Four Steps of Polya's Problem Solving Techniques

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In the world of mathematics and algorithms, problem-solving is an art which follows well-defined steps. Such steps do not follow some strict rules and each individual can come up with their steps of solving the problem. But there are some guidelines which can help to solve systematically.

In this direction, mathematician George Polya crafted a legacy that has guided countless individuals through the maze of problem-solving. In his book “ How To Solve It ,” Polya provided four fundamental steps that serve as a compass for handling mathematical challenges. 

  • Understand the problem
  • Devise a Plan
  • Carry out the Plan
  • Look Back and Reflect

Let’s look at each one of these steps in detail.

Polya’s First Principle: Understand the Problem

Before starting the journey of problem-solving, a critical step is to understand every critical detail in the problem. According to Polya, this initial phase serves as the foundation for successful solutions.

At first sight, understanding a problem may seem a trivial task for us, but it is often the root cause of failure in problem-solving. The reason is simple: We often understand the problem in a hurry and miss some important details or make some unnecessary assumptions. So, we need to clearly understand the problem by asking these essential questions:

  • Do we understand all the words used in the problem statement? 
  • What are we asked to find or show? What is the unknown? What is the information given? Is there enough information to enable you to find a solution?
  • What is the condition or constraints given in the problem? Separate the various parts of the condition: Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
  • Can you write down the problem in your own words? If required, use suitable notations, symbols, equations, or expressions to convey ideas and encapsulate critical details. This can work as our compass, which can guide us through calculations to reach the solution.
  • After knowing relevant details, visualization becomes a powerful tool. Can you think of a diagram that might help you understand the problem? This can serve as a bridge between the abstract and tangible details and reveal patterns that might not be visible after looking at the problem description.

Just as a painter understands the canvas before using the brush, understanding the problem is the first step towards the correct solution.

Polya’s Second Principle: Devise a Plan

Polya mentions that there are many reasonable ways to solve problems. If we want to learn how to choose the best problem-solving strategy, the most effective way is to solve a variety of problems and observe different steps involved in the thought process and implementation techniques.

During this practice, we can try these strategies:

  • Guess and check
  • Identification of patterns
  • Construction of orderly lists
  • Creation of visual diagrams
  • Elimination of possibilities
  • Solving simplified versions of the problem
  • Using symmetry and models
  • Considering special cases
  • Working backwards
  • Using direct reasoning
  • Using formulas and equations

Here are some critical questions at this stage:

  • Can you solve a portion of the problem? Consider retaining only a segment of conditions and discarding the rest.
  • Have you encountered this problem before? Have you encountered a similar problem in a slightly different form with the same or a similar unknown? Look closely at the unknown.
  • If the proposed problem proves challenging, try to solve related problems first. Can you imagine a more approachable related problem? A more general or specialized version? Could you utilize their solutions, results, or methods?
  • Can you derive useful insights from the data? Can you think of other data that would help determine the unknown? Did you utilize all the given data? Did you incorporate the entire set of conditions? Have you considered all essential concepts related to the problem?

Polya’s Third Principle: Carry out the Plan

This is the execution phase where we transform the blueprint of our devised strategy into a correct solution. As we proceed, our goal is to put each step into action and move towards the solution.

In general, after identifying the strategy, we need to move forward and persist with the chosen strategy. If it is not working, then we should not hesitate to discard it and try another strategy. All we need is care and patience. Don’t be misled, this is how mathematics is done, even by professionals. There is one important thing: We need to verify the correctness of each step or prove the correctness of the entire solution.

Polya’s Fourth Principle: Look Back and Reflect

In the rush to solve a problem, we often ignore learning from the completed solutions. So according to Polya, we can gain a lot of new insights by taking the time to reflect and look back at what we have done, what worked, and what didn’t. Doing this will enable us to predict what strategy to use to solve future problems.

  • Can you check the result? 
  • Can you check the concepts and theorems used? 
  • Can you derive the solution differently?
  • Can you use the result, or the method, for some other problem?

By consistently following the steps, you can observe a lot of interesting insights on your own.

George Polya's problem-solving methods give us a clear way of thinking to get better at math. These methods change the experience of dealing with math problems from something hard to something exciting. By following Polya's ideas, we not only learn how to approach math problems but also learn how to handle the difficult parts of math problems.

Shubham Gautam

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Polya’s Problem-Solving Process

Emma Moore, Teaching Excellence Program Master Teacher 

Problem-solving skills are crucial for students to navigate challenges, think critically, and find innovative solutions. In PISA, problem-solving competence is defined as “an individual’s capacity to engage in cognitive processing to understand and resolve problem situations where a method of solution is not immediately obvious” (OECD, 2014, p. 30). Returning to the classroom post-COVID, I found that students had lost their ‘grit’ for these deep-thinking tasks. They either struggled to start, gave up easily, or stopped at their first ‘answer’ without considering if it answered the problem or was the only possible solution.

To re-invigorate these skills, I investigated the impact of explicitly teaching Polya's problem-solving process in my Year Six class. This framework developed student agency and supported them to manage their feelings if they felt challenged by the work.

Here, I will share the impact of this initiative and how it empowered students to become effective and resilient problem solvers.  

Understanding Polya's Problem-Solving Process

Polya's problem-solving process, developed by mathematician George Polya, provides a structured approach to problem-solving that can be applied across various domains. This four-step process consists of understanding the problem, devising a plan, trying the plan, and revisiting the solution. (Polya, 1947)

In order to focus on the skills and knowledge of the problem-solving process, I began by using tasks where the mathematical processes were obvious. This allowed me to focus on the problem-solving process explicitly.

Polya's Problem-Solving Process - Figure 1

The question shown in Figure 2 is taken from Peter Sullivan and Pat Lilburn's Open-Ended Maths Activities book. This task was used to establish a baseline assessment for each stage of the process. I planned the prompts in dot points and revealed them one by one through the PowerPoint. After launching the task and giving the students time to think, they recorded all their possible answers in their workbook.

Understanding Polya's Problem-Solving Process - Figure 2

The student sample shown in Figure 3 demonstrates that the student followed a pattern and stuck to it but did not revisit their work. On line two, their response (1 half and 1 half is 2 quarters) is unreasonable.

Understanding Polya's Problem-Solving Process - Figure 3: Sample gathered from a small group of students

Figure 3 is a sample gathered from a small group of students. This group required support to start. They used paper folding and paper strips to model their thinking.

Over half of the class could give at least one correct answer, but only four students showed signs of checking to see if their plans addressed the problem and yielded correct answers. Understanding the problem and revisiting the solutions became the focus of my inquiry.

The following series of lessons covering operations with fractions and decimals focused on the stages of Polya’s process.  

Step 1: Understanding the Problem

The first step of Polya's problem-solving process emphasises the importance of ensuring you thoroughly comprehend the problem. In this step, students learn to read and analyse the problem statement, identify the key information, and clarify any uncertainties. This process encourages critical thinking (Bicer et al., 2020) as students develop the ability to break down complex problems into manageable parts. I facilitated this process by engaging students in discussions and guiding them to identify the essential components of the problem. By fostering a collaborative learning environment, students shared their perspectives and learned to refine their questions when they were unsure. Figure 6 shares an example of a prompt I use for Step 1.

Figure 4: Example prompt for Step 1.

Understanding Polya's Problem-Solving Process - Figure 4: Example prompt

Initially, students who were stuck provided the classic ‘white flag’ responses.

Student: I just don’t get it.

Teacher: What part don’t you get?

Student: All of it!

As a starting point, the students and I co-created a classroom display of helpful questions the students could use to develop their understanding.

These questions supported me to develop a deeper understanding of what students didn’t understand when they expressed uncertainty. This could range from not understanding specific terminology (often easy to explain) to where numbers came from and why their classmates interpreted the problem differently. I found engaging in this step made triaging their misunderstandings easier.  

Step 2: Devising a Plan

Once students had grasped the problem, the next step was to formulate a plan of action. In this step, students explored different strategies and selected the most appropriate approach. I prompted students to brainstorm possible solutions, draw diagrams, make tables, and create algorithms, all the time fostering creativity and diverse thinking.

This step had been a strength during the baseline assessment data, and a wide range of strategies were explored. Polya’s strategies were displayed in the classroom as the mathematician’s strategy tool kit, so students were comfortable acknowledging the many ways to solve the problem.

Students developed critical thinking and decision-making skills by keeping this step in problem-solving. They become adept at evaluating multiple approaches and selecting the most effective strategy to solve a problem, thus promoting the development of mathematical reasoning abilities (Barnes, 2021). Figure 7 shows a slide used in Step 2.

Figure 5: Example prompt for Step 2.

Understanding Polya's Problem-Solving Process - Figure 5: Example prompt for Step 2

Step 3: Try

The students implemented their selected strategy, performed calculations, made models, drew diagrams, created tables, and found patterns. This stage encouraged students to persevere and take ownership of their problem-solving process.

At Cowes Primary School, we have developed whole-school expectations around providing opportunities for hands-on learning, allowing students to engage in practical activities that support the development of ideas, expecting students to represent their work visually (pictures, materials and manipulatives), using language and numbers/symbols. This approach enhances students' problem-solving skills and fosters a sense of autonomy and confidence in their capabilities and ability to talk about their work (Roche et al., 2023). Figure 9 shows the slide used for Step 3.

Figure 6: Example prompt for Step 3.

Understanding Polya's Problem-Solving Process - Figure 6: Example prompt for Step 3

Step 4. Re-visiting the solution

The last step in Polya's problem-solving process is re-visit. After finding a solution, students critically analyse and evaluate their approach after finding a solution. They consider the effectiveness of their chosen strategy, identify strengths and weaknesses, and reflect on how they could improve their problem-solving techniques. This step was missing from most students’ work during the baseline assessment.

As a class, we added to the display questions to facilitate better reflective practice and developed a more critical approach to looking at our work. This process encouraged students to refine their answers, not go too far down the wrong path, fostered resilience, embrace challenge and normalise uncertainty (Buckley & Sullivan, 2023).

Figure 7: Class display showing our questions.

Understanding Polya's Problem-Solving Process - Figure 7: Class display showing questions

  Figure 8: Student samples from the task.

Understanding Polya's Problem-Solving Process - Figure 8: Fraction Wall sample task

Impact and Benefits:

Figure 9 shows four tasks, including the initial baseline assessment. The blue series shows the percentage of students who arrived at least one correct solution. The green series shows evidence that students were revisiting their initial solutions using other strategies to check they were correct or checking in with other groups and adjusting. There was a steady increase in both skills over the course of these four tasks.

Understanding Polya's Problem-Solving Process - Figure 9: Shows four tasks, including the initial baseline assessment

By explicitly teaching Polya's problem-solving process, the students cultivated valuable skills that extend beyond maths problems. Some of the key benefits observed were:

Mathematical Reasoning: Polya's process promotes the development of mathematical reasoning skills. Students analysed problems, explored different strategies, and apply logical thinking to arrive at solutions. These skills can enhance their overall mathematical proficiency.

Self-efficacy: Through problem-solving, students gained confidence in their ability to tackle problems. They become more self-reliant, taking ownership of their learning, and seeking solutions proactively.

Collaboration and Communication: The process encouraged collaboration and communication among students. They discussed problems, shared ideas, and considered multiple perspectives, students developed effective teamwork and interpersonal skills.

Metacognition: The reflective aspect of Polya's process fostered metacognitive skills, enabling students to monitor and regulate their thinking processes. They learned to identify their strengths and weaknesses, supporting continuous improvement and growth.  

Overall using the 4 steps was a really effective and an explicit way to focus on developing the problem-solving skills of my Year 6 students.

This article was originally published for the Mathematical Association of Victoria's Prime Number.    

References:

Barnes, A. (2021). Enjoyment in learning mathematics: Its role as a potential barrier to children’s perseverance in mathematical reasoning. Educational Studies in Mathematics , 106(1), 45–63. https://doi.org/10.1007/s10649-020-09992-x

Bicer, Ali, Yujin Lee, Celal Perihan, Mary M. Capraro, and Robert M. Capraro. ‘Considering Mathematical Creative Self-Efficacy with Problem Posing as a Measure of Mathematical Creativity’. Educational Studies in Mathematics 105, no. 3 (November 2020): 457–85. https://doi.org/10.1007/s10649-020-09995-8

Buckley, S., & Sullivan, P. (2023). Reframing anxiety and uncertainty in the mathematics classroom. Mathematics Education Research Journal , 35(S1), 157–170. https://doi.org/10.1007/s13394-021-00393-8

OECD (Ed.). (2014). Creative problem solving: Students’ skills in tackling real-life problems. OECD.

Pólya, G. (1988). How to solve it: A new aspect of mathematical method (2nd ed). Princeton university press.

Roche, A., Gervasoni, A., & Kalogeropoulos, P. (2023). Factors that promote interest and engagement in learning mathematics for low-achieving primary students across three learning settings. Mathematics Education Research Journal , 35(3), 525–556. https://doi.org/10.1007/s13394-021-00402-w

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2.1: George Polya's Four Step Problem Solving Process

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Step 1: Understand the Problem

  • Do you understand all the words?
  • Can you restate the problem in your own words?
  • Do you know what is given?
  • Do you know what the goal is?
  • Is there enough information?
  • Is there extraneous information?
  • Is this problem similar to another problem you have solved?

Step 2: Devise a Plan: Below are some strategies one might use to solve a problem. Can one (or more) of the following strategies be used? (A strategy is defined as an artful means to an end.)

Teaching with Artificial Intelligence Series

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Registration is now Open!

Our Teaching with Artificial Intelligence Series (June 3 - June 7, 2024) is open to the University of Guelph, University of Guelph-Humber, and Ridgetown Campus faculty, instructors, staff, and students. ​​ In partnership with CARE-AI, OpenED, OQA, McLaughlin Library, and Contact North, we are facilitating 17 AI workshops, panels, and playgrounds. Click on each Day below to explore and register for sessions.

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Monday, June 3, 2024

Packing for your generative ai journey .

Time: 9:30 AM - 10:30 AM

Facilitators: Kevin Matsui (CARE-AI) and Katie McLean (CARE-AI)

Description: Having some background understanding of Generative AI is a good starting point for successful use of GenAI in teaching and learning. The knowledge that can effectively inform use of available tools such as Microsoft Copilot, ChatGPT, GPT4o, Google Gemini and others includes awareness of the issues of privacy, copyright, sources, misinformation and ethics.  Deciding how you would like to use AI will impact your decisions – are you using AI as a tool or as a collaborator, or something in between like a touchpoint like a colleague. This session will explore some of the different options of foundational models and touch on some of the general issues related to the use of generative AI and recommendations for effective use.

AI Playground 

Time: 11:00 AM - 12:00 PM

Facilitators: Shehroze Saharan (OTL), Owen Wooding (OpenEd), and Dr. Rachael Lewitzky (OpenEd)

Description : This interactive session offers a space to explore, ask questions, and experiment with different AI tools. The session will be structured as guided experimentation with AI tools, which will include prompts, activities, scenarios, and reflections specifically designed to explore possible uses and limitations of AI. We will also discuss how to craft effective prompts for AI tools that will deliver useful outputs. Following our guided experimentation as a group, we will provide space for participants to share their experiences with using AI tools. No prior experience with AI tools necessary.

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Exploring Generative AI Tools

Time: 2:30 PM - 3:30 PM

Description : A survey of the available landscape of Generative AI tools (Microsoft Copilot, Google Gemini, DALLE-3, Adobe Firefly, Cohere, Llama 3, etc.) will be conducted followed live demos of common and highly impactful use cases focusing primarily on Microsoft Copilot (already available to all faculty and staff), Microsoft 365 Copilot (available as an extra cost add on, incorporates Copilot into Outlook, Excel, PowerPoint and Word) as well as ChatGPT, GPT-4o from OpenAI. Considerations and strategies for best practice will be discussed and highlighted. Understanding these tools will help effectively use these core tools as well as customized GPTs and bots that are built on these models.

Tuesday, June 4, 2024

Should i use generative ai in my course – and how to make that clear to students .

Facilitators: Dr. Christopher Laursen (OTL), Mary McCaffery (Library), and Alison Crerar (OQA)

Description: As a course instructor, it’s crucial to tell your students whether they can use generative AI, how they can use it, and why.  There are multiple means by which you can communicate the use of AI through your course outlines, assessment instructions, and class discussions. To assist you with this process, we have created a tool to help you determine skill-based learning objectives for your assignments and link these with uses of AI that do not undermine these objectives. You’ll get a chance to learn how instructors have effectively used this tool, and even try it out for yourself. We'll also consider a variety of other tools that will help you determine allowable uses and clearly communicate these to your students. 

Spice Up Your Announcements and Content with AI-Powered Videos and Images 

Facilitator: Dr. Victoria Chen (University of Guelph-Humber)

Description : Course trailers and video announcements are a great way to introduce your course and send reminders to students in an engaging way, but they can be intimidating to create. Whip up a video in under a minute with the magic of AI-powered tools! We will also explore OER and AI-generated images to help spruce up your PowerPoint slides.

AI Tool Drop-In Session

Time: 1:00 PM - 1:30 PM

Description : In these informal sessions, we will work through specific use cases that might be of interest. Focusing primarily on Microsoft Copilot (already available to all faculty and staff), Microsoft 365 Copilot (available as an extra cost add on, incorporates Copilot into Outlook, Excel, PowerPoint and Word) as well as ChatGPT, GPT-4o from OpenAI. Participants are welcome to submit a use case in advance.

Assessing the Impact of GPT on Faculty and Students at UofG: Boon or Bane? 

Time: 1:30 PM - 2:30 PM

Panelists:  Dr. Ritu Chaturvedi (CEPS), Dr. Soha Eid Moussa (CEPS), Dr. Karen Gordon (CEPS), and additional panelists. 

Description : The impact of GPT on faculty and students hinges on its use. As a supplementary resource for resource creation and problem-solving, it can be advantageous, but misuse as a shortcut may foster superficial understanding. Faculty and students must approach GPT-like tools with discernment to optimize their educational benefits. This investigative panel discussion delves into the (mis)use of GPT. Faculty members are prompted to consider its potential contributions to education, such as content creation and personalized feedback, as well as concerns like ethical implications. Meanwhile, students are asked about their utilization of GPT in coursework, its appealing aspects, and situations where they may feel pressured to use it. Through this session, the diverse implications of GPT within the university community are explored, aiming to foster a nuanced understanding of its role in education and its potential impact on teaching and learning dynamics. 

How to Personalize Learning and Enhance Course Development with Contact North | Contact Nord’s AI-powered Apps 

Time: 2:30 PM - 3:30 PM

Facilitator:  Dr. Ron Owston (Contact North)

Description : In this session participants will be introduced to AI Tutor Pro and AI Teaching Assistant Pro, two free GenAI apps recently launched by Contact North | Contact Nord. With AI Tutor Pro learners can engage in an interactive and responsive dialog to learn any topic at any level. Demonstrated will be features such as its international language options, file upload to base the interaction on the user’s own content, and voice interaction. AI Teaching Assistant Pro provides tools to help instructors create multiple choice and draft essay questions with scoring rubrics on any topic at any level. Additionally, instructors can build a course syllabus on any topic complete with a course description, learning outcomes, course topics, teaching notes, and PowerPoint slides. Time will be allotted in the session for participants’ questions and discussion. The session will be facilitated by the academic lead for the apps, Dr. Ron Owston, Professor Emeritus, York University, and Research Associate, AI in Higher Education, Contact North | Contact Nord. Learn more about Dr. Owsten: http://ronowston.ca.

Wednesday, June 5, 2024

Time: 9:30 AM - 10:00 AM

Description : In these informal sessions, we will work through specific use cases that might be of interest. Focusing primarily on Microsoft Copilot (already available to all faculty and staff), Microsoft 365 Copilot (available as an extra cost add on, incorporates Copilot into Outlook, Excel, PowerPoint and Word) as well as ChatGPT, GPT-4o from OpenAI. Participants are welcome to submit a use case in advance.

Instructor Panel: Navigating AI’s Role in Teaching and Assessment

Time: 10:30 AM - 11:30 AM

Panelists: Dr. Tanya Barzotti (Lang), Dr. Eric Chi (Lang), Carri-Ann Scott (University of Guelph-Humber), and Dr. Gus Skorburg (CoA)

Description : Join panelists Dr. Tanya Barzotti (Gordon S. Lang School of Business and Economics), Dr. Eric Chi (Gordon S. Lang School of Business and Economics), Carri-Ann Scott (Early Childhood Studies, University of Guelph-Humber), and Dr. Gus Skorburg (College of Arts) for an engaging discussion on integrating AI into their teaching and assessment practices. Panelists will share their motivations for incorporating AI into their teaching, their uses of AI, and the benefits and challenges of using AI in their teaching contexts. Attendees will gain insights on effective practices, innovative strategies, and practical applications of AI in the classroom.

Time: 11:30 AM - 12:00 PM

Redesigning Assessments in the Context of AI 

Time: 1:30 PM - 2:15 PM

Facilitators:  Dr. Megan De Roover (OTL) and Shehroze Saharan (OTL)

Description : Join us as we explore how to design assessments to intentionally address students’ use of AI in this hands-on workshop. Learn to integrate AI tools thoughtfully to enhance the effectiveness and fairness of assessments in your courses. Participants will discover strategies for incorporating AI to create innovative, adaptive assessments that reflect today’s learners, while also mitigating potential misuse. Whether you're looking to refine existing assessments or develop new ones, this workshop will provide the guidance and tools necessary to make AI a beneficial component of your educational approach.   

Using AI to Design Assessments 

Time: 2:30 PM - 3:15 PM

Description : This workshop offers a deep dive into leveraging AI technologies to create dynamic and effective assessments. Participants will learn how to utilize AI tools to develop assessments using a variety of tools, tips, and tricks. This session provides practical insights and hands-on experiences for enhancing student evaluation through AI.

Thursday, June 6, 2024

Ai playground: using ai for course design and course materials .

Time: 9:15 AM - 10:15 AM

Facilitators: Shehroze Saharan (OTL), Owen Wooding (OpenEd), & Dr. Rachael Lewitzky (OpenEd), Dr. Aron Fazekas (OTL), and Dr. Sara Fulmer (OTL)

Description : This interactive session offers a space to explore, ask questions, and experiment with different AI tools. This session will introduce various ways to use generative artificial intelligence (GenAI) for course design and developing course materials. The session will be structured as guided experimentation with AI tools, which will include prompts, activities, scenarios, and reflections specifically designed to explore possible uses and limitations of AI for course design and teaching. We will also discuss how to craft effective prompts for AI tools that will deliver useful outputs. Following our guided experimentation as a group, we will provide space for participants to share their experiences with using AI tools. No prior experience with AI tools necessary.

Gradescope’s AI Answer Grouping for Handwritten Tests & Assignments 

Time: 10:30 AM - 11:00 AM

Facilitators: Owen Wooding (OpenEd) and Dr. Rachael Lewitzky (OpenEd)

Description : While most of the buzz in the world of AI revolves around generative AI and chat-based interactions, there are other forms of AI that can also help improve the efficiency and effectiveness of common tasks. One example of helpful non-generative AI can be found in Gradescope, a grading and assessment platform available to all instructors at the University of Guelph and University of Guelph-Humber.  

During this brief 30-minute session, OpenEd’s instructional technology specialist (ITS) team will discuss and demonstrate Gradescope’s AI answer grouping capabilities for handwritten tests and assignments. Together, we will explore how incorporating Gradescope into your course(s) via a simple CourseLink integration and leveraging AI answer grouping has the potential to greatly improve grading efficiency and provide more fulsome feedback to your students.

Leveraging AI to Tackle your Workload 

Time: 11:00 AM - 12:00 PM

Facilitators:  Dr. Aron Fazekas (OTL) and Dr. Christopher Laursen (OTL)

Description : There are many promises being made about the potential of artificial intelligence to improve how we work, while maintaining the importance of the human components of teaching and learning. In this workshop, we’ll consider the variety of ways in which genAI can assist in managing workload, for example, streamlining tasks that take up time which could be spent doing more meaningful things. This workshop gives everyone a chance to share things that may have worked well in academic workload management.

External Session: Ethics and Equity with AI: Leading the Way

Please note, this is an external session that may be of interest to Teaching with Artificial Intelligence Series attendees: 

Time: 12:00 PM - 1:00 PM

Speakers: Dr. Vincent Del Casino, Provost and SVP for Academic Affairs, San Jose State University, David Weil, VP and Chief Information and Analytics Officer, Ithaca College, Carrie O’Donnell, Founder and CEO, Alchemy

Description : In this thought-provoking discussion, higher education leaders will gain valuable insights to hone their institutions’ strategic priorities around the equitable and ethical use of AI. We will explore best practices for leveraging AI to advance equity in teaching and learning, navigating ethical challenges in AI adoption, and developing robust policies to promote fairness and transparency. Attendees will leave with practical strategies to foster an inclusive and ethically responsible AI-driven educational environment. 

External Session: The Future of Higher Education in The Age of Artificial Intelligence 

Time: 1:00 PM - 2:00 PM

Facilitator:  Dr. Stephen Murgatroyd (Contact North)

Description : The rapid advancement of artificial intelligence (AI) is reshaping higher education, impacting student recruitment, teaching, assessment and engagement. AI's role raises questions about faculty's future responsibilities and the potential for AI-enabled platforms to offer education anytime, anywhere. This shift could democratize education and introduce new competitors like GoogleU or OpenAI College. Additionally, programs not incorporating AI may lag behind, with a significant debate on whether AI will adapt to faculty needs or vice versa. The integration and adaptation to AI in education is crucial for maintaining relevance and enhancing learning outcomes. 

Friday, June 7, 2024

The future of teaching: ai coffee chat.

Facilitators:   OTL, McLaughlin Library, OpenEd, OQA, and CARE-AI

Description : In this closing session of our Teaching with AI Series, we’ll collaboratively explore the evolving role of AI in learning, teaching, assessment, and curriculum. What are the opportunities and challenges of AI for education? How will AI continue to impact education, and what does this mean for our teaching? Join the conversation to share your thoughts, understand different perspectives, explore next steps, and discuss support needed for integrating AI into teaching and curriculum.  Whether you're new to exploring AI or currently adopting AI in your teaching practice, this session provides a collaborative space to explore, learn, and share experiences as a community.

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IMAGES

  1. what is the 4 step problem solving process

    example of polya's four step problem solving

  2. Problem Solving with Polya's Four Steps by Miss Benjamin

    example of polya's four step problem solving

  3. Polya's Four Steps in Problem Solving

    example of polya's four step problem solving

  4. how to solve a problem george polya

    example of polya's four step problem solving

  5. polya steps of problem solving

    example of polya's four step problem solving

  6. [Solved] Solve the following problems using Polya's four-step

    example of polya's four step problem solving

VIDEO

  1. Working Backwards Strategy: (using Polya's Problem Solving Strategy)

  2. Polya's 4 step Problem Solving

  3. POLYA`S FOUR STEPS IN PROBLEM SOLVING

  4. Polya's Problem Solving Strategy

  5. Polya's Problem Solving

  6. How to solve a mathematical word problem using the 4 Polya's step Presented by GROUP 4

COMMENTS

  1. 10.1: George Polya's Four Step Problem Solving Process

    Can one (or more) of the following strategies be used? (A strategy is defined as an artful means to an end.) 1. Guess and test. 11. Solve an equivalent problem. 2. Use a variable. 12.

  2. Polya's Problem Solving Process

    Polya's four step method for problem solving is. 1) Understand the Problem-Make sure you understand what the question is asking and what information will be used to solve the problem. 2) Devise a ...

  3. PDF 1. Understand Polya's problem-solving method. 2. State and apply

    Step 1: Understand the problem. It would seem unnecessary to state this obvious advice, but yet in my years of teaching, I have seen many students try to solve a problem before they completely understand it. The techniques that we will explain shortly will help you to avoid this critical mistake. Step 2: Devise a plan.

  4. Four Steps of Polya's Problem Solving Techniques

    Before starting the journey of problem-solving, a critical step is to understand every critical detail in the problem. According to Polya, this initial phase serves as the foundation for successful solutions. At first sight, understanding a problem may seem a trivial task for us, but it is often the root cause of failure in problem-solving.

  5. Problem Solving Strategies & Polya's 4-step Process

    Math in the Modern World Playlist: https://www.youtube.com/watch?v=vb-hDOm3GzU&list=PLbZl6MGLeYnsoaxa2L-xouDPHcoe9z23x&index=3A more logical answer to 13:36 ...

  6. Mastering Problem-Solving: A Guide to Polya's Four-Step Approach

    The four steps of the Polya method are as follows: Understand the problem. Devise a plan. Carry out the plan. Evaluate the solution. Let's take a closer look at each step. Step 1: Understand the ...

  7. Polya's Problem-Solving Process

    The first step of Polya's problem-solving process emphasises the importance of ensuring you thoroughly comprehend the problem. In this step, students learn to read and analyse the problem statement, identify the key information, and clarify any uncertainties. ... Figure 4: Example prompt for Step 1. Initially, students who were stuck provided ...

  8. Intermediate Algebra Tutorial 8

    The following formula will come in handy for solving example 6: Perimeter of a Rectangle = 2 (length) + 2 (width) Example 6 : In a blueprint of a rectangular room, the length is 1 inch more than 3 times the width. Find the dimensions if the perimeter is to be 26 inches. Step 1: Understand the problem.

  9. Polya's four steps to solving a problem

    Carry out the plan: Spend a reasonable amount of time trying to solve the problem using your plan. If you are not successful, go back to step 2. If you run out of strategies, go back to step 1. If you still don't have any luck, talk the problem over with a classmate. Look back: After you have a proposed solution, check your solution out.

  10. PDF Polya's Four Phases of Problem Solving

    Introduce suitable notation. Separate the various parts of the condition. Can you write them down? 2. Devising a Plan. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.

  11. PDF Polya's four-step approach to problem solving

    1. a) Act out the following: There are five people in a group and each shakes hands with every person. How many handshakes take place in a group? b) Draw/diagram what took place and write down what each part of your diagrams represents. c) List the number of handshakes for groups of 5, 6, and 7. 2. a) Solve the following problem in your head ...

  12. Module 1: Problem Solving Strategies

    In 1945, Pólya published the short book How to Solve It, which gave a four-step method for solving mathematical problems: First, you have to understand the problem. ... Make sure you use Polya's 4 problem solving steps. (12 points) Problem Solving Strategy 2 (Draw a Picture). ... Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks ...

  13. PDF Problem Solving and Critical Thinking

    Polya's Four Steps in Problem Solving Steps 3-4. Step 3: Carry out the plan and solve the problem. Step 4: Look back and check the answer. The answer should satisfy the conditions of the problem. The answer should make sense and be reasonable. If this is not the case, recheck the method and any calculations. Perhaps there is an alternative ...

  14. Polya's Four Steps in Problem Solving (1.3)

    Explanation of Polya's Four Step problem solving technique. The four steps are explained in simple terms with an example of applying Polya's method.

  15. PDF Polya's four-step approach to problem solving

    To begin this task, we now discuss a framework for thinking about problem solving: Polya's four-step approach to problem solving. Polya's four-step approach to problem solving 1. Preparation: ... two specific examples that illustrate the statement. If it is false, give a specific counterexample. (a) If a < b, then a + c < b + c.

  16. PDF Polya'S Four Step Problem Solving Process

    POLYA'S FOUR STEP PROBLEM SOLVING PROCESS Understand Devise a Plan Carry out Plan Look Back PROBLEM SOLVING STRATEGIES (exmples) Making a Drawing ... Arithmetic Sequences Examples D & E Common Differences Geometric Sequences Example F Common Ratio Triangular Numbers Example G Finite Differences Examples H & I §1.3 KEY IDEAS, page 1 of 2 ...

  17. Pólya's Four Step Method

    Step 1. Understand (or clarify) the problem; Step 2. Devise a plan; Step 3. Carry out the plan; Step 4. Look for ways to improve your work; Let's break it down step-by-step to see how it can help you when it comes to white boarding. Step 1. Understand (or clarify) the problem. When you first encounter the problem, whether it be in an ...

  18. The Problem-Solving Process in a Mathematics Classroom

    Polya's (1957) four-step process has provided a model for the teaching and assessing. problem solving in mathematics classrooms: understanding the problem, devising a plan, carrying out the plan, and looking back. Other educators have adapted these steps, but the. essence of these adaptations is very similar to what Polya initially developed.

  19. PDF 1 Polya's Problem-Solving Process

    their problem-solving skills. P´olya's Four-Step Process In his book How to Solve It, George Polya identifies a four-step process that forms the basis of any serious attempt at problem solving. These steps are: Step 1. Understand the Problem Obviously if you don't understand a problem, you won't be able to solve it.

  20. 2.1: George Polya's Four Step Problem Solving Process

    Can one (or more) of the following strategies be used? (A strategy is defined as an artful means to an end.) 1. Guess and test. 11. Solve an equivalent problem. 2. Use a variable. 12.

  21. Polya's 4 step problem solving examples

    - In this book he identifies four basic principles of problem solving. 1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back. Numeric Word Problems Example 1: Twice the difference of a number and 1 is 4 more than that number. Find the number. Step 1: Make sure that you read the question carefully several times. Since we ...

  22. Problem Solving using Polya's Four Steps

    About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ...

  23. The Impact of Applying the First Two Steps of Polya's Four

    All three of these resources indicate that problem-solving skills can provide access for the underprivileged, be a bridge to the university, and provide a discerning electorate for our democracy (Grouws, 2003; Polya, 1985; Schoenfeld, 2004). This is why it is important to investigate whether the first two steps of George Polya's problem ...

  24. Problem solving

    Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions habit from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue ...

  25. Three-body problem

    The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details

  26. Use Polya's four-step method in problem solving to

    Other Math questions and answers. Use Polya's four-step method in problem solving to solve the following problem.Five rumners, Ancly, Beth, Dale, Ella, and Tri, are in a one-mile race.Tri finished 7 second (s) before Andy. Andy finished 2 second (s) before Beth.Beth finished 5 second (s) after Ella. Dale finished 9 second ...

  27. Newton's method

    An illustration of Newton's method. In numerical analysis, Newton's method, also known as the Newton-Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.The most basic version starts with a real-valued function f, its derivative f ′, and an initial guess ...

  28. Develop Problem Solving Skills in Accounting

    Here's how you can develop the essential problem solving skills employers seek in Accounting professionals. Powered by AI and the LinkedIn community. 1. Understand Basics. 2. Analytical Thinking ...

  29. Scientific method

    The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century. The scientific method involves careful observation coupled with rigorous scepticism, because cognitive assumptions can distort the interpretation of the observation.Scientific inquiry includes creating a hypothesis through inductive reasoning ...

  30. Teaching with Artificial Intelligence Series

    Description: The impact of GPT on faculty and students hinges on its use. As a supplementary resource for resource creation and problem-solving, it can be advantageous, but misuse as a shortcut may foster superficial understanding. Faculty and students must approach GPT-like tools with discernment to optimize their educational benefits.