problem solving learning define

Problem-Based Learning (PBL)

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

By working with PBL, students will:

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

How to Begin PBL

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

Designing Classroom Instruction

How to Orchestrate a PBL Activity

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

Teacher’s Role in PBL

The Role of the Students

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

Problem-Based Learning

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

Why Use Problem-Based Learning?

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

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

Considerations for Using Problem-Based Learning

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

Students generally must:

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

Getting Started with Problem-Based Learning

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

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

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

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

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

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

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

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

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

Where can I learn more?

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

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Problem-Based Learning

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What is Problem-Based Learning

Problem-based learning & the classroom, the problem-based learning process, problem-based learning & the common core, project example: a better community, project example: preserving appalachia, project example: make an impact.

All Toolkits

A Learning is Open toolkit written by the New Learning Institute.

Problem-based learning (PBL) challenges students to identify and examine real problems, then work together to address and solve those problems through advocacy and by mobilizing resources. Importantly, every aspect of the problem solving process involves students in real work—work that is a reflection of the range of expertise required to solve issues in the world outside of school.

While problem-based learning can use any type of problem as its basis, the approach described here is deliberately focused on local ones. Local problems allow students to have a meaningful voice, and be instrumental in a process where real, recognizable change results. It also gives students opportunities to source and interact with a variety of local experts.

In many classrooms teachers give students information and then ask them to solve problems at the culmination of a unit. Problem-based learning turns this on its head by challenging students to define the problem before finding the resources necessary to address or solve it. In this approach, teachers are facilitators: they set the context for the problem, ask questions to propel students’ interests and learning forward, help students locate necessary resources and experts, and provide multiple opportunities to critique students’ process and progress. In some cases, the teacher may identify a problem that is connected to existing curriculum; in others the teacher may assign a larger topic and challenge the students to identify a specific problem they are interested in addressing.

This approach is interdisciplinary and provides natural opportunities for integrating a variety of required content areas. Because recognizing and making relationships between content areas is a necessary part of the problem-solving process—as it is in the real world—students are building skills to prepare them for life, work, and civic participation. Problem-based learning gives students a variety of ways to address and tackle a problem. It encourages everyone to contribute and rewards different kinds of success. This builds confidence in students who have not always been successful in school. With the changing needs of today’s world, there is a growing urgency for people who are competent in a range of areas including the ability to apply critical thinking to complex problems, collaborate, network and gather resources, and communicate and persuade others to actively take up a cause.

Problem-based learning builds agency & independence

Although students work collaboratively throughout the process, applying a wide range of skills to new tasks requires them to develop their own specialties that lead to greater confidence and competency. And because the process is student-driven, students are challenged to define the problem, conduct comprehensive research, sort through multiple solutions and present the one that allows them best move forward. This reinforces a sense of self-agency and independence.

Problem-based learning promotes adaptability & flexibility

Investigating and solving problems requires students to work with many different types of people and encounter many unknowns throughout the process. These experiences help students learn to be adaptable and flexible during periods of uncertainty. From an academic standpoint, this flexible mindset is an opportunity for students to develop a range of communication aptitudes and styles. For example, in the beginning research phases, students must gather multiple perspectives and gain a clear understanding of their various audiences. As they move into the later project phases they must develop more nuanced ways to communicate with each audience, from clearly presenting information to persuasion to defending the merits of a new idea.

Problem-based learning is persistent

Educators recognize that when students are working towards a real goal they care about, they show increased investment and willingness to persist through challenges. Problem-based learning requires students to navigate many variables including the diverse personalities on a project team, the decisions and perspectives of stakeholders, challenging and rigorous content, and real world deadlines. Students will experience frustration and failure, but they will learn that working though that by trying new things will be its own reward. And this is a critical lesson that will be carried on into life and work.

Problem-based learning is civically engaged

Because problem-based learning focuses on using local issues as jumping off points it gives students a meaningful context in which to voice their opinions and take the initiative to find solutions. Problems within schools and communities also provide opportunities for students to work directly with stakeholders (i.e. the school principal or a town council member) and experts (i.e. local residents, professionals, and business owners). These local connections make it more likely that students will successfully implement some aspect of their plan and gives students firsthand experience with civic processes.

A problem well put is half solved. – John Dewey

The problem-based learning process described in this toolkit has been refined and tested through the Model Classroom Program, a project of the New Learning Institute. Educators throughout the United States participated in this program by designing, implementing, and documenting projects. The resulting problem-based learning approach provides a clear process and diverse set of tools to support problem-based learning.

The problem-based learning process can help students define problems in new ways, explore multiple perspectives, challenge their thinking, and develop the real-world skills needed for planning and carrying out a project. Beyond this, because the approach emphasizes local and community-based issues, this process develops student drive and motivation as they work towards a tangible end result with the potential to impact their community.

Make it Real

The world is full of unsolved problems and opportunities just waiting to be addressed. The Make It Real phase is about identifying a real problem within the local community, then conducting further investigation to define the problem.

Identify what you do and don’t know about the problem Brainstorm what is known about the problem. What do you know about it at the local level? Is this problem globally relevant? How? What questions would you investigate further?

Discover the problem’s root causes and impacts on the community While it’s easy to find a problem, it’s much harder to understand it. Investigate how the problem impacts different people and places. As a result of these investigations, students will gain a clearer understanding of the problem.

Make it Relevant

Problems are everywhere, but it can often be difficult to convince people that a specific problem should matter to them. The word relevant is from the Latin root meaning “to raise” or “to lift up.” To Make It Relevant, elevate the problem so that people in the community and beyond will take interest and become invested in its resolution. Make important connections in order to begin a plan to address the problem.

Field Studies

Collect as much information as possible on the problem. Conduct the kind of research experts in the field—scientists and historians—conduct. While online and library research is a good starting point, it’s important that students get out into the real world to conduct their own original research! This includes using methods such as surveys, interviews, photo and video documentation, collection of evidence (such as science related activities), and working with a variety of experts and viewpoints.

Develop an action-plan Have students analyze their field studies data and create charts, graphs, and other visual representations to understand their findings. After analyzing, students will have the information needed to develop a plan of action. Importantly, they’ll need to consider how best to meet the needs of all stakeholders, which will include a diverse community such as local businesses, community members, experts, and even the natural world.

Make an Impact

Make An Impact with a creative implementation based on the best research-supported ideas. In many cases, making an impact is about solving the problem. Sometimes it’s about addressing it, making representations to stakeholders, or presenting a possible solution for future implementation. At the most rigorous level, students will implement a project that has lasting impact on their community.

Put your plan into action See the hard work of researching and analyzing the problem pay off as students begin implementing their plans. In so doing, they’ll act as part of a team creating a product to share. Depending on the problem, purpose, and audience, their products might be anything from a website to an art installation to the planning of a community-wide event.

Share your findings and make an impact Share results with important stakeholders and the larger community. Depending on the project, this effort may include awareness campaigns, a persuasive presentation to stakeholders, an action-oriented campaign, a community-wide event, or a re-designed program. In many cases this “final” act leads to the beginning of another project!

With the Common Core implementation, teachers have found different strategies and resources to help align their practice to the standards. Indeed, many schools and districts have discovered a variety of solutions. When considering Common Core alignment, the opportunity presented by methods like problem-based learning hinges on a belief in the art of teaching and the importance of developing students’ passion and love of learning. In short, with the ultimate goal of making students college-, career-, and life-ready, it’s essential that educators put students in the driver’s seat to collaboratively solve real problems.

The Common Core ELA standards draw a portrait of a college- and career-ready student. This portrait includes characteristics such as independence, the ability to adapt communication to different audiences and purposes, the ability to comprehend and critique, appreciation for the value of evidence (when reading and when creating their own work), and the capability to make strategic use of digital media. Developing creative solutions to complex problems provides students with multiple opportunities to develop all of these skills.

Independence

Students are challenged to define the problem and conduct comprehensive research, then present solutions. This student-driven process requires students to find multiple answers and think critically about the best way to act, ultimately building confidence and independence.

Adapting Communication to Different Audiences and Purposes

In the initial research phases, students must gather multiple perspectives and gain a clear understanding of who those audiences are. As they move into the later project phases, they must communicate in a variety of ways (including informative and persuasive methods) to reach diverse audiences.

Comprehending and Critiquing

In examining multiple perspectives, students must summarize various viewpoints, addressing their strengths and critiquing their weaknesses. Furthermore, as students develop solutions they must analyze each idea for its potential success, which compels them to critique their own work in addition to the work of others.

Valuing Evidence

Collecting evidence is essential to the process, whether through visual documentation of a problem, uncovering key facts, or collecting narratives from the community.

Strategic Use of Digital Media

The use of digital media is naturally integrated throughout the entire process. The problem-based learning approach not only builds the specific 21st century skills called for by the Common Core, it also embraces practices supported by hundreds of years of educational theory. This is not the next new thing – problem-based learning is one example of how vetted best educational practices will meet the needs of a future economy and society; and, more immediately, the new Common Core Standards.

Language Arts

The Key Design Considerations for the English Language Arts standards describe an integrated literacy model in which all communication processes are closely connected. Likewise, the problem-based learning approach expects students to read, write, and speak about the issue (whether through interviews or speeches) in a variety of ways (expository, persuasive). In addition, the Key Design Considerations describe how literacy is a shared responsibility across subject areas. Because problem-based learning is rooted in real issues, these naturally connect to science content areas (environmental sciences, engineering and design, innovation and invention), social studies (community history, geography/land forms), math (including operations such as graphing, statistics, economics, and mathematical modeling), and art. As part of this interdisciplinary model, problem-based learning follows a process that touches on key ELA skill areas including research, a variety of writing styles and formats (both reading and writing in these formats), publishing, and integration of digital media.

It’s also important to note that the Common Core calls for an increase in informational and nonfiction text. This objective is easily met through examining real problems. Quite simply, informational and nonfiction text is everywhere – in newspaper articles, public surveys, government documents, etc. Very often, when reading out of context, many students struggle to work through and comprehend these types of complex texts. Because problem-based learning authentically integrates a real purpose with reading informational text, students work harder to comprehend and apply their reading.

Note: Each project has the potential to meet many additional standards. The standards outlined here are only a sampling of those addressed by this approach.

Reading Standards

CCSS.ELA-Literacy.CCRA.R.6 Assess how point of view or purpose shapes the content and style of a text. In the early phases of problem-based learning, students investigate the topic by reading a range of informational and persuasive texts, and by talking to a variety of experts and community members. As an essential component to these investigations on multiple perspectives, students must be able to understand the purpose of the text, the intended audience, and the individual’s position on the issue (if applicable).

CCSS.ELA-Literacy.CCRA.R.7 Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words. As students consider multiple perspectives on their identified problem, they naturally will seek a wide range of print materials, media resources (videos, presentations), and formats (research studies, opinion pieces). Comparing and contrasting the viewpoints of these various texts will help students shape a more holistic view of the problem.

Writing Standards

CCSS.ELA-Literacy.CCRA.W.1 Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence. As students analyze the problem, multiple opportunities for persuasive writing emerge. In the early project phases, students might summarize their perspective on the problem using key evidence from a variety of research (online, community polling, and discussions with experts). In the later project phases, students might develop a proposal or presentation to persuade others to change personal habits or consider a larger change in the community.

Speaking & Listening Standards

CCSS.ELA-Literacy.CCRA.SL.1 Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively. Multiple perspectives are an essential component to any problem-based project. As students investigate, they must seek a wide range of opinions and personal stories on the issues. Furthermore, this process is collaborative. Students must trust and work with each other, they must trust and work with key experts, and, in some cases, they must convince others to collaborate with them around a shared purpose or cause.

CCSS.ELA-Literacy.CCRA.SL.5 Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations. Because each problem-based project requires students to analyze information, share their findings with others, and collaborate on a variety of levels, digital media is naturally integrated into these tasks. Students might create charts, graphs, or other illustrative/photo/video displays to communicate their research results. Students might use a variety of digital formats including graphic posters, video public service announcements (PSAs), and digital presentations to mobilize the community to their cause. Inherent to these processes is special consideration of how images, videos, and other media support key ideas and key evidence and further the effectiveness of their presentation on the intended audience.

Mathematics

Simply put, math is problem solving. Problem-based learning provides multiple opportunities for students to apply and develop their understanding of various mathematical concepts within real contexts. Through the various stages of problem-based learning, students engage in the same dispositions encouraged by the Standards for Mathematical Practice

CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them. Problem-based learning is all about problem solving. An essential first step is understanding the problem as deeply as possible, rather than rushing to solve it. This is a process that takes time and perseverance, both individually and in collaborative student groups.

CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. As students understand and deconstruct a problem, they must begin to form solutions. As part of this process, they must have evidence (including visual and mathematical evidence) to support their position. They must also understand other perspectives to solving the problem, and they must be prepared to critique those other perspectives based on verbal and mathematical reasoning.

CCSS.Math.Practice.MP4 Model with mathematics. Throughout the process, students must analyze information and data using a variety of mathematical models. These range from charts and graphs to 3-D modeling used in science or engineering projects.

CCSS.Math.Practice.MP5 Use appropriate tools strategically. According to the Common Core Math Practices standard, “Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.” In addition to providing opportunities to use these tools, problem-based learning asks students to make effective use of digital and mobile media as they collect information, document the issue, share their findings, and mobilize others to their cause.

Students informed the school about the importance of recycling, developed systems to improve recycling options and implemented a school-wide recycling program that involved all students, other teachers, school principals, school custodians, and the county recycling center.

While investigating their local county history, students were challenged to recognize their role in the community and ultimately realize the importance of stewardship for the county’s land, history and culture. Students began by researching their local history through many first hand experiences including museum visits, local resident interviews and visits to places representing the current culture.

Challenged to find ways to make “A Better Community”, students chose to investigate recycling.

They conducted hands-on research to determine the need for a recycling program through a school survey, town trash pickup and visit to the local Landfill and Recycling Center.

Students then developed a proposal for a school-wide recycling program, interviewed the principal to address their concerns and began to carry out their plan.

Students designed recycling bins for each classroom and worked with school janitors to develop a plan for collection.

Students visited each classroom to distribute the recycling bins and describe how to use them. Students developed a schedule for collecting bins and sorting materials. The program continues beyond the initial school-year; students continue to expand their efforts.

Students created Project Playhouse, a live production for the local community. Audience members included community members, parents, and other students. In addition, students designed a quilt sharing Appalachian history, and recorded their work on a community website.

Appalachia has a rich culture full of unique traditions and an impressive heritage, yet many negative stereotypes persist. 6th grade students brainstormed existing stereotypes and their consequences on the community.

Students discussions led them to realize that, in their region, stereotypes were preventing people from overcoming adversity. They set about to conduct further research demonstrating the strengths of Appalachian heritage.

Students investigated Appalachian culture by working with local experts like Tammy Horn, professor at Eastern Kentucky University and specialist in Appalachian cultural traditions; taking a field trip to Logan Hubble Park to explore the natural region; talking with a “coon” hunter and other local Appalachians including quilters, cooks, artists, and writers.

Students developed a plan to curate an exhibition and live production for the local community. Finally, students connected virtually with museum expert Rebecca Kasemeyer, Associate Director of Education at the Smithsonian National Portrait Gallery to discuss exhibition design.

For their final projects students produced a series of works exhibiting Appalachian life, work, play and community structure including a quilt, a theatrical performance and a website.

Students invited the community to view their exhibit and theatrical performance.

Engineering teacher Bryan Coburn presented a scenario to his students inspired by the community’s very real drought, a drought so bad that cars could only be washed on specific days. Students identified and examined environmental issues related to water scarcity in their community.

Based on initial brainstorming, students divided into teams based on specific problems related to a water shortage. These included topics like watering gardens and lawns, watering cars, drinking water to name a few.

Based on their topic, students conducted online research on existing solutions to their specific problem.

Students analyzed their research to develop their own prototypes and plans for addressing the problem. Throughout the planning phase students received peer and teacher feedback on the viability of their prototypes, resulting in many edits before final designs were selected for creation.

Students created online portfolios showcasing their research, 3D designs, and multimedia presentations marketing their designs. Student portfolios included documentation of each stage of the design process, a design brief, decision matrix, a prototype using Autodesk Inventor 3D professional modeling tool, and a final presentation.

Students shared their presentations and portfolios in a public forum, pitching their proposed solution to a review committee consisting of local engineers from the community, the city water manager and the school principal.

Plan Your PBL Experience

Resources to help you plan.

Problem-based learning projects are inspired by students’ real world experiences and the pressing issues and concerns they want to address. Problem-based learning projects benefit teachers by increasing student motivation and engagement, while deepening knowledge and improving essential skills. In spite of the inherent value problem-based learning brings to any educational setting, planning a large project can be an overwhelming task.

Through the New Learning Institute’s Model Classroom, a range of problem-based learning planning tools have been developed and tested in a variety of educational settings. These tools make the planning process more manageable by supporting teachers in establishing the context and/or problem for a project, planning for and procuring the necessary resources for a real-world project (including community organizations, expert involvement, and tools needed for communicating, creating and sharing), and facilitating students through the project phases.

Here are some initial considerations when planning a problem-based learning project. (More detailed tips and planning tools follow.) These questions can help you determine where to begin your project planning. Once you have a clear idea, the problem-based learning planning tools will guide you through the process.

Are you starting from the curriculum? It’s probably tempting to jump in and define a problem for students based on the unit of study. And time constraints may make a teacher-defined problem necessary. If time permits, a problem-based learning project will be more successful if time is built-in for students to define a problem they’d like to address. Do this by building in topic exploration time, and then challenging students to define a problem based on their findings. Including this extra time will allow students to develop their own interests and questions about the topic, deepening engagement and ensuring that students are investigating a problem they’re invested in—all while covering curriculum requirements.

Are you starting from student interest? Perhaps your students want to solve a problem in the school, such as bullying or lack of recycling. Perhaps they’re concerned about a larger community problem, such as a contested piece of parkland that is up for development or a pollution problem in your local waterways. Starting with student interest can help ensure students’ investment and motivation. However, this starting point provides less direct navigation than existing projects or curriculum materials. When taking on a project of this nature, be sure to identify natural intersections with your curriculum. It also helps to enlist community or expert support.

Start Small – Focus on Practices as Entry Points

If you’re new to problem-based learning it makes sense to start small. Many teachers new to this approach report that starting with the smaller practices—such as integrating research methods or having students define a specific problem within a unit of study—ultimately sets the stage for larger projects and more easily leads them to implement a problem-based learning project.

Opportunities to address and solve problems are everywhere. Just look in your own backyard or schoolyard. Better yet, ask students to identify problems within the school community or based on a topic of interest within a unit of study. As you progress through the project, find natural opportunities for research and problem solving by working with the people who are affected by the issue and invested in solving it. Finally, make sure students share their work with an authentic audience who cares about the problem and its resolution.

Be Honest About Project Constraints

When you’re new to problem-based learning, the most important consideration is your project constraints. For example, perhaps you’re required to cover a designated set of standards and content. Or perhaps you have limited time for this project experience. Whatever the constraints, determine them in advance then plan backwards to determine the length and depth of your project.

Identify Intersections With Your Curriculum

Problem-based learning projects are interdisciplinary and have the ability to meet a range of standards. Identify where these intersections naturally occur with the topic students have selected, then design some activities or project requirements to ensure these content areas are covered.

Turn Limitations Into Opportunities

Many educators work in schools with pre-defined curriculum or schedule constraints that make implementing larger projects difficult. In these cases, it may help to find small windows of opportunity during the school day or after school to implement problem-based learning. For example, some teachers implement problem-based learning in special subject courses which have a more flexible curriculum. Others host afterschool “Genius Hour” programs that challenge students to explore and investigate their interests. Whatever opportunity you find, make the work highly visible to staff and parents. Make it an intention to get the school community exploring and designing possibilities of integrating these practices more holistically.

Take Risks and Model Perseverance

The problem-based learning process is messy and full of opportunities to fail, just like real life and real jobs. Many educators share that this is incredibly difficult for their students and themselves. Despite the initial letdown that comes with small failures, it’s important that students see the value in learning from failure and persevering through these challenges. Model risk taking for your students and when you make a mistake or face a challenge, welcome it with open arms by demonstrating what you’ve learned and what you’ll do differently next time around. Let students know that it’s okay to make mistakes; that mistakes are a welcome opportunity to learn and try something new.

Be Less Helpful

A key to building problem-solving and critical thinking capacities is to be less helpful. Let students figure things out on their own. In classroom implementation, teachers repeatedly share that handing over control to the students and “being less helpful” makes for a big mindshift. This shift is often described as becoming a facilitator, which means knowing when to stand back and knowing when to step-in and offer extra support.

Be Flexible

Recognize that there is no one-size-fits-all answer to any problem. Understanding this and being able to identify unique challenges will help students understand that an initial failure is just a bump in the road. Being flexible also helps students focus on the importance of process over product.

Experts are Everywhere

Experts are everywhere; their differing perspectives and expertise help bring learning to life. But think outside the box about who experts are and integrate multiple opportunities for their involvement. Parents and community members who are not often thought of as experts can speak to life, work, and lived historical experiences. Beyond that, the people usually thought of as experts—researchers, scientists, museum professionals, business professionals, university professors—are more available than many teachers think. It’s often just a matter of asking. And don’t take sole responsibility for finding experts! Seek your students’ help in identifying and securing expert or community support. And when trying to locate experts, don’t forget: students can also be experts.

Maintain a List of Your Support Networks

Some schools have brought the practice of working with the community and outside experts to scale by building databases of parent and community expertise and their interest in working with students. See if a school administrative assistant, student intern, or parent helper can take the lead in developing and maintaining this list for your school community.

Encourage Original Research

Online research is often a great starting point. It can be a way to identify a knowledge base, locate experts, and even find interest-based communities for the topic being approached. While online research is literally right at students’ fingertips, make sure your students spend time offline as well. Original research methods include student-conducted surveys, interviewing experts, and working alongside experts in the field.

This Learning is Open toolkit includes a number of tools and resources that may be helpful as you plan and reflect on your project.

Brainstorming Project Details (Google Presentation) This tool is designed to aid teachers as they brainstorm a project from a variety of starting-points. It’s a helpful tool for independent brainstorming, and would also make a useful workshop tool for teachers who are designing problem-based learning experiences.

Guide to Writing a Problem Statement (PDF) You’ve got to start somewhere. Finding—and defining—a problem is a great place to begin. This guide is a useful tool for teachers and students alike. It will walk you through the process of identifying a problem by providing inspiration on where to look. Then it will support you through the process of defining that problem clearly.

Project Planning Templates (PDF) Need a place to plan out each project phase? Use this project planner to record your ideas in one place. This template is great used alone or in tandem with the other problem-based learning tools.

Ladder of Real World Learning Experiences (PDF) Want to determine if your project is “real” enough? This ladder can be used to help teachers assess their project design based on the real world nature of the project’s learning context, type of activities, and the application of digital tools.

Digital Toolkit (Google Doc) This toolkit was developed in collaboration with teachers and continues to be a community-edited document. The toolkit provides extensive information on digital tools that can be used for planning, brainstorming, collaborating, creating, and sharing work.

Assessing student learning is a crucial part of any dynamic, nonlinear problem-based learning project. Problem-based projects have many parts to them. It’s important to understand each project as a whole as well as each individual component. This section of the toolkit will help you understand problem-based learning assessments and help you develop assessment tools for your problem-based learning experiences.

Because the subject of assessments is so complex, it may be helpful to define how it is approached here.

Portfolio-based Assessment

Each phase of problem-based learning has important tasks and outcomes associated with it. Assessing each phase of the process allows students to receive on-time feedback about their process and associated products and gives them the opportunity to refine and revise their work throughout the process.

Feedback-based Assessment

Problem-based learning emphasizes collaboration with classmates and a range of experts. Assessment should include multiple opportunities for peer feedback, teacher feedback, and expert feedback.

Assessment as a System of Interrelated Feedback Tools

These tools may include rubrics, checklists, observation, portfolios, or quizzes. Whatever the matrix of carefully selected tools, they should optimize the feedback that students receive about what and how they are learning and growing.

Assessment Tools

One way to approach developing assessment tools for your students’ specific problem-based learning project is to deconstruct the learning experience into various categories. Together, these categories make up a simple system through which students may receive feedback on their learning.

Assessing Process

Many students and teachers alike have been conditioned to emphasize and evaluate the end product. While problem-based learning projects often result in impressive end products, it’s important to emphasize each stage of the process with students.

Each phase of problem-based learning process emphasizes important skills, from research and data gathering in the early phases to problem solving, collaboration, and persuasion in the later phases. There are many opportunities to assess student understanding and skill throughout the process. The tools here provide many methods for students to self-assess their process, get feedback from peers, and get feedback from their teachers and other adults.

The Process Portfolio Tool (PDF) provides a place for students to collect their work, define their problem and goals, and reflect throughout the process. Use this as a self-assessment tool, as well as a place to organize the materials for student portfolios.

Driving & Reflection Questioning Guidelines (PDF) is a simple tool for teachers who are integrating problem-based learning into the learning process. The tool highlights the two types of questions teachers/facilitators should consider with students: driving questions and reflection questions. Driving questions push students in their thinking, challenging them to build upon ideas and try new ways to solve problems. Reflection questions ask students to reflect on a process phase once it’s complete, challenging them to think about how they think.

The Peer Feedback Guidelines (PDF) will help students frame how they provide feedback to their peers. The guide includes tips on how and when to use these guidelines in different types of forums (i.e. whole group, gallery-style, and peer-to-peer).

The Buck Institute has also developed a series of rubrics that address various project phases. Their Collaboration Rubric (PDF) can help students be better teammates. (Being an effective teammate is critical to the problem-based learning process.) Their Presentation Rubric (PDF) can help students, adult mentors, and outside experts evaluate final presentations. Final presentations are often one of the most exciting parts of a project.

Assessing Subject Matter and Content

A common concern that emerges in any problem-based learning design is whether projects are able to meet all required subject matter content targets. Because many students are required to learn specific content, there is often tension around the student-directed nature of problem-based learning. While teachers acknowledge that students go deeper into specific content during problem-based learning experiences, teachers also want to ensure that their students are meeting all content goals.

Many teachers in the New Learning Institute’s Model Classroom Program addressed this issue directly by carefully examining their curriculum requirements throughout the planning and implementation phases. Begin by planning activities and real world explorations that address core content. As the project evolves, revisit content standards to mark off and record additional standards met and create a contingency plan for those that have not been addressed.

The Buck Institute’s Rubric for Rubrics (DOC) is an excellent source for designing a rubric to fit your needs. Developing a rubric can be the most simple and effective tool for planning a project around required content targets.

Blended learning is another emerging trend that educators are moving towards as a way to both address individualized skill needs and to create space for real world project strategies, like problem-based learning. In these learning environments, students address skill acquisition through blended experiences and then apply their skills through projects and other real world applications. To learn more about blended models, visit Blend My Learning .

Assessing Mindsets and Skills

In addition to assessing process and subject matter content, it may be helpful to consider the other important mindsets and skills that the problem-based learning project experience fosters. These include persistence, problem solving, collaboration, and adaptability. While problem-based learning supports the development of a large suite of 21st century mindsets and skills, it may be helpful to focus assessments on one or two issues that are most relevant. Some helpful tools may include:

The Buck Institute offers rubrics for Critical Thinking (PDF), Collaboration (PDF), and Creativity and Innovation (PDF) that are aligned to the Common Core State Standards. These can be used as is or tailored to your specific needs.

The Character Growth Card (PDF) from the CharacterLab at Kipp is designed for school assessments more than it is for project assessment, but the list of skills and character traits are relevant to design thinking. With the inclusion of a more relevant, effective scale, these can easily be turned into a rubric, especially when paired with the Buck Institute’s Rubric for Rubrics tool.

Host a Teacher Workshop

Teachers are instrumental in sharing and spreading best practices and innovative strategies to other teachers. Once you’re confident in your conceptual and practical grasp of problem-based learning, share your knowledge and expertise with others.

The downloadable presentation decks below (PowerPoint) are adaptable tools for helping you spread the word to other educators. The presentations vary in length and depth. A 90-minute presentation introduces problem-based learning and provides a hands-on opportunity to complete an activity. The half-day and full day presentations provide in-depth opportunities to explore projects and consider their classroom applications. While this series is structured in a way that each presentation builds on the previous one, each one can also be used individually as appropriate. Each is designed to be interactive and participatory.

Getting Started with Problem-based Learning (PPT) A presentation deck for introducing educators to the Learning is Open problem-based learning process during a 90-minute peer workshop.

Dig Deeper with Problem-based Learning – Half-day (PPT) A presentation deck for training educators on the Learning is Open problem-based learning process during a half-day peer workshop.

Dig Deeper with Problem-based Learning – Full day (PPT) A presentation deck for training educators on the Learning is Open problem-based learning process during a full day peer workshop.

Setting up Learning Experiences Using Real Problems

This New York Times Learning Blog article explores how projects can be set-up with real problems, providing many examples and suggestions for this approach.

Title: “ Guest Lesson | For Authentic Learning Start with Real Problems ” Type: Article Source: Suzie Boss. New York Times Learning Blog

Guest Lesson: Recycling as a Focus for Project-based Learning

There are many ways to set-up a project with a real world problem. This article describes the problem of recycling, providing multiple examples of student projects addressing the issue.

Title: “ Guest Lesson | Recycling as a Focus for Project-Based Learning ” Type: Article Source: Suzie Boss. New York Times Learning Blog

Problem-based Learning: Professional Development Inspires Classroom Project

This video features how the Model Classroom professional development workshop model worked in practice, challenging teachers to collaboratively problem-solve using real world places and experts. It also shows how one workshop participant used her experience to design a yearlong problem-based learning project for first-graders called the “Streamkeepers Project.”

Title: Mission Possible: the Model Classroom Type: Video Source: New Learning Institute

Problem-based Learning in an Engineering Class: Solutions to a Water Shortage

Engineering teacher Bryan Coburn used the problem of a local water shortage to inspire his students to conduct research and design solutions.

Title: “ National Project Aims to Inspire the Model Classroom ” Type: Article Source: eSchool News

Making Project-based Learning More Meaningful

This article provides great tips on how to design projects to be relevant and purposeful for students. While it addresses the larger umbrella of project-based learning, the suggestions and tips provided apply to problem-based learning.

Title: “ How to Reinvent Project-Based Learning to Make it More Meaningful ” Type: Article Source: KQED Mindshift

PBL Downloads

Guide to Writing a Problem Statement (PDF)

A walk-through guide for identifying and defining a problem.

Project Planning Templates (PDF)

A planning template for standalone use or to be used along with other problem-based learning tools.

Process Portfolio Tool (PDF)

A self-assessment tool to support students as they collect their work, define their problem and goals, and make reflections throughout the process.

More PBL Downloads

Getting Started with Problem-based Learning (PPT)

A presentation deck for introducing educators to the Project MASH problem-based learning process during a 90-minute peer workshop.

Dig Deeper with Problem-based Learning – Half-day (PPT)

A presentation deck for training educators on the PBL process during a half-day peer workshop.

Dig Deeper with Problem-based Learning – Full day (PPT)

A presentation deck for training educators on the PBL process during a full day peer workshop.

Problem-Based Learning (PBL)

Problem-Based Learning (PBL) is an instructional method of hands-on, active learning centered on the investigation and resolution of messy, real-world problems.

Contributors Key Concepts Resources and References

Contributors

Late 1960s at the medical school at McMaster University in Canada

Key Concepts

Problem-Based Learning (PBL) is a pedagogical approach and curriculum design methodology often used in higher education and K-12 settings[1][2].

The following are some of the defining characteristics of PBL:

Learning is driven by challenging, open-ended problems with no one “right” answer
Problems/cases are context specific
Students work as self-directed, active investigators and problem-solvers in small collaborative groups (typically of about five students)
A key problem is identified and a solution is agreed upon and implemented
Teachers adopt the role as facilitators of learning, guiding the learning process and promoting an environment of inquiry

Rather than having a teacher provide facts and then testing students ability to recall these facts via memorization, PBL attempts to get students to apply knowledge to new situations. Students are faced with contextualized, ill-structured problems and are asked to investigate and discover meaningful solutions.

Proponents believe that PBL:

develops critical thinking and creative skills
improves problem-solving skills
increases motivation
helps students learn to transfer knowledge to new situations

PBL’s more recent influence can be traced to the late 1960s at the medical school at McMaster University in Canada[3][4]. Shortly thereafter, three other medical schools — the University of Limburg at Maastricht (the Netherlands), the University of Newcastle (Australia), and the University of New Mexico (United States) took on the McMaster model of problem-based learning. Various adaptations were made and the model soon found its way to various other disciplines — business, dentistry, health sciences, law, engineering, education, and so on.

One common criticism of PBL is that students cannot really know what might be important for them to learn, especially in areas which they have no prior experience[3]. Therefore teachers, as facilitators, must be careful to assess and account for the prior knowledge that students bring to the classroom.

Another criticism is that a teacher adopting a PBL approach may not be able to cover as much material as a conventional lecture-based course[3]. PBL can be very challenging to implement, as it requires a lot of planning and hard work for the teacher. It can be difficult at first for the teacher to “relinquish control” and become a facilitator, encouraging the students to ask the right questions rather than handing them solutions.

Additional Resources and References

Thinking Through Project-Based Learning: Guiding Deeper Inquiry : Krauss & Boss’s book contains many practical examples of how to teach and create critical thinking experiences in project-based learning.
Essential Readings in Problem-Based Learning: Exploring and Extending the Legacy of Howard S. Barrows : Walker, Hmelo-Silver & Ertmer’s book discusses developments in the field of PBL, bridging the gap between theory and practice.
Barrows, H. S. (1986). A taxonomy of problem?based learning methods.Medical education, 20(6), 481-486.
Savery, J. R., & Duffy, T. M. (1995). Problem based learning: An instructional model and its constructivist framework. Educational technology, 35(5), 31-38.
Boud, D., & Feletti, G. (1997). The challenge of problem-based learning. Psychology Press.
Barrows, H. S. (1996). Problem?based learning in medicine and beyond: A brief overview. New directions for teaching and learning, 1996(68), 3-12.

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Situated Learning Theory (Lave)

Stereotype Threat (Steele, Aronson)

Albert bandura, erik erikson.

Encyclopedia of the Sciences of Learning pp 2680–2683 Cite as

Problem Solving

David H. Jonassen 2 &
Woei Hung 3
Reference work entry

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11 Citations

Cognition ; Problem typology ; Problem-based learning ; Problems ; Reasoning

Problem solving is the process of constructing and applying mental representations of problems to finding solutions to those problems that are encountered in nearly every context.

Theoretical Background

Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to vexing and complex social problems, such as violence in society (see Problem Typology ). Second, finding or solving for the unknown must have some social, cultural, or intellectual value. That is, someone believes that it is worth finding the unknown. If no one perceives an unknown or a need to determine an unknown, there is no perceived problem. Finding...

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Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology: Research & Development, 48 (4), 63–85.

Jonassen, D. H. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments . New York: Routledge.

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College of Education and Human Development, University of North Dakota, 231 Centennial Drive, Stop 7189, 58202, Grand Forks, ND, USA

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Jonassen, D.H., Hung, W. (2012). Problem Solving. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_208

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The Oxford Handbook of Cognitive Psychology

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48 Problem Solving

Department of Psychological and Brain Sciences, University of California, Santa Barbara

Published: 03 June 2013
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Problem solving refers to cognitive processing directed at achieving a goal when the problem solver does not initially know a solution method. A problem exists when someone has a goal but does not know how to achieve it. Problems can be classified as routine or nonroutine, and as well defined or ill defined. The major cognitive processes in problem solving are representing, planning, executing, and monitoring. The major kinds of knowledge required for problem solving are facts, concepts, procedures, strategies, and beliefs. Classic theoretical approaches to the study of problem solving are associationism, Gestalt, and information processing. Current issues and suggested future issues include decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific thinking, everyday thinking, and the cognitive neuroscience of problem solving. Common themes concern the domain specificity of problem solving and a focus on problem solving in authentic contexts.

The study of problem solving begins with defining problem solving, problem, and problem types. This introduction to problem solving is rounded out with an examination of cognitive processes in problem solving, the role of knowledge in problem solving, and historical approaches to the study of problem solving.

Definition of Problem Solving

Problem solving refers to cognitive processing directed at achieving a goal for which the problem solver does not initially know a solution method. This definition consists of four major elements (Mayer, 1992 ; Mayer & Wittrock, 2006 ):

Cognitive —Problem solving occurs within the problem solver’s cognitive system and can only be inferred indirectly from the problem solver’s behavior (including biological changes, introspections, and actions during problem solving). Process —Problem solving involves mental computations in which some operation is applied to a mental representation, sometimes resulting in the creation of a new mental representation. Directed —Problem solving is aimed at achieving a goal. Personal —Problem solving depends on the existing knowledge of the problem solver so that what is a problem for one problem solver may not be a problem for someone who already knows a solution method.

The definition is broad enough to include a wide array of cognitive activities such as deciding which apartment to rent, figuring out how to use a cell phone interface, playing a game of chess, making a medical diagnosis, finding the answer to an arithmetic word problem, or writing a chapter for a handbook. Problem solving is pervasive in human life and is crucial for human survival. Although this chapter focuses on problem solving in humans, problem solving also occurs in nonhuman animals and in intelligent machines.

How is problem solving related to other forms of high-level cognition processing, such as thinking and reasoning? Thinking refers to cognitive processing in individuals but includes both directed thinking (which corresponds to the definition of problem solving) and undirected thinking such as daydreaming (which does not correspond to the definition of problem solving). Thus, problem solving is a type of thinking (i.e., directed thinking).

Reasoning refers to problem solving within specific classes of problems, such as deductive reasoning or inductive reasoning. In deductive reasoning, the reasoner is given premises and must derive a conclusion by applying the rules of logic. For example, given that “A is greater than B” and “B is greater than C,” a reasoner can conclude that “A is greater than C.” In inductive reasoning, the reasoner is given (or has experienced) a collection of examples or instances and must infer a rule. For example, given that X, C, and V are in the “yes” group and x, c, and v are in the “no” group, the reasoning may conclude that B is in “yes” group because it is in uppercase format. Thus, reasoning is a type of problem solving.

Definition of Problem

A problem occurs when someone has a goal but does not know to achieve it. This definition is consistent with how the Gestalt psychologist Karl Duncker ( 1945 , p. 1) defined a problem in his classic monograph, On Problem Solving : “A problem arises when a living creature has a goal but does not know how this goal is to be reached.” However, today researchers recognize that the definition should be extended to include problem solving by intelligent machines. This definition can be clarified using an information processing approach by noting that a problem occurs when a situation is in the given state, the problem solver wants the situation to be in the goal state, and there is no obvious way to move from the given state to the goal state (Newell & Simon, 1972 ). Accordingly, the three main elements in describing a problem are the given state (i.e., the current state of the situation), the goal state (i.e., the desired state of the situation), and the set of allowable operators (i.e., the actions the problem solver is allowed to take). The definition of “problem” is broad enough to include the situation confronting a physician who wishes to make a diagnosis on the basis of preliminary tests and a patient examination, as well as a beginning physics student trying to solve a complex physics problem.

Types of Problems

It is customary in the problem-solving literature to make a distinction between routine and nonroutine problems. Routine problems are problems that are so familiar to the problem solver that the problem solver knows a solution method. For example, for most adults, “What is 365 divided by 12?” is a routine problem because they already know the procedure for long division. Nonroutine problems are so unfamiliar to the problem solver that the problem solver does not know a solution method. For example, figuring out the best way to set up a funding campaign for a nonprofit charity is a nonroutine problem for most volunteers. Technically, routine problems do not meet the definition of problem because the problem solver has a goal but knows how to achieve it. Much research on problem solving has focused on routine problems, although most interesting problems in life are nonroutine.

Another customary distinction is between well-defined and ill-defined problems. Well-defined problems have a clearly specified given state, goal state, and legal operators. Examples include arithmetic computation problems or games such as checkers or tic-tac-toe. Ill-defined problems have a poorly specified given state, goal state, or legal operators, or a combination of poorly defined features. Examples include solving the problem of global warming or finding a life partner. Although, ill-defined problems are more challenging, much research in problem solving has focused on well-defined problems.

Cognitive Processes in Problem Solving

The process of problem solving can be broken down into two main phases: problem representation , in which the problem solver builds a mental representation of the problem situation, and problem solution , in which the problem solver works to produce a solution. The major subprocess in problem representation is representing , which involves building a situation model —that is, a mental representation of the situation described in the problem. The major subprocesses in problem solution are planning , which involves devising a plan for how to solve the problem; executing , which involves carrying out the plan; and monitoring , which involves evaluating and adjusting one’s problem solving.

For example, given an arithmetic word problem such as “Alice has three marbles. Sarah has two more marbles than Alice. How many marbles does Sarah have?” the process of representing involves building a situation model in which Alice has a set of marbles, there is set of marbles for the difference between the two girls, and Sarah has a set of marbles that consists of Alice’s marbles and the difference set. In the planning process, the problem solver sets a goal of adding 3 and 2. In the executing process, the problem solver carries out the computation, yielding an answer of 5. In the monitoring process, the problem solver looks over what was done and concludes that 5 is a reasonable answer. In most complex problem-solving episodes, the four cognitive processes may not occur in linear order, but rather may interact with one another. Although some research focuses mainly on the execution process, problem solvers may tend to have more difficulty with the processes of representing, planning, and monitoring.

Knowledge for Problem Solving

An important theme in problem-solving research is that problem-solving proficiency on any task depends on the learner’s knowledge (Anderson et al., 2001 ; Mayer, 1992 ). Five kinds of knowledge are as follows:

Facts —factual knowledge about the characteristics of elements in the world, such as “Sacramento is the capital of California” Concepts —conceptual knowledge, including categories, schemas, or models, such as knowing the difference between plants and animals or knowing how a battery works Procedures —procedural knowledge of step-by-step processes, such as how to carry out long-division computations Strategies —strategic knowledge of general methods such as breaking a problem into parts or thinking of a related problem Beliefs —attitudinal knowledge about how one’s cognitive processing works such as thinking, “I’m good at this”

Although some research focuses mainly on the role of facts and procedures in problem solving, complex problem solving also depends on the problem solver’s concepts, strategies, and beliefs (Mayer, 1992 ).

Historical Approaches to Problem Solving

Psychological research on problem solving began in the early 1900s, as an outgrowth of mental philosophy (Humphrey, 1963 ; Mandler & Mandler, 1964 ). Throughout the 20th century four theoretical approaches developed: early conceptions, associationism, Gestalt psychology, and information processing.

Early Conceptions

The start of psychology as a science can be set at 1879—the year Wilhelm Wundt opened the first world’s psychology laboratory in Leipzig, Germany, and sought to train the world’s first cohort of experimental psychologists. Instead of relying solely on philosophical speculations about how the human mind works, Wundt sought to apply the methods of experimental science to issues addressed in mental philosophy. His theoretical approach became structuralism —the analysis of consciousness into its basic elements.

Wundt’s main contribution to the study of problem solving, however, was to call for its banishment. According to Wundt, complex cognitive processing was too complicated to be studied by experimental methods, so “nothing can be discovered in such experiments” (Wundt, 1911/1973 ). Despite his admonishments, however, a group of his former students began studying thinking mainly in Wurzburg, Germany. Using the method of introspection, subjects were asked to describe their thought process as they solved word association problems, such as finding the superordinate of “newspaper” (e.g., an answer is “publication”). Although the Wurzburg group—as they came to be called—did not produce a new theoretical approach, they found empirical evidence that challenged some of the key assumptions of mental philosophy. For example, Aristotle had proclaimed that all thinking involves mental imagery, but the Wurzburg group was able to find empirical evidence for imageless thought .

Associationism

The first major theoretical approach to take hold in the scientific study of problem solving was associationism —the idea that the cognitive representations in the mind consist of ideas and links between them and that cognitive processing in the mind involves following a chain of associations from one idea to the next (Mandler & Mandler, 1964 ; Mayer, 1992 ). For example, in a classic study, E. L. Thorndike ( 1911 ) placed a hungry cat in what he called a puzzle box—a wooden crate in which pulling a loop of string that hung from overhead would open a trap door to allow the cat to escape to a bowl of food outside the crate. Thorndike placed the cat in the puzzle box once a day for several weeks. On the first day, the cat engaged in many extraneous behaviors such as pouncing against the wall, pushing its paws through the slats, and meowing, but on successive days the number of extraneous behaviors tended to decrease. Overall, the time required to get out of the puzzle box decreased over the course of the experiment, indicating the cat was learning how to escape.

Thorndike’s explanation for how the cat learned to solve the puzzle box problem is based on an associationist view: The cat begins with a habit family hierarchy —a set of potential responses (e.g., pouncing, thrusting, meowing, etc.) all associated with the same stimulus (i.e., being hungry and confined) and ordered in terms of strength of association. When placed in the puzzle box, the cat executes its strongest response (e.g., perhaps pouncing against the wall), but when it fails, the strength of the association is weakened, and so on for each unsuccessful action. Eventually, the cat gets down to what was initially a weak response—waving its paw in the air—but when that response leads to accidentally pulling the string and getting out, it is strengthened. Over the course of many trials, the ineffective responses become weak and the successful response becomes strong. Thorndike refers to this process as the law of effect : Responses that lead to dissatisfaction become less associated with the situation and responses that lead to satisfaction become more associated with the situation. According to Thorndike’s associationist view, solving a problem is simply a matter of trial and error and accidental success. A major challenge to assocationist theory concerns the nature of transfer—that is, where does a problem solver find a creative solution that has never been performed before? Associationist conceptions of cognition can be seen in current research, including neural networks, connectionist models, and parallel distributed processing models (Rogers & McClelland, 2004 ).

Gestalt Psychology

The Gestalt approach to problem solving developed in the 1930s and 1940s as a counterbalance to the associationist approach. According to the Gestalt approach, cognitive representations consist of coherent structures (rather than individual associations) and the cognitive process of problem solving involves building a coherent structure (rather than strengthening and weakening of associations). For example, in a classic study, Kohler ( 1925 ) placed a hungry ape in a play yard that contained several empty shipping crates and a banana attached overhead but out of reach. Based on observing the ape in this situation, Kohler noted that the ape did not randomly try responses until one worked—as suggested by Thorndike’s associationist view. Instead, the ape stood under the banana, looked up at it, looked at the crates, and then in a flash of insight stacked the crates under the bananas as a ladder, and walked up the steps in order to reach the banana.

According to Kohler, the ape experienced a sudden visual reorganization in which the elements in the situation fit together in a way to solve the problem; that is, the crates could become a ladder that reduces the distance to the banana. Kohler referred to the underlying mechanism as insight —literally seeing into the structure of the situation. A major challenge of Gestalt theory is its lack of precision; for example, naming a process (i.e., insight) is not the same as explaining how it works. Gestalt conceptions can be seen in modern research on mental models and schemas (Gentner & Stevens, 1983 ).

Information Processing

The information processing approach to problem solving developed in the 1960s and 1970s and was based on the influence of the computer metaphor—the idea that humans are processors of information (Mayer, 2009 ). According to the information processing approach, problem solving involves a series of mental computations—each of which consists of applying a process to a mental representation (such as comparing two elements to determine whether they differ).

In their classic book, Human Problem Solving , Newell and Simon ( 1972 ) proposed that problem solving involved a problem space and search heuristics . A problem space is a mental representation of the initial state of the problem, the goal state of the problem, and all possible intervening states (based on applying allowable operators). Search heuristics are strategies for moving through the problem space from the given to the goal state. Newell and Simon focused on means-ends analysis , in which the problem solver continually sets goals and finds moves to accomplish goals.

Newell and Simon used computer simulation as a research method to test their conception of human problem solving. First, they asked human problem solvers to think aloud as they solved various problems such as logic problems, chess, and cryptarithmetic problems. Then, based on an information processing analysis, Newell and Simon created computer programs that solved these problems. In comparing the solution behavior of humans and computers, they found high similarity, suggesting that the computer programs were solving problems using the same thought processes as humans.

An important advantage of the information processing approach is that problem solving can be described with great clarity—as a computer program. An important limitation of the information processing approach is that it is most useful for describing problem solving for well-defined problems rather than ill-defined problems. The information processing conception of cognition lives on as a keystone of today’s cognitive science (Mayer, 2009 ).

Classic Issues in Problem Solving

Three classic issues in research on problem solving concern the nature of transfer (suggested by the associationist approach), the nature of insight (suggested by the Gestalt approach), and the role of problem-solving heuristics (suggested by the information processing approach).

Transfer refers to the effects of prior learning on new learning (or new problem solving). Positive transfer occurs when learning A helps someone learn B. Negative transfer occurs when learning A hinders someone from learning B. Neutral transfer occurs when learning A has no effect on learning B. Positive transfer is a central goal of education, but research shows that people often do not transfer what they learned to solving problems in new contexts (Mayer, 1992 ; Singley & Anderson, 1989 ).

Three conceptions of the mechanisms underlying transfer are specific transfer , general transfer , and specific transfer of general principles . Specific transfer refers to the idea that learning A will help someone learn B only if A and B have specific elements in common. For example, learning Spanish may help someone learn Latin because some of the vocabulary words are similar and the verb conjugation rules are similar. General transfer refers to the idea that learning A can help someone learn B even they have nothing specifically in common but A helps improve the learner’s mind in general. For example, learning Latin may help people learn “proper habits of mind” so they are better able to learn completely unrelated subjects as well. Specific transfer of general principles is the idea that learning A will help someone learn B if the same general principle or solution method is required for both even if the specific elements are different.

In a classic study, Thorndike and Woodworth ( 1901 ) found that students who learned Latin did not subsequently learn bookkeeping any better than students who had not learned Latin. They interpreted this finding as evidence for specific transfer—learning A did not transfer to learning B because A and B did not have specific elements in common. Modern research on problem-solving transfer continues to show that people often do not demonstrate general transfer (Mayer, 1992 ). However, it is possible to teach people a general strategy for solving a problem, so that when they see a new problem in a different context they are able to apply the strategy to the new problem (Judd, 1908 ; Mayer, 2008 )—so there is also research support for the idea of specific transfer of general principles.

Insight refers to a change in a problem solver’s mind from not knowing how to solve a problem to knowing how to solve it (Mayer, 1995 ; Metcalfe & Wiebe, 1987 ). In short, where does the idea for a creative solution come from? A central goal of problem-solving research is to determine the mechanisms underlying insight.

The search for insight has led to five major (but not mutually exclusive) explanatory mechanisms—insight as completing a schema, insight as suddenly reorganizing visual information, insight as reformulation of a problem, insight as removing mental blocks, and insight as finding a problem analog (Mayer, 1995 ). Completing a schema is exemplified in a study by Selz (Fridja & de Groot, 1982 ), in which people were asked to think aloud as they solved word association problems such as “What is the superordinate for newspaper?” To solve the problem, people sometimes thought of a coordinate, such as “magazine,” and then searched for a superordinate category that subsumed both terms, such as “publication.” According to Selz, finding a solution involved building a schema that consisted of a superordinate and two subordinate categories.

Reorganizing visual information is reflected in Kohler’s ( 1925 ) study described in a previous section in which a hungry ape figured out how to stack boxes as a ladder to reach a banana hanging above. According to Kohler, the ape looked around the yard and found the solution in a flash of insight by mentally seeing how the parts could be rearranged to accomplish the goal.

Reformulating a problem is reflected in a classic study by Duncker ( 1945 ) in which people are asked to think aloud as they solve the tumor problem—how can you destroy a tumor in a patient without destroying surrounding healthy tissue by using rays that at sufficient intensity will destroy any tissue in their path? In analyzing the thinking-aloud protocols—that is, transcripts of what the problem solvers said—Duncker concluded that people reformulated the goal in various ways (e.g., avoid contact with healthy tissue, immunize healthy tissue, have ray be weak in healthy tissue) until they hit upon a productive formulation that led to the solution (i.e., concentrating many weak rays on the tumor).

Removing mental blocks is reflected in classic studies by Duncker ( 1945 ) in which solving a problem involved thinking of a novel use for an object, and by Luchins ( 1942 ) in which solving a problem involved not using a procedure that had worked well on previous problems. Finding a problem analog is reflected in classic research by Wertheimer ( 1959 ) in which learning to find the area of a parallelogram is supported by the insight that one could cut off the triangle on one side and place it on the other side to form a rectangle—so a parallelogram is really a rectangle in disguise. The search for insight along each of these five lines continues in current problem-solving research.

Heuristics are problem-solving strategies, that is, general approaches to how to solve problems. Newell and Simon ( 1972 ) suggested three general problem-solving heuristics for moving from a given state to a goal state: random trial and error , hill climbing , and means-ends analysis . Random trial and error involves randomly selecting a legal move and applying it to create a new problem state, and repeating that process until the goal state is reached. Random trial and error may work for simple problems but is not efficient for complex ones. Hill climbing involves selecting the legal move that moves the problem solver closer to the goal state. Hill climbing will not work for problems in which the problem solver must take a move that temporarily moves away from the goal as is required in many problems.

Means-ends analysis involves creating goals and seeking moves that can accomplish the goal. If a goal cannot be directly accomplished, a subgoal is created to remove one or more obstacles. Newell and Simon ( 1972 ) successfully used means-ends analysis as the search heuristic in a computer program aimed at general problem solving, that is, solving a diverse collection of problems. However, people may also use specific heuristics that are designed to work for specific problem-solving situations (Gigerenzer, Todd, & ABC Research Group, 1999 ; Kahneman & Tversky, 1984 ).

Current and Future Issues in Problem Solving

Eight current issues in problem solving involve decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific problem solving, everyday thinking, and the cognitive neuroscience of problem solving.

Decision Making

Decision making refers to the cognitive processing involved in choosing between two or more alternatives (Baron, 2000 ; Markman & Medin, 2002 ). For example, a decision-making task may involve choosing between getting $240 for sure or having a 25% change of getting $1000. According to economic theories such as expected value theory, people should chose the second option, which is worth $250 (i.e., .25 x $1000) rather than the first option, which is worth $240 (1.00 x $240), but psychological research shows that most people prefer the first option (Kahneman & Tversky, 1984 ).

Research on decision making has generated three classes of theories (Markman & Medin, 2002 ): descriptive theories, such as prospect theory (Kahneman & Tversky), which are based on the ideas that people prefer to overweight the cost of a loss and tend to overestimate small probabilities; heuristic theories, which are based on the idea that people use a collection of short-cut strategies such as the availability heuristic (Gigerenzer et al., 1999 ; Kahneman & Tversky, 2000 ); and constructive theories, such as mental accounting (Kahneman & Tversky, 2000 ), in which people build a narrative to justify their choices to themselves. Future research is needed to examine decision making in more realistic settings.

Intelligence and Creativity

Although researchers do not have complete consensus on the definition of intelligence (Sternberg, 1990 ), it is reasonable to view intelligence as the ability to learn or adapt to new situations. Fluid intelligence refers to the potential to solve problems without any relevant knowledge, whereas crystallized intelligence refers to the potential to solve problems based on relevant prior knowledge (Sternberg & Gregorenko, 2003 ). As people gain more experience in a field, their problem-solving performance depends more on crystallized intelligence (i.e., domain knowledge) than on fluid intelligence (i.e., general ability) (Sternberg & Gregorenko, 2003 ). The ability to monitor and manage one’s cognitive processing during problem solving—which can be called metacognition —is an important aspect of intelligence (Sternberg, 1990 ). Research is needed to pinpoint the knowledge that is needed to support intelligent performance on problem-solving tasks.

Creativity refers to the ability to generate ideas that are original (i.e., other people do not think of the same idea) and functional (i.e., the idea works; Sternberg, 1999 ). Creativity is often measured using tests of divergent thinking —that is, generating as many solutions as possible for a problem (Guilford, 1967 ). For example, the uses test asks people to list as many uses as they can think of for a brick. Creativity is different from intelligence, and it is at the heart of creative problem solving—generating a novel solution to a problem that the problem solver has never seen before. An important research question concerns whether creative problem solving depends on specific knowledge or creativity ability in general.

Teaching of Thinking Skills

How can people learn to be better problem solvers? Mayer ( 2008 ) proposes four questions concerning teaching of thinking skills:

What to teach —Successful programs attempt to teach small component skills (such as how to generate and evaluate hypotheses) rather than improve the mind as a single monolithic skill (Covington, Crutchfield, Davies, & Olton, 1974 ). How to teach —Successful programs focus on modeling the process of problem solving rather than solely reinforcing the product of problem solving (Bloom & Broder, 1950 ). Where to teach —Successful programs teach problem-solving skills within the specific context they will be used rather than within a general course on how to solve problems (Nickerson, 1999 ). When to teach —Successful programs teaching higher order skills early rather than waiting until lower order skills are completely mastered (Tharp & Gallimore, 1988 ).

Overall, research on teaching of thinking skills points to the domain specificity of problem solving; that is, successful problem solving depends on the problem solver having domain knowledge that is relevant to the problem-solving task.

Expert Problem Solving

Research on expertise is concerned with differences between how experts and novices solve problems (Ericsson, Feltovich, & Hoffman, 2006 ). Expertise can be defined in terms of time (e.g., 10 years of concentrated experience in a field), performance (e.g., earning a perfect score on an assessment), or recognition (e.g., receiving a Nobel Prize or becoming Grand Master in chess). For example, in classic research conducted in the 1940s, de Groot ( 1965 ) found that chess experts did not have better general memory than chess novices, but they did have better domain-specific memory for the arrangement of chess pieces on the board. Chase and Simon ( 1973 ) replicated this result in a better controlled experiment. An explanation is that experts have developed schemas that allow them to chunk collections of pieces into a single configuration.

In another landmark study, Larkin et al. ( 1980 ) compared how experts (e.g., physics professors) and novices (e.g., first-year physics students) solved textbook physics problems about motion. Experts tended to work forward from the given information to the goal, whereas novices tended to work backward from the goal to the givens using a means-ends analysis strategy. Experts tended to store their knowledge in an integrated way, whereas novices tended to store their knowledge in isolated fragments. In another study, Chi, Feltovich, and Glaser ( 1981 ) found that experts tended to focus on the underlying physics concepts (such as conservation of energy), whereas novices tended to focus on the surface features of the problem (such as inclined planes or springs). Overall, research on expertise is useful in pinpointing what experts know that is different from what novices know. An important theme is that experts rely on domain-specific knowledge rather than solely general cognitive ability.

Analogical Reasoning

Analogical reasoning occurs when people solve one problem by using their knowledge about another problem (Holyoak, 2005 ). For example, suppose a problem solver learns how to solve a problem in one context using one solution method and then is given a problem in another context that requires the same solution method. In this case, the problem solver must recognize that the new problem has structural similarity to the old problem (i.e., it may be solved by the same method), even though they do not have surface similarity (i.e., the cover stories are different). Three steps in analogical reasoning are recognizing —seeing that a new problem is similar to a previously solved problem; abstracting —finding the general method used to solve the old problem; and mapping —using that general method to solve the new problem.

Research on analogical reasoning shows that people often do not recognize that a new problem can be solved by the same method as a previously solved problem (Holyoak, 2005 ). However, research also shows that successful analogical transfer to a new problem is more likely when the problem solver has experience with two old problems that have the same underlying structural features (i.e., they are solved by the same principle) but different surface features (i.e., they have different cover stories) (Holyoak, 2005 ). This finding is consistent with the idea of specific transfer of general principles as described in the section on “Transfer.”

Mathematical and Scientific Problem Solving

Research on mathematical problem solving suggests that five kinds of knowledge are needed to solve arithmetic word problems (Mayer, 2008 ):

Factual knowledge —knowledge about the characteristics of problem elements, such as knowing that there are 100 cents in a dollar Schematic knowledge —knowledge of problem types, such as being able to recognize time-rate-distance problems Strategic knowledge —knowledge of general methods, such as how to break a problem into parts Procedural knowledge —knowledge of processes, such as how to carry our arithmetic operations Attitudinal knowledge —beliefs about one’s mathematical problem-solving ability, such as thinking, “I am good at this”

People generally possess adequate procedural knowledge but may have difficulty in solving mathematics problems because they lack factual, schematic, strategic, or attitudinal knowledge (Mayer, 2008 ). Research is needed to pinpoint the role of domain knowledge in mathematical problem solving.

Research on scientific problem solving shows that people harbor misconceptions, such as believing that a force is needed to keep an object in motion (McCloskey, 1983 ). Learning to solve science problems involves conceptual change, in which the problem solver comes to recognize that previous conceptions are wrong (Mayer, 2008 ). Students can be taught to engage in scientific reasoning such as hypothesis testing through direct instruction in how to control for variables (Chen & Klahr, 1999 ). A central theme of research on scientific problem solving concerns the role of domain knowledge.

Everyday Thinking

Everyday thinking refers to problem solving in the context of one’s life outside of school. For example, children who are street vendors tend to use different procedures for solving arithmetic problems when they are working on the streets than when they are in school (Nunes, Schlieman, & Carraher, 1993 ). This line of research highlights the role of situated cognition —the idea that thinking always is shaped by the physical and social context in which it occurs (Robbins & Aydede, 2009 ). Research is needed to determine how people solve problems in authentic contexts.

Cognitive Neuroscience of Problem Solving

The cognitive neuroscience of problem solving is concerned with the brain activity that occurs during problem solving. For example, using fMRI brain imaging methodology, Goel ( 2005 ) found that people used the language areas of the brain to solve logical reasoning problems presented in sentences (e.g., “All dogs are pets…”) and used the spatial areas of the brain to solve logical reasoning problems presented in abstract letters (e.g., “All D are P…”). Cognitive neuroscience holds the potential to make unique contributions to the study of problem solving.

Problem solving has always been a topic at the fringe of cognitive psychology—too complicated to study intensively but too important to completely ignore. Problem solving—especially in realistic environments—is messy in comparison to studying elementary processes in cognition. The field remains fragmented in the sense that topics such as decision making, reasoning, intelligence, expertise, mathematical problem solving, everyday thinking, and the like are considered to be separate topics, each with its own separate literature. Yet some recurring themes are the role of domain-specific knowledge in problem solving and the advantages of studying problem solving in authentic contexts.

Future Directions

Some important issues for future research include the three classic issues examined in this chapter—the nature of problem-solving transfer (i.e., How are people able to use what they know about previous problem solving to help them in new problem solving?), the nature of insight (e.g., What is the mechanism by which a creative solution is constructed?), and heuristics (e.g., What are some teachable strategies for problem solving?). In addition, future research in problem solving should continue to pinpoint the role of domain-specific knowledge in problem solving, the nature of cognitive ability in problem solving, how to help people develop proficiency in solving problems, and how to provide aids for problem solving.

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

Identify the Problem
Define the Problem
Form a Strategy
Organize Information
Allocate Resources
Monitor Progress
Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

Asking questions about the problem
Breaking the problem down into smaller pieces
Looking at the problem from different perspectives
Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

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You can become a better problem solving by:

Practicing brainstorming and coming up with multiple potential solutions to problems
Being open-minded and considering all possible options before making a decision
Breaking down problems into smaller, more manageable pieces
Asking for help when needed
Researching different problem-solving techniques and trying out new ones
Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors. The Psychology of Problem Solving . Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving . Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Center for Teaching

Teaching problem solving.

Print Version

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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Article • 7 min read

What Is Problem Solving?

By the Mind Tools Content Team

We all spend a lot of our time solving problems, both at work and in our personal lives.

Some problems are small, and we can quickly sort them out ourselves. But others are complex challenges that take collaboration, creativity, and a considerable amount of effort to solve.

At work, the types of problems we face depend largely on the organizations we're in and the jobs we do. A manager in a cleaning company, for example, might spend their day untangling staffing issues, resolving client complaints, and sorting out problems with equipment and supplies. An aircraft designer, on the other hand, might be grappling with a problem about aerodynamics, or trying to work out why a new safety feature isn't working. Meanwhile, a politician might be exploring solutions to racial injustice or climate change.

But whatever issues we face, there are some common ways to tackle them effectively. And we can all boost our confidence and ability to succeed by building a strong set of problem-solving skills.

Mind Tools offers a large collection of resources to help you do just that!

How Well Do You Solve Problems?

Start by taking an honest look at your existing skills. What's your current approach to solving problems, and how well is it working? Our quiz, How Good Is Your Problem Solving? lets you analyze your abilities, and signposts ways to address any areas of weakness.

Define Every Problem

The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem – not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work. However, if you look a bit deeper, the real issue might be a general lack of training, or an unreasonable workload across the team.

Tools like 5 Whys , Appreciation and Root Cause Analysis get you asking the right questions, and help you to work through the layers of a problem to uncover what's really going on.

However, defining a problem doesn't mean deciding how to solve it straightaway. It's important to look at the issue from a variety of perspectives. If you commit yourself too early, you can end up with a short-sighted solution. The CATWOE checklist provides a powerful reminder to look at many elements that may contribute to the problem, keeping you open to a variety of possible solutions.

Understanding Complexity

As you define your problem, you'll often discover just how complicated it is. There are likely several interrelated issues involved. That's why it's important to have ways to visualize, simplify and make sense of this tangled mess!

Affinity Diagrams are great for organizing many different pieces of information into common themes, and for understanding the relationships between them.

Another popular tool is the Cause-and-Effect Diagram . To generate viable solutions, you need a solid understanding of what's causing the problem.

When your problem occurs within a business process, creating a Flow Chart , Swim Lane Diagram or a Systems Diagram will help you to see how various activities and inputs fit together. This may well highlight a missing element or bottleneck that's causing your problem.

Quite often, what seems to be a single problem turns out to be a whole series of problems. The Drill Down technique prompts you to split your problem into smaller, more manageable parts.

General Problem-Solving Tools

When you understand the problem in front of you, you’re ready to start solving it. With your definition to guide you, you can generate several possible solutions, choose the best one, then put it into action. That's the four-step approach at the heart of good problem solving.

There are various problem-solving styles to use. For example:

Constructive Controversy is a way of widening perspectives and energizing discussions.
Inductive Reasoning makes the most of people’s experiences and know-how, and can speed up solution finding.
Means-End Analysis can bring extra clarity to your thinking, and kick-start the process of implementing solutions.

Specific Problem-Solving Systems

Some particularly complicated or important problems call for a more comprehensive process. Again, Mind Tools has a range of approaches to try, including:

Simplex , which involves an eight-stage process: problem finding, fact finding, defining the problem, idea finding, selecting and evaluating, planning, selling the idea, and acting. These steps build upon the basic, four-step process described above, and they create a cycle of problem finding and solving that will continually improve your organization.
Appreciative Inquiry , which is a uniquely positive way of solving problems by examining what's working well in the areas surrounding them.
Soft Systems Methodology , which takes you through four stages to uncover more details about what's creating your problem, and then define actions that will improve the situation.

Further Problem-Solving Strategies

Good problem solving requires a number of other skills – all of which are covered by Mind Tools.

For example, we have a large section of resources to improve your Creativity , so that you come up with a range of possible solutions.

By strengthening your Decision Making , you'll be better at evaluating the options, selecting the best ones, then choosing how to implement them.

And our Project Management collection has valuable advice for strengthening the whole problem-solving process. The resources there will help you to make effective changes – and then keep them working long term.

Problems are an inescapable part of life, both in and out of work. So we can all benefit from having strong problem-solving skills.

It's important to understand your current approach to problem solving, and to know where and how to improve.

Define every problem you encounter – and understand its complexity, rather than trying to solve it too soon.

There's a range of general problem-solving approaches, helping you to generate possible answers, choose the best ones, and then implement your solution.

Some complicated or serious problems require more specific problem-solving systems, especially when they relate to business processes.

By boosting your creativity, decision-making and project-management skills, you’ll become even better at solving all the problems you face.

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Med Sci Educ
v.31(3); 2021 Jun

Effective Learning Behavior in Problem-Based Learning: a Scoping Review

Azril shahreez abdul ghani.

1 Department of Basic Medical Sciences, Kulliyah of Medicine, Bandar Indera Mahkota Campus, International Islamic University Malaysia, Kuantan, 25200 Pahang Malaysia

2 Department of Medical Education, School of Medical Sciences, Health Campus, Universiti Sains Malaysia, Kubang Kerian, Kota Bharu, 16150 Kelantan Malaysia

Ahmad Fuad Abdul Rahim

Muhamad saiful bahri yusoff, siti nurma hanim hadie.

3 Department of Anatomy, School of Medical Sciences, Health Campus, Universiti Sains Malaysia, Kubang Kerian, 16150 Kota Bharu, Kelantan Malaysia

Problem-based learning (PBL) emphasizes learning behavior that leads to critical thinking, problem-solving, communication, and collaborative skills in preparing students for a professional medical career. However, learning behavior that develops these skills has not been systematically described. This review aimed to unearth the elements of effective learning behavior in a PBL context, using the protocol by Arksey and O’Malley. The protocol identified the research question, selected relevant studies, charted and collected data, and collated, summarized, and reported results. We discovered three categories of elements—intrinsic empowerment, entrustment, and functional skills—proven effective in the achievement of learning outcomes in PBL.

Introduction

Problem-based learning (PBL) is an educational approach that utilizes the principles of collaborative learning in small groups, first introduced by McMaster Medical University [ 1 ]. The shift of the higher education curriculum from traditional, lecture-based approaches to an integrated, student-centered approach was triggered by concern over the content-driven nature of medical knowledge with minimal clinical application [ 2 ]. The PBL pedagogy uses a systematic approach, starting with an authentic, real-life problem scenario as a context in which learning is not separated from practice as students collaborate and learn [ 3 ]. The tutor acts as a facilitator who guides the students’ learning, while students are required to solve the problems by discussing them with group members [ 4 ]. The essential aspect of the PBL process is the ability of the students to recognize their current knowledge, determine the gaps in their knowledge and experience, and acquire new knowledge to bridge the gaps [ 5 ]. PBL is a holistic approach that gives students an active role in their learning.

Since its inception, PBL has been used in many undergraduate and postgraduate degree programs, such as medicine [ 6 , 7 ], nursing [ 8 ], social work education [ 9 ], law [ 10 ], architecture [ 11 ], economics [ 12 ], business [ 13 ], science [ 14 ], and engineering [ 15 ]. It has also been applied in elementary and secondary education [ 16 – 18 ]. Despite its many applications, its implementation is based on a single universal workflow framework that contains three elements: problem as the initiator for learning, tutor as a facilitator in the group versions, and group work as a stimulus for collaborative interaction [ 19 ]. However, there are various versions of PBL workflow, such as the seven-step technique based on the Maastricht “seven jumps” process. The tutor’s role is to ensure the achievement of learning objectives and to assess students’ performance [ 20 , 21 ].

The PBL process revolves around four types of learning principles: constructive, self-directed, collaborative, and contextual [ 19 ]. Through the constructive learning process, the students are encouraged to think about what is already known and integrate their prior knowledge with their new understanding. This process helps the student understand the content, form a new opinion, and acquire new knowledge [ 22 ]. The PBL process encourages students to become self-directed learners who plan, monitor, and evaluate their own learning, enabling them to become lifelong learners [ 23 ]. The contextualized collaborative learning process also promotes interaction among students, who share similar responsibilities to achieve common goals relevant to the learning context [ 24 ]. By exchanging ideas and providing feedback during the learning session, the students can attain a greater understanding of the subject matter [ 25 ].

Dolmans et al. [ 19 ] pointed out two issues related to the implementation of PBL: dominant facilitators and dysfunctional PBL groups. These problems inhibit students’ self-directed learning and reduce their satisfaction level with the PBL session. A case study by Eryilmaz [ 26 ] that evaluated engineering students’ and tutors’ experience of PBL discovered that PBL increased the students’ self-confidence and improved essential skills such as problem-solving, communications, critical thinking, and collaboration. Although most of the participants in the study found PBL satisfactory, many complained about the tutor’s poor guidance and lack of preparation. Additionally, it was noted that 64% of the first-year students were unable to adapt to the PBL system because they had been accustomed to conventional learning settings and that 43% of students were not adequately prepared for the sessions and thus were minimally involved in the discussion.

In a case study by Cónsul-giribet [ 27 ], newly graduated nursing professionals reported a lack of perceived theoretical basic science knowledge at the end of their program, despite learning through PBL. The nurses perceived that this lack of knowledge might affect their expertise, identity, and professional image.

Likewise, a study by McKendree [ 28 ] reported the outcomes of a workshop that explored the strengths and weaknesses of PBL in an allied health sciences curriculum in the UK. The workshop found that problems related to PBL were mainly caused by students, the majority of whom came from conventional educational backgrounds either during high school or their first degree. They felt anxious when they were involved in PBL, concerned about “not knowing when to stop” in exploring the learning needs. Apart from a lack of basic science knowledge, the knowledge acquired during PBL sessions remains unorganized [ 29 ]. Hence, tutors must guide students in overcoming this situation by instilling appropriate insights and essential skills for the achievement of the learning outcomes [ 30 ]. It was also evident that the combination of intention and motivation to learn and desirable learning behavior determined the quality of learning outcomes [ 31 , 32 ]. However, effective learning behaviors that help develop these skills have not been systematically described. Thus, this scoping review aimed to unearth the elements of effective learning behavior in the PBL context.

Scoping Review Protocol

This scoping review was performed using a protocol by Arksey and O’Malley [ 33 ]. The protocol comprises five phases: (i) identification of research questions, (ii) identification of relevant articles, (iii) selection of relevant studies, (iv) data collection and charting, and (v) collating, summarizing, and reporting the results.

Identification of Research Questions

This scoping review was designed to unearth the elements of effective learning behavior that can be generated from learning through PBL instruction. The review aimed to answer one research question: “What are the effective learning behavior elements related to PBL?” For the purpose of the review, an operational definition of effective learning behavior was constructed, whereby it was defined as any learning behavior that is related to PBL instruction and has been shown to successfully attain the desired learning outcomes (i.e., cognitive, skill, or affective)—either quantitatively or qualitatively—in any intervention conducted in higher education institutions.

The positive outcome variables include student viewpoint or perception, student learning experience and performance, lecturer viewpoint and expert judgment, and other indirect variables that may be important indicators of successful PBL learning (i.e., attendance to PBL session, participation in PBL activity, number of interactions in PBL activity, and improvement in communication skills in PBL).

Identification of Relevant Articles

An extensive literature search was conducted on articles published in English between 2015 and 2019. Three databases—Google Scholar, Scopus, and PubMed—were used for the literature search. Seven search terms with the Boolean combination were used, whereby the keywords were identified from the Medical Subject Headings (MeSH) and Education Resources Information Center (ERIC) databases. The search terms were tested and refined with multiple test searches. The final search terms with the Boolean operation were as follows: “problem-based learning” AND (“learning behavior” OR “learning behaviour”) AND (student OR “medical students” OR undergraduate OR “medical education”).

Selection of Relevant Articles

The articles from the three databases were exported manually into Microsoft Excel. The duplicates were removed, and the remaining articles were reviewed based on the inclusion and exclusion criteria. These criteria were tested on titles and abstracts to ensure their robustness in capturing the articles related to learning behavior in PBL. The shortlisted articles were reviewed by two independent researchers, and a consensus was reached either to accept or reject each article based on the set criteria. When a disagreement occurred between the two reviewers, the particular article was re-evaluated independently by the third and fourth researchers (M.S.B.Y and A.F.A.R), who have vast experience in conducting qualitative research. The sets of criteria for selecting abstracts and final articles were developed. The inclusion and exclusion criteria are listed in Table Table1 1 .

Inclusion and exclusion criteria

Data Charting

The selected final articles were reviewed, and several important data were extracted to provide an objective summary of the review. The extracted data were charted in a table, including the (i) title of the article, (ii) author(s), (iii) year of publication, (iv) aim or purpose of the study, (v) study design and method, (iv) intervention performed, and (v) study population and sample size.

Collating, Summarizing, and Reporting the Results

A content analysis was performed to identify the elements of effective learning behaviors in the literature by A.S.A.G and S.N.H.H, who have experience in conducting qualitative studies. The initial step of content analysis was to read the selected articles thoroughly to gain a general understanding of the articles and extract the elements of learning behavior which are available in the articles. Next, the elements of learning behavior that fulfil the inclusion criteria were extracted. The selected elements that were related to each other through their content or context were grouped into subtheme categories. Subsequently, the combinations of several subthemes expressing similar underlying meanings were grouped into themes. Each of the themes and subthemes was given a name, which was operationally defined based on the underlying elements. The selected themes and subthemes were presented to the independent researchers in the team (M.S.B.Y and A.F.A.R), and a consensus was reached either to accept or reformulate each of the themes and subthemes. The flow of the scoping review methods for this study is illustrated in Fig. 1 .

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The flow of literature search and article selection

Literature Search

Based on the keyword search, 1750 articles were obtained. Duplicate articles that were not original articles found in different databases and resources were removed. Based on the inclusion and exclusion criteria of title selection, the eligibility of 1750 abstracts was evaluated. The articles that did not fulfil the criteria were removed, leaving 328 articles for abstract screening. A total of 284 articles were screened according to the eligibility criteria for abstract selection. Based on these criteria, 284 articles were selected and screened according to the eligibility criteria for full article selection. Fourteen articles were selected for the final review. The information about these articles is summarized in Table Table2 2 .

Studies characteristics

Study Characteristics

The final 14 articles were published between 2015 and 2019. The majority of the studies were conducted in Western Asian countries ( n = 4), followed by China ( n = 3), European countries ( n = 2), Thailand ( n = 2), Indonesia ( n = 1), Singapore ( n = 1), and South Africa ( n = 1). Apart from traditional PBL, some studies incorporated other pedagogic modalities into their PBL sessions, such as online learning, blended learning, and gamification. The majority of the studies targeted a single-profession learner group, and one study was performed on mixed interprofessional health education learners.

Results of Thematic Analysis

The thematic analysis yielded three main themes of effective learning behavior: intrinsic empowerment, entrustment, and functional skills. Intrinsic empowerment overlies four proposed subthemes: proactivity, organization, diligence, and resourcefulness. For entrustment, there were four underlying subthemes: students as assessors, students as teachers, feedback-giving, and feedback-receiving. The functional skills theme contains four subthemes: time management, digital proficiency, data management, and collaboration.

Theme 1: Intrinsic Empowerment

Intrinsic empowerment enforces student learning behavior that can facilitate the achievement of learning outcomes. By empowering the development of these behaviors, students can become lifelong learners [ 34 ]. The first element of intrinsic empowerment is proactive behavior. In PBL, the students must be proactive in analyzing problems [ 35 , 36 ] and their learning needs [ 35 , 37 ], and this can be done by integrating prior knowledge and previous experience through a brainstorming session [ 35 , 38 ]. The students must be proactive in seeking guidance to ensure they stay focused and confident [ 39 , 40 ]. Finding ways to integrate content from different disciplines [ 35 , 41 ], formulate new explanations based on known facts [ 34 , 35 , 41 ], and incorporate hands-on activity [ 35 , 39 , 42 ] during a PBL session are also proactive behaviors.

The second element identified is “being organized” which reflects the ability of students to systematically manage their roles [ 43 ], ideas, and learning needs [ 34 ]. The students also need to understand the task for each learning role in PBL, such as chairperson or leader, scribe, recorder, and reflector. This role needs to be assigned appropriately to ensure that all members take part in the discussion [ 43 ]. Similarly, when discussing ideas or learning needs, the students need to follow the steps in the PBL process and organize and prioritize the information to ensure that the issues are discussed systematically and all aspects of the problems are covered accordingly [ 34 , 37 ]. This team organization and systematic thought process is an effective way for students to focus, plan, and finalize their learning tasks.

The third element of intrinsic empowerment is “being diligent.” Students must consistently conduct self-revision [ 40 ] and keep track of their learning plan to ensure the achievement of their learning goal [ 4 , 40 ]. The students must also be responsible for completing any given task and ensuring good understanding prior to their presentation [ 40 ]. Appropriate actions need to be undertaken to find solutions to unsolved problems [ 40 , 44 ]. This effort will help them think critically and apply their knowledge for problem-solving.

The fourth element identified is “being resourceful.” Students should be able to acquire knowledge from different resources, which include external resources (i.e., lecture notes, textbooks, journal articles, audiovisual instructions, the Internet) [ 38 , 40 , 45 ] and internal resources (i.e., students’ prior knowledge or experience) [ 35 , 39 ]. The resources must be evidence-based, and thus should be carefully selected by evaluating their cross-references and appraising them critically [ 37 ]. Students should also be able to understand and summarize the learned materials and explain them using their own words [ 4 , 34 ]. The subthemes of the intrinsic empowerment theme are summarized in Table Table3 3 .

Intrinsic empowerment subtheme with the learning behavior elements

Theme 2: Entrustment

Entrustment emphasizes the various roles of students in PBL that can promote effective learning. The first entrusted role identified is “student as an assessor.” This means that students evaluate their own performance in PBL [ 46 ]. The evaluation of their own performance must be based on the achievement of the learning outcomes and reflect actual understanding of the content as well as the ability to apply the learned information in problem-solving [ 46 ].

The second element identified in this review is “student as a teacher.” To ensure successful peer teaching in PBL, students need to comprehensively understand the content of the learning materials and summarize the content in an organized manner. The students should be able to explain the gist of the discussed information using their own words [ 4 , 34 ] and utilize teaching methods to cater to differences in learning styles (i.e., visual, auditory, and kinesthetic) [ 41 ]. These strategies help capture their group members’ attention and evoke interactive discussions among them.

The third element of entrustment is to “give feedback.” Students should try giving constructive feedback on individual and group performance in PBL. Feedback on individual performance must reflect the quality of the content and task presented in the PBL. Feedback on group performance should reflect the ways in which the group members communicate and complete the group task [ 47 ]. To ensure continuous constructive feedback, students should be able to generate feedback questions beforehand and immediately deliver them during the PBL sessions [ 44 , 47 ]. In addition, the feedback must include specific measures for improvement to help their peers to take appropriate action for the future [ 47 ].

The fourth element of entrustment is “receive feedback.” Students should listen carefully to the feedback given and ask questions to clarify the feedback [ 47 ]. They need to be attentive and learn to deal with negative feedback [ 47 ]. Also, if the student does not receive feedback, they should request it either from peers or teachers and ask specific questions, such as what aspects to improve and how to improve [ 47 ]. The data on the subthemes of the entrustment theme are summarized in Table Table4 4 .

Entrustment subtheme with the learning behavior elements

Theme 3: Functional Skills

Functional skills refer to essential skills that can help students learn independently and competently. The first element identified is time management skills. In PBL, students must know how to prioritize learning tasks according to the needs and urgency of the tasks [ 40 ]. To ensure that students can self-pace their learning, a deadline should be set for each learning task within a manageable and achievable learning schedule [ 40 ].

Furthermore, students should have digital proficiency, the ability to utilize digital devices to support learning [ 38 , 40 , 44 ]. The student needs to know how to operate basic software (e.g., Words and PowerPoints) and the basic digital tools (i.e., social media, cloud storage, simulation, and online community learning platforms) to support their learning [ 39 , 40 ]. These skills are important for peer learning activities, which may require information sharing, information retrieval, online peer discussion, and online peer feedback [ 38 , 44 ].

The third functional skill identified is data management, the ability to collect key information in the PBL trigger and analyze that information to support the solution in a problem-solving activity [ 39 ]. Students need to work either individually or in a group to collect the key information from a different trigger or case format such as text lines, an interview, an investigation, or statistical results [ 39 ]. Subsequently, students also need to analyze the information and draw conclusions based on their analysis [ 39 ].

The fourth element of functional skill is collaboration. Students need to participate equally in the PBL discussion [ 41 , 46 ]. Through discussion, confusion and queries can be addressed and resolved by listening, respecting others’ viewpoints, and responding professionally [ 35 , 39 , 43 , 44 ]. In addition, the students need to learn from each other and reflect on their performance [ 48 ]. Table Table5 5 summarizes the data on the subthemes of the functional skills theme.

Functional skills subtheme with the learning behavior elements

This scoping review outlines three themes of effective learning behavior elements in the PBL context: intrinsic empowerment, entrustment, and functional skills. Hence, it is evident from this review that successful PBL instruction demands students’ commitment to empower themselves with value-driven behaviors, skills, and roles.

In this review, intrinsic empowerment is viewed as enforcement of students’ internal strength in performing positive learning behaviors related to PBL. This theme requires the student to proactively engage in the learning process, organize their learning activities systematically, persevere in learning, and be intelligently resourceful. One of the elements of intrinsic empowerment is the identification and analysis of problems related to complex scenarios. This element is aligned with a study by Meyer [ 49 ], who observed students’ engagement in problem identification and clarification prior to problem-solving activities in a PBL session related to multiple engineering design. Rubenstein and colleagues [ 50 ] discovered in a semi-structured interview the importance of undergoing a problem identification process before proposing a solution during learning. It was reported that the problem identification process in PBL may enhance the attainment of learning outcomes, specifically in the domain of concept understanding [ 51 ].

The ability of the students to acquire and manage learning resources is essential for building their understanding of the learned materials and enriching discussion among team members during PBL. This is aligned with a study by Jeong and Hmelo-Silver [ 52 ], who studied the use of learning resources by students in PBL. The study concluded that in a resource-rich environment, the students need to learn how to access and understand the resources to ensure effective learning. Secondly, they need to process the content of the resources, integrate various resources, and apply them in problem-solving activities. Finally, they need to use the resources in collaborative learning activities, such as sharing and relating to peer resources.

Wong [ 53 ] documented that excellent students spent considerably more time managing academic resources than low achievers. The ability of the student to identify and utilize their internal learning resources, such as prior knowledge and experience, is also important. A study by Lee et al. [ 54 ] has shown that participants with high domain-specific prior knowledge displayed a more systematic approach and high accuracy in visual and motor reactions in solving problems compared to novice learners.

During the discussion phase in PBL, organizing ideas—e.g., arranging relevant information gathered from the learning resources into relevant categories—is essential for communicating the idea clearly [ 34 ]. This finding is in line with a typology study conducted by Larue [ 55 ] on second-year nursing students’ learning strategies during a group discussion. The study discovered that although the content presented by the student is adequate, they unable to make further progress in the group discussion until they are instructed by the tutor on how to organize the information given into a category [ 55 ].

Hence, the empowerment of student intrinsic behavior may enhance students’ learning in PBL by allowing them to make a decision in their learning objectives and instilling confidence in them to achieve goals. A study conducted by Kirk et al. [ 56 ] proved that highly empowered students obtain better grades, increase learning participation, and target higher educational aspirations.

Entrustment is the learning role given to students to be engaging and identify gaps in their learning. This theme requires the student to engage in self-assessment, prepare to teach others, give constructive feedback, and value the feedback received. One of the elements of entrustment is the ability to self-assess. In a study conducted by Mohd et al. [ 57 ] looking at the factors in PBL that can strengthen the capability of IT students, they discovered that one of the critical factors that contribute to these skills is the ability of the student to perform self-assessment in PBL. As mentioned by Daud, Kassim, and Daud [ 58 ], the self-assessment may be more reliable if the assessment is performed based on the objectives set beforehand and if the criteria of the assessment are understood by the learner. This is important to avoid the fact that the result of the self-assessment is influenced by the students’ perception of themselves rather than reflecting their true performance. However, having an assessment based on the learning objective only focuses on the immediate learning requirements in the PBL. To foster lifelong learning skills, it should also be balanced with the long-term focus of assessment, such as utilizing the assessment to foster the application of knowledge in solving real-life situations. This is aligned with the review by Boud and Falchikov [ 59 ] suggesting that students need to become assessors within the concept of participation in practice, that is, the kind that is within the context of real life and work.

The second subtheme of entrustment is “students as a teacher” in PBL. In our review, the student needs to be well prepared with the teaching materials. A cross-sectional study conducted by Charoensakulchai and colleagues discovered that student preparation is considered among the important factors in PBL success, alongside other factors such as “objective and contents,” “student assessment,” and “attitude towards group work” [ 60 ]. This is also aligned with a study conducted by Sukrajh [ 61 ] using focus group discussion on fifth-year medical students to explore their perception of preparedness before conducting peer teaching activity. In this study, the student in the focus group expressed that the preparation made them more confident in teaching others because preparing stimulated them to activate and revise prior knowledge, discover their knowledge gaps, construct new knowledge, reflect on their learning, improve their memory, inspire them to search several resources, and motivate them to learn the topics.

The next element of “student as a teacher” is using various learning styles to teach other members in the group. A study conducted by Almomani [ 62 ] showed that the most preferred learning pattern by the high school student is the visual pattern, followed by auditory pattern and then kinesthetic. However, in the university setting, Hamdani [ 63 ] discovered that students prefer a combination of the three learning styles. Anbarasi [ 64 ] also explained that incorporating teaching methods based on the student’s preferred learning style further promotes active learning among the students and significantly improved the long-term retrieval of knowledge. However, among the three learning styles group, he discovered that the kinesthetic group with the kinesthetic teaching method showed a significantly higher post-test score compared to the traditional group with the didactic teaching method, and he concluded that this is because of the involvement of more active learning activity in the kinesthetic group.

The ability of students to give constructive feedback on individual tasks is an important element in promoting student contribution in PBL because feedback from peers or teachers is needed to reassure themselves that they are on the right track in the learning process. Kamp et al. [ 65 ] performed a study on the effectiveness of midterm peer feedback on student individual cognitive, collaborative, and motivational contributions in PBL. The experimental group that received midterm peer feedback combined with goal-setting with face-to-face discussion showed an increased amount of individual contributions in PBL. Another element of effective feedback is that the feedback is given immediately after the observed behavior. Parikh and colleagues survey student feedback in PBL environments among 103 final-year medical students in five Ontario schools, including the University of Toronto, McMaster University, Queens University, the University of Ottawa, and the University of Western Ontario. They discovered that there was a dramatic difference between McMaster University and other universities in the immediacy of feedback they practiced. Seventy percent of students at McMaster reported receiving immediate feedback in PBL, compared to less than 40 percent of students from the other universities, in which most of them received feedback within one week or several weeks after the PBL had been conducted [ 66 ]. Another study, conducted among students of the International Medical University of Kuala Lumpur examining the student expectation on feedback, discovered that immediate feedback is effective if the feedback is in written form, simple but focused on the area of improvement, and delivered by a content expert. If the feedback is delivered by a content non-expert and using a model answer, it must be supplemented with teacher dialogue sessions to clarify the feedback received [ 67 ].

Requesting feedback from peers and teachers is an important element of the PBL learning environment, enabling students to discover their learning gaps and ways to fill them. This is aligned with a study conducted by de Jong and colleagues [ 68 ], who discovered that high-performing students are more motivated to seek feedback than low-performing students. The main reason for this is because high-performing students seek feedback as a tool to learn from, whereas low-performing students do so as an academic requirement. This resulted in high-performing students collecting more feedback. A study by Bose and Gijselaers [ 69 ] examined the factors that promote feedback-seeking behavior in medical residency. They discovered that feedback-seeking behavior can be promoted by providing residents with high-quality feedback to motivate them to ask for feedback for improvement.

By assigning an active role to students as teachers, assessors, and feedback providers, teachers give them the ownership and responsibility to craft their learning. The learner will then learn the skills to monitor and reflect on their learning to achieve academic success. Furthermore, an active role encourages students to be evaluative experts in their own learning, and promoting deep learning [ 70 ].

Functional skills refer to essential abilities for competently performing a task in PBL. This theme requires the student to organize and plan time for specific learning tasks, be digitally literate, use data effectively to support problem-solving, and work together efficiently to achieve agreed objectives. One of the elements in this theme is to have a schedule of learning tasks with deadlines. In a study conducted by Tadjer and colleagues [ 71 ], they discovered that setting deadlines with a restricted time period in a group activity improved students’ cognitive abilities and soft skills. Although the deadline may initially cause anxiety, coping with it encourages students to become more creative and energetic in performing various learning strategies [ 72 , 73 ]. Ballard et al. [ 74 ] reported that students tend to work harder to complete learning tasks if they face multiple deadlines.

The students also need to be digitally literate—i.e., able to demonstrate the use of technological devices and tools in PBL. Taradi et al. [ 75 ] discovered that incorporating technology in learning—blending web technology with PBL—removes time and place barriers in the creation of a collaborative environment. It was found that students who participated in web discussions achieved a significantly higher mean grade on a physiology final examination than those who used traditional methods. Also, the incorporation of an online platform in PBL can facilitate students to develop investigation and inquiry skills with high-level cognitive thought processes, which is crucial to successful problem-solving [ 76 ].

In PBL, students need to work collaboratively with their peers to solve problems. A study by Hidayati et al. [ 77 ] demonstrated that effective collaborative skills improve cognitive learning outcomes and problem-solving ability among students who undergo PBL integrated with digital mind maps. To ensure successful collaborative learning in PBL, professional communication among students is pertinent. Research by Zheng and Huang [ 78 ] has proven that co-regulation (i.e., warm and responsive communication that provides support to peers) improved collaborative effort and group performance among undergraduate and master’s students majoring in education and psychology. This is also in line with a study by Maraj and colleagues [ 79 ], which showed the strong team interaction within the PBL group leads to a high level of team efficacy and academic self-efficacy. Moreover, strengthening communication competence, such as by developing negotiation skills among partners during discussion sessions, improves student scores [ 80 ].

PBL also includes opportunities for students to learn from each other (i.e., peer learning). A study by Maraj et al. [ 79 ] discovered that the majority of the students in their study perceived improvement in their understanding of the learned subject when they learned from each other. Another study by Lyonga [ 81 ] documented the successful formation of cohesive group learning, where students could express and share their ideas with their friends and help each other. It was suggested that each student should be paired with a more knowledgeable student who has mastered certain learning components to promote purposeful structured learning within the group.

From this scoping review, it is clear that functional skills equip the students with abilities and knowledge needed for successful PBL. Studies have shown that strong time management skills, digital literacy, data management, and collaborative skills lead to positive academic achievement [ 77 , 82 , 83 ].

Limitation of the Study

This scoping review is aimed to capture the recent effective learning behavior in problem-based learning; therefore, the literature before 2015 was not included. Without denying the importance of publication before 2015, we are relying on Okoli and Schabram [ 84 ] who highlighted the impossibility of retrieving all the published articles when conducting a literature search. Based on this ground, we decided to focus on the time frame between 2015 and 2019, which is aligned with the concepts of study maturity (i.e., the more mature the field, the higher the published articles and therefore more topics were investigated) by Kraus et al. [ 85 ]. In fact, it was noted that within this time frame, a significant number of articles have been found as relevant to PBL with the recent discovery of effective learning behavior. Nevertheless, our time frame did not include the timing of the coronavirus disease 19 (COVID-19) pandemic outbreak, which began at the end of 2019. Hence, we might miss some important elements of learning behavior that are required for the successful implementation of PBL during the COVID-19 pandemic.

Surprisingly, the results obtained from this study are also applicable for the PBL sessions administration during the COVID-19 pandemic situation as one of the functional skills identified is digital proficiency. This skill is indeed important for the successful implementation of online PBL session.

This review identified the essential learning behaviors required for effective PBL in higher education and clustered them into three main themes: (i) intrinsic empowerment, (ii) entrustment, and (iii) functional skills. These learning behaviors must coexist to ensure the achievement of desired learning outcomes. In fact, the findings of this study indicated two important implications for future practice. Firstly, the identified learning behaviors can be incorporated as functional elements in the PBL framework and implementation. Secondly, the learning behaviors change and adaption can be considered to be a new domain of formative assessment related to PBL. It is noteworthy to highlight that these learning behaviors could help in fostering the development of lifelong skills for future workplace challenges. Nevertheless, considerably more work should be carried out to design a solid guideline on how to systematically adopt the learning behaviors in PBL sessions, especially during this COVID-19 pandemic situation.

This study was supported by Postgraduate Incentive Grant-PhD (GIPS-PhD, grant number: 311/PPSP/4404803).

Declarations

The study has received an ethical approval from the Human Research Ethics Committee of Universiti Sains Malaysia.

No informed consent required for the scoping review.

The authors declare no competing interests.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Pave the Way for Self-regulation and Problem-solving With Social-emotional Learning

Posted: April 3, 2024

Problem-solving is a social-emotional learning (SEL) skill children need for lifelong success. Effective problem-solving skills support children's ability to self-regulate, focus on tasks, think flexibly and creatively, work with others, and generate multiple ways to solve problems. When young children develop and build these skills, it positively impacts their interactions with others, grows their capacity to manage challenges, and boosts a sense of competence.

A group of school-age children are stacking plastic blocks with an educator.

The foundation for effective social problem-solving is grounded in self-regulation, or the ability to regulate emotions when interacting with others. It is easier to focus on one's feelings and the feelings and perspectives of others and to work cooperatively toward solutions when a child can self-regulate and calm down. Children develop self-regulation skills over time, with practice and with adult guidance. Equally important is how an adult models emotion regulation and co-regulation.

"Caregivers play a key role in cultivating the development of emotion regulation through co-regulation, or the processes by which they provide external support or scaffolding as children navigate their emotional experiences" (Paley & Hajal, 2022, p. 1).

When adults model calm and self-regulated approaches to problem-solving, it shows children how to approach problems constructively. For example, an educator says, "I'm going to take a breath and calm down so I can think better." This model helps children see and hear a strategy to support self-regulation.

Problem-solving skills help children resolve conflicts and interact with others as partners and collaborators. Developing problem-solving skills helps children learn and grow empathy for others, stand up for themselves, and build resilience and competence to work through challenges in their world.

Eight strategies to support problem-solving

Teach about emotions and use feeling words throughout the day. When children have more words to express themselves and their feelings, it is easier to address and talk about challenges when they arise.
Recognize and acknowledge children's feelings throughout the day. For example, when children enter the classroom during circle time, mealtime, and outside time, ask them how they feel. Always acknowledge children's feelings, both comfortable and uncomfortable, to support an understanding that all feelings are OK to experience.
Differentiate between feelings and behaviors. By differentiating feelings from behaviors, educators contribute to children’s understanding that all feelings are OK, but not all behaviors are OK. For example, an educator says, "It looks like you may be feeling mad because you want the red blocks, and Nila is playing with them. It's OK to feel mad but not OK to knock over your friend’s blocks."
Support children's efforts to calm down. When children are self-regulated, they can think more clearly. For example, practice taking a breath with children as a self-regulation technique during calm moments. Then, when challenges arise, children have a strategy they have practiced many times and can use to calm down before problem-solving begins.
Encourage children's efforts to voice the problem and their feelings after they are calm. For example, when a challenge arises, encourage children to use the phrase, "The problem is_______, and I feel______." This process sets the stage to begin problem-solving.
Acknowledge children's efforts to think about varied ways to solve problems. For example, an educator says, "It looks like you and Nila are trying to work out how to share the blocks. What do you think might work so you can both play with them? Do you have some other ideas about how you could share?"
Champion children's efforts as they problem-solve. For example, "You and Nila thought about two ways you could share. One way is to divide the red blocks so you can each build, and the other is to build a tower together. Great thinking, friends!"
Create opportunities for activities and play that offer problem-solving practice. For example, when children play together in the block area, it provides opportunities to negotiate plans for play and role-play, build perspective, talk about feelings, and share. The skills children learn during play, along with adult support, enhance children’s ability to solve more complex and challenging social problems and conflicts when they occur in and out of the early learning setting.

References:

Paley, B., & Hajal, N. J. (2022). Conceptualizing emotion regulation and coregulation as family-level phenomena. Clinical Child and Family Psychology Review ,  25 (1), 19-43.

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Objective 2

Translating sentences and define a process for problem solving, learning objectives.

Translate words into algebraic expressions and equations
Define a process for solving word problems

Word problems can be tricky. Often it takes a bit of practice to convert an English sentence into a mathematical sentence, which is one of the first steps to solving word problems. In the table below, words or phrases commonly associated with mathematical operators are categorized. Word problems often contain these or similar words, so it’s good to see what mathematical operators are associated with them.

How much will it cost?

Some examples follow:

[latex]x\text{ is }5[/latex] becomes [latex]x=5[/latex]
Three more than a number becomes [latex]x+3[/latex]
Four less than a number becomes [latex]x-4[/latex]
Double the cost becomes [latex]2\cdot\text{ cost }[/latex]
Groceries and gas together for the week cost $250 means [latex]\text{ groceries }+\text{ gas }=250[/latex]
The difference of 9 and a number becomes [latex]9-x[/latex]. Notice how 9 is first in the sentence and the expression

Let’s practice translating a few more English phrases into algebraic expressions.

Translate the table into algebraic expressions:

In this example video, we show how to translate more words into mathematical expressions.

The power of algebra is how it can help you model real situations in order to answer questions about them.

Here are some steps to translate problem situations into algebraic equations you can solve. Not every word problem fits perfectly into these steps, but they will help you get started.

Read and understand the problem.
Determine the constants and variables in the problem.
Translate words into algebraic expressions and equations.
Write an equation to represent the problem.
Solve the equation.
Check and interpret your answer. Sometimes writing a sentence helps.

Twenty-eight less than five times a certain number is 232. What is the number?

Following the steps provided:

Read and understand: we are looking for a number.
Constants and variables: 28 and 232 are constants, “a certain number” is our variable because we don’t know its value, and we are asked to find it. We will call it x.
Translate: five times a certain number translates to [latex]5x[/latex] Twenty-eight less than five times a certain number translates to [latex]5x-28[/latex] because subtraction is built backward. is 232 translates to [latex]=232[/latex] because “is” is associated with equals.
Write an equation: [latex]5x-28=232[/latex]

[latex]\begin{array}{r}5x-28=232\\5x=260\\x=52\,\,\,\end{array}[/latex]

[latex]\begin{array}{r}5\left(52\right)-28=232\\5\left(52\right)=260\\260=260\end{array}[/latex].

In the video that follows, we show another example of how to translate a sentence into a mathematical expression using a problem solving method.

Another type of number problem involves consecutive numbers. Consecutive numbers are numbers that come one after the other, such as 3, 4, 5. If we are looking for several consecutive numbers it is important to first identify what they look like with variables before we set up the equation.

For example, let’s say I want to know the next consecutive integer after 4. In mathematical terms, we would add 1 to 4 to get 5. We can generalize this idea as follows: the consecutive integer of any number, x , is [latex]x+1[/latex]. If we continue this pattern we can define any number of consecutive integers from any starting point. The following table shows how to describe four consecutive integers using algebraic notation.

We apply the idea of consecutive integers to solving a word problem in the following example.

The sum of three consecutive integers is 93. What are the integers?

Read and understand: We are looking for three numbers, and we know they are consecutive integers.
Constants and Variables: 93 is a constant. The first integer we will call x . Second: [latex]x+1[/latex] Third: [latex]x+2[/latex]
Translate: The sum of three consecutive integers translates to [latex]x+\left(x+1\right)+\left(x+2\right)[/latex], based on how we defined the first, second, and third integers. Notice how we placed parentheses around the second and third integers. This is just to make each integer more distinct. is 93 translates to [latex]=93[/latex] because is is associated with equals.
Write an equation: [latex]x+\left(x+1\right)+\left(x+2\right)=93[/latex]

[latex]x+x+1+x+2=93[/latex]

Combine like terms, simplify, and solve.

[latex]\begin{array}{r}x+x+1+x+2=93\\3x+3 = 93\\\underline{-3\,\,\,\,\,-3}\\3x=90\\\frac{3x}{3}=\frac{90}{3}\\x=30\end{array}[/latex]

Check and Interpret: Okay, we have found a value for x . We were asked to find the value of three consecutive integers, so we need to do a couple more steps. Remember how we defined our variables: The first integer we will call [latex]x[/latex], [latex]x=30[/latex] Second: [latex]x+1[/latex] so [latex]30+1=31[/latex] Third: [latex]x+2[/latex] so [latex]30+2=32[/latex] The three consecutive integers whose sum is [latex]93[/latex] are [latex]30\text{, }31\text{, and }32[/latex]

Writing Algebraic Expressions. Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/uD_V5t-6Kzs . License : CC BY: Attribution
Write and Solve a Linear Equations to Solve a Number Problem (1). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/izIIqOztUyI . License : CC BY: Attribution
Write and Solve a Linear Equations to Solve a Number Problem (Consecutive Integers). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/S5HZy3jKodg . License : CC BY: Attribution

Understanding the Problem You’re Trying to Solve

U nderstanding the problem you aim to solve is crucial. It’s the difference between spinning wheels and making progress. Without clarity on the issue at hand, finding solutions becomes a shot in the dark. This blog post dives into why grasping the problem is key to success, contrasting confusion with clarity.

Problem understanding importance, problem identification strategies, comprehension techniques, ensuring correct focus, deep understanding tips, addressing the right problem, problem-solving approaches, implementing solutions effectively, reflecting on the process, closing thoughts, recognizing relevance.

Understanding the problem’s relevance is crucial for effective solutions. It helps in grasping the impact of the issue within the context. By recognizing relevance, you can prioritize and address critical challenges promptly.

Highlighting the significance of understanding the problem’s impact allows for a comprehensive view of the situation. It enables you to comprehend how various factors are interconnected and influence each other. This understanding is vital for devising appropriate solutions.

Emphasizing why the problem needs attention sheds light on its urgency and potential consequences of neglect. By acknowledging this, you can allocate resources efficiently and focus on resolving pressing issues promptly.

Clarifying Importance

Clarifying the importance of the problem within the broader issue provides a clear perspective on its significance. It helps in determining how solving this specific problem contributes to overall progress. Prioritizing understanding ensures efforts are directed towards impactful solutions.

Stressing the need to prioritize understanding highlights how a clear grasp of importance drives effective problem-solving strategies. When you understand why a problem matters, you can develop targeted approaches that address root causes rather than symptoms. This clarity enhances decision-making processes significantly.

Explaining how clarity on importance drives effective strategies emphasizes the role of precise problem definition in guiding actions. It enables teams to align their efforts towards achieving common goals by focusing on issues that have substantial implications. Clear importance identification streamlines problem-solving efforts effectively.

Identifying Statement

Identifying a clear and concise statement defining the problem is essential for initiating effective solutions. A well-articulated problem statement serves as a roadmap, guiding actions towards resolution by providing a clear direction for problem-solving processes.

Emphasizing the role of a well-defined problem statement underscores its significance in structuring problem-solving approaches efficiently. It acts as a compass, ensuring all efforts are directed towards addressing core issues accurately and systematically. A precise statement minimizes ambiguity and confusion during solution development.

Discussing the significance of articulating the problem accurately highlights its role in generating effective solutions. An accurately defined problem statement sets boundaries, clarifies objectives, and facilitates focused brainstorming sessions to explore innovative resolutions effectively.

Addressing Right Issue

Identifying the right problem is crucial for effective solutions. To ensure success, validate if the issue aligns with reality. Methods like conducting research and seeking feedback help verify alignment.

Addressing the correct problem significantly impacts solution success . By focusing efforts on the right issue, outcomes improve, leading to better results.

Validating Addressed Problem

Validating the addressed problem’s accuracy and relevance is vital. Confirm that the stated problem truly reflects the underlying issue . Techniques such as data analysis and expert consultations aid in validation.

Ensuring alignment between the identified problem and the actual situation is key. It guarantees that resources are utilized efficiently towards solving the real issue at hand.

Confirming Relevance

Confirming the relevance of a problem within its context is essential. Validate that the problem holds significance and demands immediate attention. Techniques like SWOT analysis and trend evaluation assist in confirming relevance.

ving a relevant problem directly impacts achieving desired outcomes. It ensures that efforts are directed towards addressing pressing issues, leading to tangible improvements.

Strategies for Understanding

Research methods.

Explore various research methods to gain deeper insights into the problem.
Using appropriate research techniques is significant in understanding the problem better.
Research plays a crucial role in uncovering underlying factors contributing to the problem.

Questioning Techniques

Effective questioning techniques introduce ways to delve deeper into the problem.
Asking the right questions is important to uncover essential information.
Powerful questions can lead to a better understanding of the problem, such as “Why does this occur?”

Tips for Clarity

Practical tips enhance clarity in problem understanding.
Strategies include eliminating confusion and ambiguity surrounding the problem.
Actionable advice helps achieve a clear perspective on the issue, like breaking down complex problems.

Narrowing Down Issues

Understanding the goal is crucial in narrowing down complex problems effectively. By defining the specific objective, you can focus on the core problem without getting distracted by irrelevant details. This clarity helps in streamlining the entire problem-solving process.

To identify key issues, start by breaking down the larger problem into smaller components. This approach allows you to pinpoint the root cause efficiently. By prioritizing these key issues, you can allocate resources effectively towards solving them, leading to quicker resolutions.

Narrowing down issues offers several benefits, including saving time and resources. It enables a more targeted approach to problem-solving, increasing the likelihood of finding effective solutions promptly. By focusing on essential aspects, you avoid unnecessary detours that can prolong the resolution process.

Avoiding Misinterpretation

Misinterpreting the problem can lead to misguided solutions and wasted efforts. It’s essential to recognize the risks associated with misunderstanding the issue at hand. Misinterpretation often stems from incomplete information or biased perspectives.

Effective communication plays a pivotal role in avoiding misinterpretation. Clear and concise exchanges of information among team members help ensure everyone is on the same page regarding the problem at hand. Encouraging open dialogue and active listening minimizes the chances of miscommunication.

Misinterpreting the problem can have serious consequences for the overall problem-solving process. It may result in implementing ineffective solutions that do not address the root cause adequately. This can lead to repeated failures and setbacks, hindering progress towards achieving desired outcomes.

Analyzing Root Causes

To truly understand a problem, mind the importance of delving into its root causes. By taking this approach, you can uncover the kind of issues that fuel the problem. Identifying these underlying factors is crucial for effective problem-solving. Root cause analysis plays a pivotal role in addressing not just symptoms but the core issues at play. It allows you to tackle problems at their source, leading to long-lasting solutions.

When it comes to understanding a problem comprehensively, analyzing root causes is key. By identifying the fundamental reasons behind an issue, you can develop more targeted and impactful solutions. This process involves digging deep to unearth the mind of complexities that contribute to the problem’s existence. Without addressing these root causes, any solutions implemented may only scratch the surface without resolving the underlying issues.

Gathering Insights

Gathering insights is essential for gaining a holistic understanding of a problem. To effectively address challenges, it’s crucial to collect diverse perspectives and information sources. By doing so, you can gain a comprehensive view of the kind of factors influencing the situation. These insights serve as valuable inputs for developing innovative and tailored solutions that address the core of the issue.

In navigating complex problems, gathering insights from various angles is invaluable. Different perspectives offer unique viewpoints that enrich your understanding of the situation at hand. By embracing this diversity of insights, you can identify patterns, trends, and connections that might have otherwise gone unnoticed. These varied perspectives pave the way for creative problem-solving approaches that consider all facets of the issue.

Validating Assumptions

Validating assumptions is crucial in accurately identifying the problem at hand. It ensures that the focus remains on the actual issue rather than perceived ones. Methods such as conducting surveys, interviews, or data analysis can help challenge and verify assumptions effectively. By actively seeking feedback and evidence, you can align assumptions with the real problem scenario.

Re-evaluating Statements

Re-evaluating problem statements periodically is essential for maintaining clarity in the problem-solving process. It allows for adjustments based on new insights gained along the way. Continuously refining the problem statement ensures that efforts are directed towards solving the right issue. This iterative approach helps in adapting to changing circumstances and evolving needs.

Creative Solutions

Creativity plays a pivotal role in problem-solving , encouraging individuals to think beyond traditional boundaries. By exploring unique perspectives and innovative ideas, creative solutions can emerge. This approach allows for unconventional methods to tackle complex issues effectively.

Embracing creativity in problem space exploration opens up a myriad of possibilities. It fosters a dynamic environment where ways of thinking are not limited by conventional norms. Thinking outside the box enables individuals to discover fresh angles and potential breakthroughs.

Examples of creative problem-solving include using analogies from unrelated fields to inspire new approaches, employing brainstorming sessions to generate diverse ideas, or even incorporating art and design principles into analytical processes. These unconventional methods often lead to innovative problem resolutions , challenging the status quo and fostering growth.

Logical Frameworks

Introducing logical frameworks provides a structured approach to problem-solving , offering a systematic way to analyze and address issues. By breaking down problems into manageable components, individuals can navigate through the problem space more efficiently.

The advantages of employing logical frameworks lie in their ability to bring clarity and coherence to complex problems. By organizing thoughts and actions logically, individuals can establish a clear roadmap towards reaching solutions. This method ensures that each step taken is purposeful and contributes towards the overall goal.

Guidance on applying logical frameworks involves defining the problem statement clearly, identifying key variables at play, establishing causal relationships between factors, and outlining potential solutions based on logical deductions. This systematic approach enhances decision-making processes and empowers individuals to tackle even the most intricate challenges effectively.

Action Plan Development

Developing a structured action plan is crucial in tackling identified issues effectively. Firstly, define the problem clearly to establish a solid foundation. Next, set specific, measurable objectives to guide the solution process. Break down the plan into manageable steps for easier implementation.

Creating an actionable strategy involves identifying key stakeholders and assigning roles accordingly. Allocate resources efficiently to support the plan’s execution. Prioritize tasks based on urgency and impact to streamline the resolution process. Regularly review and adjust the action plan as needed to stay on track towards achieving desired outcomes.

Monitoring Progress

Monitoring progress is vital in ensuring that implemented solutions are yielding positive results. Utilize key performance indicators (KPIs) to measure success and track advancements accurately. Regularly assess data and feedback to gauge the effectiveness of chosen strategies.

Methods for tracking progress include establishing regular check-ins with team members or stakeholders to evaluate milestones achieved. Implement feedback mechanisms to gather insights on the solution’s impact and areas needing improvement. Continuous monitoring allows for timely interventions and adjustments, enhancing overall efficiency.

Incorporating progress monitoring enables teams to identify bottlenecks early on and address them promptly. By staying proactive in evaluating outcomes, organizations can optimize their problem-solving approaches for better results. Make data-driven decisions based on real-time information gathered during the implementation phase.

Learning from Outcomes

Learning from both successful and unsuccessful outcomes is crucial for personal growth and professional development. By analyzing what worked well and what didn’t, individuals can gain valuable insights into their problem-solving skills. Extracting lessons from past experiences allows individuals to refine their strategies and approaches for future challenges. This reflective process enhances one’s ability to tackle problems more effectively in the future.

Adjusting Strategies

Flexibility is key when it comes to problem-solving. Being able to adjust strategies based on the evolving dynamics of a problem is essential for success. Adapting problem-solving approaches to changing circumstances ensures that individuals can stay agile and responsive in their problem-solving efforts. Refining strategies to better align with the problem-solving process enables individuals to navigate challenges more efficiently.

Understanding the problem you aim to solve is the cornerstone of effective solutions. By honing your comprehension skills, ensuring a laser focus, and employing the right strategies, you pave the way for successful outcomes. Reflect on your process, adjust as needed, and embrace the journey of problem-solving with confidence.

In your next challenge, remember that clarity in problem understanding leads to innovation in solutions. Embrace these insights, apply them diligently, and watch as your problem-solving abilities reach new heights. Keep refining your approach, stay adaptable, and tackle each issue with the wisdom gained from understanding the core problem at hand.

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Computer Science > Computation and Language

Title: saas: solving ability amplification strategy for enhanced mathematical reasoning in large language models.

Abstract: This study presents a novel learning approach designed to enhance both mathematical reasoning and problem-solving abilities of Large Language Models (LLMs). We focus on integrating the Chain-of-Thought (CoT) and the Program-of-Thought (PoT) learning, hypothesizing that prioritizing the learning of mathematical reasoning ability is helpful for the amplification of problem-solving ability. Thus, the initial learning with CoT is essential for solving challenging mathematical problems. To this end, we propose a sequential learning approach, named SAAS (Solving Ability Amplification Strategy), which strategically transitions from CoT learning to PoT learning. Our empirical study, involving an extensive performance comparison using several benchmarks, demonstrates that our SAAS achieves state-of-the-art (SOTA) performance. The results underscore the effectiveness of our sequential learning approach, marking a significant advancement in the field of mathematical reasoning in LLMs.

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What is Problem-Based Learning (PBL)
An Overview of Problem-Based Learning. Problem-based learning (PBL) is a teaching style that pushes students to become the drivers of their learning education. Problem-based learning uses complex, real-world issues as the classroom's subject matter, encouraging students to develop problem-solving skills and learn concepts instead of just ...
Problem-based learning
A PBL group at Sydney Dental Hospital. Problem-based learning (PBL) is a student-centered pedagogy in which students learn about a subject through the experience of solving an open-ended problem found in trigger material. The PBL process does not focus on problem solving with a defined solution, but it allows for the development of other desirable skills and attributes.
Problem-Based Learning (PBL)
PBL is a student-centered approach to learning that involves groups of students working to solve a real-world problem, quite different from the direct teaching method of a teacher presenting facts and concepts about a specific subject to a classroom of students. Through PBL, students not only strengthen their teamwork, communication, and ...
Problem-Based Learning
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. ... Examine and define the problem.
Problem-Based Learning (PBL)
Problem-Based Learning (PBL) is a teaching method in which complex real-world problems are used as the vehicle to promote student learning of concepts and principles as opposed to direct presentation of facts and concepts. In addition to course content, PBL can promote the development of critical thinking skills, problem-solving abilities, and ...
Problem-Based Learning
What is Problem-Based Learning. Problem-based learning (PBL) challenges students to identify and examine real problems, then work together to address and solve those problems through advocacy and by mobilizing resources. Importantly, every aspect of the problem solving process involves students in real work—work that is a reflection of the ...
Problem-Based Learning (PBL)
Key Concepts. Problem-Based Learning (PBL) is a pedagogical approach and curriculum design methodology often used in higher education and K-12 settings [1] [2]. The following are some of the defining characteristics of PBL: Learning is driven by challenging, open-ended problems with no one "right" answer. Problems/cases are context specific.
What is Problem-Based Learning? A Complete Guide for Educators
Final Thoughts on Problem-Based Learning. Problem-based learning (PBL) is a student-centered teaching method that encourages students to learn by actively solving real-world problems. Unlike traditional instructional methods, PBL does not focus on delivering content but rather on facilitating student learning through problem-solving.
Problem-Based Learning: An Overview of its Process and Impact on
Problem-based learning (PBL) has been widely adopted in diverse fields and educational contexts to promote critical thinking and problem-solving in authentic learning situations. Its close affiliation with workplace collaboration and interdisciplinary learning contributed to its spread beyond the traditional realm of clinical education 1 to ...
Problem-Based Learning
Problem-focused. The students begin learning by simulating the process of solving an authentic, ill-structured problem. Problem-structured content. The content and skills to be learned are organized around problems, rather than as a hierarchical list of topics, so there is a reciprocal relationship between knowledge and the problem.
Problem Solving
Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to ...
Problem Solving
Cognitive—Problem solving occurs within the problem solver's cognitive system and can only be inferred indirectly from the problem solver's behavior (including biological changes, introspections, and actions during problem solving).. Process—Problem solving involves mental computations in which some operation is applied to a mental representation, sometimes resulting in the creation of ...
Problem Solving: Definition, Skills, & Strategies
This process is a crucial part of problem-solving as being able to define the problem has been identified as one of the eight steps towards coming up with a solution (D'Zurilla & Goldfried, 1971). ... productive life. Learning skills to improve problem-solving through problem-solving therapy has been shown to help a variety of physical and ...
Teaching Problem Solving
A key skill for problem solving is knowing how to define and represent the problem and its solutions. This is true for all students, regardless of discipline. For example, Berkenkotter (1982, p. 33) states, "A writer is a problem solver of a particular kind. ... We use team-based learning exercises and collaborative problem solving. Students ...
The Problem-Solving Process
Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything ...
Teaching Problem Solving
Make students articulate their problem solving process . 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.".
What is Problem Solving? Steps, Process & Techniques
1. Define the problem. Diagnose the situation so that your focus is on the problem, not just its symptoms. Helpful problem-solving techniques include using flowcharts to identify the expected steps of a process and cause-and-effect diagrams to define and analyze root causes. The sections below help explain key problem-solving steps.
Problem-Based Learning: Definition, Tips and Examples
Problem-based learning (PBL) is a teaching method that allows a group of people to solve real-world issues through concepts and scenarios. This differs from how teachers or mentors usually teach students, which is by presenting facts for them to memorize. Rather, problem-based learning helps people use critical thinking and problem-solving ...
Problem Solving
A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A "rule of thumb" is an example of a heuristic.
What Is Problem Solving?
Define Every Problem. The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem - not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work.
PDF Problem Based Learning: A Student-Centered Approach
Problem solving can incites for learning. 7). Throughout the learning process, critical reflection happens The main important point of this approach is that students are responsible for their own learning, learn how to use prior knowledge and the way of knowledge acquisition. The PBL approach gives more focus on self and peer
Effective Learning Behavior in Problem-Based Learning: a Scoping Review
Problem-based learning (PBL) emphasizes learning behavior that leads to critical thinking, problem-solving, communication, and collaborative skills in preparing students for a professional medical career. However, learning behavior that develops these skills has not been systematically described. This review aimed to unearth the elements of ...
Pave the Way for Self-regulation and Problem-solving With Social
Problem-solving is a social-emotional learning (SEL) skill children need for lifelong success. Effective problem-solving skills support children's ability to self-regulate, focus on tasks, think flexibly and creatively, work with others, and generate multiple ways to solve problems. When young children develop and build these skills, it positively impacts their interactions with others, grows ...
Translating Sentences and Define a Process for Problem Solving
Groceries and gas together for the week cost $250 means [Math Processing Error] groceries + gas = 250. The difference of 9 and a number becomes [Math Processing Error] 9 − x. Notice how 9 is first in the sentence and the expression. Let's practice translating a few more English phrases into algebraic expressions.
Understanding the Problem You're Trying to Solve
Reflect on your process, adjust as needed, and embrace the journey of problem-solving with confidence. In your next challenge, remember that clarity in problem understanding leads to innovation in ...
Creating Strategic Problem Solvers
In the latest edition of the Army War College journal Parameters, Andrew Carr argues that the rising level of complexity in the world necessitates a change in how we define strategy away from a math problem of ends + ways + means and instead look to strategy as problem-solving.1 Carr's idea is that as the amount of complexity in a situation increases, the strategy should be less focused on ...
Master Problem-Solving in Public Administration
6. Prioritize Problems. Be the first to add your personal experience. 7. Here's what else to consider. Be the first to add your personal experience. In public administration, identifying and ...
Put students' reasoning skills to the test with ERB on Kahoot!
Strengthen students' reasoning skills with new learning content from ERB on Kahoot! Put your students' problem-solving, critical thinking, and reasoning skills to the test with these compelling new kahoots! Learning isn't all about the destination; it's also about the journey! While memorizing facts before a test is certainly helpful ...
[2404.03887] SAAS: Solving Ability Amplification Strategy for Enhanced
This study presents a novel learning approach designed to enhance both mathematical reasoning and problem-solving abilities of Large Language Models (LLMs). We focus on integrating the Chain-of-Thought (CoT) and the Program-of-Thought (PoT) learning, hypothesizing that prioritizing the learning of mathematical reasoning ability is helpful for the amplification of problem-solving ability. Thus ...

Problem-Based Learning (PBL)

By working with PBL, students will:

How to Begin PBL

Designing Classroom Instruction

How to Orchestrate a PBL Activity

Teacher’s Role in PBL

The Role of the Students

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Why Use Problem-Based Learning?

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Getting Started with Problem-Based Learning

Where can I learn more?

Problem-Based Learning

What is Problem-Based Learning

Problem-based learning builds agency & independence

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Problem-based learning is persistent

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Make it Real

Make it Relevant

Field Studies

Make an Impact

Independence

Adapting Communication to Different Audiences and Purposes

Comprehending and Critiquing

Valuing Evidence

Strategic Use of Digital Media

Language Arts

Reading Standards

Writing Standards

Speaking & Listening Standards

Mathematics

Plan Your PBL Experience

Start Small – Focus on Practices as Entry Points

Be Honest About Project Constraints

Identify Intersections With Your Curriculum

Turn Limitations Into Opportunities

Take Risks and Model Perseverance

Be Less Helpful

Be Flexible

Experts are Everywhere

Maintain a List of Your Support Networks

Encourage Original Research

Portfolio-based Assessment

Feedback-based Assessment

Assessment as a System of Interrelated Feedback Tools

Assessment Tools

Assessing Process

Assessing Subject Matter and Content

Assessing Mindsets and Skills

Host a Teacher Workshop

Related Links

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