Problem-Solving Method in Teaching

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

Table of Contents

Definition of problem-solving method.

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

Meaning of Problem-Solving Method

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

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

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

Benefits of Problem-Solving Method

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

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

Steps in Problem-Solving Method

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

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

Verification of the concluded solution or Hypothesis

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

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

  • Jonassen, D. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments. Routledge.
  • Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266.
  • Mergendoller, J. R., Maxwell, N. L., & Bellisimo, Y. (2006). The effectiveness of problem-based instruction: A comparative study of instructional methods and student characteristics. Interdisciplinary Journal of Problem-based Learning, 1(2), 49-69.
  • Richey, R. C., Klein, J. D., & Tracey, M. W. (2011). The instructional design knowledge base: Theory, research, and practice. Routledge.
  • Savery, J. R., & Duffy, T. M. (2001). Problem-based learning: An instructional model and its constructivist framework. CRLT Technical Report No. 16-01, University of Michigan. Wojcikowski, J. (2013). Solving real-world problems through problem-based learning. College Teaching, 61(4), 153-156

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Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

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

Encourage Independence

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

Be sensitive

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

Encourage Thoroughness and Patience

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

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

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

example of problem solving method of teaching

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Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

  • Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
  • Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
  • Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
  • Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
  • Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
  • Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

  • The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
  • Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
  • Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
  • Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
  • Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
  • Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

  • “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
  • Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
  • Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

  • Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
  • Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

  • Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
  • Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

  • Does the answer make sense?
  • Does it fit with the criteria established in step 1?
  • Did I answer the question(s)?
  • What did I learn by doing this?
  • Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact. 

  • Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
  • Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
  • Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
  • Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

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Problem-Based Learning

Problem-based learning  (PBL) is a student-centered approach in which students learn about a subject by working in groups to solve an open-ended problem. This problem is what drives the motivation and the learning. 

Why Use Problem-Based Learning?

Nilson (2010) lists the following learning outcomes that are associated with PBL. A well-designed PBL project provides students with the opportunity to develop skills related to:

  • Working in teams.
  • Managing projects and holding leadership roles.
  • Oral and written communication.
  • Self-awareness and evaluation of group processes.
  • Working independently.
  • Critical thinking and analysis.
  • Explaining concepts.
  • Self-directed learning.
  • Applying course content to real-world examples.
  • Researching and information literacy.
  • Problem solving across disciplines.

Considerations for Using Problem-Based Learning

Rather than teaching relevant material and subsequently having students apply the knowledge to solve problems, the problem is presented first. PBL assignments can be short, or they can be more involved and take a whole semester. PBL is often group-oriented, so it is beneficial to set aside classroom time to prepare students to   work in groups  and to allow them to engage in their PBL project.

Students generally must:

  • Examine and define the problem.
  • Explore what they already know about underlying issues related to it.
  • Determine what they need to learn and where they can acquire the information and tools necessary to solve the problem.
  • Evaluate possible ways to solve the problem.
  • Solve the problem.
  • Report on their findings.

Getting Started with Problem-Based Learning

  • Articulate the learning outcomes of the project. What do you want students to know or be able to do as a result of participating in the assignment?
  • Create the problem. Ideally, this will be a real-world situation that resembles something students may encounter in their future careers or lives. Cases are often the basis of PBL activities. Previously developed PBL activities can be found online through the University of Delaware’s PBL Clearinghouse of Activities .
  • Establish ground rules at the beginning to prepare students to work effectively in groups.
  • Introduce students to group processes and do some warm up exercises to allow them to practice assessing both their own work and that of their peers.
  • Consider having students take on different roles or divide up the work up amongst themselves. Alternatively, the project might require students to assume various perspectives, such as those of government officials, local business owners, etc.
  • Establish how you will evaluate and assess the assignment. Consider making the self and peer assessments a part of the assignment grade.

Nilson, L. B. (2010).  Teaching at its best: A research-based resource for college instructors  (2nd ed.).  San Francisco, CA: Jossey-Bass. 

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Teaching problem solving

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

Introducing the problem

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

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

Working on solutions

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

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

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

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

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

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Problem-Based Learning (PBL) is a teaching method in which complex real-world problems are used as the vehicle to promote student learning of concepts and principles as opposed to direct presentation of facts and concepts. In addition to course content, PBL can promote the development of critical thinking skills, problem-solving abilities, and communication skills. It can also provide opportunities for working in groups, finding and evaluating research materials, and life-long learning (Duch et al, 2001).

PBL can be incorporated into any learning situation. In the strictest definition of PBL, the approach is used over the entire semester as the primary method of teaching. However, broader definitions and uses range from including PBL in lab and design classes, to using it simply to start a single discussion. PBL can also be used to create assessment items. The main thread connecting these various uses is the real-world problem.

Any subject area can be adapted to PBL with a little creativity. While the core problems will vary among disciplines, there are some characteristics of good PBL problems that transcend fields (Duch, Groh, and Allen, 2001):

  • The problem must motivate students to seek out a deeper understanding of concepts.
  • The problem should require students to make reasoned decisions and to defend them.
  • The problem should incorporate the content objectives in such a way as to connect it to previous courses/knowledge.
  • If used for a group project, the problem needs a level of complexity to ensure that the students must work together to solve it.
  • If used for a multistage project, the initial steps of the problem should be open-ended and engaging to draw students into the problem.

The problems can come from a variety of sources: newspapers, magazines, journals, books, textbooks, and television/ movies. Some are in such form that they can be used with little editing; however, others need to be rewritten to be of use. The following guidelines from The Power of Problem-Based Learning (Duch et al, 2001) are written for creating PBL problems for a class centered around the method; however, the general ideas can be applied in simpler uses of PBL:

  • Choose a central idea, concept, or principle that is always taught in a given course, and then think of a typical end-of-chapter problem, assignment, or homework that is usually assigned to students to help them learn that concept. List the learning objectives that students should meet when they work through the problem.
  • Think of a real-world context for the concept under consideration. Develop a storytelling aspect to an end-of-chapter problem, or research an actual case that can be adapted, adding some motivation for students to solve the problem. More complex problems will challenge students to go beyond simple plug-and-chug to solve it. Look at magazines, newspapers, and articles for ideas on the story line. Some PBL practitioners talk to professionals in the field, searching for ideas of realistic applications of the concept being taught.
  • What will the first page (or stage) look like? What open-ended questions can be asked? What learning issues will be identified?
  • How will the problem be structured?
  • How long will the problem be? How many class periods will it take to complete?
  • Will students be given information in subsequent pages (or stages) as they work through the problem?
  • What resources will the students need?
  • What end product will the students produce at the completion of the problem?
  • Write a teacher's guide detailing the instructional plans on using the problem in the course. If the course is a medium- to large-size class, a combination of mini-lectures, whole-class discussions, and small group work with regular reporting may be necessary. The teacher's guide can indicate plans or options for cycling through the pages of the problem interspersing the various modes of learning.
  • The final step is to identify key resources for students. Students need to learn to identify and utilize learning resources on their own, but it can be helpful if the instructor indicates a few good sources to get them started. Many students will want to limit their research to the Internet, so it will be important to guide them toward the library as well.

The method for distributing a PBL problem falls under three closely related teaching techniques: case studies, role-plays, and simulations. Case studies are presented to students in written form. Role-plays have students improvise scenes based on character descriptions given. Today, simulations often involve computer-based programs. Regardless of which technique is used, the heart of the method remains the same: the real-world problem.

Where can I learn more?

  • PBL through the Institute for Transforming Undergraduate Education at the University of Delaware
  • Duch, B. J., Groh, S. E, & Allen, D. E. (Eds.). (2001). The power of problem-based learning . Sterling, VA: Stylus.
  • Grasha, A. F. (1996). Teaching with style: A practical guide to enhancing learning by understanding teaching and learning styles. Pittsburgh: Alliance Publishers.

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Teaching problem solving: Let students get ‘stuck’ and ‘unstuck’

Subscribe to the center for universal education bulletin, kate mills and km kate mills literacy interventionist - red bank primary school helyn kim helyn kim former brookings expert @helyn_kim.

October 31, 2017

This is the second in a six-part  blog series  on  teaching 21st century skills , including  problem solving ,  metacognition , critical thinking , and collaboration , in classrooms.

In the real world, students encounter problems that are complex, not well defined, and lack a clear solution and approach. They need to be able to identify and apply different strategies to solve these problems. However, problem solving skills do not necessarily develop naturally; they need to be explicitly taught in a way that can be transferred across multiple settings and contexts.

Here’s what Kate Mills, who taught 4 th grade for 10 years at Knollwood School in New Jersey and is now a Literacy Interventionist at Red Bank Primary School, has to say about creating a classroom culture of problem solvers:

Helping my students grow to be people who will be successful outside of the classroom is equally as important as teaching the curriculum. From the first day of school, I intentionally choose language and activities that help to create a classroom culture of problem solvers. I want to produce students who are able to think about achieving a particular goal and manage their mental processes . This is known as metacognition , and research shows that metacognitive skills help students become better problem solvers.

I begin by “normalizing trouble” in the classroom. Peter H. Johnston teaches the importance of normalizing struggle , of naming it, acknowledging it, and calling it what it is: a sign that we’re growing. The goal is for the students to accept challenge and failure as a chance to grow and do better.

I look for every chance to share problems and highlight how the students— not the teachers— worked through those problems. There is, of course, coaching along the way. For example, a science class that is arguing over whose turn it is to build a vehicle will most likely need a teacher to help them find a way to the balance the work in an equitable way. Afterwards, I make it a point to turn it back to the class and say, “Do you see how you …” By naming what it is they did to solve the problem , students can be more independent and productive as they apply and adapt their thinking when engaging in future complex tasks.

After a few weeks, most of the class understands that the teachers aren’t there to solve problems for the students, but to support them in solving the problems themselves. With that important part of our classroom culture established, we can move to focusing on the strategies that students might need.

Here’s one way I do this in the classroom:

I show the broken escalator video to the class. Since my students are fourth graders, they think it’s hilarious and immediately start exclaiming, “Just get off! Walk!”

When the video is over, I say, “Many of us, probably all of us, are like the man in the video yelling for help when we get stuck. When we get stuck, we stop and immediately say ‘Help!’ instead of embracing the challenge and trying new ways to work through it.” I often introduce this lesson during math class, but it can apply to any area of our lives, and I can refer to the experience and conversation we had during any part of our day.

Research shows that just because students know the strategies does not mean they will engage in the appropriate strategies. Therefore, I try to provide opportunities where students can explicitly practice learning how, when, and why to use which strategies effectively  so that they can become self-directed learners.

For example, I give students a math problem that will make many of them feel “stuck”. I will say, “Your job is to get yourselves stuck—or to allow yourselves to get stuck on this problem—and then work through it, being mindful of how you’re getting yourselves unstuck.” As students work, I check-in to help them name their process: “How did you get yourself unstuck?” or “What was your first step? What are you doing now? What might you try next?” As students talk about their process, I’ll add to a list of strategies that students are using and, if they are struggling, help students name a specific process. For instance, if a student says he wrote the information from the math problem down and points to a chart, I will say: “Oh that’s interesting. You pulled the important information from the problem out and organized it into a chart.” In this way, I am giving him the language to match what he did, so that he now has a strategy he could use in other times of struggle.

The charts grow with us over time and are something that we refer to when students are stuck or struggling. They become a resource for students and a way for them to talk about their process when they are reflecting on and monitoring what did or did not work.

For me, as a teacher, it is important that I create a classroom environment in which students are problem solvers. This helps tie struggles to strategies so that the students will not only see value in working harder but in working smarter by trying new and different strategies and revising their process. In doing so, they will more successful the next time around.

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Problem-Solving

TeacherVision Staff

Jabberwocky

Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically.

Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.

Problem-solving involves three basic functions:

Seeking information

Generating new knowledge

Making decisions

Problem-solving is, and should be, a very real part of the curriculum. It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum. It provides students with opportunities to use their newly acquired knowledge in meaningful, real-life activities and assists them in working at higher levels of thinking (see Levels of Questions ).

Here is a five-stage model that most students can easily memorize and put into action and which has direct applications to many areas of the curriculum as well as everyday life:

Expert Opinion

Here are some techniques that will help students understand the nature of a problem and the conditions that surround it:

  • List all related relevant facts.
  • Make a list of all the given information.
  • Restate the problem in their own words.
  • List the conditions that surround a problem.
  • Describe related known problems.

It's Elementary

For younger students, illustrations are helpful in organizing data, manipulating information, and outlining the limits of a problem and its possible solution(s). Students can use drawings to help them look at a problem from many different perspectives.

Understand the problem. It's important that students understand the nature of a problem and its related goals. Encourage students to frame a problem in their own words.

Describe any barriers. Students need to be aware of any barriers or constraints that may be preventing them from achieving their goal. In short, what is creating the problem? Encouraging students to verbalize these impediments is always an important step.

Identify various solutions. After the nature and parameters of a problem are understood, students will need to select one or more appropriate strategies to help resolve the problem. Students need to understand that they have many strategies available to them and that no single strategy will work for all problems. Here are some problem-solving possibilities:

Create visual images. Many problem-solvers find it useful to create “mind pictures” of a problem and its potential solutions prior to working on the problem. Mental imaging allows the problem-solvers to map out many dimensions of a problem and “see” it clearly.

Guesstimate. Give students opportunities to engage in some trial-and-error approaches to problem-solving. It should be understood, however, that this is not a singular approach to problem-solving but rather an attempt to gather some preliminary data.

Create a table. A table is an orderly arrangement of data. When students have opportunities to design and create tables of information, they begin to understand that they can group and organize most data relative to a problem.

Use manipulatives. By moving objects around on a table or desk, students can develop patterns and organize elements of a problem into recognizable and visually satisfying components.

Work backward. It's frequently helpful for students to take the data presented at the end of a problem and use a series of computations to arrive at the data presented at the beginning of the problem.

Look for a pattern. Looking for patterns is an important problem-solving strategy because many problems are similar and fall into predictable patterns. A pattern, by definition, is a regular, systematic repetition and may be numerical, visual, or behavioral.

Create a systematic list. Recording information in list form is a process used quite frequently to map out a plan of attack for defining and solving problems. Encourage students to record their ideas in lists to determine regularities, patterns, or similarities between problem elements.

Try out a solution. When working through a strategy or combination of strategies, it will be important for students to …

Keep accurate and up-to-date records of their thoughts, proceedings, and procedures. Recording the data collected, the predictions made, and the strategies used is an important part of the problem solving process.

Try to work through a selected strategy or combination of strategies until it becomes evident that it's not working, it needs to be modified, or it is yielding inappropriate data. As students become more proficient problem-solvers, they should feel comfortable rejecting potential strategies at any time during their quest for solutions.

Monitor with great care the steps undertaken as part of a solution. Although it might be a natural tendency for students to “rush” through a strategy to arrive at a quick answer, encourage them to carefully assess and monitor their progress.

Feel comfortable putting a problem aside for a period of time and tackling it at a later time. For example, scientists rarely come up with a solution the first time they approach a problem. Students should also feel comfortable letting a problem rest for a while and returning to it later.

Evaluate the results. It's vitally important that students have multiple opportunities to assess their own problem-solving skills and the solutions they generate from using those skills. Frequently, students are overly dependent upon teachers to evaluate their performance in the classroom. The process of self-assessment is not easy, however. It involves risk-taking, self-assurance, and a certain level of independence. But it can be effectively promoted by asking students questions such as “How do you feel about your progress so far?” “Are you satisfied with the results you obtained?” and “Why do you believe this is an appropriate response to the problem?”

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

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Problem-Solving Method of Teaching: All You Need to Know

What is Problem-Solving Method of Teaching?

Ever wondered about the problem-solving method of teaching? We’ve got you covered, from its core principles to practical tips, benefits, and real-world examples.

The problem-solving method of teaching is a student-centered approach to learning that focuses on developing students’ problem-solving skills. In this method, students are presented with real-world problems to solve, and they are encouraged to use their own knowledge and skills to come up with solutions. The teacher acts as a facilitator, providing guidance and support as needed, but ultimately the students are responsible for finding their own solutions.

Problem-Solving Method of Teaching Example

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5 Most Important Benefits of Problem-Solving Method of Teaching

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

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

1. Enhances critical thinking: By presenting students with real-world problems to solve, the problem-solving method of teaching forces them to think critically about the situation and to come up with their own solutions. This process helps students to develop their critical thinking skills, which are essential for success in school and in life.

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

3. Encourages real-world application: The problem-solving method of teaching helps students learn how to apply their knowledge to real-world situations. By solving real-world problems, students are able to see how their knowledge is relevant to their lives and to the world around them. This helps students to become more motivated and engaged learners.

4. Builds student confidence: When students are able to successfully solve problems, they gain confidence in their abilities. This confidence is essential for success in all areas of life, both academic and personal.

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

Know 6 Steps in the Problem-Solving Method of Teaching

Know the 6 Steps

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

  • Identifying the problem. The first step is to identify the problem that students will be working on. This can be done by presenting students with a real-world problem, or by asking them to come up with their own problems.
  • Understanding the problem. Once students have identified the problem, they need to understand it fully. This may involve breaking the problem down into smaller parts or gathering more information about the problem.
  • Generating solutions. Once students understand the problem, they need to generate possible solutions. This can be done by brainstorming, or by using problem-solving techniques such as root cause analysis or the decision matrix.
  • Evaluating solutions. Students need to evaluate the pros and cons of each solution before choosing one to implement.
  • Implementing the solution. Once students have chosen a solution, they need to implement it. This may involve taking action or developing a plan.
  • Evaluating the results. Once students have implemented the solution, they need to evaluate the results to see if it was successful. If the solution is not successful, students may need to go back to step 3 and generate new solutions.

Find Out Examples of the Problem-Solving Method of Teaching

Here are a few examples of how the problem-solving method of teaching can be used in different subjects:

  • Math: Students could be presented with a real-world problem such as budgeting for a family or designing a new product. Students would then need to use their math skills to solve the problem.
  • Science: Students could be presented with a science experiment, or asked to research a scientific topic and come up with a solution to a problem. Students would then need to use their science knowledge and skills to solve the problem.
  • Social studies: Students could be presented with a historical event or current social issue, and asked to come up with a solution. Students would then need to use their social studies knowledge and skills to solve the problem.

5 How Tos For Using The Problem-Solving Method Of Teaching

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

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

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How to Choose: Let’s Draw a Comparison

The following table compares the different problem-solving methods:

Which Method is the Most Suitable?

The most suitable method of teaching will depend on a number of factors, such as the subject matter, the student’s age and ability level, and the teacher’s own preferences. However, the problem-solving method of teaching is a valuable approach that can be used in any subject area and with students of all ages.

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

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

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Some Unique Examples to Refer to Before We Conclude

Here are a few unique examples of how the problem-solving method of teaching can be used in different subjects:

  • English: Students could be presented with a challenging text, such as a poem or a short story, and asked to analyze the text and come up with their own interpretation.
  • Art: Students could be asked to design a new product or to create a piece of art that addresses a social issue.
  • Music: Students could be asked to write a song about a current event or to create a new piece of music that reflects their cultural heritage.

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

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example of problem solving method of teaching

Problem Solving Method Of Teaching

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

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

What is your preferred problem-solving technique?

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

Share it with me by commenting.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Introduce the problem

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

Explain why the problem solving method of teaching is effective.

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

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

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

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

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

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

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

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

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

What are your thoughts on this method? 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

What are Problem Solving Skills?

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

How To Solve The Problems? Practical Problem Solving Skills

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A Problem Solving Method: Brainstorming

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

How To Develop Problem Solving Skills?

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Key Tips On Problem Solving Method Of Teaching

example of problem solving method of teaching

Problem-solving skills are necessary for all strata of life, and none can be better than classroom problem-solving activities. It can be an excellent way to introduce students to problem-solving skills, get them prepped and ready to solve real problems in real-life settings.  

The ability to critically analyze a problem, map out all its elements and then prepare a solution that works is one of the most valuable skills; one must acquire in life. Educating your students about problem-solving techniques from an early age can be facilitated with in-class problem-solving activities. Such efforts encourage cognitive and social development and equip students with the tools they will need to tackle and resolve their lives.  

So, what is  a  problem-solving method of teaching ?

Problem Solving  is the act of defining a problem; determining the cause of the problem; identifying, prioritizing and selecting alternatives for a solution; and implementing a solution. In a problem-solving method, children learn by working on problems. This skill enables the students to learn new knowledge by facing the problems to be solved. It is expected of them to observe, understand, analyze, interpret, find solutions, and perform applications that lead to a holistic understanding of the concept. This method develops scientific process skills. This method helps in developing a brainstorming approach to learning concepts. 

In simple words, problem-solving is an ongoing activity in which we take what we know to discover what we do not know. It involves overcoming obstacles by generating hypotheses, testing those predictions, and arriving at satisfactory solutions. 

The problem-solving method involves three basic functions

  • Seeking information
  • Generating new knowledge 
  • Making decisions 

This post will include key strategies to help you inculcate problem-solving skills in your students. 

First and foremostly, follow the 5-step model of problem-solving presented by Wood

Woods' problem-solving model

Identify the problem .

Allow your students to identify the system under study by interpreting the information provided in the problem statement. Then, prepare a list of what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it. Once you have a list of known problems, identifying the unknown(s) becomes simpler. The unknown one is usually the answer to the problem; however, there may be other unknowns. Make sure that your students have a clear understanding of what they are expected to find. 

While teaching problem solving, it is very important to have students know how to select, interpret, and use units and symbols. Emphasize the use of units and symbols whenever appropriate. Develop a habit of using appropriate units and symbols yourself at all times. Teach your students to look for the words only and neglect or assume to help identify the constraints. 

Furthermore, help students consider from the beginning what a logical type of answer would be. What characteristics will it possess?  

Think about it

Use the next stage to ponder the identified problem. Ideally, students will develop an imaginary image of the problem at hand during this stage. They need to determine the required background knowledge from illustrations, examples and problems covered in the course and collect pertinent information such as conversion factors, constants, and tables needed to solve the problem. 

Plan a solution

Often, the type of problem will determine the type of solution. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards. 

Help your students choose the best strategy by reminding them again what they must find or calculate. 

Carry out the plan

Now that the major part of problem-solving has been done start executing the solution. There are possibilities that a plan may not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying. 

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions: 

  •  Does the answer make sense? 
  •  Does it fit with the criteria established in step 1? 
  •  Did I answer the question(s)? 
  •  What did I learn by doing this? 
  •  Could I have done the problem another way?  

Other tips include

Ask open-ended questions.

When a student seeks help, you might be willing to give them the answer they are looking for so you can both move on. But what is recommend is that instead of giving answers promptly, try using open-ended questions and prompts. For example: ask What do you think will happen if..? Why do you think so? What would you do if you get into such situations? Etc. 

Emphasize Process Over Product

For elementary students, reflecting on the process of solving a problem helps them develop a growth mindset. Getting an 'incorrect' response does not have to be a bad thing! What matters most is what they have done to achieve it and how they might change their approach next time. As a teacher, you can help students learn the process of reflection. 

Model The Strategies

As children learn creative problem-solving techniques, there will probably be times when they will be frustrated or uncertain. Here are just a few simple ways to model what creative problem-solving looks like and sounds like. 

  • Ask questions in case you don't understand anything.
  • Admit to not knowing the right answer.
  • Discuss the many possible outcomes of different situations. 
  • Verbalize what you feel when you come across a problem.
  • Practising these strategies with your students will help create an environment where struggle, failure and growth are celebrated!

Encourage Grappling

Grappling is not confined to perseverance! This includes critical thinking, asking questions, observing evidence, asking more questions, formulating hypotheses and building a deep understanding of a problem. 

There are numerous ways to provide opportunities for students to struggle. All that includes the engineering design process is right! Examples include: 

  • Engineering or creative projects
  • Design-thinking challenges
  • Informatics projects
  • Science experiments

Make problem resolution relevant to the lives of your students

Limiting problem solving to class is a bad idea. This will affect students later in life because problem-solving is an essential part of human life, and we have had a chance to look at it from a mathematical perspective. Such problems are relevant to us, and they are not things that we are supposed to remember or learn but to put into practice in real life. These are things from which we can take very significant life lessons and apply them later in life. 

What's your strategy? How do you teach Problem-Solving to your students? Do let us know in the comments. 

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Problem-Based Learning (PBL)

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

See also: Just-in-Time Teaching

Problem-Based Learning (PBL)

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

Pbl

By working with PBL, students will:

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

How to Begin PBL

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

Designing Classroom Instruction

See also: Inclusive Teaching Strategies

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

How to Orchestrate a PBL Activity

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

Teacher’s Role in PBL

See also: Flipped teaching

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

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

The Role of the Students

See also: ADDIE model

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

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

See also: Kirkpatrick Model: Four Levels of Learning Evaluation

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

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5 Teaching Mathematics Through Problem Solving

Janet Stramel

Problem Solving

In his book “How to Solve It,” George Pólya (1945) said, “One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles. The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student. The teacher should help, but not too much and not too little, so that the student shall have a reasonable share of the work.” (page 1)

What is a problem  in mathematics? A problem is “any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method” (Hiebert, et. al., 1997). Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.

According to NCTM (2010), the term “problem solving” refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. When you first hear “problem solving,” what do you think about? Story problems or word problems? Story problems may be limited to and not “problematic” enough. For example, you may ask students to find the area of a rectangle, given the length and width. This type of problem is an exercise in computation and can be completed mindlessly without understanding the concept of area. Worthwhile problems  includes problems that are truly problematic and have the potential to provide contexts for students’ mathematical development.

There are three ways to solve problems: teaching for problem solving, teaching about problem solving, and teaching through problem solving.

Teaching for problem solving begins with learning a skill. For example, students are learning how to multiply a two-digit number by a one-digit number, and the story problems you select are multiplication problems. Be sure when you are teaching for problem solving, you select or develop tasks that can promote the development of mathematical understanding.

Teaching about problem solving begins with suggested strategies to solve a problem. For example, “draw a picture,” “make a table,” etc. You may see posters in teachers’ classrooms of the “Problem Solving Method” such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no evidence that students’ problem-solving abilities are improved when teaching about problem solving. Students will see a word problem as a separate endeavor and focus on the steps to follow rather than the mathematics. In addition, students will tend to use trial and error instead of focusing on sense making.

Teaching through problem solving  focuses students’ attention on ideas and sense making and develops mathematical practices. Teaching through problem solving also develops a student’s confidence and builds on their strengths. It allows for collaboration among students and engages students in their own learning.

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

  • The problem has important, useful mathematics embedded in it.
  • The problem requires high-level thinking and problem solving.
  • The problem contributes to the conceptual development of students.
  • The problem creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
  • The problem can be approached by students in multiple ways using different solution strategies.
  • The problem has various solutions or allows different decisions or positions to be taken and defended.
  • The problem encourages student engagement and discourse.
  • The problem connects to other important mathematical ideas.
  • The problem promotes the skillful use of mathematics.
  • The problem provides an opportunity to practice important skills.

Of course, not every problem will include all of the above. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.

Key features of a good mathematics problem includes:

  • It must begin where the students are mathematically.
  • The feature of the problem must be the mathematics that students are to learn.
  • It must require justifications and explanations for both answers and methods of solving.

Needlepoint of cats

Problem solving is not a  neat and orderly process. Think about needlework. On the front side, it is neat and perfect and pretty.

Back of a needlepoint

But look at the b ack.

It is messy and full of knots and loops. Problem solving in mathematics is also like this and we need to help our students be “messy” with problem solving; they need to go through those knots and loops and learn how to solve problems with the teacher’s guidance.

When you teach through problem solving , your students are focused on ideas and sense-making and they develop confidence in mathematics!

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Teacher teaching a math lesson

Choosing the Right Task

Selecting activities and/or tasks is the most significant decision teachers make that will affect students’ learning. Consider the following questions:

  • Teachers must do the activity first. What is problematic about the activity? What will you need to do BEFORE the activity and AFTER the activity? Additionally, think how your students would do the activity.
  • What mathematical ideas will the activity develop? Are there connections to other related mathematics topics, or other content areas?
  • Can the activity accomplish your learning objective/goals?

example of problem solving method of teaching

Low Floor High Ceiling Tasks

By definition, a “ low floor/high ceiling task ” is a mathematical activity where everyone in the group can begin and then work on at their own level of engagement. Low Floor High Ceiling Tasks are activities that everyone can begin and work on based on their own level, and have many possibilities for students to do more challenging mathematics. One gauge of knowing whether an activity is a Low Floor High Ceiling Task is when the work on the problems becomes more important than the answer itself, and leads to rich mathematical discourse [Hover: ways of representing, thinking, talking, agreeing, and disagreeing; the way ideas are exchanged and what the ideas entail; and as being shaped by the tasks in which students engage as well as by the nature of the learning environment].

The strengths of using Low Floor High Ceiling Tasks:

  • Allows students to show what they can do, not what they can’t.
  • Provides differentiation to all students.
  • Promotes a positive classroom environment.
  • Advances a growth mindset in students
  • Aligns with the Standards for Mathematical Practice

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

  • YouCubed – under grades choose Low Floor High Ceiling
  • NRICH Creating a Low Threshold High Ceiling Classroom
  • Inside Mathematics Problems of the Month

Math in 3-Acts

Math in 3-Acts was developed by Dan Meyer to spark an interest in and engage students in thought-provoking mathematical inquiry. Math in 3-Acts is a whole-group mathematics task consisting of three distinct parts:

Act One is about noticing and wondering. The teacher shares with students an image, video, or other situation that is engaging and perplexing. Students then generate questions about the situation.

In Act Two , the teacher offers some information for the students to use as they find the solutions to the problem.

Act Three is the “reveal.” Students share their thinking as well as their solutions.

“Math in 3 Acts” is a fun way to engage your students, there is a low entry point that gives students confidence, there are multiple paths to a solution, and it encourages students to work in groups to solve the problem. Some examples of Math in 3-Acts can be found at the following websites:

  • Dan Meyer’s Three-Act Math Tasks
  • Graham Fletcher3-Act Tasks ]
  • Math in 3-Acts: Real World Math Problems to Make Math Contextual, Visual and Concrete

Number Talks

Number talks are brief, 5-15 minute discussions that focus on student solutions for a mental math computation problem. Students share their different mental math processes aloud while the teacher records their thinking visually on a chart or board. In addition, students learn from each other’s strategies as they question, critique, or build on the strategies that are shared.. To use a “number talk,” you would include the following steps:

  • The teacher presents a problem for students to solve mentally.
  • Provide adequate “ wait time .”
  • The teacher calls on a students and asks, “What were you thinking?” and “Explain your thinking.”
  • For each student who volunteers to share their strategy, write their thinking on the board. Make sure to accurately record their thinking; do not correct their responses.
  • Invite students to question each other about their strategies, compare and contrast the strategies, and ask for clarification about strategies that are confusing.

“Number Talks” can be used as an introduction, a warm up to a lesson, or an extension. Some examples of Number Talks can be found at the following websites:

  • Inside Mathematics Number Talks
  • Number Talks Build Numerical Reasoning

Light bulb

Saying “This is Easy”

“This is easy.” Three little words that can have a big impact on students. What may be “easy” for one person, may be more “difficult” for someone else. And saying “this is easy” defeats the purpose of a growth mindset classroom, where students are comfortable making mistakes.

When the teacher says, “this is easy,” students may think,

  • “Everyone else understands and I don’t. I can’t do this!”
  • Students may just give up and surrender the mathematics to their classmates.
  • Students may shut down.

Instead, you and your students could say the following:

  • “I think I can do this.”
  • “I have an idea I want to try.”
  • “I’ve seen this kind of problem before.”

Tracy Zager wrote a short article, “This is easy”: The Little Phrase That Causes Big Problems” that can give you more information. Read Tracy Zager’s article here.

Using “Worksheets”

Do you want your students to memorize concepts, or do you want them to understand and apply the mathematics for different situations?

What is a “worksheet” in mathematics? It is a paper and pencil assignment when no other materials are used. A worksheet does not allow your students to use hands-on materials/manipulatives [Hover: physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics]; and worksheets are many times “naked number” with no context. And a worksheet should not be used to enhance a hands-on activity.

Students need time to explore and manipulate materials in order to learn the mathematics concept. Worksheets are just a test of rote memory. Students need to develop those higher-order thinking skills, and worksheets will not allow them to do that.

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.”

You may need an “activity sheet,” a “graphic organizer,” etc. as you plan your mathematics activities/lessons, but be sure to include hands-on manipulatives. Using manipulatives can

  • Provide your students a bridge between the concrete and abstract
  • Serve as models that support students’ thinking
  • Provide another representation
  • Support student engagement
  • Give students ownership of their own learning.

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method

should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

a mathematical activity where everyone in the group can begin and then work on at their own level of engagement

20 seconds to 2 minutes for students to make sense of questions

Mathematics Methods for Early Childhood Copyright © 2021 by Janet Stramel is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Module 1: Problem Solving Strategies

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Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1

1. Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY

Screen Shot 2018-08-30 at 4.43.05 PM.png

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.

After understanding, then make a plan.

Carry out the plan.

Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

Problem Solving Strategy 1 (Guess and Test)

Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution.

Mr. Jones has a total of 25 chickens and cows on his farm. How many of each does he have if all together there are 76 feet?

Step 1: Understanding the problem

We are given in the problem that there are 25 chickens and cows.

All together there are 76 feet.

Chickens have 2 feet and cows have 4 feet.

We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.

Step 2: Devise a plan

Going to use Guess and test along with making a tab

Many times the strategy below is used with guess and test.

Make a table and look for a pattern:

Procedure: Make a table reflecting the data in the problem. If done in an orderly way, such a table will often reveal patterns and relationships that suggest how the problem can be solved.

Step 3: Carry out the plan:

Notice we are going in the wrong direction! The total number of feet is decreasing!

Better! The total number of feet are increasing!

Step 4: Looking back:

Check: 12 + 13 = 25 heads

24 + 52 = 76 feet.

We have found the solution to this problem. I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.

Videos to watch:

1. Click on this link to see an example of “Guess and Test”

http://www.mathstories.com/strategies.htm

2. Click on this link to see another example of Guess and Test.

http://www.mathinaction.org/problem-solving-strategies.html

Check in question 1:

clipboard_e6298bbd7c7f66d9eb9affcd33892ef0d.png

Place the digits 8, 10, 11, 12, and 13 in the circles to make the sums across and vertically equal 31. (5 points)

Check in question 2:

Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet . How many of each animal does he have? Make sure you use Polya’s 4 problem solving steps. (12 points)

Problem Solving Strategy 2 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric thinking visually can help!

Videos to watch demonstrating how to use "Draw a Picture".

1. Click on this link to see an example of “Draw a Picture”

2. Click on this link to see another example of Draw a Picture.

Problem Solving Strategy 3 ( Using a variable to find the sum of a sequence.)

Gauss's strategy for sequences.

last term = fixed number ( n -1) + first term

The fix number is the the amount each term is increasing or decreasing by. "n" is the number of terms you have. You can use this formula to find the last term in the sequence or the number of terms you have in a sequence.

Ex: 2, 5, 8, ... Find the 200th term.

Last term = 3(200-1) +2

Last term is 599.

To find the sum of a sequence: sum = [(first term + last term) (number of terms)]/ 2

Sum = (2 + 599) (200) then divide by 2

Sum = 60,100

Check in question 3: (10 points)

Find the 320 th term of 7, 10, 13, 16 …

Then find the sum of the first 320 terms.

Problem Solving Strategy 4 (Working Backwards)

This is considered a strategy in many schools. If you are given an answer, and the steps that were taken to arrive at that answer, you should be able to determine the starting point.

Videos to watch demonstrating of “Working Backwards”

https://www.youtube.com/watch?v=5FFWTsMEeJw

Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number?

1. We start with 11 and work backwards.

2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.

3. The opposite of doubling something is dividing by 2. 18/2 = 9

4. This should be our answer. Looking back:

9 x 2 = 18 -7 = 11

5. We have the right answer.

Check in question 4:

Christina is thinking of a number.

If you multiply her number by 93, add 6, and divide by 3, you obtain 436. What is her number? Solve this problem by working backwards. (5 points)

Problem Solving Strategy 5 (Looking for a Pattern)

Definition: A sequence is a pattern involving an ordered arrangement of numbers.

We first need to find a pattern.

Ask yourself as you search for a pattern – are the numbers growing steadily larger? Steadily smaller? How is each number related?

Example 1: 1, 4, 7, 10, 13…

Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19.

Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4.

So the next number would be

25 + 11 = 36

Example 3: 10, 7, 4, 1, -2… find the next 2 numbers.

In this sequence, the numbers are decreasing by 3. So the next 2 numbers would be -2 -3 = -5

-5 – 3 = -8

Example 4: 1, 2, 4, 8 … find the next two numbers.

This example is a little bit harder. The numbers are increasing but not by a constant. Maybe a factor?

So each number is being multiplied by 2.

16 x 2 = 32

1. Click on this link to see an example of “Looking for a Pattern”

2. Click on this link to see another example of Looking for a Pattern.

Problem Solving Strategy 6 (Make a List)

Example 1 : Can perfect squares end in a 2 or a 3?

List all the squares of the numbers 1 to 20.

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400.

Now look at the number in the ones digits. Notice they are 0, 1, 4, 5, 6, or 9. Notice none of the perfect squares end in 2, 3, 7, or 8. This list suggests that perfect squares cannot end in a 2, 3, 7 or 8.

How many different amounts of money can you have in your pocket if you have only three coins including only dimes and quarters?

Quarter’s dimes

0 3 30 cents

1 2 45 cents

2 1 60 cents

3 0 75 cents

Videos demonstrating "Make a List"

Check in question 5:

How many ways can you make change for 23 cents using only pennies, nickels, and dimes? (10 points)

Problem Solving Strategy 7 (Solve a Simpler Problem)

Geometric Sequences:

How would we find the nth term?

Solve a simpler problem:

1, 3, 9, 27.

1. To get from 1 to 3 what did we do?

2. To get from 3 to 9 what did we do?

Let’s set up a table:

Term Number what did we do

example of problem solving method of teaching

Looking back: How would you find the nth term?

example of problem solving method of teaching

Find the 10 th term of the above sequence.

Let L = the tenth term

example of problem solving method of teaching

Problem Solving Strategy 8 (Process of Elimination)

This strategy can be used when there is only one possible solution.

I’m thinking of a number.

The number is odd.

It is more than 1 but less than 100.

It is greater than 20.

It is less than 5 times 7.

The sum of the digits is 7.

It is evenly divisible by 5.

a. We know it is an odd number between 1 and 100.

b. It is greater than 20 but less than 35

21, 23, 25, 27, 29, 31, 33, 35. These are the possibilities.

c. The sum of the digits is 7

21 (2+1=3) No 23 (2+3 = 5) No 25 (2 + 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. Also we notice 25 is divisible by 5. By using the strategy elimination, we have found our answer.

Check in question 6: (8 points)

Jose is thinking of a number.

The number is not odd.

The sum of the digits is divisible by 2.

The number is a multiple of 11.

It is greater than 5 times 4.

It is a multiple of 6

It is less than 7 times 8 +23

What is the number?

Click on this link for a quick review of the problem solving strategies.

https://garyhall.org.uk/maths-problem-solving-strategies.html

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5 Problem-Solving Activities for the Classroom

Problem-solving skills are necessary in all areas of life, and classroom problem solving activities can be a great way to get students prepped and ready to solve real problems in real life scenarios. Whether in school, work or in their social relationships, the ability to critically analyze a problem, map out all its elements and then prepare a workable solution is one of the most valuable skills one can acquire in life.

Educating your students about problem solving skills from an early age in school can be facilitated through classroom problem solving activities. Such endeavors encourage cognitive as well as social development, and can equip students with the tools they’ll need to address and solve problems throughout the rest of their lives. Here are five classroom problem solving activities your students are sure to benefit from as well as enjoy doing:

1. Brainstorm bonanza

Having your students create lists related to whatever you are currently studying can be a great way to help them to enrich their understanding of a topic while learning to problem-solve. For example, if you are studying a historical, current or fictional event that did not turn out favorably, have your students brainstorm ways that the protagonist or participants could have created a different, more positive outcome. They can brainstorm on paper individually or on a chalkboard or white board in front of the class.

2. Problem-solving as a group

Have your students create and decorate a medium-sized box with a slot in the top. Label the box “The Problem-Solving Box.” Invite students to anonymously write down and submit any problem or issue they might be having at school or at home, ones that they can’t seem to figure out on their own. Once or twice a week, have a student draw one of the items from the box and read it aloud. Then have the class as a group figure out the ideal way the student can address the issue and hopefully solve it.

3. Clue me in

This fun detective game encourages problem-solving, critical thinking and cognitive development. Collect a number of items that are associated with a specific profession, social trend, place, public figure, historical event, animal, etc. Assemble actual items (or pictures of items) that are commonly associated with the target answer. Place them all in a bag (five-10 clues should be sufficient.) Then have a student reach into the bag and one by one pull out clues. Choose a minimum number of clues they must draw out before making their first guess (two- three). After this, the student must venture a guess after each clue pulled until they guess correctly. See how quickly the student is able to solve the riddle.

4. Survivor scenarios

Create a pretend scenario for students that requires them to think creatively to make it through. An example might be getting stranded on an island, knowing that help will not arrive for three days. The group has a limited amount of food and water and must create shelter from items around the island. Encourage working together as a group and hearing out every child that has an idea about how to make it through the three days as safely and comfortably as possible.

5. Moral dilemma

Create a number of possible moral dilemmas your students might encounter in life, write them down, and place each item folded up in a bowl or bag. Some of the items might include things like, “I saw a good friend of mine shoplifting. What should I do?” or “The cashier gave me an extra $1.50 in change after I bought candy at the store. What should I do?” Have each student draw an item from the bag one by one, read it aloud, then tell the class their answer on the spot as to how they would handle the situation.

Classroom problem solving activities need not be dull and routine. Ideally, the problem solving activities you give your students will engage their senses and be genuinely fun to do. The activities and lessons learned will leave an impression on each child, increasing the likelihood that they will take the lesson forward into their everyday lives.

You may also like to read

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44 Powerful Instructional Strategies Examples for Every Classroom

So many ways to help students learn!

Collage of instructional strategies examples including demonstrations and reading for meaning

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 ..

Looking for new and exciting instructional strategies examples to help all of your students learn more effectively? Get them here!

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Top 10 Challenges to Teaching Math and Science Using Real Problems

example of problem solving method of teaching

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Nine in ten educators believe that using a problem-solving approach to teaching math and science can be motivating for students, according to an EdWeek Research Center survey.

But that doesn’t mean it’s easy.

Teachers perceive lack of time as a big hurdle. In fact, a third of educators—35 percent—worry that teaching math or science through real-world problems—rather than focusing on procedures—eats up too many precious instructional minutes.

Other challenges: About another third of educators said they weren’t given sufficient professional development in how to teach using a real-world problem-solving approach. Nearly a third say reading and writing take priority over STEM, leaving little bandwidth for this kind of instruction. About a quarter say that it’s tough to find instructional materials that embrace a problem-solving perspective.

Nearly one in five cited teachers’ lack of confidence in their own problem solving, the belief that this approach isn’t compatible with standardized tests, low parent support, and the belief that student behavior is so poor that this approach would not be feasible.

The nationally representative survey included 1,183 district leaders, school leaders, and teachers, and was conducted from March 27 to April 14. (Note: The chart below lists 11 challenges because the last two on the list—dealing with teacher preparation and student behavior—received the exact percentage of responses.)

Trying to incorporate a problem-solving approach to tackling math can require rethinking long-held beliefs about how students learn, said Elham Kazemi, a professor in the teacher education program at the University of Washington.

Most teachers were taught math using a procedural perspective when they were in school. While Kazemi believes that approach has merit, she advocates for exposing students to both types of instruction.

Many educators have “grown up around a particular model of thinking of teaching and learning as the teacher in the front of the room, imparting knowledge, showing kids how to do things,” Kazemi said.

To be sure, some teachers have figured out how to incorporate some real-world problem solving alongside more traditional methods. But it can be tough for their colleagues to learn from them because “teachers don’t have a lot of time to collaborate with one another and see each other teach,” Kazemi said.

What’s more, there are limited instructional materials emphasizing problem solving, Kazemi said.

Though that’s changing, many of the resources available have “reinforced the idea that the teacher demonstrates solutions for kids,” Kazemi said.

Molly Daley, a regional math coordinator for Education Service District 112, which serves about 30 districts near Vancouver, Wash., has heard teachers raise concerns that teaching math from a problem-solving perspective takes too long—particularly given the pressure to get through all the material students will need to perform well on state tests.

Daley believes, however, that being taught to think about math in a deeper way will help students tackle math questions on state assessments that may look different from what they’ve seen before.

“It’s myth that it’s possible to cover everything that will be on the test,” as it will appear, she said. “There’s actually no way to make sure that kids have seen every single possible thing the way it will show up. That’s kind of a losing proposition.”

But rushing through the material in a purely procedural way may actually be counterproductive, she said.

Teachers don’t want kids to “sit down at the test and say, ‘I haven’t seen this and therefore I can’t do it,’” Daley said. “I think a lot of times teachers can unintentionally foster that because they’re so urgently trying to cover everything. That’s where the kind of mindless [teaching] approaches come in.”

Teachers may think to themselves: “’OK, I’m gonna make this as simple as possible, make sure everyone knows how to follow the steps and then when they see it, they can follow it,” Daley said.

But that strategy might “take away their students’ confidence that they can figure out what to do when they don’t know what to do, which is really what you want them to be thinking when they go to approach a test,” Daley said.

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Data analysis for this article was provided by the EdWeek Research Center. Learn more about the center’s work.

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COMMENTS

  1. Problem-Solving Method In Teaching

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

  2. Teaching Problem Solving

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

  3. Teaching Problem-Solving Skills

    Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill. Help students understand the problem. In order to solve problems, students need ...

  4. Problem-Based Learning

    Nilson (2010) lists the following learning outcomes that are associated with PBL. A well-designed PBL project provides students with the opportunity to develop skills related to: Working in teams. Managing projects and holding leadership roles. Oral and written communication. Self-awareness and evaluation of group processes. Working independently.

  5. Teaching problem solving

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

  6. Teaching Problem Solving

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

  7. Problem-Based Learning (PBL)

    Problem-Based Learning (PBL) is a teaching method in which complex real-world problems are used as the vehicle to promote student learning of concepts and principles as opposed to direct presentation of facts and concepts. In addition to course content, PBL can promote the development of critical thinking skills, problem-solving abilities, and ...

  8. Teaching problem solving: Let students get 'stuck' and 'unstuck'

    Teaching problem solving: Let students get 'stuck' and 'unstuck'. This is the second in a six-part blog series on teaching 21st century skills, including problem solving , metacognition ...

  9. Problem Solving Resources

    Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically. Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.

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

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

  11. Problem-Solving Method of Teaching: All You Need to Know

    The problem-solving method of teaching is a student-centered approach to learning that focuses on developing students' problem-solving skills. In this method, students are presented with real-world problems to solve, and they are encouraged to use their own knowledge and skills to come up with solutions. The teacher acts as a facilitator ...

  12. Problem Solving Method Of Teaching

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

  13. Key Tips On Problem Solving Method Of Teaching

    The problem-solving method involves three basic functions Woods' problem-solving model Identify the problem Think about it Plan a solution Carry out the plan Look back Other tips include Ask Open-Ended Questions Emphasize Process Over Product Model The Strategies Encourage Grappling Make problem resolution relevant to the lives of your students.

  14. Full article: Understanding and explaining pedagogical problem solving

    1. Introduction. The focus of this paper is on understanding and explaining pedagogical problem solving. This theoretical paper builds on two previous studies (Riordan, Citation 2020; and Riordan, Hardman and Cumbers, Citation 2021) by introducing an 'extended Pedagogy Analysis Framework' and a 'Pedagogical Problem Typology' illustrating both with examples from video-based analysis of ...

  15. Problem-Based Learning (PBL)

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

  16. PDF Problem Based Learning: A Student-Centered Approach

    principles and concept. PBL is both a teaching method and approach to the curriculum. It can develop critical thinking skill, problem solving abilities, communication skills and lifelong learning. The purpose of this study is to give the general idea of PBL in the context of language learning, as PBL has expanded in the areas of law,

  17. The process of implementing problem-based learning in a teacher

    For example, studies on topics related to problem solving (Helmi et al ... teaching methods in the cognitive field, teaching methods in the field of affective skills and skills generally, individualised teaching methods and principles, and teaching evaluation assessments. ... I observed that the higher the students' learning engagement and ...

  18. Teaching Mathematics Through Problem Solving

    Teaching about problem solving begins with suggested strategies to solve a problem. For example, "draw a picture," "make a table," etc. You may see posters in teachers' classrooms of the "Problem Solving Method" such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no ...

  19. Module 1: Problem Solving Strategies

    Step 1: Understanding the problem. We are given in the problem that there are 25 chickens and cows. All together there are 76 feet. Chickens have 2 feet and cows have 4 feet. We are trying to determine how many cows and how many chickens Mr. Jones has on his farm. Step 2: Devise a plan.

  20. 5 Problem-Solving Activities for the Classroom

    2. Problem-solving as a group. Have your students create and decorate a medium-sized box with a slot in the top. Label the box "The Problem-Solving Box.". Invite students to anonymously write down and submit any problem or issue they might be having at school or at home, ones that they can't seem to figure out on their own.

  21. 44 Instructional Strategies Examples for Every Kind of Classroom

    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.

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

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

  23. PDF A Problem With Problem Solving: Teaching Thinking Without Teaching

    Three examples of a problem solving heuristic are presented in Table 1. The first belongs to John Dewey, who explicated a method of problem solving in How We Think (1933). The second is George Polya's, whose method is mostly associated with problem solving in mathematics. The last is a more contemporary version

  24. Top 10 Challenges to Teaching Math and Science Using Real Problems

    Teachers perceive lack of time as a big hurdle. In fact, a third of educators—35 percent—worry that teaching math or science through real-world problems—rather than focusing on procedures ...

  25. Nursing Reports

    Methods: This quantitative study used a cross-sectional, descriptive, correlation design to investigate the effectiveness of standardized patient simulation as a teaching method in the Psychiatric and Mental Health nursing course in a university setting. A total of 84 nursing students were recruited for the convenience sample.

  26. Exploring large language models as an integrated tool for learning

    They found it beneficial in simplifying complex theories, facilitating problem-solving, preparing efficient study materials, and interpreting ideas with real-life examples. While recognizing these positive aspects, students also emphasized the necessity for simulation guidance and improvements in providing relevant and accurate answers.