problem solving framework for students

New Designs for School 5 Steps to Teaching Students a Problem-Solving Routine

Jeff Heyck-Williams (He, His, Him) Director of the Two Rivers Learning Institute in Washington, DC

We’ve all had the experience of truly purposeful, authentic learning and know how valuable it is. Educators are taking the best of what we know about learning, student support, effective instruction, and interpersonal skill-building to completely reimagine schools so that students experience that kind of purposeful learning all day, every day.

Students can use the 5 steps in this simple routine to solve problems across the curriculum and throughout their lives.

When I visited a fifth-grade class recently, the students were tackling the following problem:

If there are nine people in a room and every person shakes hands exactly once with each of the other people, how many handshakes will there be? How can you prove your answer is correct using a model or numerical explanation?

There were students on the rug modeling people with Unifix cubes. There were kids at one table vigorously shaking each other’s hand. There were kids at another table writing out a diagram with numbers. At yet another table, students were working on creating a numeric expression. What was common across this class was that all of the students were productively grappling around the problem.

On a different day, I was out at recess with a group of kindergarteners who got into an argument over a vigorous game of tag. Several kids were arguing about who should be “it.” Many of them insisted that they hadn’t been tagged. They all agreed that they had a problem. With the assistance of the teacher they walked through a process of identifying what they knew about the problem and how best to solve it. They grappled with this very real problem to come to a solution that all could agree upon.

Then just last week, I had the pleasure of watching a culminating showcase of learning for our 8th graders. They presented to their families about their project exploring the role that genetics plays in our society. Tackling the problem of how we should or should not regulate gene research and editing in the human population, students explored both the history and scientific concerns about genetics and the ethics of gene editing. Each student developed arguments about how we as a country should proceed in the burgeoning field of human genetics which they took to Capitol Hill to share with legislators. Through the process students read complex text to build their knowledge, identified the underlying issues and questions, and developed unique solutions to this very real problem.

Problem-solving is at the heart of each of these scenarios, and an essential set of skills our students need to develop. They need the abilities to think critically and solve challenging problems without a roadmap to solutions. At Two Rivers Public Charter School in Washington, D.C., we have found that one of the most powerful ways to build these skills in students is through the use of a common set of steps for problem-solving. These steps, when used regularly, become a flexible cognitive routine for students to apply to problems across the curriculum and their lives.

The Problem-Solving Routine

At Two Rivers, we use a fairly simple routine for problem solving that has five basic steps. The power of this structure is that it becomes a routine that students are able to use regularly across multiple contexts. The first three steps are implemented before problem-solving. Students use one step during problem-solving. Finally, they finish with a reflective step after problem-solving.

Problem Solving from Two Rivers Public Charter School

Before Problem-Solving: The KWI

The three steps before problem solving: we call them the K-W-I.

The “K” stands for “know” and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem. For example, in the math problem above students identify that they know there are nine people and each person must shake hands with each other person. Second, the student needs to activate their background knowledge about that context or other similar problems. In the case of the handshake problem, students may recognize that this seems like a situation in which they will need to add or multiply.

The “W” stands for “what” a student needs to find out to solve the problem. At this point in the routine the student always must identify the core question that is being asked in a problem or task. However, it may also include other questions that help a student access and understand a problem more deeply. For example, in addition to identifying that they need to determine how many handshakes in the math problem, students may also identify that they need to determine how many handshakes each individual person has or how to organize their work to make sure that they count the handshakes correctly.

The “I” stands for “ideas” and refers to ideas that a student brings to the table to solve a problem effectively. In this portion of the routine, students list the strategies that they will use to solve a problem. In the example from the math class, this step involved all of the different ways that students tackled the problem from Unifix cubes to creating mathematical expressions.

This KWI routine before problem solving sets students up to actively engage in solving problems by ensuring they understand the problem and have some ideas about where to start in solving the problem. Two remaining steps are equally important during and after problem solving.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them.

During Problem-Solving: The Metacognitive Moment

The step that occurs during problem solving is a metacognitive moment. We ask students to deliberately pause in their problem-solving and answer the following questions: “Is the path I’m on to solve the problem working?” and “What might I do to either stay on a productive path or readjust my approach to get on a productive path?” At this point in the process, students may hear from other students that have had a breakthrough or they may go back to their KWI to determine if they need to reconsider what they know about the problem. By naming explicitly to students that part of problem-solving is monitoring our thinking and process, we help them become more thoughtful problem solvers.

After Problem-Solving: Evaluating Solutions

As a final step, after students solve the problem, they evaluate both their solutions and the process that they used to arrive at those solutions. They look back to determine if their solution accurately solved the problem, and when time permits they also consider if their path to a solution was efficient and how it compares to other students’ solutions.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them. This empowers students to be the problem solvers that we know they can become.

Jeff Heyck-Williams (He, His, Him)

Director of the two rivers learning institute.

Jeff Heyck-Williams is the director of the Two Rivers Learning Institute and a founder of Two Rivers Public Charter School. He has led work around creating school-wide cultures of mathematics, developing assessments of critical thinking and problem-solving, and supporting project-based learning.

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Do Your Students Know How to Analyze a Case—Really?

Explore more.

• Case Teaching
• Student Engagement

J ust as actors, athletes, and musicians spend thousands of hours practicing their craft, business students benefit from practicing their critical-thinking and decision-making skills. Students, however, often have limited exposure to real-world problem-solving scenarios; they need more opportunities to practice tackling tough business problems and deciding on—and executing—the best solutions.

To ensure students have ample opportunity to develop these critical-thinking and decision-making skills, we believe business faculty should shift from teaching mostly principles and ideas to mostly applications and practices. And in doing so, they should emphasize the case method, which simulates real-world management challenges and opportunities for students.

To help educators facilitate this shift and help students get the most out of case-based learning, we have developed a framework for analyzing cases. We call it PACADI (Problem, Alternatives, Criteria, Analysis, Decision, Implementation); it can improve learning outcomes by helping students better solve and analyze business problems, make decisions, and develop and implement strategy. Here, we’ll explain why we developed this framework, how it works, and what makes it an effective learning tool.

The Case for Cases: Helping Students Think Critically

Business students must develop critical-thinking and analytical skills, which are essential to their ability to make good decisions in functional areas such as marketing, finance, operations, and information technology, as well as to understand the relationships among these functions. For example, the decisions a marketing manager must make include strategic planning (segments, products, and channels); execution (digital messaging, media, branding, budgets, and pricing); and operations (integrated communications and technologies), as well as how to implement decisions across functional areas.

Faculty can use many types of cases to help students develop these skills. These include the prototypical “paper cases”; live cases , which feature guest lecturers such as entrepreneurs or corporate leaders and on-site visits; and multimedia cases , which immerse students into real situations. Most cases feature an explicit or implicit decision that a protagonist—whether it is an individual, a group, or an organization—must make.

For students new to learning by the case method—and even for those with case experience—some common issues can emerge; these issues can sometimes be a barrier for educators looking to ensure the best possible outcomes in their case classrooms. Unsure of how to dig into case analysis on their own, students may turn to the internet or rely on former students for “answers” to assigned cases. Or, when assigned to provide answers to assignment questions in teams, students might take a divide-and-conquer approach but not take the time to regroup and provide answers that are consistent with one other.

To help address these issues, which we commonly experienced in our classes, we wanted to provide our students with a more structured approach for how they analyze cases—and to really think about making decisions from the protagonists’ point of view. We developed the PACADI framework to address this need.

PACADI: A Six-Step Decision-Making Approach

The PACADI framework is a six-step decision-making approach that can be used in lieu of traditional end-of-case questions. It offers a structured, integrated, and iterative process that requires students to analyze case information, apply business concepts to derive valuable insights, and develop recommendations based on these insights.

Prior to beginning a PACADI assessment, which we’ll outline here, students should first prepare a two-paragraph summary—a situation analysis—that highlights the key case facts. Then, we task students with providing a five-page PACADI case analysis (excluding appendices) based on the following six steps.

Step 1: Problem definition. What is the major challenge, problem, opportunity, or decision that has to be made? If there is more than one problem, choose the most important one. Often when solving the key problem, other issues will surface and be addressed. The problem statement may be framed as a question; for example, How can brand X improve market share among millennials in Canada? Usually the problem statement has to be re-written several times during the analysis of a case as students peel back the layers of symptoms or causation.

Step 2: Alternatives. Identify in detail the strategic alternatives to address the problem; three to five options generally work best. Alternatives should be mutually exclusive, realistic, creative, and feasible given the constraints of the situation. Doing nothing or delaying the decision to a later date are not considered acceptable alternatives.

Step 3: Criteria. What are the key decision criteria that will guide decision-making? In a marketing course, for example, these may include relevant marketing criteria such as segmentation, positioning, advertising and sales, distribution, and pricing. Financial criteria useful in evaluating the alternatives should be included—for example, income statement variables, customer lifetime value, payback, etc. Students must discuss their rationale for selecting the decision criteria and the weights and importance for each factor.

Step 4: Analysis. Provide an in-depth analysis of each alternative based on the criteria chosen in step three. Decision tables using criteria as columns and alternatives as rows can be helpful. The pros and cons of the various choices as well as the short- and long-term implications of each may be evaluated. Best, worst, and most likely scenarios can also be insightful.

Step 5: Decision. Students propose their solution to the problem. This decision is justified based on an in-depth analysis. Explain why the recommendation made is the best fit for the criteria.

Step 6: Implementation plan. Sound business decisions may fail due to poor execution. To enhance the likeliness of a successful project outcome, students describe the key steps (activities) to implement the recommendation, timetable, projected costs, expected competitive reaction, success metrics, and risks in the plan.

“Students note that using the PACADI framework yields ‘aha moments’—they learned something surprising in the case that led them to think differently about the problem and their proposed solution.”

PACADI’s Benefits: Meaningfully and Thoughtfully Applying Business Concepts

The PACADI framework covers all of the major elements of business decision-making, including implementation, which is often overlooked. By stepping through the whole framework, students apply relevant business concepts and solve management problems via a systematic, comprehensive approach; they’re far less likely to surface piecemeal responses.

As students explore each part of the framework, they may realize that they need to make changes to a previous step. For instance, when working on implementation, students may realize that the alternative they selected cannot be executed or will not be profitable, and thus need to rethink their decision. Or, they may discover that the criteria need to be revised since the list of decision factors they identified is incomplete (for example, the factors may explain key marketing concerns but fail to address relevant financial considerations) or is unrealistic (for example, they suggest a 25 percent increase in revenues without proposing an increased promotional budget).

In addition, the PACADI framework can be used alongside quantitative assignments, in-class exercises, and business and management simulations. The structured, multi-step decision framework encourages careful and sequential analysis to solve business problems. Incorporating PACADI as an overarching decision-making method across different projects will ultimately help students achieve desired learning outcomes. As a practical “beyond-the-classroom” tool, the PACADI framework is not a contrived course assignment; it reflects the decision-making approach that managers, executives, and entrepreneurs exercise daily. Case analysis introduces students to the real-world process of making business decisions quickly and correctly, often with limited information. This framework supplies an organized and disciplined process that students can readily defend in writing and in class discussions.

PACADI in Action: An Example

Here’s an example of how students used the PACADI framework for a recent case analysis on CVS, a large North American drugstore chain.

The CVS Prescription for Customer Value*

PACADI Stage

Summary Response

How should CVS Health evolve from the “drugstore of your neighborhood” to the “drugstore of your future”?

Alternatives

A1. Kaizen (continuous improvement)

A2. Product development

A3. Market development

A4. Personalization (micro-targeting)

Criteria (include weights)

C1. Customer value: service, quality, image, and price (40%)

C2. Customer obsession (20%)

C3. Growth through related businesses (20%)

C4. Customer retention and customer lifetime value (20%)

Each alternative was analyzed by each criterion using a Customer Value Assessment Tool

Alternative 4 (A4): Personalization was selected. This is operationalized via: segmentation—move toward segment-of-1 marketing; geodemographics and lifestyle emphasis; predictive data analysis; relationship marketing; people, principles, and supply chain management; and exceptional customer service.

Implementation

Partner with leading medical school

Curbside pick-up

Pet pharmacy

E-newsletter for customers and employees

Employee incentive program

CVS beauty days

Expand to Latin America and Caribbean

Healthier/happier corner

Holiday toy drives/community outreach

*Source: A. Weinstein, Y. Rodriguez, K. Sims, R. Vergara, “The CVS Prescription for Superior Customer Value—A Case Study,” Back to the Future: Revisiting the Foundations of Marketing from Society for Marketing Advances, West Palm Beach, FL (November 2, 2018).

Results of Using the PACADI Framework

When faculty members at our respective institutions at Nova Southeastern University (NSU) and the University of North Carolina Wilmington have used the PACADI framework, our classes have been more structured and engaging. Students vigorously debate each element of their decision and note that this framework yields an “aha moment”—they learned something surprising in the case that led them to think differently about the problem and their proposed solution.

These lively discussions enhance individual and collective learning. As one external metric of this improvement, we have observed a 2.5 percent increase in student case grade performance at NSU since this framework was introduced.

Tips to Get Started

The PACADI approach works well in in-person, online, and hybrid courses. This is particularly important as more universities have moved to remote learning options. Because students have varied educational and cultural backgrounds, work experience, and familiarity with case analysis, we recommend that faculty members have students work on their first case using this new framework in small teams (two or three students). Additional analyses should then be solo efforts.

To use PACADI effectively in your classroom, we suggest the following:

Advise your students that your course will stress critical thinking and decision-making skills, not just course concepts and theory.

Use a varied mix of case studies. As marketing professors, we often address consumer and business markets; goods, services, and digital commerce; domestic and global business; and small and large companies in a single MBA course.

As a starting point, provide a short explanation (about 20 to 30 minutes) of the PACADI framework with a focus on the conceptual elements. You can deliver this face to face or through videoconferencing.

Give students an opportunity to practice the case analysis methodology via an ungraded sample case study. Designate groups of five to seven students to discuss the case and the six steps in breakout sessions (in class or via Zoom).

Ensure case analyses are weighted heavily as a grading component. We suggest 30–50 percent of the overall course grade.

Once cases are graded, debrief with the class on what they did right and areas needing improvement (30- to 40-minute in-person or Zoom session).

Encourage faculty teams that teach common courses to build appropriate instructional materials, grading rubrics, videos, sample cases, and teaching notes.

When selecting case studies, we have found that the best ones for PACADI analyses are about 15 pages long and revolve around a focal management decision. This length provides adequate depth yet is not protracted. Some of our tested and favorite marketing cases include Brand W , Hubspot , Kraft Foods Canada , TRSB(A) , and Whiskey & Cheddar .

Art Weinstein , Ph.D., is a professor of marketing at Nova Southeastern University, Fort Lauderdale, Florida. He has published more than 80 scholarly articles and papers and eight books on customer-focused marketing strategy. His latest book is Superior Customer Value—Finding and Keeping Customers in the Now Economy . Dr. Weinstein has consulted for many leading technology and service companies.

Herbert V. Brotspies , D.B.A., is an adjunct professor of marketing at Nova Southeastern University. He has over 30 years’ experience as a vice president in marketing, strategic planning, and acquisitions for Fortune 50 consumer products companies working in the United States and internationally. His research interests include return on marketing investment, consumer behavior, business-to-business strategy, and strategic planning.

John T. Gironda , Ph.D., is an assistant professor of marketing at the University of North Carolina Wilmington. His research has been published in Industrial Marketing Management, Psychology & Marketing , and Journal of Marketing Management . He has also presented at major marketing conferences including the American Marketing Association, Academy of Marketing Science, and Society for Marketing Advances.

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Problem-Solving Model for Improving Student Achievement

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

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

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

By Andrea Canter

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

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

What Is Problem Solving?

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

Why Is a New Approach Needed?

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

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

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

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

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

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

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

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How It Works

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

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

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

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

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

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

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

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

Outcomes of Problem Solving and RTI

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

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

Is Problem Solving Worth the Effort?

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

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

Case Study: Optimizing Success Through Problem Solving

By Marcia Staum and Lourdes Ocampo

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

OSPS in Action: Juneau High School

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

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

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

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

What Is Response to Intervention?

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

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

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

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

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

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Problem-Based Learning

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

Why Use Problem-Based Learning?

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

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

Considerations for Using Problem-Based Learning

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

Students generally must:

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

Getting Started with Problem-Based Learning

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

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

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Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

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

Encourage Independence

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

Be sensitive

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

Encourage Thoroughness and Patience

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

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

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

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A Critical Thinking Framework for Elementary Students

Guiding young students to engage in critical thinking fosters their ability to create and engage with knowledge.

Critical thinking is using analysis and evaluation to make a judgment. Analysis, evaluation, and judgment are not discrete skills; rather, they emerge from the accumulation of knowledge. The accumulation of knowledge does not mean students sit at desks mindlessly reciting memorized information, like in 19th century grammar schools. Our goal is not for learners to regurgitate facts by rote without demonstrating their understanding of the connections, structures, and deeper ideas embedded in the content they are learning. To foster critical thinking in school, especially for our youngest learners, we need a pedagogy that centers knowledge and also honors the ability of children to engage with knowledge.

This chapter outlines the Critical Thinking Framework: five instructional approaches educators can incorporate into their instruction to nurture deeper thinking. These approaches can also guide intellectual preparation protocols and unit unpackings to prepare rigorous, engaging instruction for elementary students. Some of these approaches, such as reason with evidence, will seem similar to other “contentless” programs professing to teach critical thinking skills. But others, such as say it in your own words or look for structure, are targeted at ensuring learners soundly understand content so that they can engage in complex thinking. You will likely notice that every single one of these approaches requires students to talk—to themselves, to a partner, or to the whole class. Dialogue, specifically in the context of teacher-led discussions, is essential for students to analyze, evaluate, and judge (i.e., do critical thinking ). 

The Critical Thinking Framework

Say it in your own words : Students articulate ideas in their own words. They use unique phrasing and do not parrot the explanations of others. When learning new material, students who pause to explain concepts in their own words (to themselves or others) demonstrate an overall better understanding than students who do not (Nokes-Malach et al., 2013). However, it’s not enough for us to pause frequently and ask students to explain, especially if they are only being asked to repeat procedures. Explanations should be effortful and require students to make connections to prior knowledge and concepts as well as to revise misconceptions (Richey & Nokes-Malach, 2015).

Break it down : Students break down the components, steps, or smaller ideas within a bigger idea or procedure. In addition to expressing concepts in their own words, students should look at new concepts in terms of parts and wholes. For instance, when learning a new type of problem or task, students can explain the steps another student took to arrive at their answer, which promotes an understanding that transfers to other tasks with a similar underlying structure. Asking students to explain the components and rationale behind procedural steps can also lead to more flexible problem solving overall (Rittle-Johnson, 2006). By breaking down ideas into component parts, students are also better equipped to monitor the soundness of their own understanding as well as to see similar patterns (i.e., regularity) among differing tasks. For example, in writing, lessons can help students see how varying subordinating conjunction phrases at the start of sentences can support the flow and readability of a paragraph. In math, a solution can be broken down into smaller steps.

Look for structure : Students look beyond shallow surface characteristics to see deep structures and underlying principles. Learners struggle to see regularity in similar problems that have small differences (Reed et al., 1985). Even when students are taught how to complete one kind of task, they struggle to transfer their understanding to a new task where some of the superficial characteristics have been changed. This is because students, especially students who are novices in a domain, tend to emphasize the surface structure of a task rather than deep structure (Chi & Van Lehn, 2012).

By prompting students to notice deep structures—such as the characteristics of a genre or the needs of animals—rather than surface structures, teachers foster the development of comprehensive schemata in students’ long-term memories, which they are more likely to then apply to novel situations. Teachers should monitor for student understanding of deep structures across several tasks and examples.

Notice gaps or inconsistencies in ideas : Students ask questions about gaps and inconsistencies in material, arguments, and their own thinking . When students engage in explanations of material, they are more likely to notice when they misunderstand material or to detect a conflict with their prior knowledge (Richey & Nokes-Malach, 2015). In a classroom, analyzing conflicting ideas and interpretations allows students to revise misconceptions and refine mental models. Noticing gaps and inconsistencies in information also helps students to evaluate the persuasiveness of arguments and to ask relevant questions.

Reason with evidence : Students construct arguments with evidence and evaluate the evidence in others’ reasoning. Reasoning with evidence matters in every subject, but what counts for evidence in a mathematical proof differs from what is required in an English essay. Students should learn the rules and conventions for evidence across a wide range of disciplines in school. The habits of looking for and weighing evidence also intersect with some of the other critical thinking approaches discussed above. Noticing regularity in reasoning and structure helps learners find evidence efficiently, while attending to gaps and inconsistencies in information encourages caution before reaching hasty conclusions.

Countering Two Critiques

Some readers may be wondering how the Critical Thinking Framework differs from other general skills curricula. The framework differs in that it demands application in the context of students’ content knowledge, rather than in isolation. It is a pedagogical tool to help students make sense of the content they are learning. Students should never sit through a lesson where they are told to “say things in their own words” when there is nothing to say anything about. While a contentless lesson could help on the margins, it will not be as relevant or transferable. Specific content matters. A checklist of “critical thinking skills” cannot replace deep subject knowledge. The framework should not be blindly applied to all subjects without context because results will look quite different in an ELA or science class.

Other readers may be thinking about high-stakes tests: how does the Critical Thinking Framework fit in with an overwhelming emphasis on assessments aligned to national or state standards? This is a valid concern and an important point to address. For teachers, schools, and districts locked into an accountability system that values performance on state tests but does not communicate content expectations beyond general standards, the arguments I make may seem beside the point. Sure, knowledge matters, but the curriculum demands that students know how to quickly identify the main idea of a paragraph, even if they don’t have any background knowledge about the topic of the paragraph.

It is crucial that elementary practitioners be connected to both evolving research on learning and the limiting realities we teach within. Unfortunately, I can provide no easy answers beyond saying that teaching is a balancing act. The tension, while real and relevant to teachers’ daily lives, should not cloud our vision for what children need from their school experiences.

I also argue it is easier to incorporate the demands of our current standardized testing environment into a curriculum rich with history, science, art, geography, languages, and novels than the reverse. The Critical Thinking Framework presents ways to approach all kinds of knowledge in a way that presses students toward deeper processing of the content they are learning. If we can raise the bar for student work and thinking in our classrooms, the question of how students perform on standardized tests will become secondary to helping them achieve much loftier and important goals. The choice of whether to emphasize excellent curriculum or high-stakes tests, insofar as it is a choice at all, should never be existential or a zero-sum game.

From Critical Thinking in the Elementary Classroom: Engaging Young Minds with Meaningful Content (pp. 25–29) by Erin Shadowens, Arlington, VA: ASCD. Copyright © 2023 by ASCD. All rights reserved.

Students THINK: A Framework for Improving Problem Solving

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The results of research about students' and teachers' use of an interaction framework (THINK) to guide group communication about problem solving. Students who used the THINK framework demonstrated greater gains in problem-solving achievement than students who did not use the framework. Teachers reading this article will understand the THINK framework and how to apply it to classroom use.

Kelli Thomas interests include elementary mathematics teaching and learning, mathematics teacher education, and evaluation of mathematics programs.

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• Effective Classroom Management

Supporting Struggling Students Through Collaborative Problem Solving

• February 23, 2022
• David Adams, PhD, and Enoch Hale, PhD

Every semester faculty are faced with students who struggle with completing assignments, understanding the content, or just find it difficult to participate in class activities and discussions. For many, these struggles are connected to low grades, negative perceptions of the instructor and class, increased absences, and indicative of a general lack of engagement.  It is not uncommon for faculty to misinterpret these students as lazy, unmotivated, or just unprepared to do college-level work.  Faculty regularly reach out to assist, but some students are put into the university machinery of “student support,” where their worlds become more complex with emails connecting them to support services like tutoring and counseling, or notifying them that they are in danger of failing or not passing a course. Although this outreach is intended to motivate and help, there is a very real cognitive and emotional load that can be demoralizing if not debilitating. This is complicated, if not impossible terrain to navigate for all of us who genuinely want to see students succeed. Greene (2009) developed a framework for collaborative problem solving as a way to organize, support, and deeply engage students in identifying realistic ways to get back on track and succeed within the classroom. This framework has three steps that can be applied across multiple modalities.  All three steps are based on the fact that we are not merely disseminating information, but teaching human beings to think through content to build disciplinary skills, insights, and understanding. 

Step 1: Connect to identify the root cause

Meet with the underperforming student and work to identify the root causes for their classroom performance. It seems simple but getting to the root cause is quite difficult because it positions us to take into consideration different factors, many of which may be personal and that can be uncomfortable. 

• Observed behaviors/actions: Let the student know what you have observed and focus on the behaviors, not what you think may be the underlying reasons. Ask if the student agrees with your observations and/or has more to add or change.
• Seek and clarify reasons: Ask the student for clarification as to why these behaviors are occurring. 

Successfully completing Step 1 requires that we, as faculty members, be specific in identifying the behavior. This step may also be the first time you have spoken with this student in a one-on-one setting and offers an opportunity to break down the barriers that may exist while opening up the opportunity for a conversation.

Step 2: Explain impact on oneself and others

Explain to the student how their behavior is impacting their success in the classroom and what impact it is having on the rest of the class. This is an important step since often the student does not realize that their behaviors can take away an opportunity for the class to be a community of learners, where students’ voices are heard and learning is done in small and large groups through the sharing of information. This may also be the first time the student has looked beyond their own learning and viewed their own behavior as a negative impact on the learning of other students. Below are some prompts to get the conversation started.

• “Now that we understand what the problems are, let me explain the type of impact I believe it is having on you, me, and the rest of the class….”
• “How do you think that your behavior may be affecting others in the class?”
• “Have any of your class peers asked if you are doing okay?”
• “We previously discussed your reluctance to engage in the class discussions, have you thought about how that has impacted the learning of yourself and your peers?”

Step 3: Collective Problem Solving

Now is the moment for mapping out solutions. The problem(s) have been identified, the points of view and implications have been clarified, so the stage is set to create an action plan.  What makes this step different from traditional problem-solving approaches is that the student takes the responsibility to lead the discussion.  Specifically, students work to identify ways in which they can get back on track. Your job, as the instructor, is to support and guide the student, being honest of their own expectations and what is possible based on the academic expectations of the course. We should remember that most students upon meeting during office hours or after class are waiting to be told what they have to do. This system of faculty problem solving for the student does not address the larger issue. It may also further decrease the motivation of the student by putting unrealistic expectations in front of them and does not address the problem as to how the student arrived in this situation. Greene (2009) points to the power of this phase as the opportunity for the student to identify a new strategy that can support them now and in future situations that are similar.

Teaching is no easy task, but strong and consistent approaches can help us help students to help themselves. With restrictions put in place across a majority of universities, and students possibly feeling more disconnected from the instructors of their courses, the chances of students encountering different unforeseen obstacles has become heightened. What we can say with confidence is that the current landscape of higher education has reminded us that often the best path to supporting student learning is focusing on what we can control…and that is what we do in the classroom. 

David Adams, PhD, is an assistant professor of kinesiology at Cal Poly Humboldt (HSU). He teaches classes within the kinesiology department. His research focuses on improving the movement abilities for children with disabilities, as well as improving the learning experience and academic experiences of students in higher education.

Enoch Hale, PhD, is the director of the Center for Teaching and Learning at Cal Poly Humboldt. Dr. Hale has 18 years of teaching experience of which 12 of those years are in higher education. His research focuses on faculty development, teaching and learning in higher ed, and embedding critical thinking into curriculum, instruction, and classroom culture.

Greene, R. W. (2009). Lost at school: Why our kids with behavioral challenges are falling through the cracks and how we can help them . Simon and Schuster.

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Strategies to develop problem-solving skills in students.

• November 14, 2023

Students need the freedom to brainstorm, develop solutions and make mistakes — this is truly the only way to prepare them for life outside the classroom. When students are immersed in a learning environment that only offers them step-by-step guides and encourages them to focus solely on memorisation, they are not gaining the skills necessary to help them navigate in the complex, interconnected environment of the real world.

Choosing a school that emphasises the importance of future-focussed skills will ensure your child has the abilities they need to survive and thrive anywhere in the world. What are future-focussed skills? Students who are prepared for the future need to possess highly developed communication skills, self-management skills, research skills, thinking skills, social skills and problem-solving skills. In this blog, I would like to focus on problem-solving skills.

What Are Problem-Solving Skills?

The Forage defines problem-solving skills as those that allow an individual to identify a problem, come up with solutions, analyse the options and collaborate to find the best solution for the issue.

Importance of Problem-Solving in the Classroom Setting

Learning how to solve problems effectively and positively is a crucial part of child development. When children are allowed to solve problems in a classroom setting, they can test those skills in a safe and nurturing environment. Generally, when they face age-appropriate issues, they can begin building those skills in a healthy and positive manner.

Without exposure to challenging situations and scenarios, children will not be equipped with the foundational problem-solving skills needed to tackle complex issues in the real world. Experts predict that problem-solving skills will eventually be more sought after in job applicants than hard skills related to that specific profession. Students must be given opportunities in school to resolve conflicts, address complex problems and come up with their own solutions in order to develop these skills.

Benefits of Problem-Solving Skills for Students

Learning how to solve problems offers students many advantages, such as:

Improving Academic Results

When students have a well-developed set of problem-solving skills, they are often better critical and analytical thinkers as well. They are able to effectively use these 21st-century skills when completing their coursework, allowing them to become more successful in all academic areas. By prioritising problem-solving strategies in the classroom, teachers often find that academic performance improves.

Developing Confidence

Giving students the freedom to solve problems and create their own solutions is essentially permitting them to make their own choices. This sense of independence — and the natural resilience that comes with it — allows students to become confident learners who aren’t intimidated by new or challenging situations. Ultimately, this prepares them to take on more complex challenges in the future, both on a professional and social level.

Preparing Students for Real-World Challenges

The challenges we are facing today are only growing more complex, and by the time students have graduated, they are going to be facing issues that we may not even have imagined. By arming them with real-world problem-solving experience, they will not feel intimidated or stifled by those challenges; they will be excited and ready to address them. They will know how to discuss their ideas with others, respect various perspectives and collaborate to develop a solution that best benefits everyone involved.

The Best Problem-Solving Strategies for Students

No single approach or strategy will instil a set of problem-solving skills in students.  Every child is different, so educators should rely on a variety of strategies to develop this core competency in their students.  It is best if these skills are developed naturally.

These are some of the best strategies to support students problem-solving skills:

Project-Based Learning

By providing students with project-based learning experiences and allowing plenty of time for discussion, educators can watch students put their problem-solving skills into action inside their classrooms. This strategy is one of the most effective ways to fine-tune problem-solving skills in students.  During project-based learning, teachers may take notes on how the students approach a problem and then offer feedback to students for future development. Teachers can address their observations of interactions during project-based learning at the group level or they can work with students on an individual basis to help them become more effective problem-solvers.

Encourage Discussion and Collaboration in the Classroom Setting

Another strategy to encourage the development of problem-solving skills in students is to allow for plenty of discussion and collaboration in the classroom setting.  When students interact with one another, they are naturally developing problem solving skills.  Rather than the teacher delivering information and requiring the students to passively receive information, students can share thoughts and ideas with one another.  Getting students to generate their own discussion and communication requires thinking skills. 

Utilising an Inquiry-Based approach to Learning

Students should be presented with situations in which their curiosity is sparked and they are motivated to inquire further. Teachers should ask open-ended questions and encourage students to develop responses which require problem-solving. By providing students with complex questions for which a variety of answers may be correct, teachers get students to consider different perspectives and deal with potential disagreement, which requires problem-solving skills to resolve.

Model Appropriate Problem-Solving Skills

One of the simplest ways to instil effective problem-solving skills in students is to model appropriate and respectful strategies and behaviour when resolving a conflict or addressing an issue. Teachers can showcase their problem-solving skills by:

• Identifying a problem when they come across one for the class to see
• Brainstorming possible solutions with students
• Collaborating with students to decide on the best solution
• Testing that solution and examining the results with the students
• Adapting as necessary to improve results or achieve the desired goal

Prioritise Student Agency in Learning

Recent research shows that self-directed learning is one of the most effective ways to nurture 21st-century competency development in young learners. Learning experiences that encourage student agency often require problem-solving skills.  When creativity and innovation are needed, students often encounter unexpected problems along the way that must be solved. Through self-directed learning, students experience challenges in a natural situation and can fine-tune their problem-solving skills along the way.  Self-directed learning provides them with a foundation in problem-solving that they can build upon in the future, allowing them to eventually develop more advanced and impactful problem-solving skills for real life.

21st-Century Skill Development at OWIS Singapore

Problem-solving has been identified as one of the core competencies that young learners must develop to be prepared to meet the dynamic needs of a global environment.  At OWIS Singapore, we have implemented an inquiry-driven, skills-based curriculum that allows students to organically develop critical future-ready skills — including problem-solving.  Our hands-on approach to education enables students to collaborate, explore, innovate, face-challenges, make mistakes and adapt as necessary.  As such, they learn problem-solving skills in an authentic manner.

For more information about 21st-century skill development, schedule a campus tour today.

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Fostering complex problem solving for diverse learners: engaging an ethos of intentionality toward equitable access

• Published: 14 April 2020
• Volume 68 , pages 679–702, ( 2020 )

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• Krista D. Glazewski 1 &
• Peggy A. Ertmer 2 , 3  

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Complex problem solving is an effective means to engage students in disciplinary content while also furnishing critical non-cognitive and life skills. Despite increased adoption of complex problem-solving methods in K-12 classrooms today (e.g., case-, project-, or problem-based learning), we know little about how to make these approaches accessible to linguistically and culturally diverse (LCD) students. In this paper, we promote a conceptual framework, based on an ethos of intentionality , that supports culturally responsive teaching (CRT). We provide specific questions to guide teachers’ implementation of an ethos of intentionality, through critical reflection and meaningful action, and discuss a framework for culturally relevant practice that operationalizes key central tenets (e.g., high expectations, cultural competence, and critical consciousness). Finally, we include strategies that can help teachers and designers translate the principles of the CRT framework into action with a specific focus on complex problem solving in classrooms.

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Aronson, B., & Laughter, J. (2015). The theory and practice of culturally relevant education: A synthesis of research across content areas. Review of Educational Research, 86 (1), 163–206. https://doi.org/10.3102/0034654315582066 .

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Glazewski, K.D., Ertmer, P.A. Fostering complex problem solving for diverse learners: engaging an ethos of intentionality toward equitable access. Education Tech Research Dev 68 , 679–702 (2020). https://doi.org/10.1007/s11423-020-09762-9

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Adapting a theoretical framework for characterizing students' use of equations in physics problem solving

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Carina M. Rebello , N. Sanjay Rebello; Adapting a theoretical framework for characterizing students' use of equations in physics problem solving. AIP Conf. Proc. 8 February 2012; 1413 (1): 311–314. https://doi.org/10.1063/1.3680057

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Previous studies have focused on the resources that students activate and utilize while solving a given physics problem. However, few studies explore how students relate a given resource such as an equation, to various types of physics problems and contexts and how they ascertain the meaning and applicability of that resource. We explore how students view physics equations, derive meaning from those equations, and use those equations in physics problem solving. We adapt Dubinsky and McDonald's description of APOS (action-process-object-schema) theory of learning in mathematics, to construct a theoretical framework that describes how students interpret and use equations in physics in terms of actions, processes, objects, and schemas. This framework provides a lens for understanding how students construct their understanding of physics concepts and their relation to equations. We highlight how APOS theory can be operationalized to serve as a lens for studying the use of mathematics in physics problem solving.

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A Better Framework for Solving Tough Problems

Start with trust and end with speed.

• Apple Podcasts

When it comes to solving complicated problems, the default for many organizational leaders is to take their time to work through the issues at hand. Unfortunately, that often leads to patchwork solutions or problems not truly getting resolved.

But Anne Morriss offers a different framework. In this episode, she outlines a five-step process for solving any problem and explains why starting with trust and ending with speed is so important for effective change leadership. As she says, “Let’s get into dialogue with the people who are also impacted by the problem before we start running down the path of solving it.”

Morriss is an entrepreneur and leadership coach. She’s also the coauthor of the book, Move Fast and Fix Things: The Trusted Leader’s Guide to Solving Hard Problems .

Key episode topics include: strategy, decision making and problem solving, strategy execution, managing people, collaboration and teams, trustworthiness, organizational culture, change leadership, problem solving, leadership.

HBR On Strategy curates the best case studies and conversations with the world’s top business and management experts, to help you unlock new ways of doing business. New episodes every week.

• Listen to the full HBR IdeaCast episode: How to Solve Tough Problems Better and Faster (2023)
• Find more episodes of HBR IdeaCast
• Discover 100 years of Harvard Business Review articles, case studies, podcasts, and more at HBR.org .

HANNAH BATES: Welcome to HBR On Strategy , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock new ways of doing business.

When it comes to solving complicated problems, many leaders only focus on the most apparent issues. Unfortunately that often leads to patchwork or partial solutions. But Anne Morriss offers a different framework that aims to truly tackle big problems by first leaning into trust and then focusing on speed.

Morriss is an entrepreneur and leadership coach. She’s also the co-author of the book, Move Fast and Fix Things: The Trusted Leader’s Guide to Solving Hard Problems . In this episode, she outlines a five-step process for solving any problem. Some, she says, can be solved in a week, while others take much longer. She also explains why starting with trust and ending with speed is so important for effective change leadership.

This episode originally aired on HBR IdeaCast in October 2023. Here it is.

CURT NICKISCH: Welcome to the HBR IdeaCast from Harvard Business Review. I’m Curt Nickisch.

Problems can be intimidating. Sure, some problems are fun to dig into. You roll up your sleeves, you just take care of them; but others, well, they’re complicated. Sometimes it’s hard to wrap your brain around a problem, much less fix it.

And that’s especially true for leaders in organizations where problems are often layered and complex. They sometimes demand technical, financial, or interpersonal knowledge to fix. And whether it’s avoidance on the leaders’ part or just the perception that a problem is systemic or even intractable, problems find a way to endure, to keep going, to keep being a problem that everyone tries to work around or just puts up with.

But today’s guest says that just compounds it and makes the problem harder to fix. Instead, she says, speed and momentum are key to overcoming a problem.

Anne Morriss is an entrepreneur, leadership coach and founder of the Leadership Consortium and with Harvard Business School Professor Francis Frei, she wrote the new book, Move Fast and Fix Things: The Trusted Leaders Guide to Solving Hard Problems . Anne, welcome back to the show.

ANNE MORRISS: Curt, thank you so much for having me.

CURT NICKISCH: So, to generate momentum at an organization, you say that you really need speed and trust. We’ll get into those essential ingredients some more, but why are those two essential?

ANNE MORRISS: Yeah. Well, the essential pattern that we observed was that the most effective change leaders out there were building trust and speed, and it didn’t seem to be a well-known observation. We all know the phrase, “Move fast and break things,” but the people who were really getting it right were moving fast and fixing things, and that was really our jumping off point. So when we dug into the pattern, what we observed was they were building trust first and then speed. This foundation of trust was what allowed them to fix more things and break fewer.

CURT NICKISCH: Trust sounds like a slow thing, right? If you talk about building trust, that is something that takes interactions, it takes communication, it takes experiences. Does that run counter to the speed idea?

ANNE MORRISS: Yeah. Well, this issue of trust is something we’ve been looking at for over a decade. One of the headlines in our research is it’s actually something we’re building and rebuilding and breaking all the time. And so instead of being this precious, almost farbege egg, it’s this thing that is constantly in motion and this thing that we can really impact when we’re deliberate about our choices and have some self-awareness around where it’s breaking down and how it’s breaking down.

CURT NICKISCH: You said break trust in there, which is intriguing, right? That you may have to break trust to build trust. Can you explain that a little?

ANNE MORRISS:  Yeah, well, I’ll clarify. It’s not that you have to break it in order to build it. It’s just that we all do it some of the time. Most of us are trusted most of the time. Most of your listeners I imagine are trusted most of the time, but all of us have a pattern where we break trust or where we don’t build as much as could be possible.

CURT NICKISCH: I want to talk about speed, this other essential ingredient that’s so intriguing, right? Because you think about solving hard problems as something that just takes a lot of time and thinking and coordination and planning and designing. Explain what you mean by it? And also, just  how we maybe approach problems wrong by taking them on too slowly?

ANNE MORRISS: Well, Curt, no one has ever said to us, “I wish I had taken longer and done less.” We hear the opposite all the time, by the way. So what we really set out to do was to create a playbook that anyone can use to take less time to do more of the things that are going to make your teams and organizations stronger.

And the way we set up the book is okay, it’s really a five step process. Speed is the last step. It’s the payoff for the hard work you’re going to do to figure out your problem, build or rebuild trust, expand the team in thoughtful and strategic ways, and then tell a real and compelling story about the change you’re leading.

Only then do you get to go fast, but that’s an essential part of the process, and we find that either people under emphasize it or speed has gotten a bad name in this world of moving fast and breaking things. And part of our mission for sure was to rehabilitate speed’s reputation because it is an essential part of the change leader’s equation. It can be the difference between good intentions and getting anything done at all.

CURT NICKISCH: You know, the fact that nobody ever tells you, “I wish we had done less and taken more time.” I think we all feel that, right? Sometimes we do something and then realize, “Oh, that wasn’t that hard and why did it take me so long to do it? And I wish I’d done this a long time ago.” Is it ever possible to solve a problem too quickly?

ANNE MORRISS: Absolutely. And we see that all the time too. What we push people to do in those scenarios is really take a look at the underlying issue because in most cases, the solution is not to take your foot off the accelerator per se and slow down. The solution is to get into the underlying problem. So if it’s burnout or a strategic disconnect between what you’re building and the marketplace you’re serving, what we find is the anxiety that people attach to speed or the frustration people attach to speed is often misplaced.

CURT NICKISCH: What is a good timeline to think about solving a problem then? Because if we by default take too long or else jump ahead and we don’t fix it right, what’s a good target time to have in your mind for how long solving a problem should take?

ANNE MORRISS: Yeah. Well, we’re playful in the book and talking about the idea that many problems can be solved in a week. We set the book up five chapters. They’re titled Monday, Tuesday, Wednesday, Thursday, Friday, and we’re definitely having fun with that. And yet, if you count the hours in a week, there are a lot of them. Many of our problems, if you were to spend a focused 40 hours of effort on a problem, you’re going to get pretty far.

But our main message is, listen, of course it’s going to depend on the nature of the problem, and you’re going to take weeks and maybe even some cases months to get to the other side. What we don’t want you to do is take years, which tends to be our default timeline for solving hard problems.

CURT NICKISCH: So you say to start with identifying the problem that’s holding you back, seems kind of obvious. But where do companies go right and wrong with this first step of just identifying the problem that’s holding you back?

ANNE MORRISS: And our goal is that all of these are going to feel obvious in retrospect. The problem is we skip over a lot of these steps and this is why we wanted to underline them. So this one is really rooted in our observation and I think the pattern of our species that we tend to be overconfident in the quality of our thoughts, particularly when it comes to diagnosing problems.

And so we want to invite you to start in a very humble and curious place, which tends not to be our default mode when we’re showing up for work. We convince ourselves that we’re being paid for our judgment. That’s exactly what gets reinforced everywhere. And so we tend to counterintuitively, given what we just talked about, we tend to move too quickly through the diagnostic phase.

CURT NICKISCH: “I know what to do, that’s why you hired me.”

ANNE MORRISS: Exactly. “I know what to do. That’s why you hired me. I’ve seen this before. I have a plan. Follow me.” We get rewarded for the expression of confidence and clarity. And so what we’re inviting people to do here is actually pause and really lean into what are the root causes of the problem you’re seeing? What are some alternative explanations? Let’s get into dialogue with the people who are also impacted by the problem before we start running down the path of solving it.

CURT NICKISCH: So what do you recommend for this step, for getting to the root of the problem? What are questions you should ask? What’s the right thought process? What do you do on Monday of the week?

ANNE MORRISS: In our experience of doing this work, people tend to undervalue the power of conversation, particularly with other people in the organization. So we will often advocate putting together a team of problem solvers, make it a temporary team, really pull in people who have a particular perspective on the problem and create the space, make it as psychologically safe as you can for people to really, as Chris Argyris so beautifully articulated, discuss the undiscussable.

And so the conditions for that are going to look different in every organization depending on the problem, but if you can get a space where smart people who have direct experience of a problem are in a room and talking honestly with each other, you can make an extraordinary amount of progress, certainly in a day.

CURT NICKISCH: Yeah, that gets back to the trust piece.

ANNE MORRISS: Definitely.

CURT NICKISCH: How do you like to start that meeting, or how do you like to talk about it? I’m just curious what somebody on that team might hear in that meeting, just to get the sense that it’s psychologically safe, you can discuss the undiscussable and you’re also focusing on the identification part. What’s key to communicate there?

ANNE MORRISS: Yeah. Well, we sometimes encourage people to do a little bit of data gathering before those conversations. So the power of a quick anonymous survey around whatever problem you’re solving, but also be really thoughtful about the questions you’re going to ask in the moment. So a little bit of preparation can go a long way and a little bit of thoughtfulness about the power dynamic. So who’s going to walk in there with license to speak and who’s going to hold back? So being thoughtful about the agenda, about the questions you’re asking about the room, about the facilitation, and then courage is a very infectious emotion.

So if you can early on create the conditions for people to show up bravely in that conversation, then the chance that you’re going to get good information and that you’re going to walk out of that room with new insight in the problem that you didn’t have when you walked in is extraordinarily high.

CURT NICKISCH: Now, in those discussions, you may have people who have different perspectives on what the problem really is. They also bear different costs of addressing the problem or solving it. You talked about the power dynamic, but there’s also an unfairness dynamic of who’s going to actually have to do the work to take care of it, and I wonder how you create a culture in that meeting where it’s the most productive?

ANNE MORRISS: For sure, the burden of work is not going to be equitably distributed around the room. But I would say, Curt, the dynamic that we see most often is that people are deeply relieved that hard problems are being addressed. So it really can create, and more often than not in our experience, it does create this beautiful flywheel of action, creativity, optimism. Often when problems haven’t been addressed, there is a fair amount of anxiety in the organization, frustration, stagnation. And so credible movement towards action and progress is often the best antidote. So even if the plan isn’t super clear yet, if it’s credible, given who’s in the room and their decision rights and mandate, if there’s real momentum coming out of that to make progress, then that tends to be deeply energizing to people.

CURT NICKISCH: I wonder if there’s an organization that you’ve worked with that you could talk about how this rolled out and how this took shape?

ANNE MORRISS: When we started working with Uber, that was wrestling with some very public issues of culture and trust with a range of stakeholders internally, the organization, also external, that work really started with a campaign of listening and really trying to understand where trust was breaking down from the perspective of these stakeholders?

So whether it was female employees or regulators or riders who had safety concerns getting into the car with a stranger. This work, it starts with an honest internal dialogue, but often the problem has threads that go external. And so bringing that same commitment to curiosity and humility and dialogue to anyone who’s impacted by the problem is the fastest way to surface what’s really going on.

CURT NICKISCH: There’s a step in this process that you lay out and that’s communicating powerfully as a leader. So we’ve heard about listening and trust building, but now you’re talking about powerful communication. How do you do this and why is it maybe this step in the process rather than the first thing you do or the last thing you do?

ANNE MORRISS: So in our process, again, it’s the days of the week. On Monday you figured out the problem. Tuesday you really got into the sandbox in figuring out what a good enough plan is for building trust. Wednesday, step three, you made it better. You created an even better plan, bringing in new perspectives. Thursday, this fourth step is the day we’re saying you got to go get buy-in. You got to bring other people along. And again, this is a step where we see people often underinvest in the power and payoff of really executing it well.

CURT NICKISCH: How does that go wrong?

ANNE MORRISS: Yeah, people don’t know the why. Human behavior and the change in human behavior really depends on a strong why. It’s not just a selfish, “What’s in it for me?” Although that’s helpful, but where are we going? I may be invested in a status quo and I need to understand, okay, if you’re going to ask me to change, if you’re going to invite me into this uncomfortable place of doing things differently, why am I here? Help me understand it and articulate the way forward and language that not only I can understand, but also that’s going to be motivating to me.

CURT NICKISCH: And who on my team was part of this process and all that kind of stuff?

ANNE MORRISS: Oh, yeah. I may have some really important questions that may be in the way of my buy-in and commitment to this plan. So certainly creating a space where those questions can be addressed is essential. But what we found is that there is an architecture of a great change story, and it starts with honoring the past, honoring the starting place. Sometimes we’re so excited about the change and animated about the change that what has happened before or what is even happening in the present tense is low on our list of priorities.

Or we want to label it bad, because that’s the way we’ve thought about the change, but really pausing and honoring what came before you and all the reasonable decisions that led up to it, I think can be really helpful to getting people emotionally where you want them to be willing to be guided by you. Going back to Uber, when Dara Khosrowshahi came in.

CURT NICKISCH: This is the new CEO.

ANNE MORRISS: The new CEO.

CURT NICKISCH: Replaced Travis Kalanick, the founder and first CEO, yeah.

ANNE MORRISS: Yeah, and had his first all-hands meeting. One of his key messages, and this is a quote, was that he was going to retain the edge that had made Uber, “A force of nature.” And in that meeting, the crowd went wild because this is also a company that had been beaten up publicly for months and months and months, and it was a really powerful choice. And his predecessor, Travis was in the room, and he also honored Travis’ incredible work and investment in bringing the company to the place where it was.

And I would use words like grace to also describe those choices, but there’s also an incredible strategic value to naming the starting place for everybody in the room because in most cases, most people in that room played a role in getting to that starting place, and you’re acknowledging that.

CURT NICKISCH: You can call it grace. Somebody else might call it diplomatic or strategic. But yeah, I guess like it or not, it’s helpful to call out and honor the complexity of the way things have been done and also the change that’s happening.

ANNE MORRISS: Yeah, and the value. Sometimes honoring the past is also owning what didn’t work or what wasn’t working for stakeholders or segments of the employee team, and we see that around culture change. Sometimes you’ve got to acknowledge that it was not an equitable environment, but whatever the worker, everyone in that room is bringing that pass with them. So again, making it discussable and using it as the jumping off place is where we advise people to start.

Then you’ve earned the right to talk about the change mandate, which we suggest using clear and compelling language about the why. “This is what happened, this is where we are, this is the good and the bad of it, and here’s the case for change.”

And then the last part, which is to describe a rigorous and optimistic way forward. It’s a simple past, present, future arc, which will be familiar to human beings. We love stories as human beings. It’s among the most powerful currency we have to make sense of the world.

CURT NICKISCH: Yeah. Chronological is a pretty powerful order.

ANNE MORRISS: Right. But again, the change leaders we see really get it right, are investing an incredible amount of time into the storytelling part of their job. Ursula Burns, the Head of Xerox is famous for the months and years she spent on the road just telling the story of Xerox’s change, its pivot into services to everyone who would listen, and that was a huge part of her success.

CURT NICKISCH: So Friday or your fifth step, you end with empowering teams and removing roadblocks. That seems obvious, but it’s critical. Can you dig into that a little bit?

ANNE MORRISS: Yeah. Friday is the fun day. Friday’s the release of energy into the system. Again, you’ve now earned the right to go fast. You have a plan, you’re pretty confident it’s going to work. You’ve told the story of change the organization, and now you get to sprint. So this is about really executing with urgency, and it’s about a lot of the tactics of speed is where we focus in the book. So the tactics of empowerment, making tough strategic trade-offs so that your priorities are clear and clearly communicated, creating mechanisms to fast-track progress. At Etsy, CEO Josh Silverman, he labeled these projects ambulances. It’s an unfortunate metaphor, but it’s super memorable. These are the products that get to speed out in front of the other ones because the stakes are high and the clock is sticking.

CURT NICKISCH: You pull over and let it go by.

ANNE MORRISS: Yeah, exactly. And so we have to agree as an organization on how to do something like that. And so we see lots of great examples both in young organizations and big complex biotech companies with lots of regulatory guardrails have still found ways to do this gracefully.

And I think we end with this idea of conflict debt, which is a term we really love. Leanne Davey, who’s a team scholar and researcher, and anyone in a tech company will recognize the idea of tech debt, which is this weight the organization drags around until they resolve it. Conflict debt is a beautiful metaphor because it is this weight that we drag around and slows us down until we decide to clean it up and fix it. The organizations that are really getting speed right have figured out either formally or informally, how to create an environment where conflict and disagreements can be gracefully resolved.

CURT NICKISCH: Well, let’s talk about this speed more, right? Because I think this is one of those places that maybe people go wrong or take too long, and then you lose the awareness of the problem, you lose that urgency. And then that also just makes it less effective, right? It’s not just about getting the problem solved as quickly as possible. It’s also just speed in some ways helps solve the problem.

ANNE MORRISS: Oh, yeah. It really is the difference between imagining the change you want to lead and really being able to bring it to life. Speed is the thing that unlocks your ability to lead change. It needs a foundation, and that’s what Monday through Thursday is all about, steps one through four, but the finish line is executing with urgency, and it’s that urgency that releases the system’s energy, that communicates your priorities, that creates the conditions for your team to make progress.

CURT NICKISCH: Moving fast is something that entrepreneurs and tech companies certainly understand, but there’s also this awareness that with big companies, the bigger the organization, the harder it is to turn the aircraft carrier around, right? Is speed relative when you get at those levels, or do you think this is something that any company should be able to apply equally?

ANNE MORRISS: We think this applies to any company. The culture really lives at the level of team. So we believe you can make a tremendous amount of progress even within your circle of control as a team leader. I want to bring some humility to this and careful of words like universal, but we do think there’s some universal truths here around the value of speed, and then some of the byproducts like keeping fantastic people. Your best people want to solve problems, they want to execute, they want to make progress and speed, and the ability to do that is going to be a variable in their own equation of whether they stay or they go somewhere else where they can have an impact.

CURT NICKISCH: Right. They want to accomplish something before they go or before they retire or finish something out. And if you’re able to just bring more things on the horizon and have it not feel like it’s going to be another two years to do something meaningful.

ANNE MORRISS: People – I mean, they want to make stuff happen and they want to be around the energy and the vitality of making things happen, which again, is also a super infectious phenomenon. One of the most important jobs of a leader, we believe, is to set the metabolic pace of their teams and organizations. And so what we really dig into on Friday is, well, what does that look like to speed something up? What are the tactics of that?

CURT NICKISCH: I wonder if that universal truth, that a body in motion stays in motion applies to organizations, right? If an organization in motion stays in motion, there is something to that.

ANNE MORRISS: Absolutely.

CURT NICKISCH: Do you have a favorite client story to share, just where you saw speed just become a bit of a flywheel or just a positive reinforcement loop for more positive change at the organization?

ANNE MORRISS: Yeah. We work with a fair number of organizations that are on fire. We do a fair amount of firefighting, but we also less dramatically do a lot of fire prevention. So we’re brought into organizations that are working well and want to get better, looking out on the horizon. That work is super gratifying, and there is always a component of, well, how do we speed this up?

What I love about that work is there’s often already a high foundation of trust, and so it’s, well, how do we maintain that foundation but move this flywheel, as you said, even faster? And it’s really energizing because often there’s a lot of pent-up energy that… There’s a lot of loyalty to the organization, but often it’s also frustration and pent-up energy. And so when that gets released, when good people get the opportunity to sprint for the first time in a little while, it’s incredibly energizing, not just for us, but for the whole organization.

CURT NICKISCH: Anne, this is great. I think finding a way to solve problems better but also faster is going to be really helpful. So thanks for coming on the show to talk about it.

ANNE MORRISS:  Oh, Curt, it was such a pleasure. This is my favorite conversation. I’m delighted to have it anytime.

HANNAH BATES: That was entrepreneur, leadership coach, and author Anne Morriss – in conversation with Curt Nickisch on HBR IdeaCast.

We’ll be back next Wednesday with another hand-picked conversation about business strategy from Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

When you’re ready for more podcasts, articles, case studies, books, and videos with the world’s top business and management experts, you’ll find it all at HBR.org.

This episode was produced by Mary Dooe, Anne Saini, and me, Hannah Bates. Ian Fox is our editor. Special thanks to Rob Eckhardt, Maureen Hoch, Erica Truxler, Ramsey Khabbaz, Nicole Smith, Anne Bartholomew, and you – our listener. See you next week.

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The Algebra Problem: How Middle School Math Became a National Flashpoint

Top students can benefit greatly by being offered the subject early. But many districts offer few Black and Latino eighth graders a chance to study it.

By Troy Closson

From suburbs in the Northeast to major cities on the West Coast, a surprising subject is prompting ballot measures, lawsuits and bitter fights among parents: algebra.

Students have been required for decades to learn to solve for the variable x, and to find the slope of a line. Most complete the course in their first year of high school. But top-achievers are sometimes allowed to enroll earlier, typically in eighth grade.

The dual pathways inspire some of the most fiery debates over equity and academic opportunity in American education.

Do bias and inequality keep Black and Latino children off the fast track? Should middle schools eliminate algebra to level the playing field? What if standout pupils lose the chance to challenge themselves?

The questions are so fraught because algebra functions as a crucial crossroads in the education system. Students who fail it are far less likely to graduate. Those who take it early can take calculus by 12th grade, giving them a potential edge when applying to elite universities and lifting them toward society’s most high-status and lucrative professions.

But racial and economic gaps in math achievement are wide in the United States, and grew wider during the pandemic. In some states, nearly four in five poor children do not meet math standards.

To close those gaps, New York City’s previous mayor, Bill de Blasio, adopted a goal embraced by many districts elsewhere. Every middle school would offer algebra, and principals could opt to enroll all of their eighth graders in the class. San Francisco took an opposite approach: If some children could not reach algebra by middle school, no one would be allowed to take it.

The central mission in both cities was to help disadvantaged students. But solving the algebra dilemma can be more complex than solving the quadratic formula.

New York’s dream of “algebra for all” was never fully realized, and Mayor Eric Adams’s administration changed the goal to improving outcomes for ninth graders taking algebra. In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes. After a huge public outcry, the district decided to reverse course.

“You wouldn’t think that there could be a more boring topic in the world,” said Thurston Domina, a professor at the University of North Carolina. “And yet, it’s this place of incredibly high passions.”

“Things run hot,” he said.

In some cities, disputes over algebra have been so intense that parents have sued school districts, protested outside mayors’ offices and campaigned for the ouster of school board members.

Teaching math in middle school is a challenge for educators in part because that is when the material becomes more complex, with students moving from multiplication tables to equations and abstract concepts. Students who have not mastered the basic skills can quickly become lost, and it can be difficult for them to catch up.

Many school districts have traditionally responded to divergent achievement levels by simply separating children into distinct pathways, placing some in general math classes while offering others algebra as an accelerated option. Such sorting, known as tracking, appeals to parents who want their children to reach advanced math as quickly as possible.

But tracking has cast an uncomfortable spotlight on inequality. Around a quarter of all students in the United States take algebra in middle school. But only about 12 percent of Black and Latino eighth graders do, compared with roughly 24 percent of white pupils, a federal report found .

“That’s why middle school math is this flashpoint,” said Joshua Goodman, an associate professor of education and economics at Boston University. “It’s the first moment where you potentially make it very obvious and explicit that there are knowledge gaps opening up.”

In the decades-long war over math, San Francisco has emerged as a prominent battleground.

California once required that all eighth graders take algebra. But lower-performing middle school students often struggle when forced to enroll in the class, research shows. San Francisco later stopped offering the class in eighth grade. But the ban did little to close achievement gaps in more advanced math classes, recent research has found.

As the pendulum swung, the only constant was anger. Leading Bay Area academics disparaged one another’s research . A group of parents even sued the district last spring. “Denying students the opportunity to skip ahead in math when their intellectual ability clearly allows for it greatly harms their potential for future achievement,” their lawsuit said.

The city is now back to where it began: Middle school algebra — for some, not necessarily for all — will return in August. The experience underscored how every approach carries risks.

“Schools really don’t know what to do,” said Jon R. Star, an educational psychologist at Harvard who has studied algebra education. “And it’s just leading to a lot of tension.”

In Cambridge, Mass., the school district phased out middle school algebra before the pandemic. But some argued that the move had backfired: Families who could afford to simply paid for their children to take accelerated math outside of school.

“It’s the worst of all possible worlds for equity,” Jacob Barandes, a Cambridge parent, said at a school board meeting.

Elsewhere, many students lack options to take the class early: One of Philadelphia’s most prestigious high schools requires students to pass algebra before enrolling, preventing many low-income children from applying because they attend middle schools that do not offer the class.

In New York, Mr. de Blasio sought to tackle the disparities when he announced a plan in 2015 to offer algebra — but not require it — in all of the city’s middle schools. More than 15,000 eighth graders did not have the class at their schools at the time.

Since then, the number of middle schools that offer algebra has risen to about 80 percent from 60 percent. But white and Asian American students still pass state algebra tests at higher rates than their peers.

The city’s current schools chancellor, David Banks, also shifted the system’s algebra focus to high schools, requiring the same ninth-grade curriculum at many schools in a move that has won both support and backlash from educators.

And some New York City families are still worried about middle school. A group of parent leaders in Manhattan recently asked the district to create more accelerated math options before high school, saying that many young students must seek out higher-level instruction outside the public school system.

In a vast district like New York — where some schools are filled with children from well-off families and others mainly educate homeless children — the challenge in math education can be that “incredible diversity,” said Pedro A. Noguera, the dean of the University of Southern California’s Rossier School of Education.

“You have some kids who are ready for algebra in fourth grade, and they should not be denied it,” Mr. Noguera said. “Others are still struggling with arithmetic in high school, and they need support.”

Many schools are unequipped to teach children with disparate math skills in a single classroom. Some educators lack the training they need to help students who have fallen behind, while also challenging those working at grade level or beyond.

Some schools have tried to find ways to tackle the issue on their own. KIPP charter schools in New York have added an additional half-hour of math time to many students’ schedules, to give children more time for practice and support so they can be ready for algebra by eighth grade.

At Middle School 50 in Brooklyn, where all eighth graders take algebra, teachers rewrote lesson plans for sixth- and seventh-grade students to lay the groundwork for the class.

The school’s principal, Ben Honoroff, said he expected that some students would have to retake the class in high school. But after starting a small algebra pilot program a few years ago, he came to believe that exposing children early could benefit everyone — as long as students came into it well prepared.

Looking around at the students who were not enrolling in the class, Mr. Honoroff said, “we asked, ‘Are there other kids that would excel in this?’”

“The answer was 100 percent, yes,” he added. “That was not something that I could live with.”

Troy Closson reports on K-12 schools in New York City for The Times. More about Troy Closson