why is problem solving important in the classroom

Benefits of Problem-Solving in the K-12 Classroom

Posted October 5, 2022 by Miranda Marshall

From solving complex algebra problems to investigating scientific theories, to making inferences about written texts, problem-solving is central to every subject explored in school. Even beyond the classroom, problem-solving is ranked among the most important skills for students to demonstrate on their resumes, with 82.9% of employers considering it a highly valued attribute. On an even broader scale, students who learn how to apply their problem-solving skills to the issues they notice in their communities – or even globally –  have the tools they need to change the future and leave a lasting impact on the world around them.

Problem-solving can be taught in any content area and can even combine cross-curricular concepts to connect learning from all subjects. On top of building transferrable skills for higher education and beyond, read on to learn more about five amazing benefits students will gain from the inclusion of problem-based learning in their education:

• Problem-solving is inherently student-centered.

Student-centered learning refers to methods of teaching that recognize and cater to students’ individual needs. Students learn at varying paces, have their own unique strengths, and even further, have their own interests and motivations – and a student-centered approach recognizes this diversity within classrooms by giving students some degree of control over their learning and making them active participants in the learning process.

Incorporating problem-solving into your curriculum is a great way to make learning more student-centered, as it requires students to engage with topics by asking questions and thinking critically about explanations and solutions, rather than expecting them to absorb information in a lecture format or through wrote memorization.

• Increases confidence and achievement across all school subjects.

As with any skill, the more students practice problem-solving, the more comfortable they become with the type of critical and analytical thinking that will carry over into other areas of their academic careers. By learning how to approach concepts they are unfamiliar with or questions they do not know the answers to, students develop a greater sense of self-confidence in their ability to apply problem-solving techniques to other subject areas, and even outside of school in their day-to-day lives.

The goal in teaching problem-solving is for it to become second nature, and for students to routinely express their curiosity, explore innovative solutions, and analyze the world around them to draw their own conclusions.

• Encourages collaboration and teamwork.

Since problem-solving often involves working cooperatively in teams, students build a number of important interpersonal skills alongside problem-solving skills. Effective teamwork requires clear communication, a sense of personal responsibility, empathy and understanding for teammates, and goal setting and organization – all of which are important throughout higher education and in the workplace as well.

• Increases metacognitive skills.

Metacognition is often described as “thinking about thinking” because it refers to a person’s ability to analyze and understand their own thought processes. When making decisions, metacognition allows problem-solvers to consider the outcomes of multiple plans of action and determine which one will yield the best results.

Higher metacognitive skills have also widely been linked to improved learning outcomes and improved studying strategies. Metacognitive students are able to reflect on their learning experiences to understand themselves and the world around them better.

• Helps with long-term knowledge retention.

Students who learn problem-solving skills may see an improved ability to retain and recall information. Specifically, being asked to explain how they reached their conclusions at the time of learning, by sharing their ideas and facts they have researched, helps reinforce their understanding of the subject matter.

Problem-solving scenarios in which students participate in small-group discussions can be especially beneficial, as this discussion gives students the opportunity to both ask and answer questions about the new concepts they’re exploring.

At all grade levels, students can see tremendous gains in their academic performance and emotional intelligence when problem-solving is thoughtfully planned into their learning.

Interested in helping your students build problem-solving skills, but aren’t sure where to start? Future Problem Solving Problem International (FPSPI) is an amazing academic competition for students of all ages, all around the world, that includes helpful resources for educators to implement in their own classrooms!

Learn more about this year’s competition season from this recorded webinar:    https://youtu.be/AbeKQ8_Sm8U and/or email [email protected] to get started!

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Why Every Educator Needs to Teach Problem-Solving Skills

Strong problem-solving skills will help students be more resilient and will increase their academic and career success .

Want to learn more about how to measure and teach students’ higher-order skills, including problem solving, critical thinking, and written communication?

Problem-solving skills are essential in school, careers, and life.

Problem-solving skills are important for every student to master. They help individuals navigate everyday life and find solutions to complex issues and challenges. These skills are especially valuable in the workplace, where employees are often required to solve problems and make decisions quickly and effectively.

Problem-solving skills are also needed for students’ personal growth and development because they help individuals overcome obstacles and achieve their goals. By developing strong problem-solving skills, students can improve their overall quality of life and become more successful in their personal and professional endeavors.

Problem-Solving Skills Help Students…

   develop resilience.

Problem-solving skills are an integral part of resilience and the ability to persevere through challenges and adversity. To effectively work through and solve a problem, students must be able to think critically and creatively. Critical and creative thinking help students approach a problem objectively, analyze its components, and determine different ways to go about finding a solution.  

This process in turn helps students build self-efficacy . When students are able to analyze and solve a problem, this increases their confidence, and they begin to realize the power they have to advocate for themselves and make meaningful change.

When students gain confidence in their ability to work through problems and attain their goals, they also begin to build a growth mindset . According to leading resilience researcher, Carol Dweck, “in a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment.”

    Set and Achieve Goals

Students who possess strong problem-solving skills are better equipped to set and achieve their goals. By learning how to identify problems, think critically, and develop solutions, students can become more self-sufficient and confident in their ability to achieve their goals. Additionally, problem-solving skills are used in virtually all fields, disciplines, and career paths, which makes them important for everyone. Building strong problem-solving skills will help students enhance their academic and career performance and become more competitive as they begin to seek full-time employment after graduation or pursue additional education and training.

  Resolve Conflicts

In addition to increased social and emotional skills like self-efficacy and goal-setting, problem-solving skills teach students how to cooperate with others and work through disagreements and conflicts. Problem-solving promotes “thinking outside the box” and approaching a conflict by searching for different solutions. This is a very different (and more effective!) method than a more stagnant approach that focuses on placing blame or getting stuck on elements of a situation that can’t be changed.

While it’s natural to get frustrated or feel stuck when working through a conflict, students with strong problem-solving skills will be able to work through these obstacles, think more rationally, and address the situation with a more solution-oriented approach. These skills will be valuable for students in school, their careers, and throughout their lives.

    Achieve Success

We are all faced with problems every day. Problems arise in our personal lives, in school and in our jobs, and in our interactions with others. Employers especially are looking for candidates with strong problem-solving skills. In today’s job market, most jobs require the ability to analyze and effectively resolve complex issues. Students with strong problem-solving skills will stand out from other applicants and will have a more desirable skill set.

In a recent opinion piece published by The Hechinger Report , Virgel Hammonds, Chief Learning Officer at KnowledgeWorks, stated “Our world presents increasingly complex challenges. Education must adapt so that it nurtures problem solvers and critical thinkers.” Yet, the “traditional K–12 education system leaves little room for students to engage in real-world problem-solving scenarios.” This is the reason that a growing number of K–12 school districts and higher education institutions are transforming their instructional approach to personalized and competency-based learning, which encourage students to make decisions, problem solve and think critically as they take ownership of and direct their educational journey.

Problem-Solving Skills Can Be Measured and Taught

Research shows that problem-solving skills can be measured and taught. One effective method is through performance-based assessments which require students to demonstrate or apply their knowledge and higher-order skills to create a response or product or do a task.

What Are Performance-Based Assessments?

With the No Child Left Behind Act (2002), the use of standardized testing became the primary way to measure student learning in the U.S. The legislative requirements of this act shifted the emphasis to standardized testing, and this led to a  decline in nontraditional testing methods .

But   many educators, policy makers, and parents have concerns with standardized tests. Some of the top issues include that they don’t provide feedback on how students can perform better, they don’t value creativity, they are not representative of diverse populations, and they can be disadvantageous to lower-income students.

While standardized tests are still the norm, U.S. Secretary of Education Miguel Cardona is encouraging states and districts to move away from traditional multiple choice and short response tests and instead use performance-based assessment, competency-based assessments, and other more authentic methods of measuring students abilities and skills rather than rote learning. 

Performance-based assessments  measure whether students can apply the skills and knowledge learned from a unit of study. Typically, a performance task challenges students to use their higher-order skills to complete a project or process. Tasks can range from an essay to a complex proposal or design.

Preview a Performance-Based Assessment

Want a closer look at how performance-based assessments work?  Preview CAE’s K–12 and Higher Education assessments and see how CAE’s tools help students develop critical thinking, problem-solving, and written communication skills.

Performance-Based Assessments Help Students Build and Practice Problem-Solving Skills

In addition to effectively measuring students’ higher-order skills, including their problem-solving skills, performance-based assessments can help students practice and build these skills. Through the assessment process, students are given opportunities to practically apply their knowledge in real-world situations. By demonstrating their understanding of a topic, students are required to put what they’ve learned into practice through activities such as presentations, experiments, and simulations. 

This type of problem-solving assessment tool requires students to analyze information and choose how to approach the presented problems. This process enhances their critical thinking skills and creativity, as well as their problem-solving skills. Unlike traditional assessments based on memorization or reciting facts, performance-based assessments focus on the students’ decisions and solutions, and through these tasks students learn to bridge the gap between theory and practice.

Performance-based assessments like CAE’s College and Career Readiness Assessment (CRA+) and Collegiate Learning Assessment (CLA+) provide students with in-depth reports that show them which higher-order skills they are strongest in and which they should continue to develop. This feedback helps students and their teachers plan instruction and supports to deepen their learning and improve their mastery of critical skills.

Explore CAE’s Problem-Solving Assessments

CAE offers performance-based assessments that measure student proficiency in higher-order skills including problem solving, critical thinking, and written communication.

• College and Career Readiness Assessment (CCRA+) for secondary education and
• Collegiate Learning Assessment (CLA+) for higher education.

Our solution also includes instructional materials, practice models, and professional development.

We can help you create a program to build students’ problem-solving skills that includes:

• Measuring students’ problem-solving skills through a performance-based assessment    
• Using the problem-solving assessment data to inform instruction and tailor interventions
• Teaching students problem-solving skills and providing practice opportunities in real-life scenarios
• Supporting educators with quality professional development

Get started with our problem-solving assessment tools to measure and build students’ problem-solving skills today! These skills will be invaluable to students now and in the future.

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Learn more about cae’s suite of products and let’s get started measuring and teaching students important higher-order skills like problem solving..

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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Center for Teaching

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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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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Published 2018

The Problem-solving Classroom

• Visualising
• Working backwards
• Reasoning logically
• Conjecturing
• Working systematically
• Looking for patterns
• Trial and improvement.

• stage of the lesson 
• level of thinking
• mathematical skill.
• The length of student response increases (300-700%)
• More responses are supported by logical argument.
• An increased number of speculative responses.
• The number of questions asked by students increases.
• Student - student exchanges increase (volleyball).
• Failures to respond decrease.
• 'Disciplinary moves' decrease.
• The variety of students participating increases.  As does the number of unsolicited, but appropriate contributions.
• Student confidence increases.
• conceptual understanding
• procedural fluency
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Problem-Based Learning

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

Why Use Problem-Based Learning?

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

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

Considerations for Using Problem-Based Learning

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

Students generally must:

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

Getting Started with Problem-Based Learning

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

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

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• 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

The Role of the Teacher Changes in a Problem-Solving Classroom

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How can teachers help students develop problem-solving skills when they themselves, even though confronted with an array of problems every day, may need to become better problem solvers? Our experience leads us to conclude that there is an expertise in a certain kind of problem-solving that teachers possess but that broader problem-solving skills are sometimes wanting.There are a few reasons why this happens. One reason may be that teacher preparation programs remain focused on how to teach subjects and behavior management techniques. Another reason may be that professional development opportunities offered in schools are focused elsewhere. And, another reason could be that leaders still often fail to engage their faculties in solving substantive problems within the school community.

A recent issue of Education Leadership was dedicated to the topic, “Unleashing Problem Solvers”. One theme that ran through several of the articles was the changing role of the teacher. In a positive but traditional classroom, information is shared by the teacher and the students are asked to demonstrate application of that information. A problem-solving classroom is different. A problem-solving classroom requires extraordinary planning on the part of the teacher. For problems to have relevance, students are engaged in the identification of the problem. Teachers have to become experts at creating questions that require students to reach back to information and skills already attained, while figuring out what they need to learn next in order to solve the problem. Some of us are really good at asking these kinds of questions. Others are not.

Students have to become experts at reflecting on these questions as guides resulting in a gathering of new information and skills, and answers. Teachers have to be prepared to offer lessons that bridge the gaps between the skills and information already attained and those the performance of the students demonstrate remain needed. Often it involves teams of students and they are simultaneously learning collaboration and communication skills.

Problem-Based Classrooms Require Letting Go

Opportunities for teachers to work with each other, to learn from experts, to receive feedback from observers of their work, all allow for skill development. But at the same time, there is a more challenging effort required of the teacher. Problem-based classrooms require teachers to dare to let go of control of the learning and to take hold of the role of questioner, coach, supporter, and diagnostician. In addition to the lack of training teachers have in these skills, the leaders in charge of evaluating their work also have to know what problem-solving classrooms look like and how to capture that environment in an observation, how to give feedback on the teachers’ efforts. Of course, if problem- solving is a collaborative school community process, how does that change the leader’s role? Are leaders, themselves, ready to become facilitators of the process rather than the sole problem solver? Many talk about wanting that but most get rewarded for being the problem solver.

Questions are Essential

There is a place to begin and that place is the shared understanding of what problem-based learning actually is. Because teachers traditionally plan for a time for Q and A within classes, they and their leaders may think of questions as having a correct answer. In moving into a problem-based learning design, the questions also have to be more overarching, create cognitive dissonance, and provoke the learner to search for answers. Here is why it is important to come to an understanding about the types of questions to be asked and shifting the teaching and learning practices to be one of expecting more from the learner.

Students Need Problem-Solving Skills

Problem-based learning skills are skills that prepare for a changing environment in all fields. Current educators cannot imagine some of the careers our students will have over their lifetimes. We do know that change will be part of everyone’s work. Flexibility and problem-solving are key skills. Problem- solving involves collaboration, communication, critical thinking, empathy, and integrity. If we listen to the business world, we will hear that design thinking is the way of the future.

Tim Brown, CEO of IDEO says,

Design thinking is a human-centered approach to innovation that draws from the designer’s toolkit to integrate the needs of people, the possibilities of technology, and the requirements for business success.

The only way for educators to develop these skills in students is to build lessons and units that are interdisciplinary and demand these skills. If we begin from the earliest of grades and expect more as they ascend through the grades, students will have mastered not only their subjects, but the skills that will prepare them for the world of work. How do we best prepare our students? We think problem solving is key.

A nn Myers and Jill Berkowicz are the authors of The STEM Shift (2015, Corwin) a book about leading the shift into 21st century schools. Ann and Jill welcome connecting through Twitter & Email .

Photo courtesy of Pixabay

The opinions expressed in Leadership 360 are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.

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Why Schools Need to Change Purpose and Problem-Solving: Developing Leaders in the Classroom

Taiwo A. Togun (he, him, his) Faculty, Pierrepont School, and Co-Founder & Executive Director, InclusionBridge, Inc. in Connecticut

Today’s learners face an uncertain present and a rapidly changing future that demand far different skills and knowledge than were needed in the 20th century. We also know so much more about enabling deep, powerful learning than we ever did before. Our collective future depends on how well young people prepare for the challenges and opportunities of 21st-century life.

As educators transform learning in their classrooms, they can develop their students ’ talent and their own leadership while also making a difference for their community.

“Purpose is a stable and generalized intention to accomplish something that is at once meaningful to the self and consequential to the world beyond the self” –Bill Damon, Professor of Education, Stanford University

As an educator, my purpose is to nurture and develop young talents. While I have been teaching for over a decade, I only articulated my purpose as an educator last year during my master’s program in technology leadership while learning to integrate technology, strategy, and leadership. Coincidentally, I became a Project Invent fellow at the same time, which only served to embolden my sense of purpose. Clarity of purpose is a vital leadership quality that shapes my experience and something I believe ought to begin every teacher’s leadership journey. While one’s articulation of purpose may change over time, there’s something quite powerful and differently effective about writing down and reading out loud your purpose statement. In the following reflection, my goal is to share how I approach my development as an educator and a leader as one and the same and how my experience with Project Invent’s design thinking curriculum represents a continuing education in leadership.

Developing a Leadership Identity

As I work toward establishing my leadership identity and persona as an educator, I find myself reflecting on Sun Tzu’s Art Of War in which he described “ Leadership [as] a matter of intelligence, trustworthiness, humaneness, courage, and discipline. ” Additional discourses from the likes of Thomas Carlyle , Tolstoy , and Plato have all helped me arrive at an understanding of leadership as a function of nature, nurture, and situation . In addition to clarity of purpose, other leadership qualities must be deliberately nurtured through training and cultivated through practicing acts of leadership. I believe an effective leader empowers others and recognizes situations when the act of leadership is, in fact, letting others lead. This summarizes the core takeaway of my “teacher as a leader” philosophy.

In 2021, I applied to Project Invent’s educator fellowship , hoping to reinforce my leadership identity as an educator. Project Invent is a nonprofit organization that trains educators in six key teacher practices, each aimed at empowering students with the mindsets to become fearless, compassionate, and creative problem solvers. As a Project Invent Fellow, I have made significant progress in mastering these six teacher practices:

• Make failure okay
• Push to the next level
• Be a co-learner
• Let students take the wheel
• Leave room for exploration
• Challenge assumptions

Courtesy of Project Invent

Leadership in Practice

Each of these teacher practices can occur independently but are often interrelated. Deliberately committing to one can undoubtedly lead to others. For example, being comfortable with being a co-learner allows space for leaving room for exploration of alternatives. Openness to the possibility of new alternatives begets making failure okay and also encourages letting students take the wheel and drive the process, while the teacher-leader nudges them to push to the next level. Of course, the order of these is not fixed.

I teach computer science at Pierrepont School in Westport, Connecticut. My Project Invent student teams come from two classes of juniors and seniors, who originally signed up for an Applied Data Science course. We began our journey in the second semester in January, after which the students were informed that their course name had changed from “Applied Data Science” to “Essential Skills of the Emerging Economy” which has two parts: “Critical Reasoning & Storytelling with Data” and “Human-centered Problem-solving.” These are the only details my brave students had to work with. Needless to say, students had to be open-minded about how the journey would shape up. After all, it is not the first time that I would modify course requirements to marry interests and new opportunities that would benefit my students. I enjoy such flexibility and reasonable autonomy at my school; I also enjoy the flexibility and reasonable autonomy of learning as I teach. I am comfortable admitting to my students that I have absolutely no idea how to solve a challenge that I assign them, but assure them we can figure it out together… and we always do.

In January, the challenge was dauntingly ambiguous: We were going to invent a new technology intended to positively impact members of our community. Given their awareness of how little I knew about what we might need, or how to invent anything for that matter, students had to buy into taking a journey with an uncertain destination together. My job as a co-learner was to make sure to emphasize that it was all about the journey, the lessons, and the fun we have; and not necessarily the end. The humility and willingness to be a co-learner with students in the driver's seat have served me very well throughout my journey as a teacher, and I can not begin to describe the gratification of learning with and from students and seeing them rise to the challenge. This time, however, we had access to a community of resources, fellows, and mentors through the extended Project Invent team, who made it even more reassuring despite the many unknowns. From the onset of our journey, my students demonstrated creative confidence and trust in one another (most of the time) and our system as a class. Together as a team, we were ready and excited for the journey.

“Coming into this class with a limited computer science background, I was a little intimidated to embark on a project that had the potential to create such a big and meaningful improvement in our community. However, as I grew more comfortable with my team, my fears eased. I was able to develop from a quiet listener to a confident doer, not only for the duration of this project but also in my longer-term data science pursuits.” –Alexis Bienstock, Pierrepont School Junior

Project Invent as Context for Leadership Development

Human-centeredness brings a new dimension to problem-solving. It helps to establish and define a worthy purpose. My students and I began our journey on our Project Invent experience by getting to know our “client” Roderick Sewell , a Paralympic athlete and swimmer, as a person—what he enjoys doing, how he got to become a serious athlete, and what his goals and aspirations are. We focused on his abilities, accomplishments, and strengths. This set the stage for helping us—students and teachers alike—cultivate mindsets of empathy and curiosity. It is this empathic curiosity that would eventually lead to two Project Invent teams of ambitious students, who set out to address Roderick’s expressed challenges of lower back pain and efficient switch from running to walking legs:

“Because there’s nothing to absorb the load except for my lower back…If there was a little more cushioning on the soles to absorb the impact, then everything would be even more doable.” “ I can’t really run with my walking leg. One question that I always have is if something happened, how fast would I be able to get up and get away? ” –Roderick Sewell

Team SNAILS, a team of one senior and five juniors, proposed and prototyped an invention they called Quick Switch Support Shoe (“QS-cubed”), a multifunctional prosthetic foot support with adjustable springs to minimize back pain and maximize run-walk efficiency for their community partner.

Team Pierrepont Innovators with three seniors and four juniors had the ambitious goal of completely redesigning Roderick’s prosthetic ankle with a dashpot or snubber mechanism and incorporating more effective shock-absorbing materials. They wrestled with disappointments as they came to terms with reality and time constraints, and the team eventually demonstrated resilience and agency as they made a pivot to capitalize on their research of Shock-absorbing materials. They developed a pitch to prosthetic companies which can incorporate their research insights to further possible impact.

The larger purpose of our 10-week journey into design thinking was our connection with Roderick’s expressed discomfort. This purpose shaped our introduction to need-finding, synthesizing and ideation, idea selection and prototyping, prototype refinement, and pitching. Students persevered through their fears, disagreements, and disappointments; they made it work because they did not think it was about them but rather about what they could contribute to support Roderick.

“Our community partner Roderick Sewell is the first bilateral above-the-knee amputee to finish the IRONMAN World Championship. As a serious athlete, he needs to feel his best to perform his best—and that’s our charge!” –Team Pierrepont Innovators

“Working on Project Invent provided me with an appreciation for Roderick Sewell and the time I spend with my classmates. The opportunity to learn Roderick’s story as we worked with him to develop solutions to his lower back pain proved to be the most rewarding part of the process.” –Hagen Feeney, Pierrepont School Senior

Understanding the Journey

“He who has a why to live for can bear almost any how.” –Friedrich Nietzsche

By default, as educators we teach process; learning to solve problems in several different ways is central to our training, and sometimes that dominates our lessons to students. The Project Invent experience helps educators and students alike to prioritize the “why” and “what” of our learning over the “how.” The Project Invent experience added the very essential element of “purpose” which helped my students and me push the boundaries of the typical project-based, creative problem-solving classroom experience. Indeed, such an experience only thrives in and helps to foster a culture of caring, purpose, learning, and enjoyment (all in the dimension of flexibility to respond to change)—the kind of culture espoused by our school, Pierrepont culture ! Through our experience with human-centered problem-solving, students and teachers alike have cultivated practices and mindsets that are necessary to become leaders.

Every Leader Needs a Community and a Support System

“Leadership without support is like trying to make bricks without enough straw. True leaders reinforce their ideas and plan with strategic partnerships, alliances, and supportive audiences.” –Reed Markham, Ph.D.

In addition to the Pierrepont culture that presented a fertile soil for the teacher practices and students’ mindsets we needed, the Project Invent community and support system were so important for us. I recall the confidence boost and reassurance from our first session with a volunteer expert, Valerie Peng, an engineer who builds robots for a living. Not only did my team get to soak invaluable information that was relevant for advancing our project, but we were also all inspired by the passion with which she shared her work with us. Similarly, I found renewed strength and motivation with each conversation with Project Invent staff members and other fellows. In our shared space as educator-leaders, my co-fellows and I were able to explore possible solutions to shared challenges like keeping students motivated through their fears and disappointments, navigating operational logistics and schedule challenges, etc. I am indeed grateful for such a community as it helps to know you are not alone.

Beyond the Classroom

The teacher as leader practices cultivated during my Project Invent experience has affected my work beyond Pierrepont. With clarity of purpose and the necessary focus on impact and human-centeredness, my data science consulting company has embarked on a renewed mission to diversify the data science workforce and bridge the gap to full and equal participation in the emerging digital economy through InclusionBridge . Indeed, the Project Invent experience provided a complementary lens for me to refine my purpose—my journey—of nurturing and developing young talents through problem-solving and meaningful learning experiences. I enjoy creating and facilitating opportunities to help students become fearless, compassionate young leaders.

Image at top is a slide from the student project presentation by Team SNAILS, Pierrepont School.

Taiwo A. Togun (he, him, his)

Faculty, pierrepont school, and co-founder & executive director, inclusionbridge, inc..

Taiwo is an educator, a data scientist, and a social entrepreneur who is passionate about nurturing and developing young talent. He is the architect and director of the Computer Science program and Innovation Lab at Pierrepont School , a private K-12 where he enjoys the challenge of making computer programming and problem-solving skills accessible to students at all levels. Dr. Togun is a visiting scientist at the Boykin Lab at the Department of Cognitive, Linguistic, and Psychological Sciences at Brown University, supporting research to elucidate perceptions of fairness in machine learning algorithms. With a Ph.D. in computational biology & bioinformatics from Yale and a master's in technology leadership from Brown, he combines data science, technology, strategy, and leadership as co-founder and executive director of InclusionBridge . Through InclusionBridge, Taiwo and his team are on a mission to increase diversity in the data science workforce through internships and training programs for underrepresented talent. Follow Taiwo on LinkedIn .

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MSU Extension

Problem-solving skills are an important factor in academic success.

Elizabeth Gutierrez, Michigan State University Extension - May 11, 2012

Updated from an original article written by [email protected]..

Parents and caregivers can ensure their children's success by teaching and modeling effective problem-solving at home.

Helping your child learn how to problem solve is a critical skill for school readiness. Parents and caregivers are a child’s first and most important teacher; therefore, modeling good problem solving skills is very important. Children learn by watching parents and caregivers handle different situations and solve problems. If a parent handles problems by yelling, throwing things, hitting, grabbing or using other unacceptable strategies, a child will learn to do the same thing.

Often, adults will prevent their children from seeing all conflicts or disagreements. Remember, it is important for children to see adults negotiate differences, compromise and resolve conflicts. Learning to negotiate differences in a constructive way and allowing children to see how this is done is very effective and important. If parent and caregivers handle these situations privately, there is no example for the child/children to learn from.

Children can learn how to be assertive verbally as a result of seeing and listening to how adults resolve conflict. Another simple way a child can learn how to be assertive verbally is by role-playing with puppets and through pretend play with an adult. When using these techniques, it is important to help your child think of constructive ways to respond to different situations. By using puppets and role-play, your child can also learn about how others may feel in specific situations. When using these techniques, it is important not to criticize or label the child for past misbehavior.

There are some basic steps to problem solving from Incredible Years :

• Identify the problem.
• List the possible solutions or courses of action.
• Weigh the possible solutions.
• Choose a solution to try.
• Put the solution into practice.
• Evaluate the solution.

Using effective problem solving techniques will help children avoid conflict with others in a school setting and in their everyday lives. It will also strengthen children’s beginning empathy skills and help them learn more positive attributions about another person’s intentions. Effective problem solving skills is essential for academic and social success.

For more articles on child development, academic success, parenting and life skill development, please visit the Michigan State University Extension website.

This article was published by Michigan State University Extension . For more information, visit https://extension.msu.edu . To have a digest of information delivered straight to your email inbox, visit https://extension.msu.edu/newsletters . To contact an expert in your area, visit https://extension.msu.edu/experts , or call 888-MSUE4MI (888-678-3464).

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Problem-Solving

Jabberwocky

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

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

Problem-solving involves three basic functions:

Seeking information

Generating new knowledge

Making decisions

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

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

Expert Opinion

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

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

It's Elementary

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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3 steps to creative problem solving in the classroom

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Bringing creativity into the classroom came naturally to Mark Gura. He began his career as a visual arts teacher in East Harlem, and when his small school asked him to teach other topics like English and social studies, it made sense to integrate some of his artistic skills into his lessons.

“Running a creative classroom was all about the culture I established,” Gura says. “I was bringing the students into another way of being. Not of thinking, but of being.”

To do that requires restructuring “habits of mind,” as Gura puts it. For example, many people think of creativity as a solo endeavor – the artist or writer who paints or writes in solitude. But creativity doesn’t happen in a bubble. Often it’s the result of team collaboration with a lot of brainstorming and bouncing ideas off each other.

How can educators best build a creative culture in their classroom? It begins with establishing a creative space where students can share their work. Gura is a fan of blogs, where students can post essays, videos or visual art projects and get real-time feedback.

Educators can also encourage students to come up with multiple solutions to specific situations. Too often, Gura says, students get caught up with finding the single correct answer to a problem. Instead, focus on finding multiple outcomes. Here’s how:

• Develop a strategy. This involves researching the problem and its history to best understand it and then analyzing how others approached the problem and solved it. Look for mistakes made along the way and the gaps left to be filled.
• Create a prototype, test or draft. Once students truly understand the problem, they are ready to solve it. This is where the creative community truly comes into play. Through collaboration, more minds are working on prototype solutions. Not only can students tap into their peers’ ideas, the feedback turns the classroom into a thought incubator where ideas are nurtured and grow.
• Find an audience. Creative communities need a support system, someone outside of the creative team who can bring an unbiased perspective to the problem and solution. This can be done by soliciting feedback through blog posts, in a closed digital community or during classroom presentations. The idea is to use the audience to help refine the prototype or draft.

In creative classrooms, Gura says, the finished product isn’t the most important outcome. It’s the process of getting to a solution and then expanding it in new directions.

“That’s a huge shift in the habits of mind within the classroom,” he adds. “It’s ongoing, with students relying on the community for support.”

Discover ready-to-implement activities for developing student creativity in your school or classroom with Gura’s new book, Make, Learn Succeed: Building a Culture of Creativity in Your School.

• artificial intelligence

Problem-Solving Model for Improving Student Achievement

Principal Leadership Magazine, Vol. 5, Number 4, December 2004

Counseling 101 column, a problem-solving model for improving student achievement.

Problem solving is an alternative to assessments and diagnostic categories as a means to identify students who need special services.

By Andrea Canter

Andrea Canter recently retired from Minneapolis Public Schools where she served as lead psychologist and helped implement a district-wide problem solving model. She currently is a consultant to the National Association of School Psychologists (NASP) and editor of its newspaper, Communiquè . “Counseling 101” is provided by NASP ( www.nasponline.org ).

The implementation of the No Child Left Behind Act (NCLB) has prompted renewed efforts to hold schools and students accountable for meeting high academic standards. At the same time, Congress has been debating the reauthorization of the Individuals With Disabilities Education Act (IDEA), which has heightened concerns that NCLB will indeed “leave behind” many students who have disabilities or other barriers to learning. This convergence of efforts to address the needs of at-risk students while simultaneously implementing high academic standards has focused attention on a number of proposals and pilot projects that are generally referred to as problem-solving models. A more specific approach to addressing academic difficulties, response to intervention (RTI), has often been proposed as a component of problem solving.

What Is Problem Solving?

A problem-solving model is a systematic approach that reviews student strengths and weaknesses, identifies evidence-based instructional interventions, frequently collects data to monitor student progress, and evaluates the effectiveness of interventions implemented with the student. Problem solving is a model that first solves student difficulties within general education classrooms. If problem-solving interventions are not successful in general education classrooms, the cycle of selecting intervention strategies and collecting data is repeated with the help of a building-level or grade-level intervention assistance or problem-solving team. Rather than relying primarily on test scores (e.g., from an IQ or math test), the student’s response to general education interventions becomes the primary determinant of his or her need for special education evaluation and services (Marston, 2002; Reschly & Tilly, 1999).

Why Is a New Approach Needed?

Although much of the early implementation of problem-solving models has involved elementary schools, problem solving also has significant potential to improve outcomes for secondary school students. Therefore, it is important for secondary school administrators to understand the basic concepts of problem solving and consider how components of this model could mesh with the needs of their schools and students. Because Congress will likely include RTI options in its reauthorization of special education law and regulations regarding learning disabilities, it is also important for school personnel to be familiar with the pros and cons of the problem-solving model.

Student outcomes. Regardless of state or federal mandates, schools need to change the way they address academic problems. More than 25 years of special education legislation and funding have failed to demonstrate either the cost effectiveness or the validity of aligning instruction to diagnostic classifications (Fletcher et al., 2002; Reschly & Tilly, 1999; Ysseldyke & Marston, 1999). Placement in special education programs has not guaranteed significant academic gains or better life outcomes for students with disabilities. Time-consuming assessments that are intended to differentiate students with disabilities from those with low achievement have not resulted in better instruction for struggling students.

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Dilemma of learning disabilities. The learning disabilities (LD) classification has proven especially problematic. Researchers and policymakers representing diverse philosophies regarding disability are generally in agreement that the current process needs revision (Fletcher et al., 2002). Traditionally, if a student with LD is to be served in special education, an evaluation using individual intelligence tests and norm-referenced achievement tests is required to document an ability/achievement discrepancy. This model has been criticized for the following reasons:

• A reliance on intelligence tests in general and with students from ethnic and linguistic minority populations in particular
• A focus on within-child deficiencies that often ignore quality of instruction and environmental factors
• The limited applicability of norm-referenced information to actual classroom teaching
• The burgeoning identification of students as disabled
• The resulting allocation of personnel to responsibilities (classification) that are significantly removed from direct service to students (Ysseldyke & Marston, 1999).

Wait to fail. A major flaw in the current system of identifying student needs is what has been dubbed the wait to fail approach in which students are not considered eligible for support until their skills are widely discrepant from expectations. This runs counter to years of research demonstrating the importance of early intervention (President’s Commission on Excellence in Special Education, 2002). Thus, a number of students fail to receive any remedial services until they reach the intermediate grades or middle school, by which time they often exhibit motivational problems and behavioral problems as well as academic deficits.

For other students, although problems are noted when they are in the early grades, referral is delayed until they fail graduation or high school standards tests, increasing the probability that they will drop out. Their school records often indicate that teachers and parents expressed concern for these students in the early grades, which sometimes resulted in referral for assessments, but did not result in qualification for special education or other services.

Call for evidence-based programs. One of the major tenets of NCLB is the implementation of scientifically based interventions to improve student performance. The traditional models used by most schools today lack such scientifically based evidence. There are, however, many programs and instructional strategies that have demonstrated positive outcomes for diverse student populations and needs (National Reading Panel, 2000). It is clear that schools need systemic approaches to identify and resolve student achievement problems and access proven instructional strategies.

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How It Works

Although problem-solving steps can be described in several stages, the steps essentially reflect the scientific method of defining and describing a problem (e.g., Ted does not comprehend grade-level reading material); generating potential solutions (e.g., Ted might respond well to direct instruction in comprehension strategies); and implementing, monitoring, and evaluating the effectiveness of the selected intervention.

Problem-solving models have been implemented in many versions at local and state levels to reflect the unique features and needs of individual schools. However, all problem-solving models share the following components:

• Screening and assessment that is focused on student skills rather than classification
• Measuring response to instruction rather than relying on norm-referenced comparisons
• Using evidence-based strategies within general education classrooms
• Developing a collaborative partnership among general and special educators for consultation and team decision making.

Three-tiered model. One common problem-solving model is the three-tiered model. In this model, tier one includes problem-solving strategies directed by the teacher within the general education classrooms. Tier two includes problem-solving efforts at a team level in which grade-level staff members or a team of various school personnel collaborate to develop an intervention plan that is still within the general education curriculum. Tier three involves referral to a special education team for additional problem solving and, potentially, a special education assessment (Office of Special Education Programs, 2002).

Response to intervention. A growing body of research and public policy discussion has focused on problem-solving models that include evaluating a student’s RTI as an alternative to the IQ-achievement discrepancy approach to identifying learning disabilities (Gresham, 2002). RTI refers to specific procedures that align with the steps of problem solving:

• Implementing evidence-based interventions
• Frequently measuring a student’s progress to determine whether the intervention is effective
• Evaluating the quality of the instructional strategy
• Evaluating the fidelity of its implementation. (For example, did the intervention work? Was it scientifically based? Was it implemented as planned?)

Although there is considerable debate about replacing traditional eligibility procedures with RTI approaches (Vaughn & Fuchs, 2003), there is promising evidence that RTI can systematically improve the effectiveness of instruction for struggling students and provide school teams with evidence-based procedures that measures a student’s progress and his or her need for special services.

New roles for personnel. An important component of problem-solving models is the allocation (or realignment) of personnel who are knowledgeable about the applications of research to classroom practice. Whereas traditional models often limit the availability of certain personnel-for example, school psychologists-to prevention and early intervention activities (e.g., classroom consultation), problem-solving models generally enhance the roles of these service providers through a systemic process that is built upon general education consultation. Problem solving shifts the emphasis from identifying disabilities to implementing earlier interventions that have the potential to reduce referral and placement in special education.

Outcomes of Problem Solving and RTI

Anticipated benefits of problem-solving models, particularly those using RTI procedures, include emphasizing scientifically proven instructional methods, the early identification and remediation of achievement difficulties, more functional and frequent measurement of student progress, a reduction in inappropriate and disproportionate special education placements of students from diverse cultural and linguistic backgrounds, and a reallocation of instructional and behavior support personnel to better meet the needs of all students (Gresham, 2002; Ysseldyke & Marston, 1999). By using problem solving, some districts have reduced overall special education placements, increased individual and group performance on standards tests, and increased collaboration among special and general educators.

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The enhanced collaboration between general education teachers and support personnel is particularly important at the secondary level because staff members often have limited interaction with school personnel who are outside of their specialty area. Problem solving provides a vehicle to facilitate communication across disciplines to resolve student difficulties in the classroom. Secondary schools, however, face additional barriers to collaboration because each student may have five or more teachers. Special education is often even more separated from general education in secondary school settings. Secondary school teachers also have a greater tendency to see themselves as content specialists and may be less invested in addressing general learning problems, particularly when they teach five or six class periods (and 150 or more students) each day. The sheer size of the student body and the staff can create both funding and logistical difficulties for scheduling training and team meetings.

Is Problem Solving Worth the Effort?

Data from district-wide and state-level projects in rural, suburban, and urban communities around the country support the need to thoughtfully implement problem-solving models at all grade levels. There are several federally funded demonstration centers that systematically collect information about these approaches. Although national demonstration models may be a few years away, it seems likely that state and federal regulations under IDEA will include problem solving and RTI as accepted experimental options. Problem solving continues to offer much promise to secondary school administrators who are seeking to improve student performance through ongoing assessment and evidence-based instruction. PL

• Fletcher, J., Lyon, R., Barnes, M., Stuebing, K., Francis, D., Olson, R., Shaywitz, S., & Shaywitz, B. (2002). Classification of learning disabilities: An evidence-based evaluation. In R. Bradley, L. Donaldson, & D. Hallahan (Eds.), Identification of learning disabilities (pp. 185-250). Mahwah, NJ: Erlbaum.
• Gresham, F. (2002). Responsiveness to intervention: An alternative approach to the identification of learning disabilities. In R. Bradley, L. Donaldson, & D. Hallahan (Eds.), Identification of learning disabilities (pp. 467-519). Mahwah, NJ: Erlbaum.
• Marston, D. (2002). A functional and intervention-based assessment approach to establishing discrepancy for students with learning disabilities. In R. Bradley, L. Donaldson, & D. Hallahan (Eds.), Identification of learning disabilities (pp. 437-447). Mahwah, NJ: Erlbaum.
• National Reading Panel. (2000). Teaching children to read: An evidence-based assessment of the scientific literature on reading and its implications for reading instruction-Reports of the subgroups. Washington, DC: Author.
• Office of Special Education Programs, U.S. Department of Education. (2002). Specific learning disabilities: Finding common ground (Report of the Learning Disabilities Round Table). Washington, DC: Author.
• President’s Commission on Excellence in Special Education. (2002). A new era: Revitalizing special education for children and their families. Washington, DC: U.S. Department of Education.
• Reschly, D., & Tilly, W. D. III (1999). Reform trends and system design alternatives. In D. Reschly, W. D. Tilly III, & J. Grimes (Eds.), Special education in transition: Functional assessment and noncategorical programming (pp. 19-48). Longmont, CO: Sopris West.
• Vaughn, S., & Fuchs, L. (Eds.) (2003). Special issue: Response to intervention. Learning Disabilities Research & Practice, 18(3).
• Ysseldyke, J., & Marston, D. (1999). Origins of categorical special education services in schools and a rationale for changing them. In D. Reschly, W. D. Tilly III, & J. Grimes (Eds.), Special education in transition: Functional assessment and noncategorical programming (pp. 1-18). Longmont, CO: Sopris West.

Case Study: Optimizing Success Through Problem Solving

By Marcia Staum and Lourdes Ocampo

Milwaukee Public Schools, the largest school district in Wisconsin, is educating students with Optimizing Success Through Problem Solving (OSPS), a problem-solving initiative that uses a four-step, data-based, decision-making process to enhance school reform efforts. OSPS is patterned after best practices in the prevention literature and focuses on prevention, early intervention, and focused intervention levels.  Problem-solving facilitators provide staff members with the training, modeling, support, and tools they need to effectively use data to drive their instructional decision-making. The OSPS initiative began in the fall of 2000 with seven participating schools. Initially, elementary and middle level schools began to use OSPS, with an emphasis on problem solving for individual student issues. As the initiative matured, increased focus was placed on prevention and early intervention support in the schools. Today, 78 schools participate in the OSPS initiative and are serviced by a team of 18 problem-solving facilitators. 

OSPS in Action: Juneau High School

The administration of Juneau High School, a Milwaukee public charter school with 900 students, invited OSPS to become involved at Juneau for the 2003-2004 school year. Because at the time OSPS had limited involvement with high schools, two problem-solving facilitators were assigned to Juneau for one half-day each week. The problem-solving facilitators immediately joined the Juneau’s learning team, which is a small group of staff members and administrators who make educational decisions aimed at increasing student achievement.

When the problem-solving facilitators became involved with Juneau, the learning team was working to improve student participation on the Wisconsin Knowledge and Concepts Exam (WKCE). The previous year, Juneau’s 10th-grade participation on the exam had been very low. The learning team used OSPS’s four-step problem-solving process to develop and implement a plan that resulted in a 99% student participation rate on the WKCE. After this initial success, the problem-solving model was also used at Juneau to increase parent participation in parent-teacher conferences. According to Myron Cain, Juneau’s principal, “Problem solving has helped the learning team at Juneau go from dialogue into action. In addition, problem solving has supported the school within the Collaborative Support Team process and with teambuilding, which resulted in a better school climate.”

By starting at the prevention level, Juneau found that there was increased commitment from staff members. OSPS is now in the initial stages of working with Juneau to explore alternatives to suspension.  The goal is to create a working plan that will lead to creative ways of decreasing the number of suspensions at Juneau.

Marcia Staum is a school psychologist, and Lourdes Ocampo is a school social worker for Optimizing Success Through Problem Solving.

What Is Response to Intervention?

Many researchers have recommended that a student’s response to intervention or response to instruction (RTI) should be considered as an alternative or replacement to the traditional IQ-achievement discrepancy approach to identifying learning disabilities (Gresham, 2002; President’s Commission on Excellence in Special Education, 2002). Although there is considerable debate about replacing traditional eligibility procedures with RTI approaches (Vaughn & Fuchs, 2003), there is promising evidence that RTI can systematically improve the effectiveness of instruction for struggling students and provide school teams with evidence-based procedures to measure student progress and need for special services. In fact, Congress has proposed the use of research-based RTI methods (as part of a comprehensive evaluation process to reauthorize IDEA) as an allowable alternative to the use of an IQ-achievement discrepancy procedure in identifying learning disabilities.

RTI refers to specific procedures that align with the steps of problem solving. These steps include the implementation of evidence-based instructional strategies in the general education classroom and the frequent measurement of a student’s progress to determine if the intervention is effective. In settings where RTI is also a criteria for identification of disability, a student’s progress in response to intervention is an important determinant of the need and eligibility for special education services.

It is important for administrators to recognize that RTI can be implemented in various ways depending on a school’s overall service delivery model and state and federal mandates. An RTI approach benefits from the involvement of specially trained personnel, such as school psychologists and curriculum specialists, who have expertise in instructional consultation and evaluation.

• National Center on Student Progress Monitoring, www.studentprogress.org
• National Research Center on Learning Disabilities, www.nrcld.org

This article was adapted from a handout published in Helping Children at Home and School II: Handouts for Families and Educators (NASP, 2004). “Counseling 101” articles and related HCHS II handouts can be downloaded from www.naspcenter.org/principals .

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Volume III, Issue IV

Keys to Productive Discussions in the Math Classroom

To listen well is as powerful a means of influence as to talk well and is as essential to all true conversation.

– Chinese Proverb

A challenge faced by math educators of all levels is how to engage students in their mathematical content through rich discussion or discourse. In classrooms where there is high-quality mathematical discourse, teachers and students ask challenging and thought-provoking questions, and there is skillful facilitation of meaningful discussions focused on the mathematics. The discussions emphasize reasoning, proof, evaluation, and justification. Students learn from one another and value the thinking of their peers. The focus of the conversation is not simply the answer to the problem, but also the students’ strategies, discoveries, conjectures, and reasoning.

The third Standard for Mathematical Practice places a strong emphasis on meaningful discourse. In this standard, students are expected to construct viable arguments and critique the reasoning of others. Meaningful discussions in the mathematics classroom rely on purposeful instructional moves from the teacher, as well as a clear understanding of the demands that are placed on students. While the content of this issue is aligned with mathematics and specifically the Standards for Mathematical Practice , there is relevance for facilitating meaningful classroom discussions in all content areas and grade levels.

The Common Core places a strong emphasis on mathematical reasoning and deep content understanding. Creating the right conditions for these discussions and facilitating conversations that emphasize a deep study of the mathematics is a challenging task. The following keys can help teachers ensure that the discourse in their mathematics classrooms is rich and extends the learning of students. The single most important thing teachers should do to ensure the success of discussions is to ask meaningful questions and facilitate the dialogue among students. The goal in any mathematical discussion is to support the students’ in constructing viable arguments and critiquing the reasoning of others.

Keys for Preparing for the Discussion

Anticipate the strategies students might use, how they will represent their thinking, and predict students’ misconceptions. In addition to drawing on their knowledge of mathematical content, teachers must also bring to classroom discussions an understanding of their students’ prior knowledge and experiences. Once the task has been designed, the teacher must be ready to handle the different strategies that the students will propose. One way to prepare is to draft all possible student strategies, prioritize how those will be shared with the class, and anticipate places where there may be flaws in students’ thinking or misconceptions. By making these predictions in advance of the class discussion, teachers will have a clear sense of the critical “look-fors” as the students are working and an idea of how they wish to shape the classroom discussion. Undoubtedly, students will come up with strategies that the teacher has not predicted; however, teachers will be far more prepared to make sense of these approaches to problem solving when they have thought ahead about what students might bring to the experience.

For instance, consider the following problem:

Anna is collecting pennies for a school-wide penny drive. She has 357 pennies saved in the first week and 225 pennies saved in the second week. Her goal is to donate 1,000 pennies. How many more pennies will Anna need to reach her goal?

Plan questions that will guide students in answering both how they solved a problem and why they chose the solution they used. Preplanning thought-provoking questions will ensure a high level of intellectual engagement during the lesson. Including the context of the problems is essential when forming these questions. By asking students to use the context of the problem when determining their solutions, they are more likely to have solid reasoning for why they solved the problem in the way that they did. For instance, the teacher might ask:

• Why did you _____________ when the problem asked for _____________?
• What does _________ mean in terms of _________________ as it stated in the problem?
• Does this solution make sense given what the problem is asking?
• Why are we ______________ in this problem?

Decide which strategies should be prioritized when sharing with the whole class. It can be overwhelming for students to hear and understand the reasoning behind too many different strategies at once. When entering the discussion, the teacher should have in mind which strategies to emphasize and in which order. For instance, if it is a problem dealing with subtraction, the teacher may choose to emphasize the use of an unmarked number line or adding up before having discussions about adding or subtracting the same number from the minuend and subtrahend in order to create an easier problem and not change the answer.

Keys for Facilitating Discussion

Establish a safe environment where students can take risks and where there are norms for classroom discussions. In order for students to openly share their thinking and risk-making mistakes in front of their peers, it is imperative that there is a supportive classroom environment. Everyone should understand their role in the classroom through the development of classroom norms. The teacher is expected to pose thought-provoking questions, support students’ conversations, listen carefully to monitor students’ understanding and misconceptions, encourage student participation in discussions, and promote student reflection about the learning experience.

Nancy Anderson, one of the authors of the National Council of Teacher of Mathematics’ book entitled, Classroom Discussions: Using Math Talk to Help Students Learn , suggests that teachers instruct their students on the importance of and expectations for mathematical conversations at the start of the school year. She explains how talking like mathematicians can enable students to be stronger mathematical thinkers. As Anderson tells her students:

• Talking and thinking together can help all students understand math better
• It is necessary for more than one person to help solve challenging problems
• There is a great deal to be learned from listening to how other’s think
• Talking about your thinking helps you to clarify your own thoughts
• When talking about the mathematics, you practice using important math vocabulary
• You can learn a great deal about what it takes to understand the ideas of others.

Along with establishing a rationale for mathematical discussions, it is also critical to establish expectations for respectful listening. Students need to be seated where they can see and hear the speaker, and they are expected to listen actively and be prepared to respond to the ideas of others. Students are taught how to respectfully disagree and question one another. Above all, there is acceptance of all ideas and all contributions to the discussion are honored. Once the school year is under way, it is important to revisit the established norms in order to maintain the quality of conversations.

Teach students the expectations for classroom discussions. Despite efforts to establish a rationale for discussions and expectations for listening, rich discussions in mathematics do not happen by chance. The explicit teaching of how students are expected to respond and interact during a classroom discussion in mathematics is necessary. students sharing their thinking should know that their explanations require more than just a description of the strategy they used to solve a problem. Rather, students need to include some sort of visual representation, along with an explanation of how they solved the problem and why they chose to solve the problem in that way.

Students who are listening should be attentive to the thinking of others, reflect on the ideas they have heard to evaluate their efficiency, determine if they agree or disagree, if they understand the thinking of their peers, and what similarities and differences they see between their own thinking and the thinking of others. Students need to be taught how to agree and disagree and how to ask questions for clarification. Provide students with prompts to use during discussions. For instance, students might say:

• The way ______ solved the problem makes sense to me because…
• ______’s strategy was similar to mine because…
• ______’s strategy was different than mine because…
• What I don’t understand about ______’s explanation is why _______.
• I will need to hear _______ explain how _________ again.
• Why did you _____ when you were solving this problem?
• I understand how you ______, but why did you ______?

Present meaningful problems. Teachers should focus on assigning mathematical tasks that are appropriately challenging and enhance students’ learning. Mathematical tasks should investigate important mathematical ideas and have authentic contexts and relevance for students. The problems posed should have multiple solution strategies, encourage investigation, promote reasoning, and require students to provide justifications for their thinking. Ultimately, mathematical tasks should be worthy of student discussion and emphasize important mathematical concepts.

Build in opportunities for independent work and partner or small group work. In order to help students summarize and understand their thinking as well as the thinking of others, it is essential to provide opportunities for students to “turn and talk” about their ideas. For instance, after presenting a problem, students may be asked to represent or state in their own words what the problem is asking, then share that with a partner. After finding an entry point and solving a problem independently, students should share their strategies with a partner or in a group, prior to sharing with the whole class. This gives students practice constructing arguments, providing justifications, and critiquing the thinking of others. Students learn how to listen in a way that prepares them to restate their partner’s thinking in their own words, as well as listening to understand and pose questions of their partner. Partnerships ensure a higher level of accountability and student engagement than is possible with only whole class discussions.

Facilitate the sharing of strategies with the whole class. While students are engaged in discussion, it is the teacher’s role to promote students’ reasoning, ensure that multiple solutions and answers are considered, hold students accountable for sharing both how they solved a problem and why they solved it using a specific strategy, and to make sure that students are actively listening and responding to each other. Teachers can do this is through the use of meaningful questions that will support and extend students’ understanding of the reasoning of others, along with the important mathematical ideas.

The teacher should begin by collecting all students’ answers and encouraging students to think about whether or not more than one answer could be correct given the context of the problem. Then, as chosen students defend their solutions and share arguments for their strategies, the teacher ensures active listening and reflection through the use of guiding questions. For instance, the teacher might ask the student who is sharing:

• Why did you ______?
• Where did ______ come from?
• Where are the original numbers in the problem?
• How did you represent your thinking?

Questions to ask the rest of the class might be:

• Could somebody repeat what _____ has shared in their own words?
• Is _______’s reasoning reasonable? Why or why not?
• Is _______’s strategy an efficient way to solve this problem? Why or why not?
• Do you agree with ______? Why or why not?
• What do you wonder after hearing ______’s thinking?
• Can you think of a counter example? In other words, can you think of an example that would disprove an idea that has been presented?

Promote student reflection on the different strategies. A powerful instructional move after students have heard the thinking of others is to send them back to work in partners or in small groups to reflect on the arguments of others. Carefully crafted questions such as the following can help guide these discussions:

• Which strategy have you heard is the most efficient for solving this problem? Why?
• What are some similarities you have seen between the strategies being used? What are some differences?
• What new ideas did you hear today?
• What confused you?
• What strategies do you think you could try when solving future problems?

In summary, how successfully a teacher facilitates a discussion drives how mathematically rigorous the work is for students. In order for students to be successful with constructing viable arguments and critiquing the reasonableness of answers, students need ample practice solving problems in a variety of ways and defending their thinking with others. Equally important is that students know how to listen to the thinking of others, and pose questions and counter examples as a way of deepening their mathematical understanding. The success of these small and large group discussions rests on the ability of the teacher to plan thoughtfully and facilitate purposefully.

Permission is granted for reprinting and distribution of this newsletter for non-commercial use only.

Please include the following citation on all copies:

Clayton, Heather. “Keys to Productive Discussions in the Math Classroom.” Making the Common Core Come Alive! Volume III, Issue IV, 2014. Available at www.justaskpublications.com. Reproduced with permission of Just ASK Publications & Professional Development (Just ASK). ©2014 by Just ASK. All rights reserved.

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Explained: Importance of critical thinking, problem-solving skills in curriculum

F uture careers are no longer about domain expertise or technical skills. Rather, critical thinking and problem-solving skills in employees are on the wish list of every big organization today. Even curriculums and pedagogies across the globe and within India are now requiring skilled workers who are able to think critically and are analytical.

The reason for this shift in perspective is very simple.

These skills provide a staunch foundation for comprehensive learning that extends beyond books or the four walls of the classroom. In a nutshell, critical thinking and problem-solving skills are a part of '21st Century Skills' that can help unlock valuable learning for life.

Over the years, the education system has been moving away from the system of rote and other conventional teaching and learning parameters.

They are aligning their curriculums to the changing scenario which is becoming more tech-driven and demands a fusion of critical skills, life skills, values, and domain expertise. There's no set formula for success.

Rather, there's a defined need for humans to be more creative, innovative, adaptive, agile, risk-taking, and have a problem-solving mindset.

In today's scenario, critical thinking and problem-solving skills have become more important because they open the human mind to multiple possibilities, solutions, and a mindset that is interdisciplinary in nature.

Therefore, many schools and educational institutions are deploying AI and immersive learning experiences via gaming, and AR-VR technologies to give a more realistic and hands-on learning experience to their students that hone these abilities and help them overcome any doubt or fear.

ADVANTAGES OF CRITICAL THINKING AND PROBLEM-SOLVING IN CURRICULUM

Ability to relate to the real world:  Instead of theoretical knowledge, critical thinking, and problem-solving skills encourage students to look at their immediate and extended environment through a spirit of questioning, curiosity, and learning. When the curriculum presents students with real-world problems, the learning is immense.

Confidence, agility & collaboration : Critical thinking and problem-solving skills boost self-belief and confidence as students examine, re-examine, and sometimes fail or succeed while attempting to do something.

They are able to understand where they may have gone wrong, attempt new approaches, ask their peers for feedback and even seek their opinion, work together as a team, and learn to face any challenge by responding to it.

Willingness to try new things: When problem-solving skills and critical thinking are encouraged by teachers, they set a robust foundation for young learners to experiment, think out of the box, and be more innovative and creative besides looking for new ways to upskill.

It's important to understand that merely introducing these skills into the curriculum is not enough. Schools and educational institutions must have upskilling workshops and conduct special training for teachers so as to ensure that they are skilled and familiarized with new teaching and learning techniques and new-age concepts that can be used in the classrooms via assignments and projects.

Critical thinking and problem-solving skills are two of the most sought-after skills. Hence, schools should emphasise the upskilling of students as a part of the academic curriculum.

The article is authored by Dr Tassos Anastasiades, Principal- IB, Genesis Global School, Noida. 

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What Is Creative Problem Solving and Why Is It Important?

Numerous studies, including ones from the US Department of Education , World Economic Forum , and Bloomberg indicate that tomorrow’s jobs will demand “creative problem solving skills.” But what exactly are creative problem solving skills? And are they being taught effectively to the next generation who will face competition for jobs from automation? To learn more about creative problem solving in the classroom, Adobe conducted a new study to understand how educators and policymakers think about creative problem solving skills, how critical these skills are to future jobs, and how they are currently being nurtured in schools today.

We asked educators and policymakers to talk to us about creative problem solving based upon the following definition: “Creative Problem Solving is the process of redefining problems and opportunities, coming up with new, innovative responses and solutions, and then taking action.” We wanted to know how skills like independent learning, learning through success or failure, and working with diverse teams are critical to a students’ ability to succeed in the future workforce.

What we discovered was extremely illuminating. Three quarters of the educators surveyed believe that students need to develop these skills to protect their futures, as the professions that require creative problem solving are less likely to be impacted by automation. However, it isn’t just job-protection where creative problem solving makes a difference. Almost 90 percent of respondents believe students who excel at creative problem solving will have higher-earning job opportunities in the future, and 85 percent agreed that these same skills are in high demand by today’s employers for senior-level and higher-paying careers.

Knowing that 90 percent of educators believe creative problem solving should be integrated across all curricula, and that policymakers are in vehement agreement, it’s reasonable to assume that schools are already providing opportunities for students to develop these skills. Alarmingly though, this critical skillset is not emphasized enough in schools today due to the barriers educators face – from tight budgets and lack of resources to outdated testing requirements. Coupled with the fact that more than half of educators explain that they do not have the training or knowledge to help students develop creative problem solving skills, the challenge that educators and students face is vast.

Adobe believes that we need to support educators who are teaching creative problem solving, get technology into the hands of schools and students, and inspire young people to create. While technology alone is not the answer, it plays a key role. That is why Adobe is working to update its licensing models, so students – including those under the age of 13, consistent with U.S children’s privacy regulations – can access Creative Cloud in the classroom and at home using just their school I.D. to log in. This will reap benefits for the users, as the educators surveyed who use Creative Cloud in the classroom report that their students are more prepared for the jobs of the future .

Adobe is also constantly developing new storytelling tools like Spark, so students can easily create high quality, visually compelling reports, research papers, posters, writing assignments, presentations and so much more. Lastly, Adobe recognizes that it is critical to challenge students and encourage them to create and to have a positive social impact. That is why we created Project 1324 , which works with emerging creatives and leading youth arts organizations around the world to showcase artists who create the art and change they want to see in their communities.

To read the full study findings, and to learn more about how Adobe is working to get much-needed technology into the hands of students and educators, support educators in teaching creative problem solving skills, and inspire students to create, please visit Creative Problem Solving .

How to align class discussions with learning objectives

A packed curriculum means it’s important to maximize the potential of every classroom activity — including class discussions ! You can transform discussions into meaningful learning opportunities by aligning them with clear learning objectives linked to curriculum standards.

With that in mind, we’re here to share our expertise to guide you in writing actionable learning objectives for class discussions (including ones you can do on Kialo Edu !). We even have free discussion resources to help you maximize student engagement and achievement.

Why is it important to write learning objectives for class discussions?

In class discussions, learning objectives act like a roadmap to guide students toward productive conversations while staying on topic. This makes discussions more purposeful to maximize learning time.

Moreover, learning objectives help focus discussions by targeting specific cognitive skills like critical thinking , language acquisition, and problem-solving. They can also address curriculum standards in subjects like reading, writing, and interdisciplinary literacy.

Finally, aligning discussions with learning objectives facilitates assessment. Educators can use these opportunities to assess students’ progress toward curriculum standards, with the added bonus of students self- and peer-evaluating their work.

How do I write good learning objectives for class discussions?

Learning objectives for class discussions should be specific, measurable, and actionable. Here are our top tips to achieve this:

• Use clear, concise language to facilitate student understanding.
• Use action verbs aligned with cognitive frameworks like Bloom’s Taxonomy or Webb’s Depth of Knowledge framework .
• Target specific cognitive skills or curriculum standards.
• Connect objectives to unit/course goals, making the discussion integral to students’ learning journeys.
• Ensure objectives are achievable within the timeframe.

Now, let’s take a look at examples of discussion learning objectives that target a range of skills and subjects.

Learning objectives for developing students’ critical thinking skills

To develop students’ critical thinking in discussions, objectives should target higher-order skills like synthesis, analysis, and evaluation. Students can apply these skills to construct evidence-based positions in arguments and debates . Below are some examples of subject-specific class discussions: 

Students will be able to argue for their position on the ethics of a scientific issue, using two scientific studies to justify their argument.

Try it in a Kialo discussion: Should cloning humans be legal?

Civics: 

Students will be able to collaboratively identify two potential biases in a news source and explain how these could affect the audience’s perception of the information. 

Social Studies: 

Students will be able to identify two logical fallacies used in a debate on a societal issue and explain how these weaken the arguments.

Try it in a Kialo discussion: Is democracy a good form of government?

Is democracy a good form of governme — kialo-edu.com

Learning objectives for developing students’ problem-solving skills

Discussions encourage collaboration , making them ideal for developing students’ problem-solving skills. Objectives should focus on having students analyze situations, explore causes, and develop solutions. Here are some examples:

Students will be able to present and defend a solution to a labor issue within an LMIC’s supply chain and reflect on alternative solutions from peers.

Try it in a Kialo discussion: Should society reject fast fashion?

Geography: 

Students will be able to generate two potential solutions to an environmental problem, and use a decision-making framework to evaluate the potential consequences of each one.

Literature:

Students will be able to articulate the internal conflict faced by a novel’s main character and generate three possible solutions, considering the character’s motivations, limitations, and the context of the story.

Try it in a Kialo discussion: Was George right to kill Lennie in “Of Mice and Men?”

Learning objectives for developing students’ language acquisition skills

Discussions provide opportunities for students to acquire and apply new language. Objectives may target building students’ subject-specific disciplinary language, developing students’ fluency in a foreign language , or, for ESL students , applying their English language skills for different purposes. Here are some example objectives:

Students will be able to identify three key elements in an artwork and explain how they contribute to the artist’s intended meaning or message.

Try it in a Kialo discussion: Is “Fountain” really a work of art?

Religious Studies: 

Students will be able to critically evaluate opposing viewpoints using accurate religious vocabulary, and construct well-reasoned counter-arguments supported by relevant scripture or scholarly sources.

Try it in a Kialo discussion: Do all religions worship the same higher power?

Foreign language: 

Students will demonstrate fluency in using sentence structures and vocabulary from the unit when discussing the advantages and disadvantages of a topic.

Try it in a Kialo discussion ( available in multiple languages ): Which country would be the most interesting to visit?

Which country would be the most interesting to visit? — kialo-edu.com

English as a Second Language (ESL):

Students will demonstrate fluency in using transition words and phrases when summarizing key arguments for and against a topic from a class debate.

Try it in a Kialo discussion: Is it better to live in the city or the countryside?

Learning objectives for developing students’ reasoning and analysis of claims

Objectives to develop reasoning and claim analysis skills should center around having students evaluate the strength of claims and analyze relationships between factors to develop lines of reasoning. Try these examples:

Students will be able to analyze claims about the causes of a historical event from two different perspectives, citing primary or secondary sources to support each perspective.

Try it in a Kialo discussion: What was the main cause of the Great Depression?

Students will be able to evaluate evidence about the impact of four human activities on an environmental issue, ranking the activities based on the strength and credibility of supporting evidence.

Social Studies:

Students will analyze the pros and cons of a recent societal development, creating a cost-benefit assessment to analyze its potential impacts.

Try it in a Kialo discussion: Do the costs of AI outweigh the benefits?

Learning objectives for developing students’ communication skills

Classroom discussions provide a safe space for students to practice communicating respectfully and engaging with diverse perspectives . Objectives should aim to move students beyond “winning” arguments toward finding common ground. Try these with your students:

Students will be able to identify different perspectives and their supporting evidence on a scientific topic.

Try it in a Kialo discussion: Should we develop technology that can read minds?

English Language Arts:

Students will be able to articulate three perspectives on a recent news story and explain the reasoning behind each one in their own words.

In a Socratic seminar , students will be able to express their textual analysis and interpretations using appropriate tone, word choice, and organizational strategies, and provide constructive feedback to classmates.

Try it in a Kialo discussion: Does Never Let Me Go create a more effective sense of threat than The Handmaid’s Tale ?

Does Never Let Me Go create a more effective sense of threat than The Handmaid’s Tale? — kialo-edu.com

How can students achieve learning objectives in Kialo discussions?

1. kialo discussions greatly increase student participation.

The written format of Kialo discussions can help increase student participation and therefore opportunities to achieve learning objectives. That’s because all students can add their ideas simultaneously, while less confident students are free from the pressure of public speaking. Moreover, Anonymous Discussions mean all students can contribute freely, without fear of judgment.

2. Kialo discussions develop students’ critical thinking and problem-solving skills 

The branching format of Kialo discussions supports students in meeting critical thinking and problem-solving objectives. Students can visualize how ideas connect, enabling them to build sophisticated lines of reasoning. This format also prompts self-reflection, as students deconstruct their perspectives into step-by-step arguments, referencing sources to justify reasoning. 

3. Kialo discussions help educators assess students against learning objectives

Contributions to Kialo discussions are automatically saved, providing valuable assessment evidence. The argument tree and sunburst visualizations offer an overview of the entire discussion, or you can view students’ individual contributions to assess their progress toward objectives. 

You can even provide personalized, targeted feedback on individual claims, helping students address areas for development and meet the intended learning objectives.

So, it’s time to empower students to achieve learning objectives through dynamic class discussions! Head to Kialo Edu’s Topic Library , a treasure trove of over 500 free ideas for discussions spanning history , science , liter a ture , and more. You’ll find discussion topics that not only spark conversation but also directly connect to your learning objectives. Try them out today!

We’d love to hear how you are transforming class discussions into purposeful learning opportunities. Contact us at [email protected] or on social media.

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Sign up for free and use Kialo Edu to have thoughtful classroom discussions and train students’ argumentation and critical thinking skills.