching, with less focus on the methods of teaching. “No greater travesty” could happen in a preservice teacher’s development than for the supervisor to assign “a brief number of lessons, have him under inspection in practically all the time of every lesson, and then criticise him almost, if not quite, at the very end of each lesson.” Such oversight might give the person “some of the knacks and tools of the trade,” but would not “develop a thoughtful and independent teacher” (Dewey, 1904a , p. 270).

Dewey’s fifth and final stage is actual apprenticeship. He insists that apprenticeship is only useful if the program is long enough for the beginning teacher to be grounded in “educational theory and history, in subject-matter, in observation, and in practice work of the laboratory type” (Dewey, 1904a , p. 271), and if the “practice schools are sufficiently large to furnish the required number of children” to offer all prospective teachers this opportunity (Dewey, 1904a , p. 270). Even here, Dewey ( 1904a , p. 271) recommends limiting oversight and criticism, while allowing the apprentice teacher “as much responsibility and initiative as he is capable of taking.” Preservice teachers’ reflective thinking about their teaching experiences remains critical here. The goal of supervision in this period is not for supervisors to “turn out teachers who will perpetuate their own notions and methods, but in the inspiration and enlightenment that come through prolonged contact with mature and sympathetic persons” (Dewey, 1904a , p. 271).

Dewey ( 1899 , p. 39) believed that this could be accomplished best by “getting things into connection with one another, so that they work easily, flexibly, and fully.” He advocated for more connection at all levels of education from kindergarten through college, connection among content areas, connection of theory and practice, connection of school with life; failing such relationships, “each side suffers from the separation” (Dewey, 1899 , p. 43).

Developing Teaching Methods

Dewey was consistent in his aversion to binary thinking. A concept like method (Latin methodus /Greek méthodos = pursuit) is neither inherently good, nor inherently evil—it is merely a strategic pursuit. A method, after all, is a natural aspect of life and living, defined in this article as the application of intelligence to the contingencies of an ever-changing world. Teaching methods are rightly criticized when they act as proxy for teacher strategy (Allsup & Westerlund, 2012 ; Dewey, 1916 ). In Deweyian logic, the most effective methods are funded by experience and self-reflection. For example, when introducing a new plant to a flower garden, the savvy gardener will call upon her past experiences to forecast how her new addition will thrive. Likewise, a music teacher will draw upon past experience to create interest in an unsuspecting but enthusiastic beginner who wants to play an instrument. In either situation, she knows that flourishing is never guaranteed. In these examples, our hypothetical methodologist will observe and take note, but be ready to make changes should her strategy require it.

In Dewey’s ( 1916 , p. 177) vision for teacher preparation, methods arise from a thorough understanding of one’s disciplinary domain, but subject matter is always balanced by a deep understanding of the principles of learning and teaching: “In brief, the method of teaching is the method of an art, of action intelligently directed by ends.” Using aesthetic language, teaching methods are never counterfeits or copies from fellow artists, but sincere forms of self-expression: “an expression of [teachers’] own intelligent observations” of children. Dewey ( 1916 , p. 177) argues that artists both follow their own inspiration and “study the operations and results of those in the past who have succeeded greatly.” The art of choosing an appropriate method is “the problem of establishing conditions that will arouse and guide curiosity ; of setting up the connections in things experienced that will on later occasions promote the flow of suggestions , create problems and purposes that will favor consecutiveness in the succession of ideas” through productive reflection (Dewey, 1933 , p. 157).

Dewey ( 1916 ) distinguishes “general method” from “individual method.” Preservice teachers can and should learn general methods from a more experienced teacher, including “knowledge of the past, of current technique, of materials, of the ways in which one’s own best results are assured,” supplemented with “child-study, psychology, and a knowledge of social environment” and a thorough knowledge of subject matter (Dewey, 1916 , pp. 177, 180). An understanding of general methods alone, however, is “worse than useless”—or even harmful—if it “get[s] in the way of [the teacher’s] own common sense” (Dewey, 1916 , p. 179). For example, Dewey ( 1933 , p. 207) suggests that there is “nothing especially sacred about the number five” in the phases of reflection that he outlines; depending on the situation, two phases may run together or a phase may be expanded to include more small steps. Dewey ( 1916 , pp. 178–179) viewed general methods, not as “ready-made models” for instruction, but as “aids in sizing up the needs, resources, and difficulties of the unique experiences” of individual learners.

As young teachers develop “the working tendencies of observation, insight, and reflection” (Dewey, 1904a , p. 256) of their students, and of themselves as educators, they may gain confidence and be freed to create their own individual methods as needed for different learners in varied social settings. As preservice teachers deepen their understanding of curriculum and educational theory, they may become more like jazz musicians, more improvisatory—more capable of allowing “these principles to work automatically, unconsciously, and hence promptly and effectively” (Dewey, 1904a , p. 256). The specific methods used by individual teachers with particular students thus “will vary as [their] past experiences and [their] preferences vary . . . [thus] no catalogue can ever exhaust [the] diversity of form and tint” of methodological approaches (Dewey, 1916 , p. 180).

Conceptualizing method as “a statement of the way the subject matter of an experience develops most effectively and fruitfully” (Dewey, 1916 , p. 186) can help young teachers to understand how to sequence problems for children’s experimentation and reflection in ways that, through continuity of learning, build deeper and deeper conceptual understanding of various subjects. Dewey ( 1916 , p. 164) suggests that “a large part of the art of instruction lies in making the difficulty of new problems large enough to challenge thought, and small enough so that, in addition to the confusion naturally attending the novel elements, there shall be luminous familiar spots from which helpful suggestions may spring” to connect with prior learning.

As mentioned, for Dewey ( 1916 , p. 160), the basis of any method (as with all learning) is experience. He suggests that “the first stage of contact with any new material, at whatever age of maturity” and no matter the subject matter, must allow children opportunities to experiment with material through trial and error, taking action (doing) and observing the consequences of the actions (undergoing), “trying to do something and having the thing perceptibly do something to one in return.” Once students have sufficient experience with an object or concept, “memory, observation, reading, communication” may all become “avenues for supplying data” for reflection and problem solving (Dewey, 1916 , p. 164).

Dewey warns that preservice teachers are likely to teach the way they were taught; they may fail to recognize that a new generation of students will always bring new problems to the classroom, or that a different social environment requires different considerations. He believed “thoughtful and alert student[s] of education” (Dewey, 1904a , p. 256) have a moral duty to learn about their students’ interests and prior experiences in order to design appropriate and effective learning experiences for them. The more teachers know about their students’ world, the better they may “understand the forces at work that need to be directed and utilized for the formation of reflective habits” (Dewey, 1933 , pp. 140–141). The teacher should “give pupils something to do, not something to learn; and the doing is of such a nature as to demand thinking, or the intentional noting of connections; learning naturally results” (Dewey, 1916 , p. 161).

To emphasize, Dewey ( 1933 , p. 157) saw the concept of “method” as richer than a pedagogical technique or the sequence of a lesson plan. Method must be understood in its very broadest sense:

Method covers not only what [the teacher] intentionally devises and employs for the purpose of mental training, but also what he does without any conscious reference to it—anything in the atmosphere and conduct of the school that reacts in any way upon the curiosity, the responsiveness, and the orderly activity of children.

Dewey calls this unconscious transmission “collateral learning,” a notion that predates current ideas about the “hidden curriculum” (e.g., Apple, 2004 ; Eisner, 1994 ; Giroux & Penna, 1979 ). Students will learn many things in a classroom, intended or not. For example, methods that require a student to memorize “predigested materials” might inadvertently teach the student that school is not a democratic space, nor one concerned with justice. Dewey ( 1938 , p. 27) believed that inappropriate collateral learning would dull the child’s innate curiosity, and might cause her to engage “in the mental truancy of mindwandering” or to build “an emotional revulsion against the subject” or schooling in general. Collateral learning may be educative or mis-educative, but it appears to be a constant in education.

Everything the teacher does, as well as the manner in which he does it, incites the child to respond in some way or other, and each response tends to set the child’s attitude in some way or other . The teacher is rarely (and even then never entirely) a transparent medium of the access of another mind to a subject. (Dewey, 1933 , p. 159, italics in the original)

Committed and ongoing reflection, Dewey believed, helps teachers, preservice teachers, and teacher educators remain alert for the development of their students’ attitudes toward learning.

Learning in Laboratories

Dewey is sometimes referred to as America’s first postmodernist because of his deep antipathy toward dualistic thinking (Hickman, 2007 ). Dewey was specifically worried that binaries misdirect the focus of our attention. The child, for example, should never be defined in opposition to the curriculum, or seen as an unformed or “miniature” adult (Dewey, 1902 ). Importantly, for Dewey, the public school must never be viewed as somehow isolated from the larger community in which it is located. Referring to the classroom as a “laboratory” was one way that Dewey could skirt the easy dualism that most people associated with schools—those all-too-familiar spaces that, with their tiny desks and green chalkboards, do not resemble much of anything else in society. Rather, the public school in a democracy is embryonic : a nondualistic metaphor that suggests an environment that is both safely apart and protected, but also incorporated into the “body” of society.

To do this means to make each one of our schools an embryonic community life, active with types of occupations that reflect the life of the larger society, and permeated throughout with the spirit of art, history, and science. [Hence] the school introduces and trains each child of society into membership within such a little community, saturating him with the spirit of service, and providing him with the instruments of effective self-direction. (Dewey, 1899 , pp. 19–20)

Set apart, protected, and incorporated, “the school in turn will be a laboratory in which the student . . . sees theories and ideas demonstrated, tested, criticized, enforced, and the evolution of new truths” (Dewey, 1899 , p. 56).

In contrast to the factory model of education, Dewey believed that the public school could be a place where the violence of industrial life (e.g., slaughter houses, iron foundries, railroad work, indentured servitude) is remedied and remediated, where displaced persons could be taught new life skills. Jane Addams in Chicago and Grace Dodge in New York City envisioned the school as a community hub—part library, museum, gymnasium, hospital, clubhouse, and savings bank—one that was centered around learning through community-building (Addams, 2002 ; Lagemann, 1979 ). Evelyn Dewey, writing with her father, makes a case for the school as a “social settlement,” a set-aside place that is deeply committed to the unique concerns of a particular neighborhood:

Schools all over the country are finding that the most direct way of vitalizing their work is through closer relations with local interest and occupations. That period of American school history which was devoted to building up uniformity of subject matter, method, administration, was obliged to neglect everything characteristic of the local environment, for attention to that meant deviation from uniformity . . . in aiming to hit all children by exactly the same educational ammunition, none were really deeply touched. Efforts to bring the work into vital connection with people’s experiences necessarily began to vary school materials to meet the special needs and definite features of local life. (Dewey & Dewey, 1915 , p. 339)

So integrated did Dewey ( 1899 , p. 45) consider the relationship between the school and democratic society that he composed a blueprint—a visual thought experiment—of the school’s relationship to community stakeholders, as well as disciplinary boundaries to each other. On the north side of the re-imagined school are openings to commercial businesses, on the east one sees arrows pointing to home and family life. In this metaphorical blueprint, a garden is located on the school’s south side, and the local university interacts with the school through its westward opening. In another chart, the school houses a museum at the center of the building with openings on four sides leading to chemistry, biology, art, and music labs. On another floor, one finds a library that is provocatively connected to the kitchen, the dining room, the shop, and the textile industries ( 1899 , pp. 52, 49).

Dewey concedes that most people will think of the laboratory as a specialized space, reserved for experts like physicists and physicians. If we leave aside the white-coated scientists in their protected eyewear, what else might we envision?—Activity? Quiet conversation? Focused attention? Group work?

The first great characteristic of a laboratory is that in it there is carried on an activity, an activity which involves contact with technical equipment, as tools, instruments and other apparatus, and machinery which require the use of the hands and the body. There is dealing with real materials and not merely, as in the old, traditional education, with the symbols of learning. (Dewey, 1932 , p. 108)

In this activity-privileged setting, there is a distinction between discovering knowledge and taking information. “I think the laboratory gives a good example of what I mean,” Dewey ( 1923 , p. 176) writes, “The individual has to be using his hands, doing things, but his experimenting in the laboratory is not simply running wild and at random. He has to have enough physical activity to see that his ideas are made definite and precise; that he is getting principles rather than taking information on faith at the word of the teacher or textbook.”

In the early 21st-century context of benchmarks, standards, high-stakes assessment, and accountability, the laboratory provides an antidote to the problem of isolated knowledge and teacher-assigned tasks. Call them inquirers, researchers, or discoverers: laboratory students will necessarily work within and across a discipline’s standards and norms. However, in an authentic laboratory, discoverers are just as likely to reassemble or build new norms and general principles. Dewey would argue that when students test the knowledge that they are given, they will do one of three things: (1) discard that knowledge if it is not useful; (2) alter it to fit a new context; or (3) accept the knowledge as worthwhile for the time being . In this sense, learners—even young learners—are practicing freedom . Standards alone do not fund freedom; that is, they do not inherently enlarge personal capacity or directly aid in problem-solving. But standards that are tested, discarded, altered, or kept in the light of present circumstances are acts of learner agency.

Norms and standards of practice are needed in the laboratory. Indeed, they help us build warranted assertions, which if tested, may assume new forms of knowledge. As Dewey suggests in the previous paragraph, the choices that warrant an assertion, claim, or solution cannot be informed solely by authority, which alone cannot help one make good judgments. Laboratory settings are democratic spaces where debate can occur, where the usefulness or validity of an emerging truth or act of creation is tested and debated with others (Allsup, 2016 ). For all learners who participate in it—students, preservice teachers, and cooperating teachers—the laboratory school, thus, can be characterized as:

a place of creativity, construction, imagination;

a place to test, perform, critique, and verify responses to authentic problems;

a place of warranted assertability; a place of hypothesis-building;

a “real”—but supportive—community, like those that exist outside classrooms, but affording students opportunities to succeed and fail;

a place of knowledge-making, where groups can collectively add to the sum of facts (asserted and tested) and principles (emerging and verified).

Dewey believed that such a laboratory setting within a teacher education program would provide preservice teachers with imaginative experiences that could help them develop understandings of the principles of education in its most ideal sense. Formal and informal settings, no matter the design, might aim for similar ends. Thus, laboratories—in their broadest, most non-binary sense—become both places to test specialized knowledge and everyday settings where (say) a new recipe could be tried out, or a previous lesson plan could be altered and studied for its results.

Dewey’s Work in Historical Context

Dewey’s writings have demonstrated consistent staying power in educational circles, with many ideas that remain relevant well beyond the 70 years during which he wrote them ( 1882–1952 ). His educational work, however, has also been criticized for saying too little about the role of schools and other democratic institutions in addressing social inequities (e.g., Brick, 2005 ; Portelli & Vilbert, 2002 ). It is essential, however, to consider Dewey’s work in the context of his time. Dewey’s ideas about reforming education were in response to the needs of a changing society, one that was undergoing rapid industrialization and mass migration. Electricity, the telegraph, and improved mail service sped communication across great distances. New discoveries in medicine and medical practice helped people live longer. We emphasize, however, that Dewey lived in an era when many in American society, like Dewey ( 1899 , pp. 6–7, 17, 7; see also 1930 , regarding Dewey’s faith in the scientific method), clung to the era’s faith that science could solve problems that were previously intractable.

One can hardly believe there has been a revolution in all history so rapid, so extensive, so complete. Through it the face of the earth is making over, even as to its physical forms; political boundaries are wiped out and moved about, as if they were indeed only lines on a paper map. . . . Even our moral and religious ideas and interests, the most conservative because the deepest-lying things in our nature, are profoundly affected. . . . Travel has been rendered easy; freedom of movement with its accompanying exchange of ideas, indefinitely facilitated. The result has been an intellectual revolution. Learning has been put into circulation; . . . a distinctively learned class is henceforth out of the question. It is an anachronism. Knowledge is no longer an immobile solid; it has been liquefied. . . . That this revolution should not affect education in some other than a formal and superficial fashion is inconceivable.

This description, written by Dewey in 1899 , bears striking resemblance to social conditions in the first quarter of the 21st century . Writing in 1930 , Dewey (p. 275) recognized that “progress” could have negative effects as well; international tensions fostered during and after World War I meant that “race and color prejudice have never had such opportunity as they have now to poison the mind, while nationalism is elevated into a religion called patriotism.” But there remains a hopeful fascination to Dewey’s tone, an inherent faith in the inevitability of progress and growth that is contradicted by the decades that followed his death. Dewey is often described as lacking a sense of the tragic. Should he have lived to see it, the violence of the latter half of the 20th century may have surprised him, particularly as business interests have remade public education according to market principles. And the promises of progressive education are mostly located in private universities and expensive “independent” schools, undermining Dewey’s democratic ideals. While Dewey’s principles clearly address the 21st century’s global interest in the standardization, privatization, and accountability of education, we believe he would continue to argue against any totalizing, one-size-fits-all approach to any reform movement.

Dewey viewed universities as laboratory spaces for social repair and experimentation. At the end of “Theory into Practice” (1904a), Dewey believed that within “the next decade,” more normal schools would become four-year bachelor’s-degree-granting programs. Dewey was hopeful that extending the teacher preparation program from two to four years, within a model of a laboratory school in conjunction with a university, would provide adequate time for preservice teachers to develop deep understandings of theory integrated with their practice and methods of teaching. Those who would graduate from such a program would become lifelong learners and genuine “students of teaching” (Dewey, 1904a , p. 256).

One fundamental and striking element in the significance of the [University of Chicago] School of Education is the desire and resolute purpose to promote the cause of education, not only here, but everywhere, through inspiring teachers with more vital and adequate conceptions of the nature of their work, and through furnishing them with the intellectual equipment necessary to make them effective and apt in carrying out such broadened and deepened ideals. (Dewey, 1904b , pp. 274–275)

Although this goal seemed tantalizingly close in Dewey’s laboratory school experiments, he admitted the model might be challenging to replicate in other settings. Dewey ( 1899 ) cites critics who accuse him of developing his ideas in the context of ideal circumstances: a small teacher–student ratio, close collaboration between university researchers and K-12 faculty, a teaching faculty sharing common beliefs and focused on learning together in community, among other benefits not common to most educators. Dewey ( 1899 , p. 56) responded that genuine experiments, in education as much as in science and industry, required carefully controlled conditions, “working out and testing a new truth, or a new method,” before “applying it on a wide scale, making it available” to others. Ultimately, he left the lab school after seven contentious years (Knoll, 2014 ), although it has continued to offer learning experiences in the Deweyian tradition into the 21st century (University of Chicago Lab Schools, n.d. ).

We now benefit from far deeper knowledge of psychology, which was a young science in Dewey’s time. Dewey did not have access to 21st-century understandings of the intersectionality of race, ethnicity, and class, and the multiple ways these contribute to continued inequities in education and teacher education. We also must admit to a far more complex understanding of educational and social problems, arising from, as in Dewey’s ( 1899 , pp. 8–9) day, an “increase in toleration, in breadth of social judgment, the larger acquaintance with human nature, the sharpened alertness in reading signs of character and interpreting social situations, greater accuracy of adaptation to differing personalities.” We continue to expand our vision of what education in a democracy means, who it is for, and how to work toward Dewey’s vision of education for all, with the goal of citizens prepared to participate fully in a democratic society. We have experienced an additional century of research, with solutions proposed and tried with varying success, yet Dewey’s ideas continue to offer teacher educators ample food for thought and practice.

Questions for Continued Research and Practice

Dewey’s writings remain provocative; even a century later, his insights seem ahead of their time. University teacher educators in the early 21st century , like those in Dewey’s day, are still pressured by myriad stakeholders to provide preservice teachers with predetermined outcomes and conclusions. But over and again, Dewey ( 1916 , p. 183) reminds us that the reflective process cannot be rushed, that knowledge and pedagogy “take their own time to mature.” Recognizing that few preparation programs offer all the characteristics of Dewey’s ideal laboratory school, how can we best incorporate the principles of learning Dewey sets forth? What types of experiences hold the greatest educative potential? How can we include both the breadth and depth of experiences needed to develop theoretical understanding and thoughtful practice? How can university teacher educators help preservice teachers create sustained continuity among all their educational experiences? What learning experiences may guide preservice teachers to enlarge their vision of the goals and practices of education and to reconceptualize possibilities for their work with children?

The authors of this article concede that experiential learning does not present itself as “efficient,” at least not in the short term; and front-loading student teaching through reflection and observation takes more time than the apprentice or “cadet” model. Guaranteed outcomes, furthermore, are prohibited in a Deweyian framework. Learners, including preservice teachers, must always make their own meanings from their experiences, and thus no preparation program or student teaching experience can guarantee skill or expertise in teaching. Dewey wrote about teacher preparation during an era when, like ours, teacher education programs were becoming more standardized and less creative. He would be the first to argue against any single definition of teacher quality or standardized curriculum (see, e.g., Dewey & Dewey, 1915 ). What would he say about 21st-century national standards for content-area learning and teacher evaluation systems that are based on student test scores, all of which consider children and their teachers “ en masse , as an aggregate of units” (Dewey, 1899 , p. 22)? He believed this view was responsible for “the uniformity of method and curriculum . . . [with] next to no opportunity for adjustment to varying capacities and demands.” Such “ready-made results and accomplishments to be acquired by all children alike in a given time” conflicted with Dewey’s beliefs about the growing child or the developing teacher: “The moment children [or teachers] act they individualize themselves; they cease to be a mass and become the intensely distinctive beings that we are acquainted with out of school, in the home, the family, on the playground, and in the neighborhood” (Dewey, 1899 , p. 22).

Substituting “teachers” for “children” in the previous statement may offer some insight into potential concerns Dewey would have with policies that evaluate teachers in light of “ready-made results and accomplishments.” Given the policy climate in the early 21st century , how can university teacher educators meaningfully respond to calls for accountability in the preparation of a student teacher? How can we honor the individuality of a preservice teacher while preparing her to meet mandated standards? After four or five years in a preparation program (or four semesters in some), how can the beginner teacher be “holistically” evaluated and deemed ready, both for immediate placement and for potential for continued growth? What types of experiences might best help her to examine, construct, or reconstruct her experiences and then demonstrate an expansive understanding of educational theory and practice? How can she exhibit this knowledge in a way that is developmentally appropriate? And if a universal benchmark is not possible—at least according to Dewey—how then do stakeholders know when a preservice teacher is ready for her own classroom, or not?

Dewey’s ideas about reflection on experience have inspired a vast body of research in teacher education. Studies have explored various strategies for engaging preservice teachers in reflection on their personal beliefs and lived histories (e.g., Grimmett & Erickson, 1988 ; Knowles, 1992 ; Schön, 1987 ). Drawing on Deweyian premises, researchers have studied educative and mis-educative beliefs and their possible source (e.g., Dolloff, 1999 ; Fives & Gill, 2014 ; Schmidt, 2013 ); the role of teaching experience in teacher development (e.g., Boyle-Baise & McIntyre, 2008 ; Clift & Brady, 2005 ; Feiman-Nemser & Buchmann, 1985 ; Miksza & Austin, 2010 ; Tabachnick & Zeichner, 1984 ); and how beginning teachers make meaning in and through content area courses (Amador, Kimmons, Miller, & Desjardins, 2015 ; Floden & Meniketti, 2005 ; Grossman, 2005 ). The authors of this article believe that more research is needed to identify context-specific practices that engage preservice teachers in truly meaningful reflection based on genuine problems, not “so-called problems” or “simply assigned tasks ” (Dewey, 1933 , p. 233).

Most research in teacher education is focused on preservice teachers’ learning and development. But more studies could be designed to examine the experiences that help preservice teachers develop an invested and strategic curiosity about children and how they think and learn, “to see how teacher and pupils react upon each other—how mind answers to mind” (Dewey, 1904a , p. 260). How can beginning teachers, generally very concerned with their own need-to-teach, focus more on the child’s needs and interests, and learn to view their students as multifaceted individuals? As an extension of this question, what experiences might help beginning teachers better understand and serve the needs of underserved students, viewing them in terms of the potential of their minds to answer to educational opportunities, rather than through a deficit lens? Research might help us design courses to better challenge preservice teachers’ perceptions of their own learning as the norm for all students; such classes could help new teachers foster a genuine desire to learn about and understand the experiences that their future students bring to school from their home cultures (e.g., Delpit, 1995 ; Gay, 2010 ; Ladson-Billings, 1995 ; Lind & McKoy, 2016 ).

Researchers could consider more longitudinal studies, following preservice teachers’ growth throughout a program or even into the early years of teaching (e.g., Bullough, 1989 ; Bullough & Baughman, 1997 ; Wetzel, Hoffman, Roach, & Russell, 2018 ). Such studies might provide insights into ways that preservice teachers make connections among their learning experiences both in and out of class, and how they create continuity among their past, present, and future. In an age of teacher de-professionalization, what can we learn about educational experiences that help preservice teachers develop a larger vision of—and a greater commitment to—their own lifelong learning?

It goes without saying that most classic philosophers of education are encountered by contemporary readers in ways that require context and some degree of generosity. Plato’s writings on education should not probably be read too literally, but we can go to The Republic to think deeply about the ways in which a society is strategically shaped through the education of its citizens. We can read Confucius and find new questions about how personhood is shaped through tradition. But Dewey, a classic American philosopher, remains highly relevant to educational concerns in the early 21st century . Indeed, he requires little contextual apology. We can, for example, return to Dewey to find inspiration in his faith in the professional capacity of teachers. He never spoke of children through a deficit lens. Dewey’s abiding belief in hands-on learning—his constant focus on the child and the child’s interests—is a counter-narrative to contemporary educational discourses that see children as future human resources. Given his belief in the power of experiential learning, the lasting influence of his educational writings almost seems counter-intuitive. Yet based on our own experiences as university teacher educators, we have found the principles presented in this article to hold great potential for continued experimentation and reflection in our own practices.

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Problem-Solving Method in Teaching

The problem-solving method is a highly effective teaching strategy that is designed to help students develop critical thinking skills and problem-solving abilities . It involves providing students with real-world problems and challenges that require them to apply their knowledge, skills, and creativity to find solutions. This method encourages active learning, promotes collaboration, and allows students to take ownership of their learning.

Table of Contents

Definition of problem-solving method.

Problem-solving is a process of identifying, analyzing, and resolving problems. The problem-solving method in teaching involves providing students with real-world problems that they must solve through collaboration and critical thinking. This method encourages students to apply their knowledge and creativity to develop solutions that are effective and practical.

Meaning of Problem-Solving Method

The meaning and Definition of problem-solving are given by different Scholars. These are-

Woodworth and Marquis(1948) : Problem-solving behavior occurs in novel or difficult situations in which a solution is not obtainable by the habitual methods of applying concepts and principles derived from past experience in very similar situations.

Skinner (1968): Problem-solving is a process of overcoming difficulties that appear to interfere with the attainment of a goal. It is the procedure of making adjustments in spite of interference

Benefits of Problem-Solving Method

The problem-solving method has several benefits for both students and teachers. These benefits include:

  • Encourages active learning: The problem-solving method encourages students to actively participate in their own learning by engaging them in real-world problems that require critical thinking and collaboration
  • Promotes collaboration: Problem-solving requires students to work together to find solutions. This promotes teamwork, communication, and cooperation.
  • Builds critical thinking skills: The problem-solving method helps students develop critical thinking skills by providing them with opportunities to analyze and evaluate problems
  • Increases motivation: When students are engaged in solving real-world problems, they are more motivated to learn and apply their knowledge.
  • Enhances creativity: The problem-solving method encourages students to be creative in finding solutions to problems.

Steps in Problem-Solving Method

The problem-solving method involves several steps that teachers can use to guide their students. These steps include

  • Identifying the problem: The first step in problem-solving is identifying the problem that needs to be solved. Teachers can present students with a real-world problem or challenge that requires critical thinking and collaboration.
  • Analyzing the problem: Once the problem is identified, students should analyze it to determine its scope and underlying causes.
  • Generating solutions: After analyzing the problem, students should generate possible solutions. This step requires creativity and critical thinking.
  • Evaluating solutions: The next step is to evaluate each solution based on its effectiveness and practicality
  • Selecting the best solution: The final step is to select the best solution and implement it.

Verification of the concluded solution or Hypothesis

The solution arrived at or the conclusion drawn must be further verified by utilizing it in solving various other likewise problems. In case, the derived solution helps in solving these problems, then and only then if one is free to agree with his finding regarding the solution. The verified solution may then become a useful product of his problem-solving behavior that can be utilized in solving further problems. The above steps can be utilized in solving various problems thereby fostering creative thinking ability in an individual.

The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to succeed in school and in life.

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What is the most effective way to teach problem solving? A commentary on productive failure as a method of teaching

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5 Advantages and Disadvantages of Problem-Based Learning [+ Activity Design Steps]

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Written by Marcus Guido

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Advantages of Problem-Based Learning

Disadvantages of problem-based learning, steps to designing problem-based learning activities.

Used since the 1960s, many teachers express concerns about the effectiveness of problem-based learning (PBL) in certain classroom settings.

Whether you introduce the student-centred pedagogy as a one-time activity or mainstay exercise, grouping students together to solve open-ended problems can present pros and cons.

Below are five advantages and disadvantages of problem-based learning to help you determine if it can work in your classroom.

If you decide to introduce an activity, there are also design creation steps and a downloadable guide to keep at your desk for easy reference.

1. Development of Long-Term Knowledge Retention

Students who participate in problem-based learning activities can improve their abilities to retain and recall information, according to a literature review of studies about the pedagogy .

The literature review states “elaboration of knowledge at the time of learning” -- by sharing facts and ideas through discussion and answering questions -- “enhances subsequent retrieval.” This form of elaborating reinforces understanding of subject matter , making it easier to remember.

Small-group discussion can be especially beneficial -- ideally, each student will get chances to participate.

But regardless of group size, problem-based learning promotes long-term knowledge retention by encouraging students to discuss -- and answer questions about -- new concepts as they’re learning them.

2. Use of Diverse Instruction Types

explain the utility of problem solving method in history teaching

You can use problem-based learning activities to the meet the diverse learning needs and styles of your students, effectively engaging a diverse classroom in the process. In general, grouping students together for problem-based learning will allow them to:

  • Address real-life issues that require real-life solutions, appealing to students who struggle to grasp abstract concepts
  • Participate in small-group and large-group learning, helping students who don’t excel during solo work grasp new material
  • Talk about their ideas and challenge each other in a constructive manner, giving participatory learners an avenue to excel
  • Tackle a problem using a range of content you provide -- such as videos, audio recordings, news articles and other applicable material -- allowing the lesson to appeal to distinct learning styles

Since running a problem-based learning scenario will give you a way to use these differentiated instruction approaches , it can be especially worthwhile if your students don’t have similar learning preferences.

3. Continuous Engagement

explain the utility of problem solving method in history teaching

Providing a problem-based learning challenge can engage students by acting as a break from normal lessons and common exercises.

It’s not hard to see the potential for engagement, as kids collaborate to solve real-world problems that directly affect or heavily interest them.

Although conducted with post-secondary students, a study published by the Association for the Study of Medical Education reported increased student attendance to -- and better attitudes towards -- courses that feature problem-based learning.

These activities may lose some inherent engagement if you repeat them too often, but can certainly inject excitement into class.

4. Development of Transferable Skills

Problem-based learning can help students develop skills they can transfer to real-world scenarios, according to a 2015 book that outlines theories and characteristics of the pedagogy .

The tangible contexts and consequences presented in a problem-based learning activity “allow learning to become more profound and durable.” As you present lessons through these real-life scenarios, students should be able to apply learnings if they eventually face similar issues.

For example, if they work together to address a dispute within the school, they may develop lifelong skills related to negotiation and communicating their thoughts with others.

As long as the problem’s context applies to out-of-class scenarios, students should be able to build skills they can use again.

5. Improvement of Teamwork and Interpersonal Skills

explain the utility of problem solving method in history teaching

Successful completion of a problem-based learning challenge hinges on interaction and communication, meaning students should also build transferable skills based on teamwork and collaboration . Instead of memorizing facts, they get chances to present their ideas to a group, defending and revising them when needed.

What’s more, this should help them understand a group dynamic. Depending on a given student, this can involve developing listening skills and a sense of responsibility when completing one’s tasks. Such skills and knowledge should serve your students well when they enter higher education levels and, eventually, the working world.

1. Potentially Poorer Performance on Tests

explain the utility of problem solving method in history teaching

Devoting too much time to problem-based learning can cause issues when students take standardized tests, as they may not have the breadth of knowledge needed to achieve high scores. Whereas problem-based learners develop skills related to collaboration and justifying their reasoning, many tests reward fact-based learning with multiple choice and short answer questions. Despite offering many advantages, you could spot this problem develop if you run problem-based learning activities too regularly.

2. Student Unpreparedness

explain the utility of problem solving method in history teaching

Problem-based learning exercises can engage many of your kids, but others may feel disengaged as a result of not being ready to handle this type of exercise for a number of reasons. On a class-by-class and activity-by-activity basis, participation may be hindered due to:

  • Immaturity  -- Some students may not display enough maturity to effectively work in a group, not fulfilling expectations and distracting other students.
  • Unfamiliarity  -- Some kids may struggle to grasp the concept of an open problem, since they can’t rely on you for answers.
  • Lack of Prerequisite Knowledge  -- Although the activity should address a relevant and tangible problem, students may require new or abstract information to create an effective solution.

You can partially mitigate these issues by actively monitoring the classroom and distributing helpful resources, such as guiding questions and articles to read. This should keep students focused and help them overcome knowledge gaps. But if you foresee facing these challenges too frequently, you may decide to avoid or seldom introduce problem-based learning exercises.

3. Teacher Unpreparedness

If supervising a problem-based learning activity is a new experience, you may have to prepare to adjust some teaching habits . For example, overtly correcting students who make flawed assumptions or statements can prevent them from thinking through difficult concepts and questions. Similarly, you shouldn’t teach to promote the fast recall of facts. Instead, you should concentrate on:

  • Giving hints to help fix improper reasoning
  • Questioning student logic and ideas in a constructive manner
  • Distributing content for research and to reinforce new concepts
  • Asking targeted questions to a group or the class, focusing their attention on a specific aspect of the problem

Depending on your teaching style, it may take time to prepare yourself to successfully run a problem-based learning lesson.

4. Time-Consuming Assessment

explain the utility of problem solving method in history teaching

If you choose to give marks, assessing a student’s performance throughout a problem-based learning exercise demands constant monitoring and note-taking. You must take factors into account such as:

  • Completed tasks
  • The quality of those tasks
  • The group’s overall work and solution
  • Communication among team members
  • Anything you outlined on the activity’s rubric

Monitoring these criteria is required for each student, making it time-consuming to give and justify a mark for everyone.

5. Varying Degrees of Relevancy and Applicability

It can be difficult to identify a tangible problem that students can solve with content they’re studying and skills they’re mastering. This introduces two clear issues. First, if it is easy for students to divert from the challenge’s objectives, they may miss pertinent information. Second, you could veer off the problem’s focus and purpose as students run into unanticipated obstacles. Overcoming obstacles has benefits, but may compromise the planning you did. It can also make it hard to get back on track once the activity is complete. Because of the difficulty associated with keeping activities relevant and applicable, you may see problem-based learning as too taxing.

If the advantages outweigh the disadvantages -- or you just want to give problem-based learning a shot -- follow these steps:

1. Identify an Applicable Real-Life Problem

explain the utility of problem solving method in history teaching

Find a tangible problem that’s relevant to your students, allowing them to easily contextualize it and hopefully apply it to future challenges. To identify an appropriate real-world problem, look at issues related to your:

  • Students’ shared interests

You must also ensure that students understand the problem and the information around it. So, not all problems are appropriate for all grade levels.

2. Determine the Overarching Purpose of the Activity

Depending on the problem you choose, determine what you want to accomplish by running the challenge. For example, you may intend to help your students improve skills related to:

  • Collaboration
  • Problem-solving
  • Curriculum-aligned topics
  • Processing diverse content

A more precise example, you may prioritize collaboration skills by assigning specific tasks to pairs of students within each team. In doing so, students will continuously develop communication and collaboration abilities by working as a couple and part of a small group. By defining a clear purpose, you’ll also have an easier time following the next step.

3. Create and Distribute Helpful Material

explain the utility of problem solving method in history teaching

Handouts and other content not only act as a set of resources, but help students stay focused on the activity and its purpose. For example, if you want them to improve a certain math skill , you should make material that highlights the mathematical aspects of the problem. You may decide to provide items such as:

  • Data that helps quantify and add context to the problem
  • Videos, presentations and other audio-visual material
  • A list of preliminary questions to investigate

Providing a range of resources can be especially important for elementary students and struggling students in higher grades, who may not have self-direction skills to work without them.

4. Set Goals and Expectations for Your Students

Along with the aforementioned materials, give students a guide or rubric that details goals and expectations. It will allow you to further highlight the purpose of the problem-based learning exercise, as you can explain what you’re looking for in terms of collaboration, the final product and anything else. It should also help students stay on track by acting as a reference throughout the activity.

5. Participate

explain the utility of problem solving method in history teaching

Although explicitly correcting students may be discouraged, you can still help them and ask questions to dig into their thought processes. When you see an opportunity, consider if it’s worthwhile to:

  • Fill gaps in knowledge
  • Provide hints, not answers
  • Question a student’s conclusion or logic regarding a certain point, helping them think through tough spots

By participating in these ways, you can provide insight when students need it most, encouraging them to effectively analyze the problem.

6. Have Students Present Ideas and Findings

If you divided them into small groups, requiring students to present their thoughts and results in front the class adds a large-group learning component to the lesson. Encourage other students to ask questions, allowing the presenting group to elaborate and provide evidence for their thoughts. This wraps up the activity and gives your class a final chance to find solutions to the problem.

Wrapping Up

The effectiveness of problem-based learning may differ between classrooms and individual students, depending on how significant specific advantages and disadvantages are to you. Evaluative research consistently shows value in giving students a question and letting them take control of their learning. But the extent of this value can depend on the difficulties you face.It may be wise to try a problem-based learning activity, and go forward based on results.

Create or log into your teacher account on Prodigy -- an adaptive math game that adjusts content to accommodate player trouble spots and learning speeds. Aligned to US and Canadian curricula, it’s used by more than 350,000 teachers and 10 million students. It may be wise to try a problem-based learning activity, and go forward based on results.

Problem Solving Method Of Teaching

A woman stands beside an expansive screen, showing a map of different locations. She holds a clipboard in her hands as she looks intently at the map. A man in a black shirt and grey pants is pointing to something on the map. On the right-hand side of the map, there is a truck symbol with a pointer. On the left-hand side, there is a white airplane on a black and orange pin. Above the map is a yellow and black striped object, with a white object with black lines beside it. Below the map is a yellow and white logo and a yellow and grey sign with black text.

Element Synthesis Example
Active LearningTeaching through problem-solving allows for active learning.Children understand the theory better by getting involved in real-world situations
PracticeContinuous practice is integral to problem-solving teaching.Each new skill or concept is practiced after being learned in class.
RelevanceProblem-solving techniques make learning more relevant.Real-world examples related to the topic are presented.
Incremental LearningEach new topic builds on previous lessons.Relating new problems to ones solved in previous sessions.
Overcome ChallengesEnhances ability to overcome real-world situations.Children understand the application of skills learned.
VarietyProblem-solving allows flexibility in teaching methods.Problems can be practical, conceptual, or theoretical.
Critical ThinkingImproves children's critical thinking skills.Adding alternative paths to a solution.
ConfidenceBoosts children's confidence in handling problems.Children feel empowered after successfully solving a problem.
AdaptabilityIncreases adaptability to new learning situations.Children can apply learned strategies to new problems.
EngagementProblem-solving increases engagement and interest.Children find solving real-world examples interesting.

The problem-solving method of teaching is the learning method that allows children to learn by doing. This is because they are given examples and real-world situations so that the theory behind it can be understood better, as well as practice with each new concept or skill taught on top of what was previously learned in class before moving onto another topic at hand.

What is your preferred problem-solving technique?

Answers : - I like to brainstorm and see what works for me - I enjoy the trial and error method - I am a linear thinker

Share it with me by commenting.

For example, while solving a problem, the child may encounter terms he has not studied yet. These will further help him understand their use in context while developing his vocabulary. At the same time, being able to practice math concepts by tapping into daily activities helps an individual retain these skills better.

One way this type of teaching is applied for younger students particularly is through games played during lessons. By allowing them to become comfortable with the concepts taught through these games, they can put their knowledge into use later on. This is done by developing thinking processes that precede an action or behavior. These games can be used by teachers for different subjects including science and language.

For younger students still, the method of teaching using real-life examples helps them understand better. Through this, it becomes easier for them to relate what they learned in school with terms used outside of school settings so that the information sticks better than if all they were given were theoretical definitions. For instance, instead of just studying photosynthesis as part of biology lessons, children are asked to imagine plants growing inside a dark room because there is no sunlight present. When questioned about the plants, children will be able to recall photosynthesis more easily because they were able to see its importance in real life.

Despite being given specific examples, the act of solving problems helps students think for themselves. They learn how to approach situations and predict outcomes based on what they already know about concepts or ideas taught in class including the use of various skills they have acquired over time. These include problem-solving strategies like using drawings when describing a solution or asking advice if they are stuck to unlock solutions that would otherwise go beyond their reach.

Teachers need to point out in advance which method will be used for any particular lesson before having children engage with it. By doing this, individuals can prepare themselves mentally for what is to come. This is especially true for students who have difficulty with a particular subject. In these cases, the teacher can help them get started by providing a worked example for reference or breaking the problem down into manageable chunks that are easier to digest.

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Ultimately, the goal of teaching using a problem-solving method is to give children the opportunity to think for themselves and to be able to do so in different contexts. Doing this helps foster independent learners who can utilize the skills they acquired in school for future endeavors.

The problem-solving method of teaching allows children to learn by doing. This is because they are given examples and real-world situations so that the theory behind it can be understood better, as practice with each new concept or skill taught on top of what was previously learned in class before moving onto another topic at hand.

One way this type of teaching is applied for younger students particularly is through games played during lessons. By allowing them to become comfortable with the concepts taught through these games, they are able to put their knowledge into use later on. This is done by developing thinking processes that precede an action or behavior. These games can be used by teachers for different subjects including science and language.

For instance, a teacher may ask students to imagine they are plants in a dark room because there is no sunlight present. When questioned about the plants, children will be able to recall photosynthesis more easily because they were able to see its importance in real life.

It is important for teachers to point out in advance which method will be used for any particular lesson before having children engage with it. By doing this, individuals can prepare themselves mentally for what is to come. This is especially true for students who have difficulty with a particular subject. In these cases, the teacher can help them get started by providing a worked example for reference or breaking the problem down into manageable chunks that are easier to digest.

lesson before having children engage with it. By doing this, individuals can prepare themselves mentally for what is to come. This is especially true for students who have difficulty with a particular subject. In these cases, the teacher can help them get started by providing a worked example for reference or breaking the problem down into manageable chunks that are easier to digest.

The teacher should have a few different ways to solve the problem.

For example, the teacher can provide a worked example for reference or break down the problem into chunks that are easier to digest.

The goal of teaching using a problem-solving method is to give children the opportunity to think for themselves and to be able to do so in different contexts. Successful problem solving allows children to become comfortable with concepts taught through games that develop thinking processes that precede an action or behavior.

Introduce the problem

The problem solving method of teaching is a popular approach to learning that allows students to understand new concepts by doing. This approach provides students with examples and real-world situations, so they can see how the theory behind a concept or skill works in practice. In addition, students are given practice with each new concept or skill taught, before moving on to the next topic. This helps them learn and retain the information better.

Explain why the problem solving method of teaching is effective.

The problem solving method of teaching is effective because it allows students to learn by doing. This means they can see how the theory behind a concept or skill works in practice, which helps them understand and remember the information better. This would not be possible if they are only told about the new concept or skill, or read a textbook to learn on their own. Since students can see how the theory works in practice through examples and real-world situations, the information is easier for them to understand.

List some advantages of using the problem solving method of teaching.

Some advantages of using the problem solving method of teaching are that it helps students retain information better since they are able to practice with each new concept or skill taught until they master it before moving on to another topic. This also allows them to learn by doing so they will have hands-on experience with facts which helps them remember important facts faster rather than just hearing about it or reading about it on their own. Furthermore, this teaching method is beneficial for students of all ages and can be adapted to different subjects making it an approach that is versatile and easily used in a classroom setting. Lastly, the problem solving method of teaching presents new information in a way that is easy to understand so students are not overwhelmed with complex material.

The problem solving method of teaching is an effective way for students to learn new concepts and skills. By providing them with examples and real-world situations, they can see how the theory behind a concept or skill works in practice. In addition, students are given practice with each new concept or skill taught, before moving on to the next topic. This them learn and retain the information better.

What has been your experience with adopting a problem-solving teaching method?

How do you feel the usefulness of your lesson plans changed since adopting this method?

What was one of your most successful attempts in using this technique to teach students, and why do you believe it was so successful?

Were there any obstacles when trying to incorporate this technique into your class? 

Did it take a while for all students to get used to the new type of teaching style before they felt comfortable enough to participate in discussions and ask questions about their newly acquired knowledge?

What are your thoughts on this method? 

“I have had the opportunity to work in several districts, including one where they used problem solving for all subjects. I never looked back after that experience--it was exciting and motivating for students and teachers alike." 

"The problem solving method of teaching is great because it makes my subject matter more interesting with hands-on activities."

Active Learning, Teaching through problem-solving allows for active learning, Children understand the theory better by getting involved in real-world situations, Practice, Continuous practice is integral to problem-solving teaching, Each new skill or concept is practiced after being learned in class, Relevance, Problem-solving techniques make learning more relevant, Real-world examples related to the topic are presented, Incremental Learning, Each new topic builds on previous lessons, Relating new problems to ones solved in previous sessions, Overcome Challenges, Enhances ability to overcome real-world situations, Children understand the application of skills learned, Variety, Problem-solving allows flexibility in teaching methods, Problems can be practical, conceptual, or theoretical, Critical Thinking, Improves children's critical thinking skills, Adding alternative paths to a solution, Confidence, Boosts children's confidence in handling problems, Children feel empowered after successfully solving a problem, Adaptability, Increases adaptability to new learning situations, Children can apply learned strategies to new problems, Engagement, Problem-solving increases engagement and interest, Children find solving real-world examples interesting

What is the role of educators in facilitating problem-solving method of teaching?

Role of Educators in Facilitating Problem-Solving Understanding the Problem-Solving Method The problem-solving method of teaching encourages students to actively engage their critical thinking skills to analyze and seek solutions to real-world problems. As such, educators play a crucial part in facilitating this learning style to ensure the effective attainment of desired skills. Encouraging Collaboration and Communication One of the ways educators can facilitate problem-solving is by promoting collaboration and communication among students. Working as a team allows students to share diverse perspectives while considering multiple solutions, thereby fostering an open-minded and inclusive environment that is crucial for effective problem-solving. Creating a Safe Space for Failure Educators must recognize that failure is an integral component of the learning process in a problem-solving method. By establishing a safe environment that allows students to fail without facing judgment or embarrassment, teachers enable students to develop perseverance, resilience, and an enhanced ability to learn from mistakes. Designing Relevant and Engaging Problems The selection and design of appropriate problems contribute significantly to the success of the problem-solving method of teaching. Educators should focus on presenting issues that are relevant, engaging, and age-appropriate, thereby sparking curiosity and interest amongst students, which further improves their problem-solving abilities. Scaffolding Learning Scaffolding is essential in the problem-solving method for providing adequate support when required. Teachers need to break down complex problems into smaller, manageable steps, and gradually remove support as students develop the necessary skills, thus promoting their self-reliance and independent thinking. Providing Constructive Feedback Constructive feedback from educators is invaluable in facilitating the problem-solving method of teaching, as it enables students to reflect on their progress, recognize areas for improvement, and actively develop their critical thinking and problem-solving abilities. In conclusion, the role of educators in facilitating the problem-solving method of teaching comprises promoting collaboration, creating a safe space for failure, designing relevant problems, scaffolding learning, and providing constructive feedback. By integrating these elements, educators can help students develop essential life-long skills and effectively navigate the complex world they will experience.

The problem-solving method of teaching is a dynamic and interactive instructional strategy that engages students directly with challenges that resemble those they might encounter outside of the classroom. Within this framework, educators are not just conveyors of knowledge, but rather facilitators of learning who empower their students to think critically and deeply. Below, we look into the nuanced role educators play in making the problem-solving method impactful.Firstly, educators must curate an atmosphere that is conducive to inquiry and exploration. They set the tone by modeling an inquisitive mindset, posing thought-provoking questions, and encouraging students to ask why, how, and what if without hesitation. This intellectual curiosity promotes the kind of deep thinking that underpins successful problem-solving.Another key responsibility is to scaffold the complexity of problems. Educators do so by assessing the readiness of their students and designing tasks that are at the appropriate level of difficulty. They must ensure challenges are neither too easy – risking boredom and disengagement – nor too difficult – potentially causing frustration and disheartenment. By striking this balance, educators help students to experience incremental success and build their problem-solving capacities over time.Educators must also provide students with relevant tools and methodologies. This might involve teaching specific problem-solving strategies such as the scientific method, design thinking, or computational thinking. Educators help students to become conversant in these approaches, allowing them to tackle problems methodically and effectively.Assessment is another pivotal area where educators play a vital role in the problem-solving method. The traditional means of assessment may not always capture the depth of understanding and learning that occurs in problem-solving scenarios. Therefore, educators develop alternative forms of assessment, such as reflective journals, portfolios, and presentations, to better gauge student learning and thinking processes.Finally, educators must be adept at facilitating group dynamics. Collaborative problem-solving can be powerful, but it also invites a range of interpersonal challenges. Thus, educators need to guide students in conflict resolution, equitable participation, and recognizing the contribution of each member to the collective effort.Educators facilitate the problem-solving method by fostering inquiry, balancing problem difficulty, equipping students with methodologies, rethinking assessment, and nurturing group cooperation. In doing so, they are not simply providing students with content knowledge but are equipping them with crucial life skills that transcend educational settings and prepare them for real-world challenges.

Can interdisciplinary approaches be incorporated into problem-solving teaching methods, and if so, how?

Interdisciplinary Approaches in Problem-Solving Teaching Methods Integration of Interdisciplinary Approaches Incorporating interdisciplinary approaches into problem-solving teaching methods can be achieved by integrating various subject areas when presenting complex problems that require students to draw from different fields of knowledge. By doing so, learners will develop a deeper understanding of the interconnectedness of various disciplines and improve their problem-solving skills. Project-Based Learning Activities Implementing project-based learning activities in the classroom allows students to work collaboratively on real-world problems. By involving learners in tasks that necessitate the integration of diverse subjects, they develop the ability to transfer skills acquired in one context to novel situations, thereby expanding their problem-solving abilities. Role of Teachers in Interdisciplinary Teaching Teachers play a crucial role in the successful incorporation of interdisciplinary methods in problem-solving teaching. They must be prepared to facilitate student-centered learning and engage in ongoing professional development tailored towards interdisciplinary education. In doing so, educators can create inclusive learning environments that encourage individualized discovery and the application of diverse perspectives to solve complex problems. Benefits of Interdisciplinary Teaching Methods Adopting interdisciplinary teaching methods in problem-solving education not only enhances students' problem-solving abilities but also fosters the development of critical thinking, creativity, and collaboration. These essential skills enable learners to navigate and adapt to an increasingly interconnected world and have been shown to contribute to students' academic and professional success. In conclusion, incorporating interdisciplinary approaches into problem-solving teaching methods can be achieved through the integration of various subject areas, implementing project-based learning activities, and the active role of teachers in interdisciplinary education. These methods benefit students by developing problem-solving skills, critical thinking, creativity, and collaboration, preparing them for future success in an interconnected world.

Interdisciplinary approaches in problem-solving teaching methods present a contemporary framework for preparing students to tackle the complexities of real-world issues. This approach can bridge the gap between various academic disciplines, offering students a more holistic and connected way of thinking.**Embracing Complexity through Interdisciplinary Problem-Solving**Problem-solving in education is no longer confined to single-subject exercises. Interdisciplinary problem-solving recognizes the multifaceted nature of real issues and encourages students to tackle them by drawing from multiple disciplines. For instance, when examining the impacts of urbanization, students might incorporate knowledge from sociology, economics, environmental science, and urban planning.**Strategies for Implementing an Interdisciplinary Approach**Various strategies can be employed to incorporate interdisciplinary methods effectively:1. **Cross-Curricular Projects**: These require students to apply knowledge and skills across different subject areas, fostering an understanding of each discipline’s unique contribution to the whole problem.2. **Thematic Units**: By designing units around broad themes, educators can seamlessly weave multiple subjects into the exploration of a single topic, prompting students to see connections between different areas of study.3. **Collaborative Teaching**: When educators from different disciplines co-teach, they can provide a combined perspective that enriches the learning experience and demonstrates the value of integrating knowledge.4. **Inquiry-Based Learning**: Encourages students to ask questions and conduct research across multiple disciplines, leading to comprehensive investigations and solutions.**Outcome-Benefits of Interdisciplinary Teaching**The merits of an interdisciplinary approach within problem-solving teaching methods are manifold:1. **Complex Problem Understanding**: It can elevate a student’s ability to deconstruct complicated issues by understanding various factors and viewpoints.2. **Adaptability**: Students learn to apply knowledge pragmatically, enabling them to adapt to new and unforeseen problems.3. **Enhanced Cognitive Abilities**: The process can promote cognitive growth, supporting the development of higher-order thinking skills like analysis and synthesis.4. **Real-World Relevance**: Students find meaning and motivation in their work when they see its relevance outside the classroom walls.In summary, integrating interdisciplinary approaches into problem-solving methods is a highly effective way to provide students with robust and adaptable skills for the future. By engaging in project-based learning activities, enjoying the support of proactive educators, and seeing the interconnectivity across subjects, students can foster critical thinking, creativity, and collaborative abilities that transcend traditional learning boundaries. As we navigate a rapidly evolving and interrelated global landscape, such approaches to education become not just advantageous but essential.

In what ways can technology be integrated into the problem-solving method of instruction?

**Role of Technology in Problem-Solving Instruction** Technology can be integrated into the problem-solving method of instruction by enhancing student engagement, promoting collaboration, and supporting personalized learning. **Enhancing Student Engagement** One way technology supports the problem-solving method is by increasing students' interest through interactive and dynamic tools. For instance, digital simulations and educational games can help students develop critical thinking and problem-solving skills in a fun, engaging manner. These tools provide real-world contexts and immediate feedback, allowing students to experiment, take risks, and learn from their mistakes. **Promoting Collaboration** Technology also promotes collaboration among students, as online platforms facilitate communication and cooperation. Utilizing tools like video conferencing and shared workspaces, students can collaborate on group projects, discuss ideas, and solve problems together. This collaborative approach fosters a sense of community, mutual support, and collective problem-solving. Moreover, it helps students develop essential interpersonal skills, such as teamwork and communication, which are crucial in today's workplaces. **Supporting Personalized Learning** Finally, technology can be used to provide personalized learning experiences tailored to individual learners' needs, interests, and abilities. With access to adaptive learning platforms or online resources, students can progress at their own pace, focus on areas where they need improvement, and explore topics that interest them. This kind of personalized approach allows instructors to identify areas where students struggle and offer targeted support, enhancing the problem-solving learning experience. In conclusion, integrating technology into the problem-solving method of instruction can improve the learning process in various ways. By fostering student engagement, promoting collaboration, and facilitating personalized learning experiences, technology can be employed as a valuable resource to develop students' problem-solving skills effectively.

The integration of technology into the problem-solving method of instruction can significantly enhance the educational process, as it offers diverse opportunities for students to engage with challenging concepts and develop practical skills. The deliberate use of technology can stimulate student interaction with course material and encourage a more dynamic approach to learning.**Interactive Problem-Solving Scenarios**Technology can simulate complex scenarios requiring students to apply their knowledge creatively to solve problems. Through interactive case studies and gamified learning environments, students can engage with these scenarios in a manner that is both compelling and educative. Such simulations often incorporate branching choices, offering an exploration of consequences which creates a deeper understanding of the material.**Data Analysis Tools**Incorporating data analysis tools into problem-solving instruction can offer students hands-on experience with real-world data sets. By learning to manipulate and analyze data through software, students can identify patterns, test hypotheses, and make evidence-based conclusions. These skills are particularly valuable in STEM fields, economics, and social sciences.**Global Connectivity & Resources**Through global connectivity, technology enables access to a vast array of resources that can be utilized to enrich problem-solving tasks. Platforms such as IIENSTITU offer courses that are designed to incorporate technology into pedagogical strategies effectively. Moreover, access to international databases, research materials, and expert lectures from around the world ensures that students are exposed to diverse perspectives and approaches to problem-solving.**Interactive Whiteboards and Projection**Interactive whiteboards and projection technology make it possible to visualize complex problems and work though them interactively in the classroom. This technology allows for collaborative diagramming and mapping of ideas, which can aid in visual learning and the synthesis of information in group settings.**Adaptive Learning Software**Educational technology that adapts to individual student performance and preferences enables personalized instruction. Adaptive learning software assesses students' skills and tailors the difficulty of problems accordingly, ensuring that each student is engaged at the appropriate level of challenge.**Formative Assessment through Technology**Technology-enabled formative assessments give teachers and students real-time feedback on understanding and performance. These tools can help identify areas of difficulty, track progress, and adjust teaching strategies to help students develop their problem-solving abilities more effectively.**Facilitating Research and Inquiry**The ability to conduct research and inquiry is central to problem solving. When students are provided with the tools to explore, research, and verify information on the internet securely, they are empowered to seek out answers to their questions and develop solutions based on evidence.**Closing Thoughts**In integrating technology into problem-solving instruction, it's important to ensure that the use of any tool or platform is pedagogically sound, enhances the learning objectives, and actually serves to improve students' problem-solving capabilities. As education evolves with the digital age, so too does the art and science of teaching problem solving, where technology becomes an indispensable ally in preparing students for the challenges of the future.

I graduated from the Family and Consumption Sciences Department at Hacettepe University. I hold certificates in blogging and personnel management. I have a Master's degree in English and have lived in the US for three years.

A rectangular puzzle piece with a light green background and a blue geometric pattern sits in the center of the image. The puzzle piece has a curved edge along the top, and straight edges along the bottom and sides. The pattern on the piece consists of a thin green line that wraps around the outside edge and a thick blue line that follows the contours of the shape. The inside of the piece is filled with various shapes of the same color, including circles, triangles, and squares. The overall effect of the piece is calming and serene. It could be part of a larger puzzle that has yet to be solved.

What are Problem Solving Skills?

A woman in a white shirt is looking down and holding her head in her hands. She has long blonde hair and blue eyes. Her lips are slightly pursed, and her eyebrows are slightly furrowed. She looks sad and contemplative, as if she is lost in thought. Her arms are crossed in front of her chest, and her head is slightly tilted to the side. Her expression is thoughtful and her posture is relaxed. She is standing in front of a plain white wall, and the light casts shadows on her face. She appears to be alone in the room, and her posture conveys a sense of loneliness and introspection.

How To Solve The Problems? Practical Problem Solving Skills

A group of people, including a man holding a laptop, a woman with her hands in her pockets, and another woman wearing a striped shirt, are standing together in a closeknit formation. One woman is holding a cup of coffee, and another has their butt partially visible in blue jeans. Everyone is smiling, and the man with the laptop appears to be engaged in conversation. The group is bathed in warm sunlight, creating a friendly atmosphere.

A Problem Solving Method: Brainstorming

A close-up of a group of people holding puzzle pieces in their hands. A man is looking at the piece he is holding, while two other people are carefully looking at the pieces they are holding in their hands. The pieces have a wooden texture, and each one is a different color. One person is holding a light blue piece, while another person is holding a red piece. All the pieces are shaped differently, and some are curved while others are straight. The pieces all fit together to form a larger puzzle.

How To Develop Problem Solving Skills?

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  3. 5 Step Problem Solving Process

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  6. Problem-Solving Strategies: Definition and 5 Techniques to Try

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  5. Problem solving method of teaching Steps in problem Solving Method समस्या समाधान विधि के चरण #ctet

  6. Video: Solving Problems Using the Scientific Method

COMMENTS

  1. 6 Teaching Undergraduate History: A Problem-Based Approach

    problem solving, historical thinking skills, learning assessment . Introduction. Among the challenges that faculty encounter is facilitating active engagement with their discipline within classrooms of diverse undergraduate students (Calder, 2006; Rendon, 2009). We face this challenge regularly when teaching history.

  2. PDF Teaching Methods in History Learning

    There are several methods a teacher can use to make history more vibrant. Active learning techniques, films, library research, and historical fiction can all be used to make teaching and learning on history more invigorating. Regardless of what methods are used, however, it is important to apply a humanistic approach when teaching history.

  3. Effective Teaching: Examples in History, Mathematics, and Science

    The first two strategies display an excellent understanding of the principles, justification, and procedures that could be used to solve the problem (the what, why, and how for solving the problem). The last two strategies are largely a shopping list of physics terms or equations that were covered in the course, but the students are not able to ...

  4. (Pdf) Teaching Philosophy and History Through the Problem-solving

    The problem solving may reveal as one of the most important pedagogical methods as it addresses the central question of pedagogy: by what means may we affect the representations of a human person ...

  5. Teaching Problem Solving

    Problem-Solving Fellows Program Undergraduate students who are currently or plan to be peer educators (e.g., UTAs, lab TAs, peer mentors, etc.) are encouraged to take the course, UNIV 1110: The Theory and Teaching of Problem Solving. Within this course, we focus on developing effective problem solvers through students' teaching practices.

  6. Full article: Understanding and explaining pedagogical problem solving

    Teachers are far too busy teaching in class, and expertise with pedagogical problem solving is, we argue, largely tacit. Teacher educators make the tacit explicit for novices, so the Pedagogical Problem Typology may help this dialogue. We now explain each problem before illustrating them with a thick description of excerpts from the data.

  7. Teaching problem solving

    Working on solutions. In the solution phase, one develops and then implements a coherent plan for solving the problem. As you help students with this phase, you might ask them to: identify the general model or procedure they have in mind for solving the problem. set sub-goals for solving the problem. identify necessary operations and steps.

  8. Classroom discussion and individual problem-solving in the teaching of

    The first teaching approach was based on individual problem-solving, the second involved problem-solving through discussion. Students in the discussion condition were prompted to discuss the value of studying history with the entire class, and were required to solve historical problems in groups.

  9. Teaching Problem Solving

    Make students articulate their problem solving process . In a one-on-one tutoring session, ask the student to work his/her problem out loud. This slows down the thinking process, making it more accurate and allowing you to access understanding. When working with larger groups you can ask students to provide a written "two-column solution.".

  10. Classroom discussion and individual problem-solving in the teaching of

    In this study, 100 Italian eighth graders were divided into two groups to compare the effects of two instructional interventions - the first based on problem-solving through discussion, the ...

  11. Defining Authenticity in Historical Problem Solving

    By "living" the decisions through problem-based simulations, our students would collectively be better prepared to engage in the larger questions that are debated in the discipline of history. Challenge Cycles. What did this look like in World History? We created challenge cycles based on each of the eras into which the course was divided.

  12. Problem-Based Learning (PBL)

    PBL is a student-centered approach to learning that involves groups of students working to solve a real-world problem, quite different from the direct teaching method of a teacher presenting facts and concepts about a specific subject to a classroom of students. Through PBL, students not only strengthen their teamwork, communication, and ...

  13. Problem-Solving Method in Teaching the Social Sciences

    A last word, in which is stated what the writer believes to be a sensible, conservative attitude toward the use of problem solving in. teaching the social sciences. 1. Concepts must be present in the mind which are germane to problem on hand-. is the power to profit by experience with effort. The experience.

  14. Problem-Solving Method of Teaching Made Easy

    The problem-solving method of teaching is a student-centered approach to learning that focuses on developing students' problem-solving skills. In this method, students have to face real-world problems to solve. They are encouraged to use their knowledge and skills to provide solutions. The teacher acts as a facilitator, providing guidance and ...

  15. John Dewey and Teacher Education

    In Dewey's (1916, p. 177) vision for teacher preparation, methods arise from a thorough understanding of one's disciplinary domain, but subject matter is always balanced by a deep understanding of the principles of learning and teaching: "In brief, the method of teaching is the method of an art, of action intelligently directed by ends ...

  16. Problem-Solving Method In Teaching

    The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to ...

  17. The Problem Method of Teaching Research Methods

    Abstract. I describe the application of the problem method, sometimes known as the case study method, to the teaching of undergraduate research methods. Problems are assigned in advance, students use course material to solve the problem, and the solutions are discussed in class. This method is particularly applicable to courses in research ...

  18. What is the most effective way to teach problem solving? A commentary

    The teaching methods described in these papers involve two phases: first a generation (or invention) phase where students struggle to come up with a solution to the problem posed and second, a consolidation (or instruction) phase where they are given the canonical solution to the problem together with direct instruction in applying the canonical solution.

  19. 5 Advantages and Disadvantages of Problem-Based Learning [+ Activity

    Advantages of Problem-Based Learning. 1. Development of Long-Term Knowledge Retention. Students who participate in problem-based learning activities can improve their abilities to retain and recall information, according to a literature review of studies about the pedagogy.. The literature review states "elaboration of knowledge at the time of learning" -- by sharing facts and ideas ...

  20. (Pdf) Learning and Problem Solving: the Use of Problem Solving Method

    Abstract. Problem-based learning is a recognized teaching method in which complex real-world problems are used as the vehicle to promote student learning of concepts and principles as opposed to ...

  21. PDF Mind Maps in Classroom Teaching and Learning

    maps traces back centuries. These pictorial methods record knowledge and model systems, and have a long history in learning, brainstorming, memory, visual thinking, and problem solving by educators, engineers, psychologists, and others. Buzan (1993) argues that traditional outlines rely

  22. Problem Solving Method Of Teaching

    The problem-solving method of teaching is the learning method that allows children to learn by doing. This is because they are given examples and real-world situations so that the theory behind it can be understood better, as well as practice with each new concept or skill taught on top of what was previously learned in class before moving onto another topic at hand.

  23. What is the problem solving method of teaching?

    What is the problem solving method of teaching? Luther A. Mahan, Luther A. Mahan. Stout State University, Menomonie, Wisconsin. Search for more papers by this author. Luther A. Mahan, Luther A. Mahan. Stout State University, Menomonie, Wisconsin. Search for more papers by this author.