problem solving examples teaching

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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.

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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

• Classroom Activities for Introverted Students
• Activities for Teaching Tolerance in the Classroom
• 5 Problem-Solving Activities for Elementary Classrooms
• 10 Ways to Motivate Students Outside the Classroom
• Motivating Introverted Students to Excel in the Classroom
• How to Engage Gifted and Talented Students in the Classroom

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Don’t Just Tell Students to Solve Problems. Teach Them How.

The positive impact of an innovative uc san diego problem-solving educational curriculum continues to grow.

• Daniel Kane - [email protected]

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Problem solving is a critical skill for technical education and technical careers of all types. But what are best practices for teaching problem solving to high school and college students? 

The University of California San Diego Jacobs School of Engineering is on the forefront of efforts to improve how problem solving is taught. This UC San Diego approach puts hands-on problem-identification and problem-solving techniques front and center. Over 1,500 students across the San Diego region have already benefited over the last three years from this program. In the 2023-2024 academic year, approximately 1,000 upper-level high school students will be taking the problem solving course in four different school districts in the San Diego region. Based on the positive results with college students, as well as high school juniors and seniors in the San Diego region, the project is getting attention from educators across the state of California, and around the nation and the world.

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In Summer 2023, th e 27 community college students who took the unique problem-solving course developed at the UC San Diego Jacobs School of Engineering thrived, according to Alex Phan PhD, the Executive Director of Student Success at the UC San Diego Jacobs School of Engineering. Phan oversees the project. 

Over the course of three weeks, these students from Southwestern College and San Diego City College poured their enthusiasm into problem solving through hands-on team engineering challenges. The students brimmed with positive energy as they worked together. 

What was noticeably absent from this laboratory classroom: frustration.

“In school, we often tell students to brainstorm, but they don’t often know where to start. This curriculum gives students direct strategies for brainstorming, for identifying problems, for solving problems,” sai d Jennifer Ogo, a teacher from Kearny High School who taught the problem-solving course in summer 2023 at UC San Diego. Ogo was part of group of educators who took the course themselves last summer.

The curriculum has been created, refined and administered over the last three years through a collaboration between the UC San Diego Jacobs School of Engineering and the UC San Diego Division of Extended Studies. The project kicked off in 2020 with a generous gift from a local philanthropist.

Not getting stuck

One of the overarching goals of this project is to teach both problem-identification and problem-solving skills that help students avoid getting stuck during the learning process. Stuck feelings lead to frustration – and when it’s a Science, Technology, Engineering and Math (STEM) project, that frustration can lead students to feel they don’t belong in a STEM major or a STEM career. Instead, the UC San Diego curriculum is designed to give students the tools that lead to reactions like “this class is hard, but I know I can do this!” –  as Ogo, a celebrated high school biomedical sciences and technology teacher, put it. 

Three years into the curriculum development effort, the light-hearted energy of the students combined with their intense focus points to success. On the last day of the class, Mourad Mjahed PhD, Director of the MESA Program at Southwestern College’s School of Mathematics, Science and Engineering came to UC San Diego to see the final project presentations made by his 22 MESA students.

“Industry is looking for students who have learned from their failures and who have worked outside of their comfort zones,” said Mjahed. The UC San Diego problem-solving curriculum, Mjahed noted, is an opportunity for students to build the skills and the confidence to learn from their failures and to work outside their comfort zone. “And from there, they see pathways to real careers,” he said. 

What does it mean to explicitly teach problem solving? 

This approach to teaching problem solving includes a significant focus on learning to identify the problem that actually needs to be solved, in order to avoid solving the wrong problem. The curriculum is organized so that each day is a complete experience. It begins with the teacher introducing the problem-identification or problem-solving strategy of the day. The teacher then presents case studies of that particular strategy in action. Next, the students get introduced to the day’s challenge project. Working in teams, the students compete to win the challenge while integrating the day’s technique. Finally, the class reconvenes to reflect. They discuss what worked and didn't work with their designs as well as how they could have used the day’s problem-identification or problem-solving technique more effectively. 

The challenges are designed to be engaging – and over three years, they have been refined to be even more engaging. But the student engagement is about much more than being entertained. Many of the students recognize early on that the problem-identification and problem-solving skills they are learning can be applied not just in the classroom, but in other classes and in life in general. 

Gabriel from Southwestern College is one of the students who saw benefits outside the classroom almost immediately. In addition to taking the UC San Diego problem-solving course, Gabriel was concurrently enrolled in an online computer science programming class. He said he immediately started applying the UC San Diego problem-identification and troubleshooting strategies to his coding assignments. 

Gabriel noted that he was given a coding-specific troubleshooting strategy in the computer science course, but the more general problem-identification strategies from the UC San Diego class had been extremely helpful. It’s critical to “find the right problem so you can get the right solution. The strategies here,” he said, “they work everywhere.”

Phan echoed this sentiment. “We believe this curriculum can prepare students for the technical workforce. It can prepare students to be impactful for any career path.”

The goal is to be able to offer the course in community colleges for course credit that transfers to the UC, and to possibly offer a version of the course to incoming students at UC San Diego. 

As the team continues to work towards integrating the curriculum in both standardized high school courses such as physics, and incorporating the content as a part of the general education curriculum at UC San Diego, the project is expected to impact thousands more students across San Diego annually. 

Portrait of the Problem-Solving Curriculum

On a sunny Wednesday in July 2023, an experiential-learning classroom was full of San Diego community college students. They were about half-way through the three-week problem-solving course at UC San Diego, held in the campus’ EnVision Arts and Engineering Maker Studio. On this day, the students were challenged to build a contraption that would propel at least six ping pong balls along a kite string spanning the laboratory. The only propulsive force they could rely on was the air shooting out of a party balloon.

A team of three students from Southwestern College – Valeria, Melissa and Alondra – took an early lead in the classroom competition. They were the first to use a plastic bag instead of disposable cups to hold the ping pong balls. Using a bag, their design got more than half-way to the finish line – better than any other team at the time – but there was more work to do. 

As the trio considered what design changes to make next, they returned to the problem-solving theme of the day: unintended consequences. Earlier in the day, all the students had been challenged to consider unintended consequences and ask questions like: When you design to reduce friction, what happens? Do new problems emerge? Did other things improve that you hadn’t anticipated? 

Other groups soon followed Valeria, Melissa and Alondra’s lead and began iterating on their own plastic-bag solutions to the day’s challenge. New unintended consequences popped up everywhere. Switching from cups to a bag, for example, reduced friction but sometimes increased wind drag. 

Over the course of several iterations, Valeria, Melissa and Alondra made their bag smaller, blew their balloon up bigger, and switched to a different kind of tape to get a better connection with the plastic straw that slid along the kite string, carrying the ping pong balls. 

One of the groups on the other side of the room watched the emergence of the plastic-bag solution with great interest. 

“We tried everything, then we saw a team using a bag,” said Alexander, a student from City College. His team adopted the plastic-bag strategy as well, and iterated on it like everyone else. They also chose to blow up their balloon with a hand pump after the balloon was already attached to the bag filled with ping pong balls – which was unique. 

“I don’t want to be trying to put the balloon in place when it's about to explode,” Alexander explained. 

Asked about whether the structured problem solving approaches were useful, Alexander’s teammate Brianna, who is a Southwestern College student, talked about how the problem-solving tools have helped her get over mental blocks. “Sometimes we make the most ridiculous things work,” she said. “It’s a pretty fun class for sure.” 

Yoshadara, a City College student who is the third member of this team, described some of the problem solving techniques this way: “It’s about letting yourself be a little absurd.”

Alexander jumped back into the conversation. “The value is in the abstraction. As students, we learn to look at the problem solving that worked and then abstract out the problem solving strategy that can then be applied to other challenges. That’s what mathematicians do all the time,” he said, adding that he is already thinking about how he can apply the process of looking at unintended consequences to improve both how he plays chess and how he goes about solving math problems.

Looking ahead, the goal is to empower as many students as possible in the San Diego area and  beyond to learn to problem solve more enjoyably. It’s a concrete way to give students tools that could encourage them to thrive in the growing number of technical careers that require sharp problem-solving skills, whether or not they require a four-year degree. 

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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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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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Worked Examples

What are worked examples?

Worked examples are step-by-step illustrations of the process required to complete a task or solve a problem. In a worked example, students are provided with the task or problem formulation, the procedure or the step-by-step process for solving the problem, and the solution. When using worked examples effectively, instructors engage students in self-explaining these procedures or solutions, encouraging them to reflect more deeply on the principles illustrated in the worked example. Worked examples can be designed to teach well-structured tasks, such as applying Newton’s Second Law, as well as more ill-structured tasks, such as constructing an argument, modeling biological pathways, or devising a mathematical proof (Renkl, 2023).

Worked examples are useful in the initial acquisition of cognitive skills because they allow students to understand principles and their applications more deeply before applying them on their own (Renkl, 2014b). Worked examples have shown to be particularly effective for novice learners, who may experience high levels of cognitive load when learning new concepts and procedures simultaneously (Renkl, 2014a). In fact, worked examples tend to be more efficient and effective for initial skill acquisition compared to problem solving (Renkl, 2014a). If designed well, worked examples can provide models for learners to follow when tackling similar problems, allowing them to transfer knowledge from one task to another (see Caveats section below).

Worked examples can be applied to a wide range of disciplines and contexts beyond STEM.

Worked examples can be created for any procedural task. For instance, in the field of law, worked examples have been used to teach students how to reason through legal cases and construct legal arguments (Nievelstein et al ., 2013; Schworm & Renkl, 2007), while worked examples have similarly been used to assist learners in understanding negotiation strategies (Gentner et al. , 2003). In language and literature, worked examples can be used to help students write essays or understand different writing styles (Kyun et al ., 2013), while in the arts, worked examples have been used to teach students to differentiate between artistic styles (Rourke & Sweller, 2009).

Furthermore, worked examples can be used inside and outside of class time and for a variety of class types. For instance, during class, instructors can either demonstrate a worked example interactively or provide students with a written worked example for students to work on individually and/or in groups. Outside of class, worked examples can be provided for students to study on their own time (see Caveats section for what to avoid when implementing worked examples). In lab-based courses, for example, instructors can convert any demonstration, which is often performed when modeling a procedure, into an effective worked example by asking students to reflect on specific and important aspects of the demonstration (e.g., Why would you do X instead of Y first? What are the advantages and disadvantages of using this type of protocol for isolating X?).

Why are worked examples important?

Early research conducted by Sweller and Cooper (1985) showed that after an initial introduction to a series of algebraic problems, replacing practice problems with worked example counterparts resulted in higher learning gains. The worked example condition was also more efficient; learners given problems to solve took almost six times longer to complete the learning sequence and had more errors than those provided with worked examples to study from. Subsequent studies have supported the finding that if implemented well, studying worked examples is more effective in the initial stages of learning than learning primarily through problem solving (Figure 1 and Salden, Koedinger, Renkl, Aleven, & McLaren, 2010). Though students may usually be provided with examples or demonstrations in the initial stages of learning, the number of worked examples is typically low and insufficient for learning underlying principles. These demonstrations are also often done passively with little student engagement, which does not lead to deep learning and neutralizes the worked example effect. In fact, when implementing worked examples with features that get students to actively study the solutions (see the Caveats section for more), the worked example effect nearly doubles (Hattie, 2009).

Why are worked examples more effective for initial skill acquisition than practice?

When introducing a new task or skill, it may seem counterintuitive to provide students with worked examples to study instead of giving them practice time to solve or complete the task. When students are introduced to a new task, they often do not have a firm grasp of the material and principles being represented in the task and may resort to ineffective problem-solving strategies such as aimless trial-and-error or plug-and-chug (Renkl, A., 2023). Trial-and-error involves trying various solutions without a proper problem-solving strategy, while plug-and-chug involves looking for existing problems with similar surface-level features without considering if their underlying structure aligns with the current problem. For example, when faced with a mechanics problem presented in the context of an inclined plane, novice students may search for another “inclined plane problem” without considering whether the underlying concept is the same (Figure 2 and Chi et al ., 1989).

These ineffective problem-solving strategies are taxing on cognitive load because they lead students down unproductive paths while already processing a lot of new information, including understanding newly introduced concepts and making sense of the problem being presented. Engaging prematurely in problem solving without fully understanding the task domain and procedure leaves little working memory capacity for learners to understand the validity of a particular solution or the ability to integrate new knowledge for future use (Sweller, 1988).

Providing step-by-step illustrations of a solution or procedure in worked examples reduces cognitive load by allowing students to focus their cognitive resources on understanding the principles illustrated in the solution. Therefore, providing worked examples for students to study can help them understand the principles and strategies needed to approach the task effectively, without overtaxing cognitive load (Clark & Mayer, 2011).

As learners become more proficient, educators can transition to more practice exercises and tasks to help students automate problem-solving strategies or procedures (see Caveats section below). In fact, when students have sufficient prior knowledge about the specific task or problem, asking students to study worked examples can decrease competence in performing said task (often called expertise reversal, Kalyuga & Renkl 2010). It is important for instructors to balance the use of worked examples with independent practice to maximize learning outcomes for students at different stages of proficiency within a learning sequence.

7.013 – Introductory Biology

During recitations, students were provided with a handout containing worked examples. The teaching assistants (TAs) would lead the class through at least one of the worked examples, step by step, to ensure that students understood the problem-solving strategies illustrated in those worked examples. Then, students were given a set of slightly more complex but similar additional problems to solve independently. One or several students would then volunteer to guide the class through the steps they used to solve these additional problems. By incorporating both worked examples and problems to solve for a given concept, students had the opportunity to more deeply understand the concepts learned, and instructors could better monitor progress by observing what happened when the surface features and the complexity of the problems changed.

21A.819.1X – How To Conduct Conversational Social Science Research

Students were provided with two examples of an informal interview protocol and informed which one was well constructed and which was not. After reading both worked examples, students were asked to annotate each example and provide suggestions for improvement. They were then able to review the instructor’s own annotations and explanations for suggestions. By beginning with the knowledge of which examples demonstrated good or poor interview protocol (correct and incorrect worked examples), students could engage more meaningfully with the worked examples, reflecting on their annotations and exploring their reasoning for suggested improvements. Using incorrect worked examples, either alone or in combination with correct examples, has been shown to be more effective than using correct worked examples alone (Booth et al ., 2013).

The instructors in this course also utilized worked examples of interview techniques by providing example videos of interviews. One video demonstrated good interview techniques (a correct worked example), while the other demonstrated poor interview techniques (an incorrect worked example). After watching these videos, students were asked to assess them for improvements regarding best practices in conversational interviewing. They were then able to compare their assessments with the instructor’s explanations, designed to help reinforce their understanding of effective interview techniques.

Caveats (and how to address them)

Worked examples effectively teach new tasks or solve new problem types. However, the worked example effect can be negated if certain design features are not considered. Here are some concerns that instructors have often brought up about worked examples and strategies for ameliorating them:

1. Students might passively read solutions without extracting underlying principles.

While worked examples have shown to be effective, their effectiveness depends on students cognitively engaging with them. Unfortunately, worked examples are often presented passively, without requiring engagement. Research shows that few students will naturally engage in self-explanation strategies when studying solutions. To address this issue, it is recommended that students be encouraged to self-explain the solutions. This can be accomplished in a variety of ways using self-explanation strategies. For example, instructors can present a solution step by step and embed pertinent questions that help students reflect on the deeper structure of the problem, such as “Why was this strategy used?” and “What was the principle applied here?” Self-explanation strategies promote deeper thinking by requiring students to explain the rationale of the solution to themselves and its relation to the core concepts. For additional information on self-explanation strategies, see the Resources section.

2. Students might memorize solutions without deepening their understanding.

It is important to vary the surface features of example tasks or problems to prevent rote memorization of solutions. This can be achieved by presenting multiple worked examples that appear dissimilar on the surface, but are representations of the same concept (see Figures 1 & 2). When exposed to contrasting problems that address the same core concept, students can more easily identify the commonalities that unify all the example problems, the deeper structure, and will be less likely to memorize solutions based on surface features (Renkl, 2014a and Paas & van Merrienboer, 1994).

3. Worked examples may not prepare students to approach tasks or solve problems independently.

When students are introduced to a new task, worked examples are more effective than having students problem solve. However, as they deepen in understanding how to perform the task or solve the problem, it is beneficial to encourage them to attempt the tasks independently to develop proficiency and automaticity (Renkl, 2014b). Instructors can do this by alternating worked examples and problems to solve in an increasingly more complex task sequence. Additionally, instructors can reduce the support provided in worked examples, such as having students solve more parts of the example and providing fewer worked-out steps. Faded support is helpful in transitioning from studying worked examples to problem solving (Renkl & Atkinson, 2003), particularly if tasks and problems are complex and challenging.

• Renkl, A. (2014a). Learning from worked examples: How to prepare students for meaningful problem solving. In V. A. Benassi, C. E. Overson, & C. M. Hakala (Eds.), Applying science of learning in education: Infusing psychological science into the curriculum (pp. 118–130). Society for the Teaching of Psychology. HTTP (downloaded PDF freely available)
• Renkl, A. (2023). Using Worked Examples for Ill-Structured Learning Content. In Overson, C. E., Hakala, C. M., Kordonowy, L.L., and Benassi, V. A. & (Eds.), In Their Own Words: What Scholars and Teachers Want You To Know About Why and How To Apply the Science of Learning in Your Academic Setting (pp. 207–224). Society for the Teaching of Psychology. HTTP (downloaded PDF freely available)

Booth, J. L., Lange, K. E., Koedinger, K. R., & Newton, K. J. (2013). Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction , 25, 24–34. http://doi.org/10.1016/j.learninstruc.2012.11.002

Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self‐Explanations: How Students Study and Use Examples in Learning to Solve Problems. Cognitive Science , 13(2), 145–182. http://doi.org/10.1207/s15516709cog1302_1

Chi, M.T.H., Feltovich, P.J. and Glaser, R. (1981). Categorization and Representation of Physics Problems by Experts and Novices. Cognitive Science , 5, 121-152. https://doi.org/10.1207/s15516709cog0502_2

Clark, R.C. & Mayer, R.E. (2011). Leveraging Examples in e-Learning. In e-Learning and the Science of Instruction (eds R.C. Clark and R.E. Mayer). https://doi.org/10.1002/9781118255971.ch11

Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. Journal of Educational Psychology , 95(2), 393-408. https://doi.org/10.1037/0022- 0663.95.2.393

Hattie, J. A. C. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. New York, NY: Routledge.

Kalyuga, S., & Renkl, A. (2010). Expertise reversal effect and its instructional implications: Introduction to the special issue. Instructional Science , 38(3), 209–215. http://doi.org/10.1007/s11251-009-9102-0

Kyun, S., Kalyuga, S., & Sweller, J. (2013). The Effect of Worked Examples When Learning to Write Essays in English Literature. The Journal of Experimental Education , 81(3), 385–408. http://doi.org/10.1080/00220973.2012.727884

Nievelstein, F., van Gog, T., van Dijck, G., & Boshuizen, H. P. A. (2013). The worked example and expertise reversal effect in less structured tasks: Learning to reason about legal cases. Contemporary Educational Psychology , 38(2), 118-125. https://doi.org/10.1016/j.cedpsych.2012.12.004

Paas, F. G. W. C., & van Merrienboer, J. J. G. (1994). Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach. Journal of Educational Psychology , 86(1), 122–133. http://doi.org/10.1037/0022-0663.86.1.122

Renkl, A. (2014a). Learning from worked examples: How to prepare students for meaningful problem solving. In V. A. Benassi, C. E. Overson, & C. M. Hakala (Eds.), Applying science of learning in education: Infusing psychological science into the curriculum (pp. 118–130). Society for the Teaching of Psychology.

Renkl, A. (2014b). Toward an instructionally oriented theory of example-based learning. Cognitive Science: a Multidisciplinary Journal , 38(1), 1–37. http://doi.org/10.1111/cogs.12086

Renkl, A., & Atkinson, R. K. (2010). Structuring the Transition From Example Study to Problem Solving in Cognitive Skill Acquisition: A Cognitive Load Perspective. Educational Psychologist . http://doi.org/10.1207/S15326985EP3801_3

Renkl, A. (2023). Using Worked Examples for Ill-Structured Learning Content. In Overson, C. E.,  Hakala, C. M., Kordonowy, L.L., and Benassi, V. A.  & (Eds.), In Their Own Words: What Scholars and Teachers Want You To KNow About Why and How To Apply the Science of Learning in Your Academic Setting (pp. 207–224). Society for the Teaching of Psychology.

Rourke, A., & Sweller, J. (2009). The worked-example effect using ill-defined problems: Learning to recognise designers’ styles. Learning and Instruction, 19(2), 185–199. http://doi.org/10.1016/j.learninstruc.2008.03.006

Salden, R. J. C. M., Koedinger, K. R., Renkl, A., Aleven, V., & McLaren, B. M. (2010). Accounting for Beneficial Effects of Worked Examples in Tutored Problem Solving. Educational Psychology Review, 22(4), 379–392. http://doi.org/10.1007/s10648-010-9143-6

Schworm, S., & Renkl, A. (2007). Learning argumentation skills through the use of prompts for self-explaining examples. Journal of Educational Psychology , 99(2), 285–296. http://doi.org/10.1037/0022-0663.99.2.285

Sweller, J. (1988). Cognitive Load During Problem Solving: Effects on Learning. Cognitive Science, 12: 257–285. http://doi.org/10.1207/s15516709cog1202_4

Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2 (1), 59–89. https://doi.org/10.1207/s1532690xci0201_3

Center for Teaching Innovation

Resource library.

• Establishing Community Agreements and Classroom Norms
• Sample group work rubric
• Problem-Based Learning Clearinghouse of Activities, University of Delaware

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. 

• Faculty & Staff

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 Solving in STEM

Solving problems is a key component of many science, math, and engineering classes.  If a goal of a class is for students to emerge with the ability to solve new kinds of problems or to use new problem-solving techniques, then students need numerous opportunities to develop the skills necessary to approach and answer different types of problems.  Problem solving during section or class allows students to develop their confidence in these skills under your guidance, better preparing them to succeed on their homework and exams. This page offers advice about strategies for facilitating problem solving during class.

How do I decide which problems to cover in section or class?

In-class problem solving should reinforce the major concepts from the class and provide the opportunity for theoretical concepts to become more concrete. If students have a problem set for homework, then in-class problem solving should prepare students for the types of problems that they will see on their homework. You may wish to include some simpler problems both in the interest of time and to help students gain confidence, but it is ideal if the complexity of at least some of the in-class problems mirrors the level of difficulty of the homework. You may also want to ask your students ahead of time which skills or concepts they find confusing, and include some problems that are directly targeted to their concerns.

You have given your students a problem to solve in class. What are some strategies to work through it?

• Try to give your students a chance to grapple with the problems as much as possible.  Offering them the chance to do the problem themselves allows them to learn from their mistakes in the presence of your expertise as their teacher. (If time is limited, they may not be able to get all the way through multi-step problems, in which case it can help to prioritize giving them a chance to tackle the most challenging steps.)
• When you do want to teach by solving the problem yourself at the board, talk through the logic of how you choose to apply certain approaches to solve certain problems.  This way you can externalize the type of thinking you hope your students internalize when they solve similar problems themselves.
• Start by setting up the problem on the board (e.g you might write down key variables and equations; draw a figure illustrating the question).  Ask students to start solving the problem, either independently or in small groups.  As they are working on the problem, walk around to hear what they are saying and see what they are writing down. If several students seem stuck, it might be a good to collect the whole class again to clarify any confusion.  After students have made progress, bring the everyone back together and have students guide you as to what to write on the board.
• It can help to first ask students to work on the problem by themselves for a minute, and then get into small groups to work on the problem collaboratively.
• If you have ample board space, have students work in small groups at the board while solving the problem.  That way you can monitor their progress by standing back and watching what they put up on the board.
• If you have several problems you would like to have the students practice, but not enough time for everyone to do all of them, you can assign different groups of students to work on different – but related - problems.

When do you want students to work in groups to solve problems?

• Don’t ask students to work in groups for straightforward problems that most students could solve independently in a short amount of time.
• Do have students work in groups for thought-provoking problems, where students will benefit from meaningful collaboration.
• Even in cases where you plan to have students work in groups, it can be useful to give students some time to work on their own before collaborating with others.  This ensures that every student engages with the problem and is ready to contribute to a discussion.

What are some benefits of having students work in groups?

• Students bring different strengths, different knowledge, and different ideas for how to solve a problem; collaboration can help students work through problems that are more challenging than they might be able to tackle on their own.
• In working in a group, students might consider multiple ways to approach a problem, thus enriching their repertoire of strategies.
• Students who think they understand the material will gain a deeper understanding by explaining concepts to their peers.

What are some strategies for helping students to form groups?  

• Instruct students to work with the person (or people) sitting next to them.
• Count off.  (e.g. 1, 2, 3, 4; all the 1’s find each other and form a group, etc)
• Hand out playing cards; students need to find the person with the same number card. (There are many variants to this.  For example, you can print pictures of images that go together [rain and umbrella]; each person gets a card and needs to find their partner[s].)
• Based on what you know about the students, assign groups in advance. List the groups on the board.
• Note: Always have students take the time to introduce themselves to each other in a new group.

What should you do while your students are working on problems?

• Walk around and talk to students. Observing their work gives you a sense of what people understand and what they are struggling with. Answer students’ questions, and ask them questions that lead in a productive direction if they are stuck.
• If you discover that many people have the same question—or that someone has a misunderstanding that others might have—you might stop everyone and discuss a key idea with the entire class.

After students work on a problem during class, what are strategies to have them share their answers and their thinking?

• Ask for volunteers to share answers. Depending on the nature of the problem, student might provide answers verbally or by writing on the board. As a variant, for questions where a variety of answers are relevant, ask for at least three volunteers before anyone shares their ideas.
• Use online polling software for students to respond to a multiple-choice question anonymously.
• If students are working in groups, assign reporters ahead of time. For example, the person with the next birthday could be responsible for sharing their group’s work with the class.
• Cold call. To reduce student anxiety about cold calling, it can help to identify students who seem to have the correct answer as you were walking around the class and checking in on their progress solving the assigned problem. You may even want to warn the student ahead of time: "This is a great answer! Do you mind if I call on you when we come back together as a class?"
• Have students write an answer on a notecard that they turn in to you.  If your goal is to understand whether students in general solved a problem correctly, the notecards could be submitted anonymously; if you wish to assess individual students’ work, you would want to ask students to put their names on their notecard.  
• Use a jigsaw strategy, where you rearrange groups such that each new group is comprised of people who came from different initial groups and had solved different problems.  Students now are responsible for teaching the other students in their new group how to solve their problem.
• Have a representative from each group explain their problem to the class.
• Have a representative from each group draw or write the answer on the board.

What happens if a student gives a wrong answer?

• Ask for their reasoning so that you can understand where they went wrong.
• Ask if anyone else has other ideas. You can also ask this sometimes when an answer is right.
• Cultivate an environment where it’s okay to be wrong. Emphasize that you are all learning together, and that you learn through making mistakes.
• Do make sure that you clarify what the correct answer is before moving on.
• Once the correct answer is given, go through some answer-checking techniques that can distinguish between correct and incorrect answers. This can help prepare students to verify their future work.

How can you make your classroom inclusive?

• The goal is that everyone is thinking, talking, and sharing their ideas, and that everyone feels valued and respected. Use a variety of teaching strategies (independent work and group work; allow students to talk to each other before they talk to the class). Create an environment where it is normal to struggle and make mistakes.
• See Kimberly Tanner’s article on strategies to promoste student engagement and cultivate classroom equity. 

A few final notes…

• Make sure that you have worked all of the problems and also thought about alternative approaches to solving them.
• Board work matters. You should have a plan beforehand of what you will write on the board, where, when, what needs to be added, and what can be erased when. If students are going to write their answers on the board, you need to also have a plan for making sure that everyone gets to the correct answer. Students will copy what is on the board and use it as their notes for later study, so correct and logical information must be written there.

For more information...

Tipsheet: Problem Solving in STEM Sections

Tanner, K. D. (2013). Structure matters: twenty-one teaching strategies to promote student engagement and cultivate classroom equity . CBE-Life Sciences Education, 12(3), 322-331.

• Designing Your Course
• A Teaching Timeline: From Pre-Term Planning to the Final Exam
• The First Day of Class
• Group Agreements
• Classroom Debate
• Flipped Classrooms
• Leading Discussions
• Polling & Clickers
• Teaching with Cases
• Engaged Scholarship
• Devices in the Classroom
• Beyond the Classroom
• On Professionalism
• Getting Feedback
• Equitable & Inclusive Teaching
• Advising and Mentoring
• Teaching and Your Career
• Teaching Remotely
• Tools and Platforms
• The Science of Learning
• Bok Publications
• Other Resources Around Campus

18 Problem-Based Learning Examples

Problem-based learning (PBL) is a student-centered teaching method where students are given the opportunity to solve open-ended real-world problems. The teacher provides limited guidance and is usually referred to as a “facilitator”.

The burden of responsibility for the majority of the work rests squarely on the shoulders of the students.

Problem-Based Learning Examples

• Broad problem posing: A teacher writes the question on the board: “Are organic fertilizers better than commercial fertilizers?” The question is purposively broad and requires student teams to clarify the question before even beginning to address it.
• Solving problems through inquiry: Problem-based learning has strong overlaps with inquiry based learning, where the teacher presents a problem and the students must develop a study to inquire about answers.
• Divergent thinking problems: Students in the first grade have to create a way to communicate with another group without speaking if both are lost in a forest.
• Product development: The professor of a Design course has student teams create product packaging that complies with rigorous environmental standards.
• Real-life problem solving: Students in second grade are given the task of studying the causes of potholes and creating ways to fill them.  
• Role playing a problem: IT majors play the role of government compliance officers and evaluate various social media apps regarding free-speech and privacy regulations.
• Solving real-life mathematical problems: Fourth graders use math to estimate crop yields of a hypothetical farm and then represent the results graphically.
• Multidisciplinary problem solving: Business majors work with students in a nutrition course to create a pizzeria franchise.
• Authentic learning scenarios: Medical students are given a clinical scenario that includes the patient’s chart, X-rays and results of various tests. They work in groups to diagnosis the patient’s disease and design a treatment program.
• Solving hypothetical problems: Anthropology students create a public holiday for an underserved class or people in a foreign country.
• Solving social problems: Students in a Civil Engineering course have to design housing for the poor in an isolated region using only local materials.
• Escape rooms: The popular trend of escape rooms can be seen as a form of problem-based learning. Learners must solve the problem of ‘how to escape’.
• Solving a riddle: The teacher presents students with a riddle, which they must work together to solve. This may require the application of curriculum-based outcomes like using certain math equations.
• Situated learning: Students work on problems in the workplace or ‘real life’ rather than in the classroom, helping them to see how the theory gets applied in a real world context.
• Turning exams into challenges: Instead of using paper-based exams, the teacher poses a challenge and the students need to present a report on the solution to the challenge.
• Creating an app: Students in a university programming class don’t just demonstrate their knowledge of programming; they have to create an app that solves a real-life problem.
• Developing an environmental regeneration plan: Students identify problems with the current ecosystem and then create a plan to solve the problem. Next, they can actually put the plan into action and report on results.
• Working on a social problem: Students are presented with a social problem that can be solved through policy. Students must come up with a social policy that maximizes benefits while also working through potential side-effects and collateral of an intervention.

Benefits of Problem Based Learning

There are numerous benefits of PBL for students. According to Nilson (2010), PBL promotes:

• development of critical thinking skills
• problem-solving abilities
• communication skills
• how to handle project management demands
• oral and written communication
• researching and information literacy
• self-awareness
• understanding of group dynamics
• leadership and teamwork
• self-directed learning

Case Studies

1. invasive species.

Students in environmental studies are given a problem-based assignment on an invasive species. The teacher provides a little early support as possible, simply instructing each group to identify the species and develop an action plan to mitigate its impact.

The students form work teams and conduct a brainstorming session on which invasive species exist in a nearby habitat. Then they examine the impact of the species in great detail, identifying the origin of the species, how it effects other plant and wildlife, human activities connected to the problem, and trajectories of consequences in the future.

Once that thorough analysis has occurred, students then begin exploring possible solutions. They have to construct a detailed plan of action and carefully consider the short and long-term effects of each step.

The plan should include government policy, educational programs, and scientific research programs that should be put in place to monitor their plan’s results.

2. Collaborative PBL: Home for the Handicapped

Real-world problems often require an interdisciplinary approach. That means professionals from different backgrounds and perspectives have to collaborate, which is sometimes easier said than done.

In this project, architecture and product design students have to work together to design a house suitable for the handicapped. This means that the floorplan must be easily navigated and that furniture and appliances have to be modified.

The project can be as demanding as the instructors require, from simply making the plans on paper, to actually constructing mock-ups of products and having them tested by affected individuals.

3. Cybersecurity

Issues related to cybersecurity as a result of globalization and technological dependence continue to escalate. Therefore, in addition to teaching future programmers about how to write gaming code, students also need to develop expertise in more serious issues.

Cybersecurity presents an opportunity for students to work in teams on a real-world issue that can have serious consequences. Students are assigned to develop a protocol to protect a nuclear reactor or financial depository.

The programs they design have to be able to handle a variety of potential threats, both internal and external. To make the assignment more realistic, the instructor will activate several programs designed to attack the organization the students are supposed to protect.

Not only do the students need to create programs that defend the organization, but they also must devise protocols to activate in case of a successful breach.

4. Design a Board Game

Students are eager to express their creativity and enjoy working independent of a lot of rules and restrictions. These characteristics are well-suited for PBL activities and result in greater student engagement and deep learning.

Recognizing these features of PBL has led to one teacher giving the students the task of designing their own board game. The facilitator/teacher leaves everything up to the students, and only supplies a set of dice.

The students then hold a class-wide brainstorming session on possible game themes. Once a list is generated, they divide up into teams based on common interests. The facilitator distributes the dice to each group and then steps aside.

The students then get to work on formulating the rules of the game and working out the process of how to play. Eventually they get to the point of being ready to construct a game prototype.

At the end, each team gets to play each other’s games and then engage in a reflection activity. Reflection can involve a worksheet or class discussion, as students consider their performance in the task and key learning outcomes they may have experienced.

5. Increasing Voter Registration

Voter turnout has been low in the U.S. for quite some time. For a democracy, this is not only a problem of people’s voices not being heard, but it can reflect feelings of disappointment in the political process as well.

To address these issues, students in a political science course must work together to understand the issues impacting low voter turnout and devise an action plan to address those factors.

The students start by researching the causal factors through a variety of methods. They might read the relevant literature on the subject, and/or conduct interviews and surveys involving non-voters.

By thoroughly understanding the issues, they can then formulate a plan to encourage voter turnout. That plan is completely up to them. It is important that the facilitator/course instructor provide as little intervention or assistance as possible.

Problem-based learning is a great way for students to learn. Instead of reading a textbook, writing term papers, or listening to hours of lectures, student take an active role in the learning process.

It starts with the instructor, referred to as a facilitator, simply presenting an open-ended problem in a real-world scenario. The students are then given an opportunity to work collaboratively to examine the problem and develop a solution.

Students benefit from this type of learning activity in numerous ways. They learn how to work with others, gain experience and insights into leadership and group dynamics, and develop critical thinking and problem-solving skills.

But perhaps the most significant benefit, is that students become more engaged and enthusiastic about the learning process.

Ali, S. S. (2019). Problem based learning: A student-centered approach. English language teaching , 12(5), 73-78.

Duch, B. J., Groh, S. E, & Allen, D. E. (Eds.). (2001). The power of problem-based learning . Sterling, VA: Stylus.

Hmelo-Silver, C.E., Eberbach, C. (2012). Learning theories and problem-based learning. In: Bridges, S., McGrath, C., Whitehill, T. (Eds.), Problem-based learning in clinical education (pp. 3-17). Innovation and Change in Professional Education, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2515-7_1

Malmia, W., et al. (2019). Problem-based learning as an effort to improve student learning outcomes. Int. J. Sci. Technol. Res, 8 (9), 1140-1143.

Moust, J., Bouhuijs, P., & Schmidt, H. (2021). Introduction to problem-based learning: A guide for students. London: Routledge.

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

Wirkala, C., & Kuhn, D. (2011). Problem-based learning in K–12 education: Is it effective and how does it achieve its effects? American Educational Research Journal, 48 (5), 1157–1186. https://doi.org/10.3102/0002831211419491

Dave Cornell (PhD)

Dr. Cornell has worked in education for more than 20 years. His work has involved designing teacher certification for Trinity College in London and in-service training for state governments in the United States. He has trained kindergarten teachers in 8 countries and helped businessmen and women open baby centers and kindergartens in 3 countries.

• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 25 Positive Punishment Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 25 Dissociation Examples (Psychology)
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 15 Zone of Proximal Development Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ Perception Checking: 15 Examples and Definition

Chris Drew (PhD)

This article was peer-reviewed and edited by Chris Drew (PhD). The review process on Helpful Professor involves having a PhD level expert fact check, edit, and contribute to articles. Reviewers ensure all content reflects expert academic consensus and is backed up with reference to academic studies. Dr. Drew has published over 20 academic articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education and holds a PhD in Education from ACU.

• Chris Drew (PhD) #molongui-disabled-link 25 Positive Punishment Examples
• Chris Drew (PhD) #molongui-disabled-link 25 Dissociation Examples (Psychology)
• Chris Drew (PhD) #molongui-disabled-link 15 Zone of Proximal Development Examples
• Chris Drew (PhD) #molongui-disabled-link Perception Checking: 15 Examples and Definition

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5 Teaching Mathematics Through Problem Solving

Janet Stramel

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.

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

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

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?

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

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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6 Tips for Teaching Math Problem-Solving Skills

Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

A growing concern with students is the ability to problem-solve, especially with complex, multistep problems. Data shows that students struggle more when solving word problems than they do with computation , and so problem-solving should be considered separately from computation. Why?

Consider this. When we’re on the way to a new destination and we plug in our location to a map on our phone, it tells us what lane to be in and takes us around any detours or collisions, sometimes even buzzing our watch to remind us to turn. When I experience this as a driver, I don’t have to do the thinking. I can think about what I’m going to cook for dinner, not paying much attention to my surroundings other than to follow those directions. If I were to be asked to go there again, I wouldn’t be able to remember, and I would again seek help.

If we can switch to giving students strategies that require them to think instead of giving them too much support throughout the journey to the answer, we may be able to give them the ability to learn the skills to read a map and have several ways to get there.

Here are six ways we can start letting students do this thinking so that they can go through rigorous problem-solving again and again, paving their own way to the solution. 

1. Link problem-solving to reading

When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools like counters or base 10 blocks, drawing a quick sketch of the problem, retelling the story in their own words, etc., can really help them to utilize the skills they already have to make the task less daunting.

We can break these skills into specific short lessons so students have a bank of strategies to try on their own. Here's an example of an anchor chart that they can use for visualizing . Breaking up comprehension into specific skills can increase student independence and help teachers to be much more targeted in their problem-solving instruction. This allows students to build confidence and break down the barriers between reading and math to see they already have so many strengths that are transferable to all problems.

2. Avoid boxing students into choosing a specific operation

It can be so tempting to tell students to look for certain words that might mean a certain operation. This might even be thoroughly successful in kindergarten and first grade, but just like when our map tells us where to go, that limits students from becoming deep thinkers. It also expires once they get into the upper grades, where those words could be in a problem multiple times, creating more confusion when students are trying to follow a rule that may not exist in every problem.

We can encourage a variety of ways to solve problems instead of choosing the operation first. In first grade, a problem might say, “Joceline has 13 stuffed animals and Jordan has 17. How many more does Jordan have?” Some students might choose to subtract, but a lot of students might just count to find the amount in between. If we tell them that “how many more” means to subtract, we’re taking the thinking out of the problem altogether, allowing them to go on autopilot without truly solving the problem or using their comprehension skills to visualize it. 

3. Revisit ‘representation’

The word “representation” can be misleading. It seems like something to do after the process of solving. When students think they have to go straight to solving, they may not realize that they need a step in between to be able to support their understanding of what’s actually happening in the problem first.

Using an anchor chart like one of these ( lower grade , upper grade ) can help students to choose a representation that most closely matches what they’re visualizing in their mind. Once they sketch it out, it can give them a clearer picture of different ways they could solve the problem.

Think about this problem: “Varush went on a trip with his family to his grandmother’s house. It was 710 miles away. On the way there, three people took turns driving. His mom drove 214 miles. His dad drove 358 miles. His older sister drove the rest. How many miles did his sister drive?”

If we were to show this student the anchor chart, they would probably choose a number line or a strip diagram to help them understand what’s happening.

If we tell students they must always draw base 10 blocks in a place value chart, that doesn’t necessarily match the concept of this problem. When we ask students to match our way of thinking, we rob them of critical thinking practice and sometimes confuse them in the process. 

4. Give time to process

Sometimes as educators, we can feel rushed to get to everyone and everything that’s required. When solving a complex problem, students need time to just sit with a problem and wrestle with it, maybe even leaving it and coming back to it after a period of time.

This might mean we need to give them fewer problems but go deeper with those problems we give them. We can also speed up processing time when we allow for collaboration and talk time with peers on problem-solving tasks. 

5. Ask questions that let Students do the thinking

Questions or prompts during problem-solving should be very open-ended to promote thinking. Telling a student to reread the problem or to think about what tools or resources would help them solve it is a way to get them to try something new but not take over their thinking.

These skills are also transferable across content, and students will be reminded, “Good readers and mathematicians reread.” 

6. Spiral concepts so students frequently use problem-solving skills

When students don’t have to switch gears in between concepts, they’re not truly using deep problem-solving skills. They already kind of know what operation it might be or that it’s something they have at the forefront of their mind from recent learning. Being intentional within their learning stations and assessments about having a variety of rigorous problem-solving skills will refine their critical thinking abilities while building more and more resilience throughout the school year as they retain content learning in the process. 

Problem-solving skills are so abstract, and it can be tough to pinpoint exactly what students need. Sometimes we have to go slow to go fast. Slowing down and helping students have tools when they get stuck and enabling them to be critical thinkers will prepare them for life and allow them multiple ways to get to their own destination.

Teaching Problem Solving in Math

• Freebies , Math , Planning

Every year my students can be fantastic at math…until they start to see math with words. For some reason, once math gets translated into reading, even my best readers start to panic. There is just something about word problems, or problem-solving, that causes children to think they don’t know how to complete them.

Every year in math, I start off by teaching my students problem-solving skills and strategies. Every year they moan and groan that they know them. Every year – paragraph one above. It was a vicious cycle. I needed something new.

I put together a problem-solving unit that would focus a bit more on strategies and steps in hopes that that would create problem-solving stars.

The Problem Solving Strategies

First, I wanted to make sure my students all learned the different strategies to solve problems, such as guess-and-check, using visuals (draw a picture, act it out, and modeling it), working backward, and organizational methods (tables, charts, and lists). In the past, I had used worksheet pages that would introduce one and provide the students with plenty of problems practicing that one strategy. I did like that because students could focus more on practicing the strategy itself, but I also wanted students to know when to use it, too, so I made sure they had both to practice.

I provided students with plenty of practice of the strategies, such as in this guess-and-check game.

There’s also this visuals strategy wheel practice.

I also provided them with paper dolls and a variety of clothing to create an organized list to determine just how many outfits their “friend” would have.

Then, as I said above, we practiced in a variety of ways to make sure we knew exactly when to use them. I really wanted to make sure they had this down!

Anyway, after I knew they had down the various strategies and when to use them, then we went into the actual problem-solving steps.

The Problem Solving Steps

I wanted students to understand that when they see a story problem, it isn’t scary. Really, it’s just the equation written out in words in a real-life situation. Then, I provided them with the “keys to success.”

S tep 1 – Understand the Problem.   To help students understand the problem, I provided them with sample problems, and together we did five important things:

• read the problem carefully
• restated the problem in our own words
• crossed out unimportant information
• circled any important information
• stated the goal or question to be solved

We did this over and over with example problems.

Once I felt the students had it down, we practiced it in a game of problem-solving relay. Students raced one another to see how quickly they could get down to the nitty-gritty of the word problems. We weren’t solving the problems – yet.

Then, we were on to Step 2 – Make a Plan . We talked about how this was where we were going to choose which strategy we were going to use. We also discussed how this was where we were going to figure out what operation to use. I taught the students Sheila Melton’s operation concept map.

We talked about how if you know the total and know if it is equal or not, that will determine what operation you are doing. So, we took an example problem, such as:

Sheldon wants to make a cupcake for each of his 28 classmates. He can make 7 cupcakes with one box of cupcake mix. How many boxes will he need to buy?

We started off by asking ourselves, “Do we know the total?” We know there are a total of 28 classmates. So, yes, we are separating. Then, we ask, “Is it equal?” Yes, he wants to make a cupcake for EACH of his classmates. So, we are dividing: 28 divided by 7 = 4. He will need to buy 4 boxes. (I actually went ahead and solved it here – which is the next step, too.)

Step 3 – Solving the problem . We talked about how solving the problem involves the following:

• taking our time
• working the problem out
• showing all our work
• estimating the answer
• using thinking strategies

We talked specifically about thinking strategies. Just like in reading, there are thinking strategies in math. I wanted students to be aware that sometimes when we are working on a problem, a particular strategy may not be working, and we may need to switch strategies. We also discussed that sometimes we may need to rethink the problem, to think of related content, or to even start over. We discussed these thinking strategies:

• switch strategies or try a different one
• rethink the problem
• think of related content
• decide if you need to make changes
• check your work
• but most important…don’t give up!

To make sure they were getting in practice utilizing these thinking strategies, I gave each group chart paper with a letter from a fellow “student” (not a real student), and they had to give advice on how to help them solve their problem using the thinking strategies above.

Finally, Step 4 – Check It.   This is the step that students often miss. I wanted to emphasize just how important it is! I went over it with them, discussing that when they check their problems, they should always look for these things:

• compare your answer to your estimate
• check for reasonableness
• check your calculations
• add the units
• restate the question in the answer
• explain how you solved the problem

Then, I gave students practice cards. I provided them with example cards of “students” who had completed their assignments already, and I wanted them to be the teacher. They needed to check the work and make sure it was completed correctly. If it wasn’t, then they needed to tell what they missed and correct it.

To demonstrate their understanding of the entire unit, we completed an adorable lap book (my first time ever putting together one or even creating one – I was surprised how well it turned out, actually). It was a great way to put everything we discussed in there.

Once we were all done, students were officially Problem Solving S.T.A.R.S. I just reminded students frequently of this acronym.

Stop – Don’t rush with any solution; just take your time and look everything over.

Think – Take your time to think about the problem and solution.

Act  – Act on a strategy and try it out.

Review – Look it over and see if you got all the parts.

Wow, you are a true trooper sticking it out in this lengthy post! To sum up the majority of what I have written here, I have some problem-solving bookmarks FREE to help you remember and to help your students!

You can grab these problem-solving bookmarks for FREE by clicking here .

You can do any of these ideas without having to purchase anything. However, if you are looking to save some time and energy, then they are all found in my Math Workshop Problem Solving Unit . The unit is for grade three, but it  may work for other grade levels. The practice problems are all for the early third-grade level.

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Promising Practices in Undergraduate Science, Technology, Engineering, and Mathematics Education: Summary of Two Workshops (2011)

Chapter: 4 scenario-, problem-, and case-based teaching and learning, 4 scenario-, problem-, and case-based teaching and learning.

The primary purpose of the October workshop was to thoughtfully examine the evidence behind a select set of promising practices that came to light during the June workshop. Susan Singer opened the October workshop by linking its agenda to key themes of the June workshop (see Chapter 3 ). Although these practices are not perfect and do not represent the universe of evidence-based innovations, she said, they are recognized by experts as promising, and each is supported by some evidence.

The promising practices discussed include scenario-, problem-, and case-based teaching and learning (this chapter); assessments to guide teaching and learning ( Chapter 5 ); efforts to restructure the learning environment ( Chapter 6 ); and faculty professional development ( Chapter 7 ). Singer explained that the presentations were based on papers prepared following a template the steering committee developed after the June workshop. 1 The authors were asked to describe the context in which the promising practice was implemented, identify examples of how the practice was used, and provide evidence to support the claim that the practice was promising, including evidence of its impact or efficacy.

FIGURE 4-1 Problem-based learning.

SOURCE: Gijbels (2008). Reprinted with permission. Problem

PROBLEM-BASED LEARNING

David Gijbels (University of Antwerp) described the cycle of problem-based learning (see Figure 4-1 ). After the instructors present a problem to the class, students meet in small groups to discuss what they know about it and what they need to learn. During a short period of independent self-study, students gather the needed resources to solve the problem. They then reconvene their small groups to re-assess their collective understanding of the problem. When they solve the problem, the instructor provides a different problem and the cycle begins anew.

Noting that problem-based learning has many possible definitions and permutations, Gijbels nonetheless stressed the importance of identifying a core set of principles that characterize this type of learning. Having a core definition enables researchers to compare problem-based learning with other types of learning environments. In his research, Gijbels uses a model developed by Howard Barrows (1996) that identifies six characteristics of problem-based learning:

Student-centered learning.

Small groups.

Tutor as a facilitator or guide.

Problems first.

The problem is the tool to achieve knowledge and problem-solving skills.

Self-directed learning.

Gijbels then described a meta-analysis conducted to examine the effects of problem-based learning on students’ knowledge and their application of knowledge, and to identify factors that mediated those effects (Dochy et al., 2003). The meta-analysis focused on empirical studies that compared problem-based learning with lecture-based education in postsecondary classrooms in Europe, and almost all of the studies that met the criteria focused on medical education. 2 Through the analysis, Gijbels and his colleagues found the following:

Students’ content knowledge was slightly lower in problem-based learning courses than in traditional lecture courses.

Although students in problem-based learning environments demonstrated less knowledge in the short term, they retained more knowledge over the long term.

Students in problem-based learning settings were better able to apply their knowledge than students in traditional courses.

These findings prompted Gijbels and his colleagues to undertake a deeper analysis of the assessment of problem-based learning (Gijbels et al., 2005). That analysis focused on three levels of knowledge that were assessed in the selected studies: (1) knowledge of concepts, (2) understanding of principles that link concepts, and (3) the application of knowledge. Gijbels noted that of the 56 studies in the analysis, 31 focused on concepts, 17 focused on principles, and 8 focused on the application of knowledge. The analysis revealed the following:

Students in problem-based learning environments and traditional lecture-based learning environments exhibited no differences in the understanding of concepts.

Students in problem-based learning environments had a deeper understanding of principles that link concepts together.

Students in problem-based learning environments demonstrated a slightly better ability to apply their knowledge than students in lecture-based classes.

Gijbels concluded by stating that problem-based learning has not completely fulfilled its potential. He suggested that students might become better problem solvers if faculty members assessed them more on problem solving. Noting that students often do not develop a sense of shared cognition when working in teams in problem-based learning environments, he also stressed the importance of attending to group developmental processes when implementing problem-based learning.

CASE-BASED TEACHING

Mary Lundeberg (Michigan State University) defined some key elements of case-based teaching. In the paper she wrote for the workshop (Lundeberg, 2008, p. 1), she said:

Cases involve an authentic portrayal of a person(s) in a complex situation(s) constructed for particular pedagogical purposes. Two features are essential: interactions involving explanations, and challenges to student thinking. Interactions involving explanations could occur among student teams, the instructor and a class; among distant colleagues; or students constructing interpretations in a multimedia environment. Cases may challenge students’ thinking in many ways, e.g., applying concepts to a real life situation; connecting concepts [and/or] interdisciplinary ideas; examining a situation from multiple perspectives; reflecting on how one approaches or solves a problem; making decisions; designing projects; considering ethical dimensions of situations. Brief vignettes, quick examples, or unedited documents are not cases.

She presented four examples to illustrate the wide range of cases that might be used in undergraduate science, technology, engineering, and mathematics (STEM) education: 3

The Deforestation of the Amazon: A Case Study in Understanding Ecosystems and Their Value, a problem-based case used in a biology seminar for nonmajors.

Cross-Dressing or Crossing-Over: Sex Testing of Women Athletes, a historical case used in large lecture courses with clicker technology (handheld wireless devices through which students register their responses to multiple-choice questions that are projected on a screen).

Case It!, in-depth problem-based multimedia cases used in biology labs.

Project-based scenarios used in engineering.

Citing the National Research Council (2002), Lundeberg identified three types of research questions often investigated in studies of educational activities—those that focus on description, cause, and process. She explained that there is much more descriptive research (i.e., faculty and student perceptions of what is happening) than research showing causal effects or describing the process of learning.

Lundeberg described the research that she and her colleagues have conducted on case-based learning. The descriptive aspects of their research involved surveys of 101 faculty members in 23 states and Canada who were using cases from the National Center on Case Study Teaching and Science (see http://library.buffalo.edu/libraries/projects/cases/case.html ). On the surveys, faculty members reported that cases make students more engaged and active learners and help them to develop multiple perspectives, gain deeper conceptual understanding, engage in critical thinking, enhance their communications skills, and develop positive peer relationships (Lundeberg, 2008). Lundeberg also reported that faculty members cited the increased time needed to prepare lessons and assess students as obstacles to implementing case-based learning.

To identify the systematic effects of case-based learning, Lundeberg and her colleagues conducted a year-long study of the use of cases in large undergraduate biology classes equipped with clickers. The study combined a design involving random assignment to experimental and control groups with an A-B-A-B design in which 12 participating faculty members alternated the use of cases and lectures systematically across two semesters. They found that “students (n = 4,366) who responded to cases using ‘clicker’ technology performed significantly better than their peers on five of the eight biology topics (cells, Mendelian genetics, cellular division, scientific method, and cancer), and in five of the eight areas in which they were asked to transfer information (cells, cellular division, scientific method, microevolution and DNA)” (Lundeberg, 2008, p. 8).

Students in the clicker classes also performed significantly better on tests of data interpretation than students in lecture classes. However, students who used cases with clicker technology showed no difference or lower effects on standardized tests measuring accumulated medical knowledge, on one topic in biology (characteristics of life), and on standardized tests of critical thinking.

Lundeberg argued that cases are effective for several reasons. First, stories are a powerful mechanism for organizing and storing information. In addition, the real-life context engages students. Cases also challenge students’ thinking and require them to integrate knowledge, reflect on their ideas, and articulate them. Lundeberg noted that role-playing during case-based education engages students and enables them to consider multiple perspectives.

In closing, Lundeberg reiterated that cases have an impact on understanding, scientific thinking, and engagement. She cited the need for more multiyear, mixed-methods studies on the effectiveness of case-based teaching, particularly classroom experiments that do not confound instructor or student effects. She also identified several gaps in the knowledge base at the undergraduate level: Which students benefit from cases? What content is most suitable? What benefits do different types of cases afford? What kinds of interaction between students and faculty matter? Do cases promote scientific literacy?

USE OF COMPLEX PROBLEMS IN TEACHING PHYSICS

Tom Foster (Southern Illinois University) discussed the use of complex problems in teaching physics. He explained that complex problems are rooted in cooperative group problem solving, which is characterized by the following traits (Foster, 2008):

positive interdependence among group members;

individual accountability;

monitoring of interpersonal skills;

frequent processing of group interactions and functioning; and

aspects of the task or learning activity that require ongoing conversation, dialogue, exchange, and support.

Foster emphasized the importance of designing the appropriate task in using this teaching method. He noted that if the problems are simple enough to be solved moderately well alone, students will not abandon their independence to work in a group. Students also will not abandon their independence if the problems are too complex for the group to initially succeed in solving them.

Context-rich problems are one example of an appropriate task for group problem solving. Foster creates such problems by converting traditional end-of-chapter problems into complex problems that students solve cooperatively, placing students in the problem by using the word “you.” Foster and his colleagues prefer not to include pictures in the problem, as a way of encouraging the group to decide whether and how to illustrate it. According to Foster, context-rich problems also provide many other decision points to foster ongoing interaction among group members. For example, problems might include extra information, omit information, or leave variables unnamed. These problems also “hide the physics” by avoiding technical terms and focusing on real-world settings. By hiding the physics, the problems demonstrate that the world is rich in physics and require students to determine which fundamental physical principles to apply (Foster, 2008).

In physics, context-rich problems are closed-ended, meaning that there is essentially one correct answer that is dictated by the rules of mathematics and physics. Even though they are closed-ended, the problems still require creativity to define and apply the correct principles and equations. Citing Schwartz, Bransford, and Sears (2005), Foster said that this balance between effectiveness and innovation is vital to the transfer of knowledge from one situation to another.

Foster noted that context-rich problems are an excellent way to challenge students’ misconceptions about problem solving. For example, students often believe that the aim of solving a physics problem is to reduce it to a mathematical exercise, and that it is always necessary to use all the information in a problem. Faculty members can address these misconceptions by structuring the problems differently, as described in previous paragraphs.

In Foster’s experience, it is easy to make context-rich problems too difficult. He and his colleagues have developed a set of 21 “difficulty traits” that fall into the broad categories of approach, analysis of the problem, and mathematical solution. Faculty members can use the traits as a checklist to design context-rich problems and to assess and adjust their level of difficulty.

Turning to the evidence, Foster explained that he uses traditional instruments, such as the Force Concept Inventory and conceptual surveys on electricity and magnetism, to measure students’ concept development. He has found that students who solve context-rich problems in cooperative group settings score as well on these measures as their peers who are taught using other interactive methods. To assess problem solving, Foster uses a rubric developed at the University of Minnesota that includes five dimensions: (1) description of the problem, (2) physics approach (i.e., whether students used the correct physics), (3) specific application of the physics, (4) mathematical procedures, and (5) logical progression. Foster reported that students’ problem-solving abilities improve through the use of context-rich problems, but he cautioned that the method does not result in quantum leaps in problem-solving abilities. Foster called his evidence on students’ attitudes and behaviors about context-rich problems anecdotal but positive.

He closed by identifying future directions for this method of physics instruction. Citing the need to create more context-rich problems in physics, he mentioned problems that begin with an answer and require the formulation of a question (such as on the television show “Jeopardy!”) as well as problems in which students identify and correct errors. He also stressed the importance of developing context-rich problems outside physics to assess the transfer of knowledge from one domain to another.

Remarking on the differences in terminology across disciplines, Karen Cummings (Southern Connecticut State University) observed that these differences pose a challenge for researchers. She asked Gijbels how he distinguished between knowledge of concepts and application of knowledge in his study. Gijbels agreed and explained that for his review of the literature he examined actual assessment questions to determine what type of knowledge they were assessing. Lundeberg added that it was a challenge for the faculty members in her study to develop assessments that measure higher order thinking, because it is easier for them to write questions that focus on definitions and conceptual knowledge.

Martha Narro (University of Arizona) asked Gijbels to clarify some of the findings that he discussed in his presentation. He explained that, across studies that assessed student learning of concepts, there was no significant difference between students in problem-based and traditional settings. Across studies that assessed student learning of principles and application of conceptual knowledge, however, students in problem-based environments performed better. He also pointed out that the findings varied depending on the context (specifically, whether the students were in their first or last year of medical school) and the curriculum, and that he was reporting on the overall trends in the data.

Responding to another question, Lundeberg and Foster discussed the issue of relevance when constructing scenarios, problems, and cases. They agreed that there is very little research on what it means to be relevant. Lundeberg related several examples of cases that faculty members designed to be relevant but that did not resonate with students. In her experience, allowing students to design their own cases is a powerful way to make the cases relevant. Foster added that many college students are still developing their identities, which makes the notion of relevance more challenging. An audience member, referring to a paper by Mayberry (1998) about pedagogies that encourage students to develop their own sense of science, cautioned faculty members to be careful about coming across as knowing more than students about what is relevant.

Following another question, the speakers engaged in a discussion about the importance of longitudinal research to understand the longer term impact of these pedagogical strategies. Lundeberg mentioned some examples of longitudinal studies of innovative instructional strategies that show mixed results. Foster added that it is difficult to measure long-term knowledge or to trace it back to its origins. As an example, he said that although students might not demonstrate understanding of a concept after a certain

course, the exposure they gained to that concept might facilitate later learning. In that situation, the initial course had an effect that is impossible to measure. The panelists noted that longitudinal research is important, difficult to conduct, difficult to fund, and relatively rare.

Numerous teaching, learning, assessment, and institutional innovations in undergraduate science, technology, engineering, and mathematics (STEM) education have emerged in the past decade. Because virtually all of these innovations have been developed independently of one another, their goals and purposes vary widely. Some focus on making science accessible and meaningful to the vast majority of students who will not pursue STEM majors or careers; others aim to increase the diversity of students who enroll and succeed in STEM courses and programs; still other efforts focus on reforming the overall curriculum in specific disciplines. In addition to this variation in focus, these innovations have been implemented at scales that range from individual classrooms to entire departments or institutions.

By 2008, partly because of this wide variability, it was apparent that little was known about the feasibility of replicating individual innovations or about their potential for broader impact beyond the specific contexts in which they were created. The research base on innovations in undergraduate STEM education was expanding rapidly, but the process of synthesizing that knowledge base had not yet begun. If future investments were to be informed by the past, then the field clearly needed a retrospective look at the ways in which earlier innovations had influenced undergraduate STEM education.

To address this need, the National Research Council (NRC) convened two public workshops to examine the impact and effectiveness of selected STEM undergraduate education innovations. This volume summarizes the workshops, which addressed such topics as the link between learning goals and evidence; promising practices at the individual faculty and institutional levels; classroom-based promising practices; and professional development for graduate students, new faculty, and veteran faculty. The workshops concluded with a broader examination of the barriers and opportunities associated with systemic change.

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44 Powerful Instructional Strategies Examples for Every Classroom

So many ways to help students learn!

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

What are instructional strategies?

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

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

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

Direct Instruction Instructional Strategies Examples

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

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

Didactic Questioning

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

Demonstration

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

Drill & Practice

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

Indirect Instruction Instructional Strategies Examples

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

Problem-Solving

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

Project-Based Learning

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

Learn more: What Is Project-Based Learning?

Concept Mapping

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

Case Studies

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

Reading for Meaning

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

Flipped Classroom

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

Learn more: What Is a Flipped Classroom?

Experiential Learning Instructional Strategies Examples

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

Science Experiments

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

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

Field Trips

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

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

Games and Gamification

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

Learn more: Classic Classroom Games and Best Online Educational Games

Service Learning

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

Learn more: What Is Service Learning?

Interactive Instruction Instructional Strategies Examples

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

Peer Instruction

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

Reciprocal Teaching

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

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

Learn more: High School Debate Topics To Challenge Every Student

Class or Small-Group Discussion

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

Learn more: Strategies To Improve Classroom Discussions

Socratic Seminar and Fishbowl

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

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

Brainstorming

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

Role-Playing

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

Think-Pair-Share

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

Learn more: Think-Pair-Share and Fun Alternatives

Independent Learning Instructional Strategies Examples

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

Learning Centers

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

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

Computer-Based Instruction

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

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

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

Research Projects

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

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

Learn more: The Benefits of Journaling in the Classroom

Play-Based Learning

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

Learn more: What Is Play-Based Learning?

More Instructional Strategies Examples

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

Simulations

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

Storytelling

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

Learn more: Teaching as Storytelling

Scaffolding

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

Learn more: What Is Scaffolding in Education?

Spaced Repetition

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

Graphic Organizers

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

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

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

Multidisciplinary Instruction

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

Interdisciplinary Instruction

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

Differentiated Instruction

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

Learn more: What Is Differentiated Instruction?

Culturally Responsive Teaching

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

Learn more: What Is Culturally Responsive Teaching?

Response to Intervention

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

Learn more: What Is Response to Intervention?

Inquiry-Based Learning

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

Learn more: What Is Inquiry-Based Learning?

Growth Mindset

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

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

Blended Learning

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

Asynchronous (Self-Paced) Learning

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

Learn more: Synchronous vs. Asynchronous Learning

Essential Questions

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

Learn more: Questions That Set a Purpose for Reading

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

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

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

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

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Problem-Solving Method in Teaching

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

Table of Contents

Definition of problem-solving method.

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

Meaning of Problem-Solving Method

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

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

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

Benefits of Problem-Solving Method

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

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

Steps in Problem-Solving Method

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

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

Verification of the concluded solution or Hypothesis

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

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

• 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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Professional Development & Training

What you will learn, tools & materials.

Teaching Methods for Solving Word Problems

This teacher professional development course will teach you about the challenges students often encounter when solving word problems and present varied solutions for teaching problem-solving skills to your students. You will be provided with a detailed plan for teaching two different problem-solving strategies in your classroom, depending on your students' needs: the GUESS method and the CUBES method for word problems. The course also comes with a downloadable PDF of the course content, graphic organizers, and supporting student resources.

• The video and article will provide you with two specific methods for solving word problems and ideas for teaching your students these skills. You will learn about common strategies required for solving word problems and challenges that arise so you can help correct and support your students. The course also includes some “Reflect or Discuss” prompts to help you connect with the course content and ends with a “Try This Task” to guide you explicitly on how you might implement the ideas into the classroom. 
• You will answer questions related to strategies for solving word problems. Quizzes are automatically scored and provide feedback on answer choice rationale. 
• The reflection prompt requires you to plan for use of the “try this task” by either reflecting on the content yourself or discussing them with the colleague. You will then discuss a new concept you can attempt to implement in the future based on something you learned in the course. 
• This short statement helps you reflect on your ideas and assess whether you might be successful in your implementation. 
• Additional content suggestions are provided to enhance and expand your understanding of supporting students in word probably analysis.

Requirements:

Hardware Requirements:

• This course can be taken on either a PC, Mac, or Chromebook.

Software Requirements:

• PC: Windows 10 or later.
• Mac: macOS 10.6 or later.
• Browser: The latest version of Google Chrome or Mozilla Firefox is preferred. Microsoft Edge and Safari are also compatible.
• Microsoft Word Online
• Editing of a Microsoft Word document is required in this course. You may use a free version of Microsoft Word Online, or Google Docs if you do not have Microsoft Office installed on your computer. Model Teaching can provide support for this.
• Adobe Acrobat Reader
• Software must be installed and fully operational before the course begins.
• Email capabilities and access to a personal email account.

Instructional Material Requirements:

The instructional materials required for this course are included in enrollment and will be available online.

Interview Questions

Comprehensive Interview Guide: 60+ Professions Explored in Detail

26 Good Examples of Problem Solving (Interview Answers)

By Biron Clark

Published: November 15, 2023

Employers like to hire people who can solve problems and work well under pressure. A job rarely goes 100% according to plan, so hiring managers will be more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical in your approach.

But how do they measure this?

They’re going to ask you interview questions about these problem solving skills, and they might also look for examples of problem solving on your resume and cover letter. So coming up, I’m going to share a list of examples of problem solving, whether you’re an experienced job seeker or recent graduate.

Then I’ll share sample interview answers to, “Give an example of a time you used logic to solve a problem?”

Problem-Solving Defined

It is the ability to identify the problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation. 

Problem-solving also involves critical thinking, communication, listening, creativity, research, data gathering, risk assessment, continuous learning, decision-making, and other soft and technical skills.

Solving problems not only prevent losses or damages but also boosts self-confidence and reputation when you successfully execute it. The spotlight shines on you when people see you handle issues with ease and savvy despite the challenges. Your ability and potential to be a future leader that can take on more significant roles and tackle bigger setbacks shine through. Problem-solving is a skill you can master by learning from others and acquiring wisdom from their and your own experiences. 

It takes a village to come up with solutions, but a good problem solver can steer the team towards the best choice and implement it to achieve the desired result.

Watch: 26 Good Examples of Problem Solving

Examples of problem solving scenarios in the workplace.

• Correcting a mistake at work, whether it was made by you or someone else
• Overcoming a delay at work through problem solving and communication
• Resolving an issue with a difficult or upset customer
• Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
• Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
• Troubleshooting and resolving technical issues
• Handling and resolving a conflict with a coworker
• Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
• Taking initiative when another team member overlooked or missed something important
• Taking initiative to meet with your superior to discuss a problem before it became potentially worse
• Solving a safety issue at work or reporting the issue to those who could solve it
• Using problem solving abilities to reduce/eliminate a company expense
• Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
• Changing how a process, team, or task is organized to make it more efficient
• Using creative thinking to come up with a solution that the company hasn’t used before
• Performing research to collect data and information to find a new solution to a problem
• Boosting a company or team’s performance by improving some aspect of communication among employees
• Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem Solving Examples for Recent Grads/Entry Level Job Seekers

• Coordinating work between team members in a class project
• Reassigning a missing team member’s work to other group members in a class project
• Adjusting your workflow on a project to accommodate a tight deadline
• Speaking to your professor to get help when you were struggling or unsure about a project
• Asking classmates, peers, or professors for help in an area of struggle
• Talking to your academic advisor to brainstorm solutions to a problem you were facing
• Researching solutions to an academic problem online, via Google or other methods
• Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

You can share all of the examples above when you’re asked questions about problem solving in your interview. As you can see, even if you have no professional work experience, it’s possible to think back to problems and unexpected challenges that you faced in your studies and discuss how you solved them.

Interview Answers to “Give an Example of an Occasion When You Used Logic to Solve a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” since you’re likely to hear this interview question in all sorts of industries.

Example Answer 1:

At my current job, I recently solved a problem where a client was upset about our software pricing. They had misunderstood the sales representative who explained pricing originally, and when their package renewed for its second month, they called to complain about the invoice. I apologized for the confusion and then spoke to our billing team to see what type of solution we could come up with. We decided that the best course of action was to offer a long-term pricing package that would provide a discount. This not only solved the problem but got the customer to agree to a longer-term contract, which means we’ll keep their business for at least one year now, and they’re happy with the pricing. I feel I got the best possible outcome and the way I chose to solve the problem was effective.

Example Answer 2:

In my last job, I had to do quite a bit of problem solving related to our shift scheduling. We had four people quit within a week and the department was severely understaffed. I coordinated a ramp-up of our hiring efforts, I got approval from the department head to offer bonuses for overtime work, and then I found eight employees who were willing to do overtime this month. I think the key problem solving skills here were taking initiative, communicating clearly, and reacting quickly to solve this problem before it became an even bigger issue.

Example Answer 3:

In my current marketing role, my manager asked me to come up with a solution to our declining social media engagement. I assessed our current strategy and recent results, analyzed what some of our top competitors were doing, and then came up with an exact blueprint we could follow this year to emulate our best competitors but also stand out and develop a unique voice as a brand. I feel this is a good example of using logic to solve a problem because it was based on analysis and observation of competitors, rather than guessing or quickly reacting to the situation without reliable data. I always use logic and data to solve problems when possible. The project turned out to be a success and we increased our social media engagement by an average of 82% by the end of the year.

Answering Questions About Problem Solving with the STAR Method

When you answer interview questions about problem solving scenarios, or if you decide to demonstrate your problem solving skills in a cover letter (which is a good idea any time the job description mention problem solving as a necessary skill), I recommend using the STAR method to tell your story.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them. So before jumping in and talking about the problem that needed solving, make sure to describe the general situation. What job/company were you working at? When was this? Then, you can describe the task at hand and the problem that needed solving. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact.

Finally, describe a positive result you got.

Whether you’re answering interview questions about problem solving or writing a cover letter, you should only choose examples where you got a positive result and successfully solved the issue.

Example answer:

Situation : We had an irate client who was a social media influencer and had impossible delivery time demands we could not meet. She spoke negatively about us in her vlog and asked her followers to boycott our products. (Task : To develop an official statement to explain our company’s side, clarify the issue, and prevent it from getting out of hand). Action : I drafted a statement that balanced empathy, understanding, and utmost customer service with facts, logic, and fairness. It was direct, simple, succinct, and phrased to highlight our brand values while addressing the issue in a logical yet sensitive way.   We also tapped our influencer partners to subtly and indirectly share their positive experiences with our brand so we could counter the negative content being shared online.  Result : We got the results we worked for through proper communication and a positive and strategic campaign. The irate client agreed to have a dialogue with us. She apologized to us, and we reaffirmed our commitment to delivering quality service to all. We assured her that she can reach out to us anytime regarding her purchases and that we’d gladly accommodate her requests whenever possible. She also retracted her negative statements in her vlog and urged her followers to keep supporting our brand.

What Are Good Outcomes of Problem Solving?

Whenever you answer interview questions about problem solving or share examples of problem solving in a cover letter, you want to be sure you’re sharing a positive outcome.

Below are good outcomes of problem solving:

• Saving the company time or money
• Making the company money
• Pleasing/keeping a customer
• Obtaining new customers
• Solving a safety issue
• Solving a staffing/scheduling issue
• Solving a logistical issue
• Solving a company hiring issue
• Solving a technical/software issue
• Making a process more efficient and faster for the company
• Creating a new business process to make the company more profitable
• Improving the company’s brand/image/reputation
• Getting the company positive reviews from customers/clients

Every employer wants to make more money, save money, and save time. If you can assess your problem solving experience and think about how you’ve helped past employers in those three areas, then that’s a great start. That’s where I recommend you begin looking for stories of times you had to solve problems.

Tips to Improve Your Problem Solving Skills

Throughout your career, you’re going to get hired for better jobs and earn more money if you can show employers that you’re a problem solver. So to improve your problem solving skills, I recommend always analyzing a problem and situation before acting. When discussing problem solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Next, to get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t. Think about how you can get better at researching and analyzing a situation, but also how you can get better at communicating, deciding the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem solving ability.

If you practice the tips above, you’ll be ready to share detailed, impressive stories and problem solving examples that will make hiring managers want to offer you the job. Every employer appreciates a problem solver, whether solving problems is a requirement listed on the job description or not. And you never know which hiring manager or interviewer will ask you about a time you solved a problem, so you should always be ready to discuss this when applying for a job.

Related interview questions & answers:

• How do you handle stress?
• How do you handle conflict?
• Tell me about a time when you failed

About the Author

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