method is also known as problem solving method

What is STEM Education?

STEM education, now also know as STEAM, is a multi-discipline approach to teaching.

• Importance of STEAM education

STEAM blended learning

• Inequalities in STEAM

Additional resources

Bibliography.

STEM education is a teaching approach that combines science, technology, engineering and math . Its recent successor, STEAM, also incorporates the arts, which have the "ability to expand the limits of STEM education and application," according to Stem Education Guide . STEAM is designed to encourage discussions and problem-solving among students, developing both practical skills and appreciation for collaborations, according to the Institution for Art Integration and STEAM .

Rather than teach the five disciplines as separate and discrete subjects, STEAM integrates them into a cohesive learning paradigm based on real-world applications. 

According to the U.S. Department of Education "In an ever-changing, increasingly complex world, it's more important than ever that our nation's youth are prepared to bring knowledge and skills to solve problems, make sense of information, and know how to gather and evaluate evidence to make decisions." 

In 2009, the Obama administration announced the " Educate to Innovate " campaign to motivate and inspire students to excel in STEAM subjects. This campaign also addresses the inadequate number of teachers skilled to educate in these subjects. 

The Department of Education now offers a number of STEM-based programs , including research programs with a STEAM emphasis, STEAM grant selection programs and general programs that support STEAM education.

In 2020, the U.S. Department of Education awarded $141 million in new grants and $437 million to continue existing STEAM projects a breakdown of grants can be seen in their investment report .  

The importance of STEM and STEAM education

STEAM education is crucial to meet the needs of a changing world. According to an article from iD Tech , millions of STEAM jobs remain unfilled in the U.S., therefore efforts to fill this skill gap are of great importance. According to a report from the U.S. Bureau of Labor Statistics there is a projected growth of STEAM-related occupations of 10.5% between 2020 and 2030 compared to 7.5% in non-STEAM-related occupations. The median wage in 2020 was also higher in STEAM occupations ($89,780) compared to non-STEAM occupations ($40,020).

Between 2014 and 2024, employment in computer occupations is projected to increase by 12.5 percent between 2014 and 2024, according to a STEAM occupation report . With projected increases in STEAM-related occupations, there needs to be an equal increase in STEAM education efforts to encourage students into these fields otherwise the skill gap will continue to grow. 

STEAM jobs do not all require higher education or even a college degree. Less than half of entry-level STEAM jobs require a bachelor's degree or higher, according to skills gap website Burning Glass Technologies . However, a four-year degree is incredibly helpful with salary — the average advertised starting salary for entry-level STEAM jobs with a bachelor's requirement was 26 percent higher than jobs in the non-STEAM fields.. For every job posting for a bachelor's degree recipient in a non-STEAM field, there were 2.5 entry-level job postings for a bachelor's degree recipient in a STEAM field. 

What separates STEAM from traditional science and math education is the blended learning environment and showing students how the scientific method can be applied to everyday life. It teaches students computational thinking and focuses on the real-world applications of problem-solving. As mentioned before, STEAM education begins while students are very young:

Elementary school — STEAM education focuses on the introductory level STEAM courses, as well as awareness of the STEAM fields and occupations. This initial step provides standards-based structured inquiry-based and real-world problem-based learning, connecting all four of the STEAM subjects. The goal is to pique students' interest into them wanting to pursue the courses, not because they have to. There is also an emphasis placed on bridging in-school and out-of-school STEAM learning opportunities. 

– Best microscopes for kids

– What is a scientific theory?

– Science experiments for kids  

Middle school — At this stage, the courses become more rigorous and challenging. Student awareness of STEAM fields and occupations is still pursued, as well as the academic requirements of such fields. Student exploration of STEAM-related careers begins at this level, particularly for underrepresented populations. 

High school — The program of study focuses on the application of the subjects in a challenging and rigorous manner. Courses and pathways are now available in STEAM fields and occupations, as well as preparation for post-secondary education and employment. More emphasis is placed on bridging in-school and out-of-school STEAM opportunities.

Much of the STEAM curriculum is aimed toward attracting underrepresented populations. There is a significant disparity in the female to male ratio when it comes to those employed in STEAM fields, according to Stem Women . Approximately 1 in 4 STEAM graduates is female.  

Inequalities in STEAM education

Ethnically, people from Black backgrounds in STEAM education in the UK have poorer degree outcomes and lower rates of academic career progression compared to other ethnic groups, according to a report from The Royal Society . Although the proportion of Black students in STEAM higher education has increased over the last decade, they are leaving STEAM careers at a higher rate compared to other ethnic groups. 

"These reports highlight the challenges faced by Black researchers, but we also need to tackle the wider inequalities which exist across our society and prevent talented people from pursuing careers in science." President of the Royal Society, Sir Adrian Smith said. 

Asian students typically have the highest level of interest in STEAM. According to the Royal Society report in 2018/19 18.7% of academic staff in STEAM were from ethnic minority groups, of these groups 13.2% were Asian compared to 1.7% who were Black. 

If you want to learn more about why STEAM is so important check out this informative article from the University of San Diego . Explore some handy STEAM education teaching resources courtesy of the Resilient Educator . Looking for tips to help get children into STEAM? Forbes has got you covered.  

• Lee, Meggan J., et al. ' If you aren't White, Asian or Indian, you aren't an engineer': racial microaggressions in STEM education. " International Journal of STEM Education 7.1 (2020): 1-16. 
• STEM Occupations: Past, Present, And Future . Stella Fayer, Alan Lacey, and Audrey Watson. A report. 2017. 
• Institution for Art Integration and STEAM What is STEAM education? 
• Barone, Ryan, ' The state of STEM education told through 18 stats ', iD Tech.  
• U.S. Department of Education , Science, Technology, Engineering, and Math, including Computer Science.  
• ' STEM sector must step up and end unacceptable disparities in Black staff ', The Royal Society. A report, March 25, 2021.  
• 'Percentages of Women in STEM Statistics' Stemwomen.com  

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Working with objects

JavaScript is designed on a simple object-based paradigm. An object is a collection of properties , and a property is an association between a name (or key ) and a value. A property's value can be a function, in which case the property is known as a method .

Objects in JavaScript, just as in many other programming languages, can be compared to objects in real life. In JavaScript, an object is a standalone entity, with properties and type. Compare it with a cup, for example. A cup is an object, with properties. A cup has a color, a design, weight, a material it is made of, etc. The same way, JavaScript objects can have properties, which define their characteristics.

In addition to objects that are predefined in the browser, you can define your own objects. This chapter describes how to use objects, properties, and methods, and how to create your own objects.

Creating new objects

You can create an object using an object initializer . Alternatively, you can first create a constructor function and then instantiate an object by invoking that function with the new operator.

Using object initializers

Object initializers are also called object literals . "Object initializer" is consistent with the terminology used by C++.

The syntax for an object using an object initializer is:

Each property name before colons is an identifier (either a name, a number, or a string literal), and each valueN is an expression whose value is assigned to the property name. The property name can also be an expression; computed keys need to be wrapped in square brackets. The object initializer reference contains a more detailed explanation of the syntax.

In this example, the newly created object is assigned to a variable obj — this is optional. If you do not need to refer to this object elsewhere, you do not need to assign it to a variable. (Note that you may need to wrap the object literal in parentheses if the object appears where a statement is expected, so as not to have the literal be confused with a block statement.)

Object initializers are expressions, and each object initializer results in a new object being created whenever the statement in which it appears is executed. Identical object initializers create distinct objects that do not compare to each other as equal.

The following statement creates an object and assigns it to the variable x if and only if the expression cond is true:

The following example creates myHonda with three properties. Note that the engine property is also an object with its own properties.

Objects created with initializers are called plain objects , because they are instances of Object , but not any other object type. Some object types have special initializer syntaxes — for example, array initializers and regex literals .

Using a constructor function

Alternatively, you can create an object with these two steps:

• Define the object type by writing a constructor function. There is a strong convention, with good reason, to use a capital initial letter.
• Create an instance of the object with new .

To define an object type, create a function for the object type that specifies its name, properties, and methods. For example, suppose you want to create an object type for cars. You want this type of object to be called Car , and you want it to have properties for make, model, and year. To do this, you would write the following function:

Notice the use of this to assign values to the object's properties based on the values passed to the function.

Now you can create an object called myCar as follows:

This statement creates myCar and assigns it the specified values for its properties. Then the value of myCar.make is the string "Eagle" , myCar.model is the string "Talon TSi" , myCar.year is the integer 1993 , and so on. The order of arguments and parameters should be the same.

You can create any number of Car objects by calls to new . For example,

An object can have a property that is itself another object. For example, suppose you define an object called Person as follows:

and then instantiate two new Person objects as follows:

Then, you can rewrite the definition of Car to include an owner property that takes a Person object, as follows:

To instantiate the new objects, you then use the following:

Notice that instead of passing a literal string or integer value when creating the new objects, the above statements pass the objects rand and ken as the arguments for the owners. Then if you want to find out the name of the owner of car2 , you can access the following property:

You can always add a property to a previously defined object. For example, the statement

adds a property color to car1 , and assigns it a value of "black" . However, this does not affect any other objects. To add the new property to all objects of the same type, you have to add the property to the definition of the Car object type.

You can also use the class syntax instead of the function syntax to define a constructor function. For more information, see the class guide .

Using the Object.create() method

Objects can also be created using the Object.create() method. This method can be very useful, because it allows you to choose the prototype object for the object you want to create, without having to define a constructor function.

Objects and properties

A JavaScript object has properties associated with it. Object properties are basically the same as variables, except that they are associated with objects, not scopes . The properties of an object define the characteristics of the object.

For example, this example creates an object named myCar , with properties named make , model , and year , with their values set to "Ford" , "Mustang" , and 1969 :

Like JavaScript variables, property names are case sensitive. Property names can only be strings or Symbols — all keys are converted to strings unless they are Symbols. Array indices are, in fact, properties with string keys that contain integers.

Accessing properties

You can access a property of an object by its property name. Property accessors come in two syntaxes: dot notation and bracket notation . For example, you could access the properties of the myCar object as follows:

An object property name can be any JavaScript string or symbol , including an empty string. However, you cannot use dot notation to access a property whose name is not a valid JavaScript identifier. For example, a property name that has a space or a hyphen, that starts with a number, or that is held inside a variable can only be accessed using the bracket notation. This notation is also very useful when property names are to be dynamically determined, i.e. not determinable until runtime. Examples are as follows:

In the above code, the key anotherObj is an object, which is neither a string nor a symbol. When it is added to the myObj , JavaScript calls the toString() method of anotherObj , and use the resulting string as the new key.

You can also access properties with a string value stored in a variable. The variable must be passed in bracket notation. In the example above, the variable str held "myString" and it is "myString" that is the property name. Therefore, myObj.str will return as undefined.

This allows accessing any property as determined at runtime:

However, beware of using square brackets to access properties whose names are given by external input. This may make your code susceptible to object injection attacks .

Nonexistent properties of an object have value undefined (and not null ).

Enumerating properties

There are three native ways to list/traverse object properties:

• for...in loops. This method traverses all of the enumerable string properties of an object as well as its prototype chain.
• Object.keys() . This method returns an array with only the enumerable own string property names ("keys") in the object myObj , but not those in the prototype chain.
• Object.getOwnPropertyNames() . This method returns an array containing all the own string property names in the object myObj , regardless of if they are enumerable or not.

You can use the bracket notation with for...in to iterate over all the enumerable properties of an object. To illustrate how this works, the following function displays the properties of the object when you pass the object and the object's name as arguments to the function:

The term "own property" refers to the properties of the object, but excluding those of the prototype chain. So, the function call showProps(myCar, 'myCar') would print the following:

The above is equivalent to:

There is no native way to list inherited non-enumerable properties. However, this can be achieved with the following function:

For more information, see Enumerability and ownership of properties .

Deleting properties

You can remove a non-inherited property using the delete operator. The following code shows how to remove a property.

Inheritance

All objects in JavaScript inherit from at least one other object. The object being inherited from is known as the prototype, and the inherited properties can be found in the prototype object of the constructor. See Inheritance and the prototype chain for more information.

Defining properties for all objects of one type

You can add a property to all objects created through a certain constructor using the prototype property. This defines a property that is shared by all objects of the specified type, rather than by just one instance of the object. The following code adds a color property to all objects of type Car , and then reads the property's value from an instance car1 .

Defining methods

A method is a function associated with an object, or, put differently, a method is a property of an object that is a function. Methods are defined the way normal functions are defined, except that they have to be assigned as the property of an object. See also method definitions for more details. An example is:

where objectName is an existing object, methodName is the name you are assigning to the method, and functionName is the name of the function.

You can then call the method in the context of the object as follows:

Methods are typically defined on the prototype object of the constructor, so that all objects of the same type share the same method. For example, you can define a function that formats and displays the properties of the previously-defined Car objects.

Notice the use of this to refer to the object to which the method belongs. Then you can call the displayCar method for each of the objects as follows:

Using this for object references

JavaScript has a special keyword, this , that you can use within a method to refer to the current object. For example, suppose you have 2 objects, Manager and Intern . Each object has its own name , age and job . In the function sayHi() , notice the use of this.name . When added to the 2 objects, the same function will print the message with the name of the respective object it's attached to.

this is a "hidden parameter" of a function call that's passed in by specifying the object before the function that was called. For example, in Manager.sayHi() , this is the Manager object, because Manager comes before the function sayHi() . If you access the same function from another object, this will change as well. If you use other methods to call the function, like Function.prototype.call() or Reflect.apply() , you can explicitly pass the value of this as an argument.

Defining getters and setters

A getter is a function associated with a property that gets the value of a specific property. A setter is a function associated with a property that sets the value of a specific property. Together, they can indirectly represent the value of a property.

Getters and setters can be either

• defined within object initializers , or
• added later to any existing object.

Within object initializers , getters and setters are defined like regular methods , but prefixed with the keywords get or set . The getter method must not expect a parameter, while the setter method expects exactly one parameter (the new value to set). For instance:

The myObj object's properties are:

• myObj.a — a number
• myObj.b — a getter that returns myObj.a plus 1
• myObj.c — a setter that sets the value of myObj.a to half of the value myObj.c is being set to

Getters and setters can also be added to an object at any time after creation using the Object.defineProperties() method. This method's first parameter is the object on which you want to define the getter or setter. The second parameter is an object whose property names are the getter or setter names, and whose property values are objects for defining the getter or setter functions. Here's an example that defines the same getter and setter used in the previous example:

Which of the two forms to choose depends on your programming style and task at hand. If you can change the definition of the original object, you will probably define getters and setters through the original initializer. This form is more compact and natural. However, if you need to add getters and setters later — maybe because you did not write the particular object — then the second form is the only possible form. The second form better represents the dynamic nature of JavaScript, but it can make the code hard to read and understand.

Comparing objects

In JavaScript, objects are a reference type. Two distinct objects are never equal, even if they have the same properties. Only comparing the same object reference with itself yields true.

For more information about comparison operators, see equality operators .

• Inheritance and the prototype chain

Academic Experience

How to identify and resolve research problems

Updated July 12, 2023

In this article, we’re going to take you through one of the most pertinent parts of conducting research: a research problem (also known as a research problem statement).

When trying to formulate a good research statement, and understand how to solve it for complex projects, it can be difficult to know where to start.

Not only are there multiple perspectives (from stakeholders to project marketers who want answers), you have to consider the particular context of the research topic: is it timely, is it relevant and most importantly of all, is it valuable?

In other words: are you looking at a research worthy problem?

The fact is, a well-defined, precise, and goal-centric research problem will keep your researchers, stakeholders, and business-focused and your results actionable.

And when it works well, it's a powerful tool to identify practical solutions that can drive change and secure buy-in from your workforce.

Free eBook: The ultimate guide to market research

What is a research problem?

In social research methodology and behavioral sciences , a research problem establishes the direction of research, often relating to a specific topic or opportunity for discussion.

For example: climate change and sustainability, analyzing moral dilemmas or wage disparity amongst classes could all be areas that the research problem focuses on.

As well as outlining the topic and/or opportunity, a research problem will explain:

• why the area/issue needs to be addressed,
• why the area/issue is of importance,
• the parameters of the research study
• the research objective
• the reporting framework for the results and
• what the overall benefit of doing so will provide (whether to society as a whole or other researchers and projects).

Having identified the main topic or opportunity for discussion, you can then narrow it down into one or several specific questions that can be scrutinized and answered through the research process.

What are research questions?

Generating research questions underpinning your study usually starts with problems that require further research and understanding while fulfilling the objectives of the study.

A good problem statement begins by asking deeper questions to gain insights about a specific topic.

For example, using the problems above, our questions could be:

"How will climate change policies influence sustainability standards across specific geographies?"

"What measures can be taken to address wage disparity without increasing inflation?"

Developing a research worthy problem is the first step - and one of the most important - in any kind of research.

It’s also a task that will come up again and again because any business research process is cyclical. New questions arise as you iterate and progress through discovering, refining, and improving your products and processes. A research question can also be referred to as a "problem statement".

Note: good research supports multiple perspectives through empirical data. It’s focused on key concepts rather than a broad area, providing readily actionable insight and areas for further research.

Research question or research problem?

As we've highlighted, the terms “research question” and “research problem” are often used interchangeably, becoming a vague or broad proposition for many.

The term "problem statement" is far more representative, but finds little use among academics.

Instead, some researchers think in terms of a single research problem and several research questions that arise from it.

As mentioned above, the questions are lines of inquiry to explore in trying to solve the overarching research problem.

Ultimately, this provides a more meaningful understanding of a topic area.

It may be useful to think of questions and problems as coming out of your business data – that’s the O-data (otherwise known as operational data) like sales figures and website metrics.

What's an example of a research problem?

Your overall research problem could be: "How do we improve sales across EMEA and reduce lost deals?"

This research problem then has a subset of questions, such as:

"Why do sales peak at certain times of the day?"

"Why are customers abandoning their online carts at the point of sale?"

As well as helping you to solve business problems, research problems (and associated questions) help you to think critically about topics and/or issues (business or otherwise). You can also use your old research to aid future research -- a good example is laying the foundation for comparative trend reports or a complex research project.

(Also, if you want to see the bigger picture when it comes to research problems, why not check out our ultimate guide to market research? In it you'll find out: what effective market research looks like, the use cases for market research, carrying out a research study, and how to examine and action research findings).

The research process: why are research problems important?

A research problem has two essential roles in setting your research project on a course for success.

1. They set the scope

The research problem defines what problem or opportunity you’re looking at and what your research goals are. It stops you from getting side-tracked or allowing the scope of research to creep off-course .

Without a strong research problem or problem statement, your team could end up spending resources unnecessarily, or coming up with results that aren’t actionable - or worse, harmful to your business - because the field of study is too broad.

2. They tie your work to business goals and actions

To formulate a research problem in terms of business decisions means you always have clarity on what’s needed to make those decisions. You can show the effects of what you’ve studied using real outcomes.

Then, by focusing your research problem statement on a series of questions tied to business objectives, you can reduce the risk of the research being unactionable or inaccurate.

It's also worth examining research or other scholarly literature (you’ll find plenty of similar, pertinent research online) to see how others have explored specific topics and noting implications that could have for your research.

Four steps to defining your research problem

Image credit: http://myfreeschooltanzania.blogspot.com/2014/11/defining-research-problem.html

1. Observe and identify

Businesses today have so much data that it can be difficult to know which problems to address first. Researchers also have business stakeholders who come to them with problems they would like to have explored. A researcher’s job is to sift through these inputs and discover exactly what higher-level trends and key concepts are worth investing in.

This often means asking questions and doing some initial investigation to decide which avenues to pursue. This could mean gathering interdisciplinary perspectives identifying additional expertise and contextual information.

Sometimes, a small-scale preliminary study might be worth doing to help get a more comprehensive understanding of the business context and needs, and to make sure your research problem addresses the most critical questions.

This could take the form of qualitative research using a few in-depth interviews , an environmental scan, or reviewing relevant literature.

The sales manager of a sportswear company has a problem: sales of trail running shoes are down year-on-year and she isn’t sure why. She approaches the company’s research team for input and they begin asking questions within the company and reviewing their knowledge of the wider market.

2. Review the key factors involved

As a marketing researcher, you must work closely with your team of researchers to define and test the influencing factors and the wider context involved in your study. These might include demographic and economic trends or the business environment affecting the question at hand. This is referred to as a relational research problem.

To do this, you have to identify the factors that will affect the research and begin formulating different methods to control them.

You also need to consider the relationships between factors and the degree of control you have over them. For example, you may be able to control the loading speed of your website but you can’t control the fluctuations of the stock market.

Doing this will help you determine whether the findings of your project will produce enough information to be worth the cost.

You need to determine:

• which factors affect the solution to the research proposal.
• which ones can be controlled and used for the purposes of the company, and to what extent.
• the functional relationships between the factors.
• which ones are critical to the solution of the research study.

The research team at the running shoe company is hard at work. They explore the factors involved and the context of why YoY sales are down for trail shoes, including things like what the company’s competitors are doing, what the weather has been like – affecting outdoor exercise – and the relative spend on marketing for the brand from year to year.

The final factor is within the company’s control, although the first two are not. They check the figures and determine marketing spend has a significant impact on the company.

3. Prioritize

Once you and your research team have a few observations, prioritize them based on their business impact and importance. It may be that you can answer more than one question with a single study, but don’t do it at the risk of losing focus on your overarching research problem.

Questions to ask:

• Who? Who are the people with the problem? Are they end-users, stakeholders, teams within your business? Have you validated the information to see what the scale of the problem is?
• What? What is its nature and what is the supporting evidence?
• Why? What is the business case for solving the problem? How will it help?
• Where? How does the problem manifest and where is it observed?

To help you understand all dimensions, you might want to consider focus groups or preliminary interviews with external (including consumers and existing customers) and internal (salespeople, managers, and other stakeholders) parties to provide what is sometimes much-needed insight into a particular set of questions or problems.

After observing and investigating, the running shoe researchers come up with a few candidate questions, including:

• What is the relationship between US average temperatures and sales of our products year on year?
• At present, how does our customer base rank Competitor X and Competitor Y’s trail running shoe compared to our brand?
• What is the relationship between marketing spend and trail shoe product sales over the last 12 months?

They opt for the final question, because the variables involved are fully within the company’s control, and based on their initial research and stakeholder input, seem the most likely cause of the dive in sales. The research question is specific enough to keep the work on course towards an actionable result, but it allows for a few different avenues to be explored, such as the different budget allocations of offline and online marketing and the kinds of messaging used.

Get feedback from the key teams within your business to make sure everyone is aligned and has the same understanding of the research problem and questions, and the actions you hope to take based on the results. Now is also a good time to demonstrate the ROI of your research and lay out its potential benefits to your stakeholders.

Different groups may have different goals and perspectives on the issue. This step is vital for getting the necessary buy-in and pushing the project forward.

The running shoe company researchers now have everything they need to begin. They call a meeting with the sales manager and consult with the product team, marketing team, and C-suite to make sure everyone is aligned and has bought into the direction of the research topic. They identify and agree that the likely course of action will be a rethink of how marketing resources are allocated, and potentially testing out some new channels and messaging strategies .

Can you explore a broad area and is it practical to do so?

A broader research problem or report can be a great way to bring attention to prevalent issues, societal or otherwise, but are often undertaken by those with the resources to do so.

Take a typical government cybersecurity breach survey, for example. Most of these reports raise awareness of cybercrime, from the day-to-day threats businesses face to what security measures some organizations are taking. What these reports don't do, however, is provide actionable advice - mostly because every organization is different.

The point here is that while some researchers will explore a very complex issue in detail, others will provide only a snapshot to maintain interest and encourage further investigation. The "value" of the data is wholly determined by the recipients of it - and what information you choose to include.

To summarize, it can be practical to undertake a broader research problem, certainly, but it may not be possible to cover everything or provide the detail your audience needs. Likewise, a more systematic investigation of an issue or topic will be more valuable, but you may also find that you cover far less ground.

It's important to think about your research objectives and expected findings before going ahead.

Ensuring your research project is a success

A complex research project can be made significantly easier with clear research objectives, a descriptive research problem, and a central focus. All of which we've outlined in this article.

If you have previous research, even better. Use it as a benchmark

Remember: what separates a good research paper from an average one is actually very simple: valuable, empirical data that explores a prevalent societal or business issue and provides actionable insights.

And we can help.

Sophisticated research made simple with Qualtrics

Trusted by the world's best brands, our platform enables researchers from academic to corporate to tackle the hardest challenges and deliver the results that matter.

Our CoreXM platform supports the methods that define superior research and delivers insights in real-time. It's easy to use (thanks to drag-and-drop functionality) and requires no coding, meaning you'll be capturing data and gleaning insights in no time.

It also excels in flexibility; you can track consumer behavior across segments , benchmark your company versus competitors , carry out complex academic research, and do much more, all from one system.

It's one platform with endless applications, so no matter your research problem, we've got the tools to help you solve it. And if you don't have a team of research experts in-house, our market research team has the practical knowledge and tools to help design the surveys and find the respondents you need.

Of course, you may want to know where to begin with your own market research . If you're struggling, make sure to download our ultimate guide using the link below.

It's got everything you need and there’s always information in our research methods knowledge base.

Scott Smith

Scott Smith, Ph.D. is a contributor to the Qualtrics blog.

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44 Powerful Instructional Strategies Examples for Every Classroom

So many ways to help students learn!

Looking for some new ways to teach and learn in your classroom? This roundup of instructional strategies examples includes methods that will appeal to all learners and work for any teacher.

What are instructional strategies?

In the simplest of terms, instructional strategies are the methods teachers use to achieve learning objectives. In other words, pretty much every learning activity you can think of is an example of an instructional strategy. They’re also known as teaching strategies and learning strategies.

The more instructional strategies a teacher has in their tool kit, the more they’re able to reach all of their students. Different types of learners respond better to various strategies, and some topics are best taught with one strategy over another. Usually, teachers use a wide array of strategies across a single lesson. This gives all students a chance to play to their strengths and ensures they have a deeper connection to the material.

There are a lot of different ways of looking at instructional strategies. One of the most common breaks them into five basic types. It’s important to remember that many learning activities fall into more than one of these categories, and teachers rarely use one type of strategy alone. The key is to know when a strategy can be most effective, for the learners or for the learning objective. Here’s a closer look at the five basic types, with instructional strategies examples for each.

Direct Instruction Instructional Strategies Examples

Direct instruction can also be called “teacher-led instruction,” and it’s exactly what it sounds like. The teacher provides the information, while the students watch, listen, and learn. Students may participate by answering questions asked by the teacher or practicing a skill under their supervision. This is a very traditional form of teaching, and one that can be highly effective when you need to provide information or teach specific skills.

This method gets a lot of flack these days for being “boring” or “old-fashioned.” It’s true that you don’t want it to be your only instructional strategy, but short lectures are still very effective learning tools. This type of direct instruction is perfect for imparting specific detailed information or teaching a step-by-step process. And lectures don’t have to be boring—just look at the success of TED Talks .

Didactic Questioning

These are often paired with other direct instruction methods like lecturing. The teacher asks questions to determine student understanding of the material. They’re often questions that start with “who,” “what,” “where,” and “when.”

Demonstration

In this direct instruction method, students watch as a teacher demonstrates an action or skill. This might be seeing a teacher solving a math problem step-by-step, or watching them demonstrate proper handwriting on the whiteboard. Usually, this is followed by having students do hands-on practice or activities in a similar manner.

Drill & Practice

If you’ve ever used flash cards to help kids practice math facts or had your whole class chant the spelling of a word out loud, you’ve used drill & practice. It’s another one of those traditional instructional strategies examples. When kids need to memorize specific information or master a step-by-step skill, drill & practice really works.

Indirect Instruction Instructional Strategies Examples

This form of instruction is learner-led and helps develop higher-order thinking skills. Teachers guide and support, but students drive the learning through reading, research, asking questions, formulating ideas and opinions, and more. This method isn’t ideal when you need to teach detailed information or a step-by-step process. Instead, use it to develop critical thinking skills , especially when more than one solution or opinion is valid.

Problem-Solving

In this indirect learning method, students work their way through a problem to find a solution. Along the way, they must develop the knowledge to understand the problem and use creative thinking to solve it. STEM challenges are terrific examples of problem-solving instructional strategies.

Project-Based Learning

When kids participate in true project-based learning, they’re learning through indirect and experiential strategies. As they work to find solutions to a real-world problem, they develop critical thinking skills and learn by research, trial and error, collaboration, and other experiences.

Learn more: What Is Project-Based Learning?

Concept Mapping

Students use concept maps to break down a subject into its main points and draw connections between these points. They brainstorm the big-picture ideas, then draw lines to connect terms, details, and more to help them visualize the topic.

Case Studies

When you think of case studies, law school is probably the first thing that jumps to mind. But this method works at any age, for a variety of topics. This indirect learning method teaches students to use material to draw conclusions, make connections, and advance their existing knowledge.

Reading for Meaning

This is different than learning to read. Instead, it’s when students use texts (print or digital) to learn about a topic. This traditional strategy works best when students already have strong reading comprehension skills. Try our free reading comprehension bundle to give students the ability to get the most out of reading for meaning.

Flipped Classroom

In a flipped classroom, students read texts or watch prerecorded lectures at home. Classroom time is used for deeper learning activities, like discussions, labs, and one-on-one time for teachers and students.

Learn more: What Is a Flipped Classroom?

Experiential Learning Instructional Strategies Examples

In experiential learning, students learn by doing. Rather than following a set of instructions or listening to a lecture, they dive right into an activity or experience. Once again, the teacher is a guide, there to answer questions and gently keep learning on track if necessary. At the end, and often throughout, the learners reflect on their experience, drawing conclusions about the skills and knowledge they’ve gained. Experiential learning values the process over the product.

Science Experiments

This is experiential learning at its best. Hands-on experiments let kids learn to establish expectations, create sound methodology, draw conclusions, and more.

Learn more: Hundreds of science experiment ideas for kids and teens

Field Trips

Heading out into the real world gives kids a chance to learn indirectly, through experiences. They may see concepts they already know put into practice or learn new information or skills from the world around them.

Learn more: The Big List of PreK-12 Field Trip Ideas

Games and Gamification

Teachers have long known that playing games is a fun (and sometimes sneaky) way to get kids to learn. You can use specially designed educational games for any subject. Plus, regular board games often involve a lot of indirect learning about math, reading, critical thinking, and more.

Learn more: Classic Classroom Games and Best Online Educational Games

Service Learning

This is another instructional strategies example that takes students out into the real world. It often involves problem-solving skills and gives kids the opportunity for meaningful social-emotional learning.

Learn more: What Is Service Learning?

Interactive Instruction Instructional Strategies Examples

As you might guess, this strategy is all about interaction between the learners and often the teacher. The focus is on discussion and sharing. Students hear other viewpoints, talk things out, and help each other learn and understand the material. Teachers can be a part of these discussions, or they can oversee smaller groups or pairings and help guide the interactions as needed. Interactive instruction helps students develop interpersonal skills like listening and observation.

Peer Instruction

It’s often said the best way to learn something is to teach it to others. Studies into the so-called “ protégé effect ” seem to prove it too. In order to teach, you first must understand the information yourself. Then, you have to find ways to share it with others—sometimes more than one way. This deepens your connection to the material, and it sticks with you much longer. Try having peers instruct one another in your classroom, and see the magic in action.

Reciprocal Teaching

This method is specifically used in reading instruction, as a cooperative learning strategy. Groups of students take turns acting as the teacher, helping students predict, clarify, question, and summarize. Teachers model the process initially, then observe and guide only as needed.

Some teachers shy away from debate in the classroom, afraid it will become too adversarial. But learning to discuss and defend various points of view is an important life skill. Debates teach students to research their topic, make informed choices, and argue effectively using facts instead of emotion.

Learn more: High School Debate Topics To Challenge Every Student

Class or Small-Group Discussion

Class, small-group, and pair discussions are all excellent interactive instructional strategies examples. As students discuss a topic, they clarify their own thinking and learn from the experiences and opinions of others. Of course, in addition to learning about the topic itself, they’re also developing valuable active listening and collaboration skills.

Learn more: Strategies To Improve Classroom Discussions

Socratic Seminar and Fishbowl

Take your classroom discussions one step further with the fishbowl method. A small group of students sits in the middle of the class. They discuss and debate a topic, while their classmates listen silently and make notes. Eventually, the teacher opens the discussion to the whole class, who offer feedback and present their own assertions and challenges.

Learn more: How I Use Fishbowl Discussions To Engage Every Student

Brainstorming

Rather than having a teacher provide examples to explain a topic or solve a problem, students do the work themselves. Remember the one rule of brainstorming: Every idea is welcome. Ensure everyone gets a chance to participate, and form diverse groups to generate lots of unique ideas.

Role-Playing

Role-playing is sort of like a simulation but less intense. It’s perfect for practicing soft skills and focusing on social-emotional learning . Put a twist on this strategy by having students model bad interactions as well as good ones and then discussing the difference.

Think-Pair-Share

This structured discussion technique is simple: First, students think about a question posed by the teacher. Pair students up, and let them talk about their answer. Finally open it up to whole-class discussion. This helps kids participate in discussions in a low-key way and gives them a chance to “practice” before they talk in front of the whole class.

Learn more: Think-Pair-Share and Fun Alternatives

Independent Learning Instructional Strategies Examples

Also called independent study, this form of learning is almost entirely student-led. Teachers take a backseat role, providing materials, answering questions, and guiding or supervising. It’s an excellent way to allow students to dive deep into topics that really interest them, or to encourage learning at a pace that’s comfortable for each student.

Learning Centers

Foster independent learning strategies with centers just for math, writing, reading, and more. Provide a variety of activities, and let kids choose how they spend their time. They often learn better from activities they enjoy.

Learn more: The Big List of K-2 Literacy Centers

Computer-Based Instruction

Once a rarity, now a daily fact of life, computer-based instruction lets students work independently. They can go at their own pace, repeating sections without feeling like they’re holding up the class. Teach students good computer skills at a young age so you’ll feel comfortable knowing they’re focusing on the work and doing it safely.

Writing an essay encourages kids to clarify and organize their thinking. Written communication has become more important in recent years, so being able to write clearly and concisely is a skill every kid needs. This independent instructional strategy has stood the test of time for good reason.

Learn more: The Big List of Essay Topics for High School

Research Projects

Here’s another oldie-but-goodie! When kids work independently to research and present on a topic, their learning is all up to them. They set the pace, choose a focus, and learn how to plan and meet deadlines. This is often a chance for them to show off their creativity and personality too.

Personal journals give kids a chance to reflect and think critically on topics. Whether responding to teacher prompts or simply recording their daily thoughts and experiences, this independent learning method strengthens writing and intrapersonal skills.

Learn more: The Benefits of Journaling in the Classroom

Play-Based Learning

In play-based learning programs, children learn by exploring their own interests. Teachers identify and help students pursue their interests by asking questions, creating play opportunities, and encouraging students to expand their play.

Learn more: What Is Play-Based Learning?

More Instructional Strategies Examples

Don’t be afraid to try new strategies from time to time—you just might find a new favorite! Here are some of the most common instructional strategies examples.

Simulations

This strategy combines experiential, interactive, and indirect learning all in one. The teacher sets up a simulation of a real-world activity or experience. Students take on roles and participate in the exercise, using existing skills and knowledge or developing new ones along the way. At the end, the class reflects separately and together on what happened and what they learned.

Storytelling

Ever since Aesop’s fables, we’ve been using storytelling as a way to teach. Stories grab students’ attention right from the start and keep them engaged throughout the learning process. Real-life stories and fiction both work equally well, depending on the situation.

Learn more: Teaching as Storytelling

Scaffolding

Scaffolding is defined as breaking learning into bite-sized chunks so students can more easily tackle complex material. It builds on old ideas and connects them to new ones. An educator models or demonstrates how to solve a problem, then steps back and encourages the students to solve the problem independently. Scaffolding teaching gives students the support they need by breaking learning into achievable sizes while they progress toward understanding and independence.

Learn more: What Is Scaffolding in Education?

Spaced Repetition

Often paired with direct or independent instruction, spaced repetition is a method where students are asked to recall certain information or skills at increasingly longer intervals. For instance, the day after discussing the causes of the American Civil War in class, the teacher might return to the topic and ask students to list the causes. The following week, the teacher asks them once again, and then a few weeks after that. Spaced repetition helps make knowledge stick, and it is especially useful when it’s not something students practice each day but will need to know in the long term (such as for a final exam).

Graphic Organizers

Graphic organizers are a way of organizing information visually to help students understand and remember it. A good organizer simplifies complex information and lays it out in a way that makes it easier for a learner to digest. Graphic organizers may include text and images, and they help students make connections in a meaningful way.

Learn more: Graphic Organizers 101: Why and How To Use Them

Jigsaw combines group learning with peer teaching. Students are assigned to “home groups.” Within that group, each student is given a specialized topic to learn about. They join up with other students who were given the same topic, then research, discuss, and become experts. Finally, students return to their home group and teach the other members about the topic they specialized in.

Multidisciplinary Instruction

As the name implies, this instructional strategy approaches a topic using techniques and aspects from multiple disciplines, helping students explore it more thoroughly from a variety of viewpoints. For instance, to learn more about a solar eclipse, students might explore scientific explanations, research the history of eclipses, read literature related to the topic, and calculate angles, temperatures, and more.

Interdisciplinary Instruction

This instructional strategy takes multidisciplinary instruction a step further, using it to synthesize information and viewpoints from a variety of disciplines to tackle issues and problems. Imagine a group of students who want to come up with ways to improve multicultural relations at their school. They might approach the topic by researching statistical information about the school population, learning more about the various cultures and their history, and talking with students, teachers, and more. Then, they use the information they’ve uncovered to present possible solutions.

Differentiated Instruction

Differentiated instruction means tailoring your teaching so all students, regardless of their ability, can learn the classroom material. Teachers can customize the content, process, product, and learning environment to help all students succeed. There are lots of differentiated instructional strategies to help educators accommodate various learning styles, backgrounds, and more.

Learn more: What Is Differentiated Instruction?

Culturally Responsive Teaching

Culturally responsive teaching is based on the understanding that we learn best when we can connect with the material. For culturally responsive teachers, that means weaving their students’ various experiences, customs, communication styles, and perspectives throughout the learning process.

Learn more: What Is Culturally Responsive Teaching?

Response to Intervention

Response to Intervention, or RTI, is a way to identify and support students who need extra academic or behavioral help to succeed in school. It’s a tiered approach with various “levels” students move through depending on how much support they need.

Learn more: What Is Response to Intervention?

Inquiry-Based Learning

Inquiry-based learning means tailoring your curriculum to what your students are interested in rather than having a set agenda that you can’t veer from—it means letting children’s curiosity take the lead and then guiding that interest to explore, research, and reflect upon their own learning.

Learn more: What Is Inquiry-Based Learning?

Growth Mindset

Growth mindset is key for learners. They must be open to new ideas and processes and believe they can learn anything with enough effort. It sounds simplistic, but when students really embrace the concept, it can be a real game-changer. Teachers can encourage a growth mindset by using instructional strategies that allow students to learn from their mistakes, rather than punishing them for those mistakes.

Learn more: Growth Mindset vs. Fixed Mindset and 25 Growth Mindset Activities

Blended Learning

This strategy combines face-to-face classroom learning with online learning, in a mix of self-paced independent learning and direct instruction. It’s incredibly common in today’s schools, where most students spend at least part of their day completing self-paced lessons and activities via online technology. Students may also complete their online instructional time at home.

Asynchronous (Self-Paced) Learning

This fancy term really just describes strategies that allow each student to work at their own pace using a flexible schedule. This method became a necessity during the days of COVID lockdowns, as families did their best to let multiple children share one device. All students in an asynchronous class setting learn the same material using the same activities, but do so on their own timetable.

Learn more: Synchronous vs. Asynchronous Learning

Essential Questions

Essential questions are the big-picture questions that inspire inquiry and discussion. Teachers give students a list of several essential questions to consider as they begin a unit or topic. As they dive deeper into the information, teachers ask more specific essential questions to help kids make connections to the “essential” points of a text or subject.

Learn more: Questions That Set a Purpose for Reading

How do I choose the right instructional strategies for my classroom?

When it comes to choosing instructional strategies, there are several things to consider:

• Learning objectives: What will students be able to do as a result of this lesson or activity? If you are teaching specific skills or detailed information, a direct approach may be best. When you want students to develop their own methods of understanding, consider experiential learning. To encourage critical thinking skills, try indirect or interactive instruction.
• Assessments : How will you be measuring whether students have met the learning objectives? The strategies you use should prepare them to succeed. For instance, if you’re teaching spelling, direct instruction is often the best method, since drill-and-practice simulates the experience of taking a spelling test.
• Learning styles : What types of learners do you need to accommodate? Most classrooms (and most students) respond best to a mix of instructional strategies. Those who have difficulty speaking in class might not benefit as much from interactive learning, and students who have trouble staying on task might struggle with independent learning.
• Learning environment: Every classroom looks different, and the environment can vary day by day. Perhaps it’s testing week for other grades in your school, so you need to keep things quieter in your classroom. This probably isn’t the time for experiments or lots of loud discussions. Some activities simply aren’t practical indoors, and the weather might not allow you to take learning outside.

Come discuss instructional strategies and ask for advice in the We Are Teachers HELPLINE group on Facebook !

Plus, check out the things the best instructional coaches do, according to teachers ..

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• Al-Khwarizmi – The Father of Algebra

MUHAMMAD IBN MUSA AL-KHWARIZMI: The Father Of Algebra. Muslim Mathematician

One of the first Directors of the House of Wisdom in Bagdad in the early 9th Century was an outstanding Persian mathematician called Muhammad Al-Khwarizmi . He oversaw the translation of the major Greek and Indian mathematical and astronomy works (including those of Brahmagupta ) into Arabic, and produced original work which had a lasting influence on the advance of Muslim and (after his works spread to Europe through Latin translations in the 12th Century) later European mathematics.

The word “ algorithm ” is derived from the Latinization of his name, and the word “ algebra ” is derived from the Latinization of “ al-jabr “, part of the title of his most famous book, in which he introduced the fundamental algebraic methods and techniques for solving equations.

Perhaps his most important contribution to mathematics was his strong advocacy of the Hindu numerical system, which Al-Khwarizmi recognized as having the power and efficiency needed to revolutionize Islamic and Western mathematics. The Hindu numerals 1 – 9 and 0 – which have since become known as Hindu-Arabic numerals – were soon adopted by the entire Islamic world. Later, with translations of Al-Khwarizmi’s work into Latin by Adelard of Bath and others in the 12th Century, and with the influence of Fibonacci ’s “Liber Abaci” they would be adopted throughout Europe as well.

Who created algebra – The Father Of Algebra

Al-Khwarizmi’s other important contribution was algebra , a word derived from the title of a mathematical text he published in about 830 called “Al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala” (“The Compendious Book on Calculation by Completion and Balancing”). Al-Khwarizmi wanted to go from the specific problems considered by the Indians and Chinese to a more general way of analyzing problems, and in doing so he created an abstract mathematical language which is used across the world today.

His book is considered the foundational text of modern algebra , although he did not employ the kind of algebraic notation used today (he used words to explain the problem, and diagrams to solve it). But the book provided an exhaustive account of solving polynomial equations up to the second degree, and introduced for the first time the fundamental algebraic methods of “reduction” (rewriting an expression in a simpler form), “completion” (moving a negative quantity from one side of the equation to the other side and changing its sign) and “balancing” (subtraction of the same quantity from both sides of an equation, and the cancellation of like terms on opposite sides).

In particular, Al-Khwarizmi developed a formula for systematically solving quadratic equations (equations involving unknown numbers to the power of 2, or x 2 ) by using the methods of completion and balancing to reduce any equation to one of six standard forms, which were then solvable. He described the standard forms in terms of “squares” (what would today be “ x 2 “), “roots” (what would today be “ x “) and “numbers” (regular constants, like 42), and identified the six types as: squares equal roots ( ax 2 = bx ), squares equal number ( ax 2 = c ), roots equal number ( bx = c ), squares and roots equal number ( ax 2 + bx = c ), squares and number equal roots ( ax 2 + c = bx ), and roots and number equal squares ( bx + c = ax 2 ).

Al-Khwarizmi is usually credited with the development of lattice (or sieve) multiplication method of multiplying large numbers, a method algorithmically equivalent to long multiplication. His lattice method was later introduced into Europe by Fibonacci .

In addition to his work in mathematics, Al-Khwarizmi made important contributions to astronomy, also largely based on methods from India , and he developed the first quadrant (an instrument used to determine time by observations of the Sun or stars), the second most widely used astronomical instrument during the Middle Ages after the astrolabe. He also produced a revised and completed version of Ptolemy’s “Geography”, consisting of a list of 2,402 coordinates of cities throughout the known world.

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How to use Solver in Excel with examples

The tutorial explains how to add and where to find Solver in different Excel versions, from 2016 to 2003. Step-by-step examples show how to use Excel Solver to find optimal solutions for linear programming and other kinds of problems.

Everyone knows that Microsoft Excel contains a lot of useful functions and powerful tools that can save you hours of calculations. But did you know that it also has a tool that can help you find optimal solutions for decision problems?

In this tutorial, we are going to cover all essential aspects of the Excel Solver add-in and provide a step-by-step guide on how to use it most effectively.

What is Excel Solver?

Excel Solver belongs to a special set of commands often referred to as What-if Analysis Tools. It is primarily purposed for simulation and optimization of various business and engineering models.

The Excel Solver add-in is especially useful for solving linear programming problems, aka linear optimization problems, and therefore is sometimes called a linear programming solver . Apart from that, it can handle smooth nonlinear and non-smooth problems. Please see Excel Solver algorithms for more details.

How to add Solver to Excel

The Solver add-in is included with all versions of Microsoft Excel beginning with 2003, but it is not enabled by default.

To add Solver to your Excel, perform the following steps:

• In Excel 2010 - Excel 365, click File > Options . In Excel 2007, click the Microsoft Office button, and then click Excel Options .

To get Solver on Excel 2003 , go to the Tools menu, and click Add-Ins . In the Add-Ins available list, check the Solver Add-in box, and click OK .

Where is Solver in Excel?

Where is Solver in Excel 2003?

Now that you know where to find Solver in Excel, open a new worksheet and let's get started!

How to use Solver in Excel

Before running the Excel Solver add-in, formulate the model you want to solve in a worksheet. In this example, let's find a solution for the following simple optimization problem.

Problem . Supposing, you are the owner of a beauty salon and you are planning on providing a new service to your clients. For this, you need to buy a new equipment that costs $40,000, which should be paid by instalments within 12 months.

Goal : Calculate the minimal cost per service that will let you pay for the new equipment within the specified timeframe.

And now, let's see how Excel Solver can find a solution for this problem.

1. Run Excel Solver

2. define the problem.

The Solver Parameters window will open where you have to set up the 3 primary components:

• Objective cell

Variable cells

Constraints.

Exactly what does Excel Solver do with the above parameters? It finds the optimal value (maximum, minimum or specified) for the formula in the Objective cell by changing the values in the Variable cells, and subject to limitations in the Constraints cells.

The Objective cell ( Target cell in earlier Excel versions) is the cell containing a formula that represents the objective, or goal, of the problem. The objective can be to maximize, minimize, or achieve some target value.

Variable cells ( Changing cells or Adjustable cells in earlier versions) are cells that contain variable data that can be changed to achieve the objective. Excel Solver allows specifying up to 200 variable cells.

In this example, we have a couple of cells whose values can be changed:

• Projected clients per month (B4) that should be less than or equal to 50; and
• Cost per service (B5) that we want Excel Solver to calculate.

The Excel Solver Constrains are restrictions or limits of the possible solutions to the problem. To put it differently, constraints are the conditions that must be met.

To add a constraint(s), do the following:

• Click the Add button right to the " Subject to the Constraints " box.

• In the Constraint window, enter a constraint.
• Click the Add button to add the constraint to the list.

• Continue entering other constraints.
• After you have entered the final constraint, click OK to return to the main Solver Parameters window.

Excel Solver allows specifying the following relationships between the referenced cell and the constraint.

• Less than or equal to , equal to , and greater than or equal to . You set these relationships by selecting a cell in the Cell Reference box, choosing one of the following signs: <= , =, or >= , and then typing a number, cell reference / cell name, or formula in the Constraint box (please see the above screenshot).
• Integer . If the referenced cell must be an integer, select int , and the word integer will appear in the Constraint box.
• Different values . If each cell in the referenced range must contain a different value, select dif , and the word AllDifferent will appear in the Constraint box.
• Binary . If you want to limit a referenced cell either to 0 or 1, select bin , and the word binary will appear in the Constraint box.

To edit or delete an existing constraint do the following:

• In the Solver Parameters dialog box, click the constraint.
• To modify the selected constraint, click Change and make the changes you want.
• To delete the constraint, click the Delete button.

In this example, the constraints are:

• B3=40000 - cost of the new equipment is $40,000.
• B4<=50 - the number of projected patients per month in under 50.

3. Solve the problem

After you've configured all the parameters, click the Solve button at the bottom of the Solver Parameters window (see the screenshot above) and let the Excel Solver add-in find the optimal solution for your problem.

Depending on the model complexity, computer memory and processor speed, it may take a few seconds, a few minutes, or even a few hours.

The Solver Result window will close and the solution will appear on the worksheet right away.

• If the Excel Solver has been processing a certain problem for too long, you can interrupt the process by pressing the Esc key. Excel will recalculate the worksheet with the last values found for the Variable cells.
• To get more details about the solved problem, click a report type in the Reports box, and then click OK . The report will be created on a new worksheet:

Excel Solver examples

Below you will find two more examples of using the Excel Solver addin. First, we will find a solution for a well-known puzzle, and then solve a real-life linear programming problem.

Excel Solver example 1 (magic square)

I believe everyone is familiar with "magic square" puzzles where you have to put a set of numbers in a square so that all rows, columns and diagonals add up to a certain number.

For instance, do you know a solution for the 3x3 square containing numbers from 1 to 9 where each row, column and diagonal adds up to 15?

It's probably no big deal to solve this puzzle by trial and error, but I bet the Solver will find the solution faster. Our part of the job is to properly define the problem.

With all the formulas in place, run Solver and set up the following parameters:

• Set Objective . In this example, we don't need to set any objective, so leave this box empty.
• Variable Cells . We want to populate numbers in cells B2 to D4, so select the range B2:D4.
• $B$2:$D$4 = AllDifferent - all of the Variable cells should contain different values.
• $B$2:$D$4 = integer - all of the Variable cells should be integers.
• $B$5:$D$5 = 15 - the sum of values in each column should equal 15.
• $E$2:$E$4 = 15 - the sum of values in each row should equal 15.
• $B$7:$B$8 = 15 - the sum of both diagonals should equal 15.

Excel Solver example 2 (linear programming problem)

This is an example of a simple transportation optimization problem with a linear objective. More complex optimization models of this kind are used by many companies to save thousands of dollars each year.

Problem : You want to minimize the cost of shipping goods from 2 different warehouses to 4 different customers. Each warehouse has a limited supply and each customer has a certain demand.

Goal : Minimize the total shipping cost, not exceeding the quantity available at each warehouse, and meeting the demand of each customer.

Source data

Formulating the model

To define our linear programming problem for the Excel Solver, let's answer the 3 main questions:

• What decisions are to be made? We want to calculate the optimal quantity of goods to deliver to each customer from each warehouse. These are Variable cells (B7:E8).
• What are the constraints? The supplies available at each warehouse (I7:I8) cannot be exceeded, and the quantity ordered by each customer (B10:E10) should be delivered. These are Constrained cells .
• What is the goal? The minimal total cost of shipping. And this is our Objective cell (C12).

To make our transportation optimization model easier to understand, create the following named ranges:

The last thing left for you to do is configure the Excel Solver parameters:

• Objective: Shipping_cost set to Min
• Variable cells: Products_shipped
• Constraints: Total_received = Ordered and Total_shipped <= Available

How to save and load Excel Solver scenarios

When solving a certain model, you may want to save your Variable cell values as a scenario that you can view or re-use later.

For example, when calculating the minimal service cost in the very first example discussed in this tutorial, you may want to try different numbers of projected clients per month and see how that affects the service cost. At that, you may want to save the most probable scenario you've already calculated and restore it at any moment.

Saving an Excel Solver scenario boils down to selecting a range of cells to save the data in. Loading a Solver model is just a matter of providing Excel with the range of cells where your model is saved. The detailed steps follow below.

Saving the model

To save the Excel Solver scenario, perform the following steps:

• Open the worksheet with the calculated model and run the Excel Solver.

• Excel will save your current model, which may look something similar to this:

Loading the saved model

When you decide to restore the saved scenario, do the following:

• In the Solver Parameters window, click the Load/Save button.

• This will open the main Excel Solver window with the parameters of the previously saved model. All you need to do is to click the Solve button to re-calculate it.

Excel Solver algorithms

When defining a problem for the Excel Solver, you can choose one of the following methods in the Select a Solving Method dropdown box:

• GRG Nonlinear. Generalized Reduced Gradient Nonlinear algorithm is used for problems that are smooth nonlinear, i.e. in which at least one of the constraints is a smooth nonlinear function of the decision variables. More details can be found here .
• LP Simplex . The Simplex LP Solving method is based the Simplex algorithm created by an American mathematical scientist George Dantzig. It is used for solving so called Linear Programming problems - mathematical models whose requirements are characterized by linear relationships, i.e. consist of a single objective represented by a linear equation that must be maximized or minimized. For more information, please check out this page .
• Evolutionary . It is used for non-smooth problems, which are the most difficult type of optimization problems to solve because some of the functions are non-smooth or even discontinuous, and therefore it's difficult to determine the direction in which a function is increasing or decreasing. For more information, please see this page .

This is how you can use Solver in Excel to find the best solutions for your decision problems. At the end of this post, you can download the sample workbook with all the examples discussed in this tutorial and reverse-engineer them for better understanding. I thank you for reading and hope to see you on our blog next week.

Practice workbook for download

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