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Physical Review Physics Education Research

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Conceptual problem solving in high school physics

Jennifer l. docktor, natalie e. strand, josé p. mestre, and brian h. ross, phys. rev. st phys. educ. res. 11 , 020106 – published 1 september 2015.

• Citing Articles (55)

Supplemental Material

• INTRODUCTION
• RESULTS AND DISCUSSION
• GENERAL DISCUSSION
• ACKNOWLEDGMENTS

Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in writing before solving a problem. The CPS approach was implemented by high school physics teachers at three schools for major theorems and conservation laws in mechanics and CPS-taught classes were compared to control classes taught using traditional problem solving methods. Information about the teachers’ implementation of the approach was gathered from classroom observations and interviews, and the effectiveness of the approach was evaluated from a series of written assessments. Results indicated that teachers found CPS easy to integrate into their curricula, students engaged in classroom discussions and produced problem solutions of a higher quality than before, and students scored higher on conceptual and problem solving measures.

• Received 30 April 2015

DOI: https://doi.org/10.1103/PhysRevSTPER.11.020106

This article is available under the terms of the Creative Commons Attribution 3.0 License . Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

• 1 Department of Physics, University of Wisconsin–La Crosse, La Crosse, Wisconsin 54601, USA
• 2 Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
• 3 Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, USA
• 4 Department of Educational Psychology, University of Illinois, Champaign, Illinois 61820, USA
• 5 Department of Psychology, University of Illinois, Champaign, Illinois 61820, USA
• * [email protected]

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Vol. 11, Iss. 2 — July - December 2015

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Conceptual Problem Solving in Physics

Research output : Contribution to journal › Article › peer-review

Students taking introductory physics courses focus on quantitative manipulations at the expense of learning concepts deeply and understanding how they apply to problem solving. This proclivity toward manipulating equations leads to shallow understanding and poor long-term retention. We discuss an alternative approach to physics problem solving, which we call conceptual problem solving (CPS), that highlights and emphasizes the role of conceptual knowledge in solving problems. We present studies that explored the impact of three different implementations of CPS on conceptual learning and problem solving. One was a lab-based study using a computer tool to scaffold conceptual analyses of problems. Another was a classroom-based study in a large introductory college course in which students wrote conceptual strategies prior to solving problems. The third was an implementation in high school classrooms where students identified the relevant principle, wrote a justification for why the principle could be applied, and provided a plan for executing the application of the principle (which was then used for generating the equations). In all three implementations benefits were found as measured by various conceptual and problem solving assessments. We conclude with a summary of what we have learned from the CPS approach, and offer some views on the current and future states of physics instruction.

• Conceptual assessment
• Conceptual problem solving
• High school
• Introductory physics
• Problem solving
• Science assessment
• Science cognition
• Science education
• Strategy writing

ASJC Scopus subject areas

• Social Psychology
• Developmental and Educational Psychology

Online availability

• 10.1016/B978-0-12-387691-1.00009-0

Library availability

Related links.

• Link to publication in Scopus
• Link to the citations in Scopus

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• Problem Solving Keyphrases 100%
• Conceptual Problems Keyphrases 100%
• Conceptual Knowledge Psychology 100%
• Concept Learning Psychology 100%
• Introductory Physics Keyphrases 16%
• Proclivity Keyphrases 16%
• Physics Problem Solving Keyphrases 16%
• High School Classrooms Keyphrases 16%

T1 - Conceptual Problem Solving in Physics

AU - Mestre, Jose P.

AU - Docktor, Jennifer L.

AU - Strand, Natalie E.

AU - Ross, Brian H.

N1 - Funding Information: Work in part supported by the Institute of Education Sciences of the US Department of Education under Award No. DE R305B070085. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the Institute of Education Sciences.

N2 - Students taking introductory physics courses focus on quantitative manipulations at the expense of learning concepts deeply and understanding how they apply to problem solving. This proclivity toward manipulating equations leads to shallow understanding and poor long-term retention. We discuss an alternative approach to physics problem solving, which we call conceptual problem solving (CPS), that highlights and emphasizes the role of conceptual knowledge in solving problems. We present studies that explored the impact of three different implementations of CPS on conceptual learning and problem solving. One was a lab-based study using a computer tool to scaffold conceptual analyses of problems. Another was a classroom-based study in a large introductory college course in which students wrote conceptual strategies prior to solving problems. The third was an implementation in high school classrooms where students identified the relevant principle, wrote a justification for why the principle could be applied, and provided a plan for executing the application of the principle (which was then used for generating the equations). In all three implementations benefits were found as measured by various conceptual and problem solving assessments. We conclude with a summary of what we have learned from the CPS approach, and offer some views on the current and future states of physics instruction.

AB - Students taking introductory physics courses focus on quantitative manipulations at the expense of learning concepts deeply and understanding how they apply to problem solving. This proclivity toward manipulating equations leads to shallow understanding and poor long-term retention. We discuss an alternative approach to physics problem solving, which we call conceptual problem solving (CPS), that highlights and emphasizes the role of conceptual knowledge in solving problems. We present studies that explored the impact of three different implementations of CPS on conceptual learning and problem solving. One was a lab-based study using a computer tool to scaffold conceptual analyses of problems. Another was a classroom-based study in a large introductory college course in which students wrote conceptual strategies prior to solving problems. The third was an implementation in high school classrooms where students identified the relevant principle, wrote a justification for why the principle could be applied, and provided a plan for executing the application of the principle (which was then used for generating the equations). In all three implementations benefits were found as measured by various conceptual and problem solving assessments. We conclude with a summary of what we have learned from the CPS approach, and offer some views on the current and future states of physics instruction.

KW - Assessment

KW - Conceptual

KW - Conceptual assessment

KW - Conceptual problem solving

KW - High school

KW - Introductory physics

KW - Problem solving

KW - Science assessment

KW - Science cognition

KW - Science education

KW - Strategy writing

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What are the steps for solving conceptual problems?

List and describe the two steps for solving conceptual problems. Analyze and Solve. Analust the conceptual problem and then solve it.

Table of Contents

How do you solve a conceptual physics problem?

• Focus on the Problem. Establish a clear mental image of the problem. A.
• Describe the Physics. Refine and quantify your mental image of the problem. A.
• Plan a Solution. Turn the concepts into math. A.
• Execute the Plan. This is the easiest step – it’s just the algebra/calculus/etc. A.
• Evaluate the Answer. Be skeptical.

What is conceptual problem solving?

This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in writing before solving a problem.

What is an example of a conceptual problem?

When we are starting out, what we really have to worry about are conceptual problems, for example: “This population of people live in a dense, urban setting where everything they would possibly need is within walking distance.”

What problems can be solved using physics?

• Global warming. Global warming is a real threat that needs no further explanation.
• Food production.
• Medical applications.
• Energy crisis.

What are the four steps for solving physics problems?

There may be more than one way to solve the problem so group the equations by the type of possible solution. Solve the equation(s). Solve algebraically for the unknown(s). Substitute known values into the solved equation.

What are the five steps to solving a physics problem?

The strategy we would like you to learn has five major steps: Focus the Problem, Physics Description, Plan a Solution, Execute the Plan, and Evaluate the Solution. Let’s take a detailed look at each of these steps and then do an sample problem following the strategy.

What is an example of conceptual thinking?

Conceptual thinking means that when a new project lands on your plate, you’re not one to roll up your sleeves and jump into tasks or start delegating responsibilities. You prefer to step back and conceptualize or theorize the project before getting into action.

What are some examples of conceptual skills?

• Able to ignore extraneous information.
• Broad thinking.
• Critical thinking.
• Breaking down a project into manageable pieces.
• Decision making.
• Executing solutions.
• Formulating effective courses of action.

What is a conceptual question in physics?

Physics concept questions or concept checking questions are questions prepared to examine learners’ understanding of core physics topics. Asking questions is one of the fundamental ways of understanding any physics topic. If students can answer all such questions, they have understood the concept well.

What is the difference between practical and conceptual problems?

The main difference is that the practical claim explains the causes of the problem to later propose a feasible solution to the problem. However, the conceptual claim focuses on understanding the situation and decoding it in some way to use as information.

What are conceptual answers?

Conceptual questions or conceptual problems in science, technology, engineering, and mathematics (STEM) education are questions that can be answered based only on the knowledge of relevant concepts, rather than performing extensive calculations.

What is the last thing you should do when solving a problem physics?

Answer and Explanation: The last thing that we do is rechecking of the answer, our answer should be correct and full fill all the requirements. Also, at last, recheck the unit and if there is not the unit, then provide the sign for the answer, checking all these things, at last, improve the accuracy of the answer.

How is physics used in everyday life?

• Alarm Clock. Physics gets involved in your daily life right after you wake up in the morning.
• Steam Iron.
• Ball Point Pen.
• Headphones/Earphones.
• Car Seat-Belts.
• Camera Lens.
• Cell Phones.

What is the importance of physics in our daily life?

Physics improves our quality of life by providing the basic understanding necessary for developing new instrumentation and techniques for medical applications, such as computer tomography, magnetic resonance imaging, positron emission tomography, ultrasonic imaging, and laser surgery.

Who is the father of problem solving method?

George Polya, known as the father of modern problem solving, did extensive studies and wrote numerous mathematical papers and three books about problem solving.

How do you think logically in physics?

The best way to deal with this is to “start with the basics” of any subject you are studying. In physics, go back to main principles. Acceleration is velocity/time because acceleration is the rate at which velocity changes. Just like that, take a basic principle that you do understand and move forward from there.

Is physics easy or hard?

Students and researchers alike have long understood that physics is challenging. But only now have scientists managed to prove it. It turns out that one of the most common goals in physics—finding an equation that describes how a system changes over time—is defined as “hard” by computer theory.

How many steps of problem solving are there?

All six steps are followed in order – as a cycle, beginning with “1. Identify the Problem.” Each step must be completed before moving on to the next step. redefine the problem.

How can I improve my physics?

• Master the Basics.
• Learn How to Basic Equations Came About.
• Always Account For Small Details.
• Work on Improving Your Math Skills.
• Simplify the Situations.
• Use Drawings.
• Always Double-Check Your Answers.
• Use Every Source of Physics Help Available.

How do you solve NEET physics Numericals?

• Study and practice Physics every day.
• Don’t miss your classes and make class notes.
• Read/ Preview the topic before the class.
• Revise everything after the class.
• Follow NEET study material to understand concepts well.
• Solve problems from NCERT and coaching modules.

What are the 7 steps of problem-solving?

• 7 Steps for Effective Problem Solving.
• Step 1: Identifying the Problem.
• Step 2: Defining Goals.
• Step 3: Brainstorming.
• Step 4: Assessing Alternatives.
• Step 5: Choosing the Solution.
• Step 6: Active Execution of the Chosen Solution.
• Step 7: Evaluation.

What are the three problem-solving techniques?

• Trial and Error.
• Difference Reduction.
• Means-End Analysis.
• Working Backwards.

What are the 3 steps of problem-solving?

Stop 1: Problem (Define the problems in the case.) Stop 2: Cause of the Problem (Identify the OB concepts or theories to use to solve the problem.) Stop 3: Recommendation (Explain what you would do to correct the situation.)

What is conceptual example?

Conceptual definition An example of conceptual is when you formulate an abstract philosophy to explain the world which cannot be proven or seen. Of, or relating to concepts or mental conception; existing in the imagination. We defined a conceptual model before designing the real thing.

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McKinsey Problem Solving: Six steps to solve any problem and tell a persuasive story

The McKinsey problem solving process is a series of mindset shifts and structured approaches to thinking about and solving challenging problems. It is a useful approach for anyone working in the knowledge and information economy and needs to communicate ideas to other people.

Over the past several years of creating StrategyU, advising an undergraduates consulting group and running workshops for clients, I have found over and over again that the principles taught on this site and in this guide are a powerful way to improve the type of work and communication you do in a business setting.

When I first set out to teach these skills to the undergraduate consulting group at my alma mater, I was still working at BCG. I was spending my day building compelling presentations, yet was at a loss for how to teach these principles to the students I would talk with at night.

Through many rounds of iteration, I was able to land on a structured process and way of framing some of these principles such that people could immediately apply them to their work.

While the “official” McKinsey problem solving process is seven steps, I have outline my own spin on things – from experience at McKinsey and Boston Consulting Group. Here are six steps that will help you solve problems like a McKinsey Consultant:

Step #1: School is over, stop worrying about “what” to make and worry about the process, or the “how”

When I reflect back on my first role at McKinsey, I realize that my biggest challenge was unlearning everything I had learned over the previous 23 years. Throughout school you are asked to do specific things. For example, you are asked to write a 5 page paper on Benjamin Franklin — double spaced, 12 font and answering two or three specific questions.

In school, to be successful you follow these rules as close as you can. However, in consulting there are no rules on the “what.” Typically the problem you are asked to solve is ambiguous and complex — exactly why they hire you. In consulting, you are taught the rules around the “how” and have to then fill in the what.

The “how” can be taught and this entire site is founded on that belief. Here are some principles to get started:

Step #2: Thinking like a consultant requires a mindset shift

There are two pre-requisites to thinking like a consultant. Without these two traits you will struggle:

• A healthy obsession looking for a “better way” to do things
• Being open minded to shifting ideas and other approaches

In business school, I was sitting in one class when I noticed that all my classmates were doing the same thing — everyone was coming up with reasons why something should should not be done.

As I’ve spent more time working, I’ve realized this is a common phenomenon. The more you learn, the easier it becomes to come up with reasons to support the current state of affairs — likely driven by the status quo bias — an emotional state that favors not changing things. Even the best consultants will experience this emotion, but they are good at identifying it and pushing forward.

Key point : Creating an effective and persuasive consulting like presentation requires a comfort with uncertainty combined with a slightly delusional belief that you can figure anything out.

Step #3: Define the problem and make sure you are not solving a symptom

Before doing the work, time should be spent on defining the actual problem. Too often, people are solutions focused when they think about fixing something. Let’s say a company is struggling with profitability. Someone might define the problem as “we do not have enough growth.” This is jumping ahead to solutions — the goal may be to drive more growth, but this is not the actual issue. It is a symptom of a deeper problem.

Consider the following information:

• Costs have remained relatively constant and are actually below industry average so revenue must be the issue
• Revenue has been increasing, but at a slowing rate
• This company sells widgets and have had no slowdown on the number of units it has sold over the last five years
• However, the price per widget is actually below where it was five years ago
• There have been new entrants in the market in the last three years that have been backed by Venture Capital money and are aggressively pricing their products below costs

In a real-life project there will definitely be much more information and a team may take a full week coming up with a problem statement . Given the information above, we may come up with the following problem statement:

Problem Statement : The company is struggling to increase profitability due to decreasing prices driven by new entrants in the market. The company does not have a clear strategy to respond to the price pressure from competitors and lacks an overall product strategy to compete in this market.

Step 4: Dive in, make hypotheses and try to figure out how to “solve” the problem

Now the fun starts!

There are generally two approaches to thinking about information in a structured way and going back and forth between the two modes is what the consulting process is founded on.

First is top-down . This is what you should start with, especially for a newer “consultant.” This involves taking the problem statement and structuring an approach. This means developing multiple hypotheses — key questions you can either prove or disprove.

Given our problem statement, you may develop the following three hypotheses:

• Company X has room to improve its pricing strategy to increase profitability
• Company X can explore new market opportunities unlocked by new entrants
• Company X can explore new business models or operating models due to advances in technology

As you can see, these three statements identify different areas you can research and either prove or disprove. In a consulting team, you may have a “workstream leader” for each statement.

Once you establish the structure you you may shift to the second type of analysis: a bottom-up approach . This involves doing deep research around your problem statement, testing your hypotheses, running different analysis and continuing to ask more questions. As you do the analysis, you will begin to see different patterns that may unlock new questions, change your thinking or even confirm your existing hypotheses. You may need to tweak your hypotheses and structure as you learn new information.

A project vacillates many times between these two approaches. Here is a hypothetical timeline of a project:

Step 5: Make a slides like a consultant

The next step is taking the structure and research and turning it into a slide. When people see slides from McKinsey and BCG, they see something that is compelling and unique, but don’t really understand all the work that goes into those slides. Both companies have a healthy obsession (maybe not to some people!) with how things look, how things are structured and how they are presented.

They also don’t understand how much work is spent on telling a compelling “story.” The biggest mistake people make in the business world is mistaking showing a lot of information versus telling a compelling story. This is an easy mistake to make — especially if you are the one that did hours of analysis. It may seem important, but when it comes down to making a slide and a presentation, you end up deleting more information rather than adding. You really need to remember the following:

Data matters, but stories change hearts and minds

Here are four quick ways to improve your presentations:

Tip #1 — Format, format, format

Both McKinsey and BCG had style templates that were obsessively followed. Some key rules I like to follow:

• Make sure all text within your slide body is the same font size (harder than you would think)
• Do not go outside of the margins into the white space on the side
• All titles throughout the presentation should be 2 lines or less and stay the same font size
• Each slide should typically only make one strong point

Tip #2 — Titles are the takeaway

The title of the slide should be the key insight or takeaway and the slide area should prove the point. The below slide is an oversimplification of this:

Even in consulting, I found that people struggled with simplifying a message to one key theme per slide. If something is going to be presented live, the simpler the better. In reality, you are often giving someone presentations that they will read in depth and more information may make sense.

To go deeper, check out these 20 presentation and powerpoint tips .

Tip #3 — Have “MECE” Ideas for max persuasion

“MECE” means mutually exclusive, collectively exhaustive — meaning all points listed cover the entire range of ideas while also being unique and differentiated from each other.

An extreme example would be this:

• Slide title: There are seven continents
• Slide content: The seven continents are North America, South America, Europe, Africa Asia, Antarctica, Australia

The list of continents provides seven distinct points that when taken together are mutually exclusive and collectively exhaustive . The MECE principle is not perfect — it is more of an ideal to push your logic in the right direction. Use it to continually improve and refine your story.

Applying this to a profitability problem at the highest level would look like this:

Goal: Increase profitability

2nd level: We can increase revenue or decrease costs

3rd level: We can increase revenue by selling more or increasing prices

Each level is MECE. It is almost impossible to argue against any of this (unless you are willing to commit accounting fraud!).

Tip #4 — Leveraging the Pyramid Principle

The pyramid principle is an approach popularized by Barbara Minto and essential to the structured problem solving approach I learned at McKinsey. Learning this approach has changed the way I look at any presentation since.

Here is a rough outline of how you can think about the pyramid principle as a way to structure a presentation:

As you build a presentation, you may have three sections for each hypothesis. As you think about the overall story, the three hypothesis (and the supporting evidence) will build on each other as a “story” to answer the defined problem. There are two ways to think about doing this — using inductive or deductive reasoning:

If we go back to our profitability example from above, you would say that increasing profitability was the core issue we developed. Lets assume that through research we found that our three hypotheses were true. Given this, you may start to build a high level presentation around the following three points:

These three ideas not only are distinct but they also build on each other. Combined, they tell a story of what the company should do and how they should react. Each of these three “points” may be a separate section in the presentation followed by several pages of detailed analysis. There may also be a shorter executive summary version of 5–10 pages that gives the high level story without as much data and analysis.

Step 6: The only way to improve is to get feedback and continue to practice

Ultimately, this process is not something you will master overnight. I’ve been consulting, either working for a firm or on my own for more than 10 years and am still looking for ways to make better presentations, become more persuasive and get feedback on individual slides.

The process never ends.

The best way to improve fast is to be working on a great team . Look for people around you that do this well and ask them for feedback. The more feedback, the more iterations and more presentations you make, the better you will become. Good luck!

If you enjoyed this post, you’ll get a kick out of all the free lessons I’ve shared that go a bit deeper. Check them out here .

Do you have a toolkit for business problem solving? I created Think Like a Strategy Consultant as an online course to make the tools of strategy consultants accessible to driven professionals, executives, and consultants. This course teaches you how to synthesize information into compelling insights, structure your information in ways that help you solve problems, and develop presentations that resonate at the C-Level. Click here to learn more or if you are interested in getting started now, enroll in the self-paced version ($497) or hands-on coaching version ($997). Both versions include lifetime access and all future updates.

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How to master the seven-step problem-solving process

In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.

Podcast transcript

Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.

Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].

Charles and Hugo, welcome to the podcast. Thank you for being here.

Hugo Sarrazin: Our pleasure.

Charles Conn: It’s terrific to be here.

Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”

You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”

I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.

I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.

Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.

Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.

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Simon London: So this is a concise problem statement.

Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.

Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.

How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.

Hugo Sarrazin: Yeah.

Charles Conn: And in the wrong direction.

Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?

Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.

What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.

Simon London: What’s a good example of a logic tree on a sort of ratable problem?

Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.

If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.

When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.

Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.

Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.

People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.

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Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?

Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.

Simon London: Not going to have a lot of depth to it.

Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.

Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.

Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.

Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.

Both: Yeah.

Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.

Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.

Simon London: Right. Right.

Hugo Sarrazin: So it’s the same thing in problem solving.

Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.

Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?

Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.

Simon London: Would you agree with that?

Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.

You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.

Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?

Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.

Simon London: Step six. You’ve done your analysis.

Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”

Simon London: But, again, these final steps are about motivating people to action, right?

Charles Conn: Yeah.

Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.

Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.

Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.

Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.

Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?

Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.

You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.

Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.

Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”

Hugo Sarrazin: Every step of the process.

Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?

Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.

Simon London: Problem definition, but out in the world.

Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.

Simon London: So, Charles, are these complements or are these alternatives?

Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.

Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?

Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.

The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.

Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.

Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.

Hugo Sarrazin: Absolutely.

Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.

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Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.

Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.

Charles Conn: It was a pleasure to be here, Simon.

Hugo Sarrazin: It was a pleasure. Thank you.

Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.

Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.

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Linking traditional teaching to innovative approaches: student conceptions in kinematics.

1. Introduction

2. pedagogical principles, student conceptions and conceptual knowledge.

“Learners need to develop an understanding of the characteristics of scientific inquiry, the role and status of the knowledge it generates, the social and intellectual circumstances surrounding the origin and development of important scientific theories, how the scientific community established and monitors professional practice, including robust knowledge of linguistic conventions for reporting, defending, scrutinizing and validating scientific claims, and awareness of the complex interactions among science, technology, society, and environment [ 20 ] (p. 2537).”

3.1. Context

3.2. participants, 3.3. data collection and analysis, 4.1. how do frequencies for knowledge level differ across gender, grade, and department, 4.2. how does the distribution of knowledge level, skill type, and logical progression level differ across grades, 4.3. do knowledge scores of male and female students differ significantly, 4.4. is being in the physics, physics education, and engineering department significantly different across logical progression levels, 4.5. do knowledge level and skill types have significant correlations, 4.6. is there a significant correlation between knowledge level and logical progression level, 4.7. how do knowledge and skill types predict logical progression, 4.8. how do knowledge, skill, and logical progression scores predict gender and grade separately in problem-solving in physics, 5. discussion.

• More PHYS and PEDU students had surface knowledge, but more ENG students indicated deep knowledge for question 1. For question 2, a more significant proportion of ENG students displayed surface knowledge. Junior and senior male PHYS students tended to have surface knowledge in both questions; however, sophomore ENG male students approached with surface knowledge. Sophomore and Junior male ENG students tended to have procedural knowledge when the purpose was to design an experiment.
• The sophomore PEDU students tended to show profound knowledge associated with mathematical skills accurately for question 1. However, there were fewer sophomore PEDU students in the sample. Sophomore PHYS students and junior and sophomore ENG students presented a procedural approach with intuitive and mathematical skills at a nearly good level of accuracy. For question 2, students from three departments presented surface and procedural knowledge approaches associated with qualitative and mathematical skills at neutral accuracy.
• There were differences in knowledge approach for male and female students in two questions. Question 1 was a graphical question requiring the interpretation of position versus time graphs. The responses showed a significant difference in knowledge approaches for males and females. In contrast, a negative z score meant that females tended to have a higher level- deep or procedural approach. In the second question, the design included three ramps to measure the speed of balls on the ramps. Data involved the second and third ramps to find the speed of the ball on the first ramp. The question asked students to design an experiment to find the speed of ball one at different time points. The results showed statistically insignificant differences between males and females in knowledge approaches. This result suggested that gender did not contribute to knowledge scores when college science students participated in designing an experiment.
• Logical progression addressed how students appropriately and accurately solved the question. The study investigated whether students’ logical progression scores differed across departments, PHYS, PEDU, and ENG. For question 1, there was a significant difference across the departments: the differences between the departments were high for highly sampled PHYS and ENG departments. For question 2, the results showed statistically significant differences, but the difference across the departments was less than in question 1.
• Both questions showed a significant difference between knowledge level and skill type. Students utilized consistent skills, for example, intuitive and mathematical for the first question and qualitative and mathematical for the second question.
• The knowledge approach and logical progression level had a direct positive correlation. For example, the deep approach displayed a good or excellent-level progression, but the surface approach indicated a fair or poor-level progression.
• There was a positive and significant relationship between knowledge and progression levels, but skill type was not an indicator of logical progression. This result showed that even though students preferred mathematical or blended skills, they might have a poor logical progression.
• Gender was likely to contribute to knowledge and logical progression levels, but grades might not show a positive relationship with knowledge level. For example, for question 2, senior students displayed a surface approach to solving physics problems.

5.1. Scientific Significance of the Study

5.2. limitations, 5.3. implications, supplementary materials, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

• Docktor, J.L.; Mestre, J.P. Synthesis of discipline-based education research in physics. Phys. Rev. Spéc. Top. Phys. Educ. Res. 2014 , 10 , 020119. [ Google Scholar ] [ CrossRef ]
• Teodorescu, R.E. Cognitive Development in Introductory Physics: A Research-Based Approach to Curriculum Reform. Ph.D. Thesis, The George Washington University, Washington, DC, USA, 2009. [ Google Scholar ]
• Strelan, P.; Osborn, A.; Palmer, E. The flipped classroom: A meta-analysis of effects on student performance across disciplines and education levels. Educ. Res. Rev. 2020 , 30 , 100314. [ Google Scholar ] [ CrossRef ]
• Redish, E.F.; Smith, K.A. Looking Beyond Content: Skill Development for Engineers. J. Eng. Educ. 2008 , 97 , 295–307. [ Google Scholar ] [ CrossRef ]
• Odden, T.O.B. How conceptual blends support sensemaking: A case study from introductory physics. Sci. Educ. 2021 , 105 , 989–1012. [ Google Scholar ] [ CrossRef ]
• Robertson, A.D.; Goodhew, L.M.; Bauman, L.C.; Hansen, B.; Alesandrini, A.T. Identifying student conceptual resources for understanding physics: A practical guide for researchers. Phys. Rev. Phys. Educ. Res. 2023 , 19 , 020138. [ Google Scholar ] [ CrossRef ]
• Børte, K.; Nesje, K.; Lillejord, S. Barriers to student active learning in higher education. Teach. High. Educ. 2020 , 28 , 597–615. [ Google Scholar ] [ CrossRef ]
• NGSS Lead States. Following Generation Science Standards: For States, by States ; National Academies Press: Washington, DC, USA, 2013. [ Google Scholar ]
• Henderson, C.; Dancy, M.; Niewiadomska-Bugaj, M. Use of research-based instructional strategies in introductory physics: Where do faculty leave the innovation-decision process? Phys. Rev. Phys. Ed. Res. 2012 , 8 , 020104. [ Google Scholar ] [ CrossRef ]
• National Research Council. A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas ; National Academies Press: Washington, DC, USA, 2012. [ Google Scholar ]
• Banilower, E.R. Understanding the Big Picture for Science Teacher Education: The 2018 NSSME+. J. Sci. Teach. Educ. 2019 , 30 , 201–208. [ Google Scholar ] [ CrossRef ]
• Hake, R.R. Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. Am. J. Phys. 1998 , 66 , 64–74. [ Google Scholar ] [ CrossRef ]
• Beichner, R.J.; Saul, J.M.; Abbott, D.S.; Morse, J.J.; Deardorff, D.; Allain, R.J.; Bonham, S.W.; Risley, J.S. The student-centred activities for large enrollment undergraduate programs (SCALE-UP) project. Res. Based Reform Univ. Phys. 2007 , 1 , 2–39. [ Google Scholar ]
• West, E.A.; Paul, C.A.; Webb, D.; Potter, W.H. Variation of instructor-student interactions in an introductory interactive physics course. Phys. Rev. Spéc. Top. Phys. Educ. Res. 2013 , 9 , 010109. [ Google Scholar ] [ CrossRef ]
• Etkina, E.; van Heuvelen, A.; White-Brahmia, S.; Brookes, D.T.; Gentile, M.; Murthy, S.; Rosengrant, D.; Warren, A. Scientific abilities and their assessment. Phys. Rev. Spéc. Top. Phys. Educ. Res. 2006 , 2 , 020103. [ Google Scholar ] [ CrossRef ]
• Navajas, A. Life Cycle Assessment in Higher Education: Design and Implementation of a Teaching Sequence Activity. Sustainability 2024 , 16 , 1614. [ Google Scholar ] [ CrossRef ]
• Pozuelo-Muñoz, J.; Calvo-Zueco, E.; Sánchez-Sánchez, E.; Cascarosa-Salillas, E. Science Skills Development through Problem-Based Learning in Secondary Education. Educ. Sci. 2023 , 13 , 1096. [ Google Scholar ] [ CrossRef ]
• Krajcik, J.; Shin, N. Student Conceptions, Conceptual Change, and Learning Progressions. In Handbook of Research on Science Education ; Routledge: Abingdon, UK, 2023; pp. 121–157. [ Google Scholar ]
• Maries, A.; Singh, C. Helping Students Become Proficient Problem Solvers Part I: A Brief Review. Educ. Sci. 2023 , 13 , 156. [ Google Scholar ] [ CrossRef ]
• Hodson, D. Learning Science, Learning about Science, Doing Science: Different goals demand different learning methods. Int. J. Sci. Educ. 2014 , 36 , 2534–2553. [ Google Scholar ] [ CrossRef ]
• Sirnoorkar, A.; Bergeron, P.D.O.; Laverty, J.T. Sensemaking and scientific modeling: Intertwined processes analyzed in the context of physics problem solving. Phys. Rev. Phys. Educ. Res. 2023 , 19 , 010118. [ Google Scholar ] [ CrossRef ]
• Potvin, P.; Boissard, B.; Durocher, É.; Hasni, A.; Riopel, M. Empowering professional learning communities of secondary science teachers to uncover and address their students’ misconceptions via research-oriented practices. Front. Educ. 2024 , 9 , 1419714. [ Google Scholar ] [ CrossRef ]
• McDermott, L.C. Millikan Lecture 1990: What we teach and what is learned—Closing the gap. Am. J. Phys. 1991 , 59 , 301–315. [ Google Scholar ] [ CrossRef ]
• McDermott, L.C.; Shaffer, P.S. The Physics Education Group at the University of Washington, Physics by Inquiry ; John Wiley & Sons Inc.: New York, NY, USA, 1996; Volume 1–2. [ Google Scholar ]
• Docktor, J.L.; Dornfeld, J.; Frodermann, E.; Heller, K.; Hsu, L.; Jackson, K.A.; Mason, A.; Ryan, Q.X.; Yang, J. Assessing student written problem solutions: A problem-solving rubric with application to introductory physics. Phys. Rev. Phys. Educ. Res. 2016 , 12 , 010130. [ Google Scholar ] [ CrossRef ]
• Walsh, E.; Dall’Alba, G.; Bowden, J.; Martin, E.; Marton, F.; Masters, G.; Ramsden, P.; Stephanou, A. Physics students’ understanding of relative speed: A phenomenographic study. J. Res. Sci. Teach. 1993 , 30 , 1133–1148. [ Google Scholar ] [ CrossRef ]
• Testa, I.; Monroy, G.; Sassi, E. Students’ reading images in kinematics: The case of real-time graphs. Int. J. Sci. Educ. 2002 , 24 , 235–256. [ Google Scholar ] [ CrossRef ]
• Christensen, W.M.; Thompson, J.R. Investigating graphical representations of slope and derivative without a physics context. Phys. Rev. Sp. Top. Phys. Ed. Res. 2012 , 8 , 023101. [ Google Scholar ] [ CrossRef ]
• Temiz, B.K. Designing a simple apparatus for measuring kinematic variables. Phys. Educ. 2014 , 49 , 574–579. [ Google Scholar ] [ CrossRef ]
• Bell, P.; Linn, M.C. Scientific arguments as learning artifacts: Designing for learning from the web with KIE. Int. J. Sci. Educ. 2000 , 22 , 797–817. [ Google Scholar ] [ CrossRef ]

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Sengul, O. Linking Traditional Teaching to Innovative Approaches: Student Conceptions in Kinematics. Educ. Sci. 2024 , 14 , 973. https://doi.org/10.3390/educsci14090973

Sengul O. Linking Traditional Teaching to Innovative Approaches: Student Conceptions in Kinematics. Education Sciences . 2024; 14(9):973. https://doi.org/10.3390/educsci14090973

Sengul, Ozden. 2024. "Linking Traditional Teaching to Innovative Approaches: Student Conceptions in Kinematics" Education Sciences 14, no. 9: 973. https://doi.org/10.3390/educsci14090973

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Conceptual Model-Based Problem Solving

• First Online: 30 April 2016

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• Yan Ping Xin Ph.D. 6  

Part of the book series: Research in Mathematics Education ((RME))

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While mathematics problem-solving skills are well recognized as critical for virtually all areas of daily life and successful functioning on the job, many students with learning disabilities or difficulties in mathematics (LDM) fail to acquire these skills during their early school studies, thereby subjecting themselves to lifelong challenges with mathematical problem solving. This chapter will introduce a conceptual model-based problem-solving (COMPS) approach that aims to promote elementary students’ generalized word problem-solving skills. With the emphasis on algebraic representation of mathematical relations in cohesive mathematical models, the COMPS program makes connections among mathematical ideas; it offers elementary school teachers a way to bridge the gap between algebraic and arithmetic teaching and learning. The COMPS program may be especially helpful for students with LDM who are likely to experience disadvantages in working memory and information organization. Findings from a series of empirical research studies will be presented, and implications for elementary mathematics education will be discussed pertinent to all students meeting the new Common Core State Standards for Mathematics (CCSSM, 2012).

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The effect of a conceptual model-based approach on ‘additive’ word problem solving of elementary students struggling in mathematics

Reflections on Problem-Solving

Problem Posing as Reformulation and Sense-Making Within Problem Solving

Baxter, J., Woodward, J., & Olson, D. (2001). Effects of reform-based mathematics instruction in five third grade classrooms. Elementary School Journal, 101 (5), 529–548.

Article   Google Scholar  

Bloom, B. S. (1976). Human characteristics and school learning . New York: McGraw-Hill.

Google Scholar  

Blomhøj, M. (2004). Mathematical Modelling – A Theory for Practice . In B. Clarke et al. (Eds.), International Perspectives on Learning and Teaching Mathematics (pp. 145–159). Göteborg: National Center for Mathematics Education.

Blum, W., & Leiss, D. (2005). Modellieren mit der “Tanken”-Aufgaben. Mathematic Lehren, 128 , 18–21.

Boulineau, T., Fore, C., Hagan-Burke, S., & Burke, M. D. (2004). Use of story-mapping to increase the story-grammar text comprehension of elementary students with learning disabilities. Learning Disability Quarterly, 27 , 105–121.

Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Duran, R., Reed, B. S., et al. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34 (4), 663–689.

Bryant, D. P., Bryant, B. R., Roberts, G., Vaughn, S., Pfannenstiel, K. H., Porterfield, J., et al. (2011). Early numeracy intervention program for first-grade students with mathematics difficulties. Council for Exceptional Children, 78 (1), 7–23.

Carpenter, T., Fennema, E., Franke, M., Levi, L., & Empson, S. (1999). Children’s mathematics: Cognitively guided instruction . Portsmouth, NH: Heinemann.

Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2006). Learning mathematics in elementary and middle schools: A learner-centered approach (4th ed.). Upper Saddle River, NJ: Pearson Merrill Prentice Hall.

Cawley, J., Parmar, R., Foley, T. E., Salmon, S., & Roy, S. (2001). Arithmetic performance of students: Implications for standards and programming. Exceptional Children, 67 , 311–328.

Chen, Z. (1999). Schema induction in children’s analogical problem solving. Journal of Educational Psychology, 91 , 703–715.

Common Core State Standards Initiative. (2012). Introduction: Standards for mathematical practice. Retrieved from http://www.corestandards.org/the-standards/mathematics

Ding, M., & Li, X. (2014). Transition from concrete to abstract representations: The distributive property in a Chinese textbook series. Educational Studies in Mathematics, 87 (1), 103–121.

Fuchs, D., & Deshler, D. D. (2007). What we need to know about responsiveness to intervention (and shouldn’t be afraid to ask). Learning Disabilities Research and Practice, 22 , 129–136.

Fuchs, L. S., Fuchs, D., & Hollenbeck, K. N. (2007). Expanding responsiveness to intervention to mathematics at first and third grade. Learning Disabilities Research and Practice, 22 , 13–24.

Gick, M., & Holyoak, K. H. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15 , 1–38.

Greer, B. (1992). Multiplication and division as models of situations. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276–295). New York: Macmillan.

Horner, R. D., & Baer, D. M. (1978). Multiple-probe technique: A variation of the multiple baseline. Journal of Applied Behavior Analysis, 11 , 189–196.

Hamson, M. J. (2003). The place of mathematical modeling in mathematics education. In S. J. Lamon, W. A. Parker, & K. Houston (Eds.), Mathematical modeling: A way of life . Chichester, England: Horwood.

Hutchison, L. F. (2012). Addressing the STEM teacher shortage in American schools: Ways to recruit and retain effective STEM teachers. Action in Teacher Education, 34 , 541–550.

Jonassen, D. H. (2003). Designing research-based instruction for story problems. Educational Psychology Review, 15 , 267–296.

Kazdin, A. E. (1982). Single-case research designs: Methods for clinical and applied settings . New York: Oxford.

Lesh, R., Doerr, H. M., Carmona, G., & Hjalmarson, M. (2003). Beyond constructivism. Mathematical Thinking and Learning, 5 (2&3), 211–233.

Lesh, R., Landau, M., & Hamilton, E. (1983). Conceptual models in applied mathematical problem solving research. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts & processes (pp. 263–343). New York: Academic Press.

Lewis, A. B. (1989). Training students to represent arithmetic word problems. Journal of Educational Psychology, 81 , 521–531.

Maletsky, E. M., et al. (2004). Harcourt math (Indianath ed.). Chicago: Harcourt.

Mevarech, Z. R., & Kramarski, B. (2008). Mathematical modeling and meta-cognitive instruction . Retrieved November 10, 2008, from http://www.icme-organisers.dk/tsg18/S32MevarechKramarski.pdf

National Assessment of Educational Progress Result. (NAEP, 2013). Are higher and lower performing students making gains? Retrieved November 12, 2013, from http://nationsreportcard.gov/reading_math_2013/#/gains-percentiles

Pressley, M. (1986). The relevance of the good strategy user model to the teaching of mathematics. Educational Psychologist, 21 (1–2), 139–161.

Schmidt, S., & Weiser, W. (1995). Semantic structures of one-step word problems involving multiplication or division. Educational Studies in Mathematics, 28 , 55–72.

Schwartz, J. (1988). Intensive quantity and referent transforming arithmetic operations. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 41–52). Reston, VA: National Council of Teachers of Mathematics.

Sherin, B. (2001). How students understand physics equations. Cognition and Instruction, 19 (4), 479–541.

Sowder, L. (1988). Children’s solutions of story problems. Journal of Mathematical Behavior, 7 , 227–238.

Thompson, P. (1989). Artificial intelligence, advanced technology, and learning and teaching algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 135–161). Reston, VA: National Council of Teachers of Mathematics.

Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally (5th ed.). Boston: Allyn and Bacon.

Xin, Y. P. (2007). Word-problem-solving tasks presented in textbooks and their relation to student performance: A cross-curriculum comparison case Study. Journal of Educational Research, 100 , 347–359.

Xin, Y. P. (2008). The effect of schema-based instruction in solving word problems: An emphasis on pre-algebraic conceptualization of multiplicative relations. Journal for Research in Mathematics Education, 39 , 526–551.

Xin, Y. P. (2012). Conceptual model-based problem-solving (COMPS) approach: Teach students with learning difficulties to solve math problems . Boston: Sense.

Book   Google Scholar  

Xin, Y. P., Kastberg, S., & Chen, V. (2015). Conceptual Model-based Problem Solving (COMPS): A Response to Intervention Program for Students with LDM . National Science Foundation funded project.

Xin, Y. P., Liu, J., & Zheng, X. (2011). A cross-cultural lesson comparison on teaching the connection between multiplication and division. School Science and Mathematics, 111 (7), 354–367.

Xin, Y. P., Tzur, R., & Si, L. (2008). Nurturing multiplicative reasoning in students with learning disabilities in a computerized conceptual-modeling environment . Grant received from the National Science Foundation.

Xin, Y. P., Wiles, B., & Lin, Y. (2008). Teaching conceptual model-based word-problem story grammar to enhance mathematics problem solving. Journal of Special Education, 42 , 163–178.

Xin, Y. P., & Zhang, D. (2009). Exploring a conceptual model-based approach to teaching situated word problems. Journal of Educational Research, 102 (6), 427–441.

Xin, Y. P., Tzur, R., Si, L., Hord, C., Liu, J., Park, J. Y., Cordova, M., & Ruan, L. Y. (2013, April). A comparison of teacher-delivered instruction and an intelligent tutor-assisted math problem-solving intervention program . Paper presented at the 2013 American Educational Research Association (AERA) Annual Meeting, San Francisco.

Xin, Y. P., Si, L., Hord, C., Zhang, D., Cetintas, S., & Park, J. Y. (2012). The effects of computer-assisted instruction in teaching conceptual model-based problem solving. Learning Disabilities: A Multidisciplinary Journal, 18 (2), 71–85.

Xin, Y. P., Zhang, D., Park, J. Y., Tom, K., Whipple, A., & Si, L. (2011). A comparison of two mathematics problem-solving strategies: Facilitate algebra-readiness. Journal of Educational Research, 104 , 381–395.

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Xin, Y.P. (2016). Conceptual Model-Based Problem Solving. In: Felmer, P., Pehkonen, E., Kilpatrick, J. (eds) Posing and Solving Mathematical Problems. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-28023-3_14

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How Do You Solve a Problem Like Polestar?

If you're thinking of getting a Polestar, you might want to keep in mind the premium EV brand may not be a standalone for much longer, if predictions from auto industry analysts and academics are anything to go by. “Fold it back into Volvo,” advises Peter Wells, a business professor and director of the Centre for Automotive Industry Research at Cardiff University in Wales.

Polestar started life in 2005 as the brand name for a Volvo-tuning, gasoline-powered Swedish motorsports team. It was transformed into an EV marque when Volvo bought the team 10 years later. Polestar has operated independently of Volvo since 2017, but both still have production facilities next to each other in Torslanda, Sweden, and both have been ultimately owned since 2010 by automotive giant Geely of China .

Earlier this year, Volvo decreased its stake in Polestar to 18 percent and cut funding. Via an outstanding convertible loan, Polestar still owes the mothership $1 billion.

According to Andy Palmer, former COO of Nissan, the Sisyphean task of making Polestar profitable sooner rather than later can’t be done by cost-cutting alone. “I can easily imagine that there’ll be a conversation going on which considers making Polestar a sub-brand of Volvo, or a sub-brand of Geely,” says Palmer, who has four decades of experience in the automotive industry and was also formerly CEO of Aston Martin Lagonda.

Palmer adds: “Operating as a separate brand is extremely expensive. You’ve got huge marketing costs without having the economies of scale.”

And Polestar—which states it has sold 170,000 cars since it began—isn’t generally viewed as a standalone brand, says Palmer: “I think most people in the industry view Polestar as the EV version of Volvo, so having it as a separate brand doesn’t make any sense.”

After Volvo cut its funding earlier this year, Polestar secured a $950 million three-year loan from a banking syndicate led by BNP Paribas, and at the end of August raised a further $300 million in the form of a one-year revolving term loan facility.

This lifeline funding was secured under the leadership of CEO Thomas Ingenlath, a former chief designer for Volkswagen and Škoda. However, following losses deepening to $1.46 billion amid slowing EV demand, Ingenlath resigned from Polestar on August 27, although his LinkedIn page continues to state he’s still the Polestar CEO; his contract runs until October 1.

Ingenlath has been replaced as CEO by Michael Lohscheller , an automotive industry veteran who previously helmed Stellantis -owned car maker Opel. On September 3, Lohscheller was joined by Jean-Francois Mady, a former senior Stellantis beancounter (full title: Senior VP of Global Accounting Operations and Finance Transformation). Mady replaces Per Ansgar, who had been CFO on a transitional basis since January.

Ansgar told investors on an earnings call at the end of August that Polestar’s sub-$1 share price wasn’t optimal. “We have been trading below $1 for quite some time,” he said, adding ominously that “we have up to early next year to heal this deficiency.” Polestar's stock high since listing was more than $15 in November 2021—on August 7, 2024, it closed at just 63 cents.

Nevertheless, Ansgar looked on the bright side: “With our increased deliveries and sales on Polestar 3 and Polestar 4, and continued good feedback from customers, the share price should go up above $1.”

In a press release , Lohscheller said new CFO Mady brings a “wealth of experience and best practice competence from our industry,” and that the pair’s goal is to “make Polestar a financial success.”

That’s a tough ask in today’s slowing EV market. In 2023, Polestar missed its sales target of 60,000 vehicles (lowered from 80,000 earlier in 2023), delivering 54,600 vehicles, the vast majority of which being the aging, and China-made , Polestar 2. The company revealed its revenue in the second quarter of this year had decreased by $319.6 million, or 26 percent, “due to lower global vehicle sales and higher discounts in a competitive market.”

The Polestar 2

Dislodging a design-led CEO and installing two numbers-focused executives is an obvious move, says Palmer, now the chair of Pod Point , a UK provider of EV charging stations.

Putting a designer at the head of Polestar had been a “brave experiment,” Palmer says, but adds: “I don’t know whether appointing accountants [in Ingenlath’s place] is automatically the right answer, but having executives with car industry experience that understand financing and the manufacturing of vehicles is kind of mandatory.”

Notwithstanding the new hires, Polestar could be on borrowed time as a standalone, says Palmer. “I think we’re going to see a lot of car companies fail, especially those operating in the premium space.”

Professor Wells agrees, but says that “appointing beancounters is not the only solution” for Polestar. “The key problem is that consumers don’t know what the brand is supposed to represent, and how it is distinguishable from Volvo. [The new executive team] have to decide whether they are going to keep it as a separate brand or reduce it to a sub-brand. In practical terms, the [sub-brand option] might be the best answer for them.”

Wells says Polestar, which was contacted for this piece, hasn’t distanced itself sufficiently from Volvo. “There’s not enough space between the design language of the two brands,” he offered. Indeed, Volvo’s new EV flagship, the EX90 , is basically a family-friendly version of the Polestar 3, as it has nearly the same underpinnings.

The Volvo EX90

To set itself as truly apart from Volvo, Polestar should have provided more “visual differentiation,” says Wells, as well as offering “differences in terms of performance, but also the other features in the car.” He adds that Polestar “needed to have better surprises and delights” rather than “position [its] cars as being a slightly higher price than a Volvo equivalent.”

And Polestar is one of many EV brands exposed by a falling tide, he believes. “In a growing market, there’s room to make mistakes,” says Wells. “But in a static or depressed market, the pressure [to be profitable] is intense.” The new executives should “fold [Polestar] back into Volvo to a greater extent, and accept that it will be a niche brand for quite some time to come.”

Polestar’s branding problems began early, says Wells. “It was odd that [Polestar was] started by [Volvo] acquiring this high-performance petrol business, and then rebadging it as an electric premium brand.” That was a “mistake,” judges Wells. “[Polestar] was also too slow to bring product into the market and too slow to make money when the sun was shining.”

Polestar’s new plant in South Carolina should help it dodge the latest US tariffs against China-manufactured cars , but avoiding these extreme costs is “just part of the story,” says Wells, venturing that current market volatility has many causes, not just protectionist ones.

This market volatility is a “blip,” said Dominic Vergine, the CEO of British startup Monumo , a company that applies machine learning and AI to improve EV powertrains. “I see technology coming through on the battery side and on the engineering side in EVs that are going to lower costs,” he says, which is an opportunity that brands such as Polestar could leverage, he suggests. “There is going to be a huge shift in engineering over the next decade because of what AI is enabling, and the early adopters of this technology will be much more successful than the laggards.”

Vergine places Polestar into a second tier of EV brands. “Are they as well known as Tesla? No. Are they better known than BYD? Yes. But they’re second tier, and that’s a challenge for the new executives.”

“Whether Polestar stays as a standalone brand likely won’t be their decision to make,” says Vergine. “I’m assuming that Geely must have a greater strategy for Volvo and Polestar. The new executives will be charged to run a very competent ship, keep the budget down, and then changes will be made once the market lifts again.”

Wells agrees with the assessment that today’s slowing market is temporary. “We know that in terms of the big picture, we are very close to the edge. We’re most likely to exceed the 1.5 degrees centigrade threshold this year, so the pressure of doing something about climate change will only grow. Despite the short-term pressures, despite the issues around not being able to sell enough electric vehicles and the emergence once again of hybrids —despite all of that, in the long term, the market will go electric.”

However, for standalone EV brands like Polestar, the tide may rise too late. “How long will [Polestar] be able to continue to fund the business under current circumstances?” asks Wells. “The upmarket part [of the auto business] is too crowded” for every premium EV brand to survive, he says. “[Polestar] haven’t been able to sell enough cars to justify all the costs [of manufacturing and marketing]. Yes, they have beautifully designed cars, but they can’t sell enough of them. That’s the grim reality.”

This is due at least in part to Polestar’s relative lack of brand recognition, which is not an issue for the 97-year-old Volvo . “Who is Polestar?” asks Stephanie Valdez Streaty, director of industry insights for Cox Automotive, publisher of the Kelley Blue Book vehicle valuer. “The average consumer doesn’t know. If I asked 10 of my friends, maybe only two or three would have heard of Polestar.” But all of them have heard of Volvo. “It will be critical for the new CEO to get in there and really increase their brand awareness," she says.

According to Streaty, the rollout to customers this month of the sporty built-in-the-USA Polestar 3 SUV could boost the brand's bottom line. "US consumers love SUVs," she says. "So depending on how that rollout goes, it could be effective for Polestar." Lohscheller will certainly be hoping so, especially considering the swing needed from the China-made Polestar 2 sales to the new models.

Polestar 3 has a starting sticker price of $74,800, with the highest-spec 3 Long Range Dual Motor Plus & Performance costing $86,300. The Polestar 4 SUV coupé (which, despite the numbering convention, sits in price and size between the 2 and the new 3) has no rear window, but four doors.

The current Polestar lineup.

“I think [Polestar] has a great sustainability story,” says Streaty, “and building in South Carolina is going to help them, but when you’re competing against legacy brands with a long-established retail network, it’s tough to be a standalone.” Indeed. Just ask Fisker .

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Get it from Amazon for $17.75 .

9. A revitalizing hair protein treatment  for conditioning and repairing dry, damaged, and over-processed hair. This collagen-rich formula is designed to work on all hair types. TBH I'm already obsessed with your hair evolution!

Promising review: "I have used this product three times now, and it has changed my hair drastically; it's so soft and glossy looking. I don’t even have to use any leave-in products because it’s so easy to comb through right out of the shower. So inexpensive and better than any hair salon products I’ve used in the past. Works better than K18 or Olaplex." — Alyx Ming

Get it from Amazon for $7.40 .

Read our  Elizavecca CER-100 Collagen Coating Hair Protein Treatment review  to learn more.

10. A clinical-strength Secret deodorant  because it provides 72 hours of sweat and odor protection. Stress, heat, and activity are no match for this antiperspirant. 

Promising review:  "I have been trying all kinds of deodorants for months, trying to find one that works! I sweat a lot at work, and this stuff works! I don’t have to reapply. This doesn’t leave any staining on my clothes. The smell is nice and light. Finally found something that works!" — Zindarella

Get it from Amazon for $8.35 .

11. Or some unscented and paraben-free  SweatBlock antiperspirant wipes  that can help control excessive sweating for up to seven days per use! Staying dry just got a little easier.

These are strong, so you should spot-test them first! Each box lasts two months.

Promising review: "For anyone who might be a skeptic, please allow me to put you at ease. If you have hyperhidrosis, meaning it can be 9 degrees outside and you're still sweating under your arms, this product has the potential to change your life. I would sweat THROUGH a sports coat before noon. Enter the Sweat Block product. I've had it for three weeks, and it is life-changing. I DO NOT sweat under my arms anymore. I'm still on the original box that I bought three weeks ago. I had to write a review after I was cleaning the garage today in 85-degree heat...I was sweating through my shirt on my back...BUT NOT MY UNDERARMS. It is amazing!" — Frosty McGee

Get a pack of 10 from Amazon for $19.99+  (also available in packs of 20 and 30).

12. A fungal nail renewal formula  if you've been living with thick, discolored, and brittle nails, which has meant not wearing open-toed shoes. This can help improve the look of your nails in as little as two days!

Promising review : "I tried EVERYTHING! I tried tree tea oil and various other products for years. Nothing worked. The reviews were so great on this that I decided to try to cure it one more time. But when you have had a condition for 35 years, you aren't too hopeful! I followed the suggestions of some of the reviewers and cut my toenails (I only had it on my big toes) everywhere that the fungus was present, even below the quick. I started applying this gel, which is super easy to use. I swear to you that I noticed a difference after one application. " — WIAPilot  

Get it from Amazon for  $18.50 .

13. A pore-control  Anua heartleaf extract cleansing oil  for gently and effectively ridding your face of dirt, makeup, and blackheads. This hypoallergenic K-beauty formula has soothing ingredients that won't cause clogged pores.

Promising review:  "My go-to cleansing oil.  It melts makeup and SPF quickly and without much effort. I like using it more as a skin cleanser than a makeup remover just because it has helped my skin glow by making my skin texture better and getting rid of blackheads!" — Ravishankar Rao

Get it from Amazon for $17.69 .

14. A bottle of dandruff shampoo made with ketoconazole because it can help relieve and control flaking, scaling, and itching caused by dandruff. Clean and clear scalps for all!

Read more about ketoconazole shampoo at  Cleveland Clinic .

Promising review: "If I could give this product more than 5 stars, then I would!! My husband has suffered from extreme dandruff/Psoriasis for years to the point that he would pick constantly at his scalp. I would be able to visually see large sores and peeling skin chunks constantly, no matter what shampoo/treatment he would use. I found this product by chance and told my husband about it, who was willing to give it a chance (he’d more than given up on finding a solution to his problem at this point). After two shampoos he said that he absolutely noticed a difference and did not feel that he had to scratch his scalp. His sores healed within a week, and now he has a clean, itch- and flake-free scalp! This stuff worked absolute wonders for us, and I would recommend it to anyone with slight dandruff issues to extreme psoriasis conditions!" — Tabitha C.

Get it from Amazon for $15.88 .

15. Or a therapeutic Neutrogena shampoo containing salicylic acid to help treat scalp buildup and dandruff. If you find that your psoriasis acts up more in the summer, try this fragrance-free and dermatologist-recommended shampoo.

Promising review:  "When it comes to breaking out on the scalp (yes, it happens to me when it's hot), I need something to relieve the inflammation. That's where this product comes in handy." — BlurredVision

Get it from Amazon for $7.32 .

16. An antimicrobial facial mist  that contains hypochlorous acid, which can help soothe minor burns, rashes, and irritations. This cheaper Tower 28 alternative removes sweat and dirt, unclogs pores, and targets acne-causing bacteria, all without drying out your skin. If you have sensitive skin, consider adding this on-the-go spray to your skincare routine.

This spray is safe to be used daily and won't leave behind any residue.

Promising review:  "Great spray! You get a lot of product for the price, and it’s an alternative to the Tower 28 spray . I’ve been using it for a week consistently now, and I have noticed improvements in my skin; the blemishes I had before are now gone and I don’t see any new ones forming. Great to use during the summer if you sweat a lot. You can refresh your face throughout the day if needed to get rid of any extra bacteria from sweating." — Dogmom99

Get it from Amazon for $17.46 .

17. A pair of stainless steel tongue scrapers  if you've been wracking your brain as to why your breath still smells even though you floss, brush, and use mouthwash. It could be the bacteria living on your tongue. Now, you won't need to fear having close conversations with friends and strangers.

They even come with their own convenient little case. 

Promising review:  "I recently purchased this tongue scraper, and I must say, it has made a significant difference in my oral hygiene routine. The scraper is easy to use and efficient in removing any buildup on my tongue. I have noticed that my breath stays fresher for longer, and my tongue feels cleaner throughout the day. The scraper is also easy to clean and store, making it a convenient addition to my daily routine. Overall, I highly recommend using a tongue scraper, and this one in particular is a great choice." — Kelsey

Get it from Amazon for $2.99+ (also available in different styles).

18. A nose wax kit  because tweezing individual nose hairs is just...no. Safely remove those noticeable nose hairs and know that they'll stay away longer.

The hairs in your nose play an important role in filtering out any harmful debris. But of course, it's your body, and if you want to wax your nose hairs, you're more than welcome to — just be careful, as plucking nose hairs can lead to infection and ingrown hairs.

This kit includes 100 grams of nose wax beads, 30 wax applicators, 10 mustache protectors, a measuring cup, and 15 paper cups.

Promising reviews: "This is the easiest to use and takes care of nose hair. My new favorite beauty aid. 😉" — Jackie Phillips

"The instructions were super easy to follow, and it worked perfectly! I was a little nervous to pull the sticks out once the two minutes were up, however it didn't even hurt." — Julie J.

Get it from Amazon for $13.85 .

19. A mattifying dry shampoo powder  whose benzene-free formula is designed to absorb excess sweat, oil, and dirt without leaving behind a white cast. If constantly washing your oily hair has left it feeling dry, refresh your hair with this volumizing powder!

Promising review:  "I have tried IGK, Living Proof, Not Your Mother's, Amika, and so many others, but THIS LASTS THE LONGEST! I am impressed by this product. Don't listen to the haters because I have severely fine and oily hair, and this product allows me to last for one week without washing, and it gives me volume without the toxicity of spray dry shampoo." — 473X

Get it from Amazon for $18 .

20. A CeraVe body wash  with salicylic acid and ceramides that'll help you deal with any "chicken skin" flare-ups caused by warmer weather. This will exfoliate your skin and leave it feeling moisturized!

Promising review: "I started using this product on my arms a few weeks ago to manage the little bumps I get, especially during the summer. I noticed a difference after a couple of uses, and my skin is much smoother now." — CoachJoe19

Get it from Amazon for $13.99 .

21. A pack of thin and discreet  incontinence pads  if your bladder has a mind of its own. These super-absorbent pads will help you (and your pants) stay dry so you can move about your day in complete comfort.

Promising review:  "I use these for nighttime. They are the best ones for me so far. Regular length, they don't scrunch up, they stay put and absorb really great. Plus, they are not perfumed. I have tried many other brands, and Poise is the one for me! I also use Poise Light during the day (regular length). You can't tell you have them on like the old days when wearing a period pad." — Leeloo

Get a box of 144 from Amazon for $30.73+ (available in five styles and smaller pack sizes).

22. An oil-absorbing face roller made using absorbent volcanic stone because it'll soak up any excess oil. Instant matte skin FTW!

Promising review: "I have super oily skin and am always looking for something to help control it during the day. The linen squares are good, but you have to keep them around (and keep replacing them), and they end up in the landfill.  This little contraption really works, and I just rinse it at the end of the day and start over again the next.  I kept one on my desk and bought a second for my purse. This is magic for my shiny skin, especially on camera in my hours of Zoom every day." — Jennifer Helseth

Get it from Amazon for $9.48 .

23. A rejuvenating eye cream with vegan ingredients that absorb quickly into the skin to start the process of brightening and lifting your under-eye area. Perpetual late nights got nothing on this cream!

LilyAna Naturals  is a family-owned small business using natural ingredients to craft high-quality skincare products.

Promising review: "I never ever write reviews. I have tried every eye cream out there. Not one does what it says. This was immediate! I saw the softening of my wrinkles and crow's-feet. It’s amazing. I will be buying this again and again." — melisa delaney

Get it from LilyAna Naturals on Amazon for $11.99+  (available in three sizes).

The reviews for this post have been edited for length and clarity.

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