Everyone misses this problem solving step

Summary

The video script emphasizes the importance of integrating conceptual understanding with procedural skills in problem-solving, particularly in physics. It outlines a four-step process from identifying concepts to evaluating answers, highlighting the crucial step of making a conceptual prediction before executing mathematical solutions. This approach ensures that students don't merely memorize procedures but deeply understand the principles, allowing them to catch errors and improve both their conceptual and mathematical competencies.

Takeaways

• 📚 The script discusses the problem-solving advice from a physics book that can be applied to various types of problems beyond physics.
• 🧠 It emphasizes the importance of learning both procedural skills and conceptual knowledge simultaneously to avoid misconceptions.
• 🔍 The four-step problem-solving process outlined in the book includes identifying concepts, setting up the problem, executing the solution, and evaluating the answer.
• 📝 A crucial part of the 'set up the problem' step is to make an estimate or conceptual prediction before doing any calculations.
• 🤔 The conceptual prediction is meant to be based on an understanding of the problem and applicable physics principles, not just symbolic manipulation.
• 📉 The 'evaluate' step involves comparing the numerical solution to the conceptual prediction to check for consistency and logical sense.
• 🚫 Skipping the conceptual prediction leads to superficial evaluation and a lack of deep understanding of the problem-solving process.
• 🤓 Making a conceptual prediction and comparing it to the numerical solution is a cognitive process that helps in learning and understanding physics concepts better.
• 🔄 When there's a conflict between the conceptual prediction and the numerical solution, it provides an opportunity for learning and improving both conceptual understanding and mathematical skills.
• 🧐 The process of making and comparing predictions can reveal misunderstandings in either the conceptual model or the mathematical application.
• 📈 By consistently following this problem-solving approach, students can integrate their conceptual understanding with their mathematical abilities.
• 👋 The speaker invites viewers to watch another video for more details on problem-solving and thanks them for watching.

Q & A

What is the main advice given in the physics book about problem-solving that is applicable to all kinds of problems?

The main advice is to integrate conceptual knowledge with procedural skills while solving problems, emphasizing the importance of making a conceptual prediction before executing the mathematical solution.

What are the four steps outlined in the book for the problem-solving process?

The four steps are: 1) Identify the concepts, 2) Set up the problem, 3) Execute the plan to find the solution, and 4) Evaluate the answer to see if it makes sense.

Why is making a conceptual prediction before solving the problem considered key in the problem-solving process?

Making a conceptual prediction is key because it allows students to compare their numerical solution with their initial understanding, which can highlight any discrepancies and lead to a deeper understanding of the physics principles involved.

What is the purpose of estimating results and predicting physical behavior before executing the mathematical solution?

The purpose is to form a conceptual understanding of the problem and the expected outcome, which is then used to evaluate the numerical solution and ensure it aligns with the physics principles.

How does the process of comparing numerical solutions with conceptual predictions help in learning?

This process helps in learning by challenging students to reconcile any differences between their intuitive understanding and the mathematical solution, leading to improvements in both conceptual knowledge and procedural skills.

What is the potential consequence of skipping the conceptual prediction step in problem-solving?

Skipping the conceptual prediction step may result in students solving problems without truly understanding the underlying physics concepts, leading to superficial evaluations and a lack of deep learning.

What does the script suggest about the relationship between conceptual models and mathematical models in problem-solving?

The script suggests that when there is a conflict between the conceptual model based on physics intuition and the mathematical model, it presents an opportunity for learning and improving both models.

How does the script address the issue of students learning to solve problems without understanding the underlying concepts?

The script addresses this issue by advocating for a problem-solving approach that integrates conceptual predictions with mathematical solutions, ensuring that students develop a comprehensive understanding of both.

What is the importance of evaluating the answer in the context of the problem-solving process described in the script?

Evaluating the answer is important as it serves as a check to ensure the numerical solution aligns with the conceptual prediction, fostering a deeper understanding and highlighting areas for improvement.

What cognitive process does the script differentiate between when students only evaluate their answers after obtaining a numerical solution?

The script differentiates between solving the problem and checking if the answer makes sense versus making a conceptual prediction and then comparing it with the numerical solution, with the latter being a more effective learning process.

What additional insight does the script offer about the nature of problem-solving in physics?

The script offers the insight that problem-solving in physics is not just about finding numerical solutions but also about developing and integrating conceptual understanding with procedural skills for effective learning.

Outlines

00:00

📚 Enhancing Problem-Solving Skills in Physics

This paragraph discusses the importance of integrating conceptual understanding with procedural skills in problem-solving, particularly in physics. The author highlights a method from a recommended physics book that emphasizes making a conceptual prediction before executing mathematical solutions. The process involves identifying concepts, setting up the problem with an estimate, executing the math, and evaluating the answer by comparing it with the initial prediction. This approach aims to avoid misconceptions and improve both intuitive and mathematical understanding of physics principles.

05:00

🚀 Avoiding Misconceptions in Physics Learning

The second paragraph builds on the previous discussion, stressing the pitfalls of learning to solve physics problems without grasping the underlying concepts. It warns against students who can mechanically solve problems but lack a true understanding of physics. The author suggests that by following the outlined problem-solving steps and making conceptual predictions, students can avoid superficial learning and instead develop a deeper, more integrated knowledge of physics. The paragraph concludes with a reference to another video for further exploration of problem-solving techniques.

Keywords

💡Problem Solving

Problem solving is a cognitive process that involves finding solutions to issues or challenges. In the context of the video, problem solving is not only about finding answers but also about understanding the underlying concepts. The script emphasizes the importance of integrating both procedural skills and conceptual knowledge in the process of solving physics problems to avoid misconceptions.

💡Physics Principles

Physics principles are the fundamental laws and theories that govern the behavior of matter and energy. The video discusses the importance of understanding these principles for effective problem solving. Students are cautioned against merely learning to solve problems without grasping the fundamental physics concepts.

💡Conceptual Knowledge

Conceptual knowledge refers to an understanding of the underlying ideas and theories in a subject, as opposed to just memorizing procedures or formulas. The script highlights the need for students to develop a conceptual understanding of physics alongside their ability to perform calculations, to ensure a holistic learning experience.

💡Procedural Skills

Procedural skills are the techniques and methods used to perform tasks or solve problems. In the video, the speaker contrasts these skills with conceptual knowledge, suggesting that students often focus on the procedural aspects of problem solving in physics, potentially neglecting the conceptual understanding that is equally important.

💡Standardized Test

A standardized test is an examination that is administered and scored in a consistent manner to ensure fairness and reliability. The script mentions that students often solve numerous problems in preparation for such tests, but may still end up with misconceptions about basic physics principles despite this practice.

💡Misconceptions

Misconceptions are false beliefs or misunderstandings about a concept or idea. The video script warns that students might develop misconceptions about physics principles even after solving many problems, if they do not integrate conceptual understanding with their procedural skills.

💡Conceptual Prediction

A conceptual prediction is an estimate or forecast made based on an understanding of the underlying concepts, rather than on mathematical calculations. The script emphasizes the importance of making a conceptual prediction before executing a mathematical solution, as it helps in evaluating the answer against the understanding of the physics principles involved.

💡Numerical Solution

A numerical solution is a specific answer obtained through mathematical calculations. The video script discusses the process of comparing the numerical solution to the conceptual prediction to evaluate if the answer makes sense, which is a crucial step in the problem-solving process.

💡Evaluate

To evaluate in the context of problem solving means to assess the validity or accuracy of a solution. The script explains that evaluating an answer by comparing it with a conceptual prediction is more effective than simply checking if the answer meets superficial criteria, such as being positive or negative.

💡Cognitive Process

A cognitive process refers to the mental activities involved in thinking, understanding, learning, and remembering. The video script describes the problem-solving process as a series of cognitive steps, including identifying concepts, setting up the problem, executing the solution, and evaluating the answer, which together contribute to a deeper understanding of physics.

💡Physics Intuition

Physics intuition is an intuitive understanding or 'gut feeling' about how physical systems should behave based on experience or exposure to physics concepts. The script suggests that making a conceptual prediction involves using this intuition to predict outcomes before performing the actual calculations.

Highlights

The physics book offers excellent advice on problem-solving applicable to various types of problems beyond just physics.

Students often solve numerous problems but may still have fundamental misconceptions about basic physics principles.

The book emphasizes learning both procedural skills and conceptual knowledge simultaneously to avoid misconceptions.

The problem-solving process involves four steps: identifying concepts, setting up the problem, executing the solution, and evaluating the answer.

Conceptual prediction is crucial and should be made before executing the mathematical solution.

Conceptual prediction is based on understanding of the problem and applicable physics principles, not symbolic manipulation.

The 'set up the problem' step includes estimating results and predicting the physical behavior of the system.

Evaluating the answer involves comparing the numerical solution to the conceptual prediction made earlier.

Skipping the conceptual prediction leads to superficial evaluation of answers, missing deeper understanding.

Making a conceptual prediction and comparing it with the numerical solution is a more cognitive process than just evaluating the answer.

When conceptual prediction conflicts with numerical solution, it leads to learning by understanding the discrepancy.

Discrepancies between conceptual prediction and numerical solution can improve either conceptual understanding or procedural skills.

The book suggests a method to integrate conceptual predictions with mathematical skills to enhance problem-solving.

Students who skip conceptual understanding may solve problems without truly grasping physics concepts.

The video provides more detailed insights into the nature of problem-solving and its importance in learning physics.

The importance of not just solving problems, but also understanding the underlying physics concepts for effective learning.

Transcripts

This extremely good physics book has some  extremely good advice about problem solving  

which students rarely follow. And it applies  to all kinds of different problems - not just  

physics problems. If you're longtime viewer, you  may have seen an old video of mine talking about  

how students can learn to solve physics problems  without actually learning physics. So students  

will solve thousands of problems in preparation  for a standardized test, but they will walk away  

with fundamental misconceptions about basic  physics principles. I didn't really answer  

the important question in that video, which was  how can we avoid this result? How can we learn  

procedural skills and conceptual knowledge at  the same time? This physics book has a pretty  

good answer. Let's take a look at the book's  description of the problem solving process.

Now, I'm not going to read everything here, I'm  going to simplify the process that they give  

and then we're going to focus on the important  sentence. Step one is to identify the concepts.  

What are the known quantities, what are the  implied quantities, and what are you trying to  

figure out? Step two is to set up the problem. So  you might draw a little picture that explains the  

situation in the problem and choose equations that  you are going to use. Step three is to execute.  

That is, to do the math to get to the solution,  based on how you set up the problem. And step  

four is to evaluate the answer. That is,  to see if your answer makes some sense.

This seems like the usual problem-solving advice.  It's good, but so far there is nothing here that  

is going to knit your conceptual knowledge  and your procedural skills together. The  

important sentence is in the "set up the  problem" step. So I'm going to read that  

right now. "As best you can, estimate what your  results will be and, as appropriate, predict what  

the physical behavior of a system will be." This  is the key sentence. Notice that it happens after  

you set up the problem, but before you execute  your plan for a solution - before you do any  

mathematics. What is this direction telling us to  do? It's telling us to come up with a conceptual  

prediction - one that's not based on symbolic  manipulation - one that's just based on our  

understanding of the problem and our understanding  of the applicable physics principles.

The conceptual prediction comes up again in the  last step, the "evaluate" step. So we're supposed  

to check to see if our answer makes sense. Well,  what is it that we do? We compare our numerical  

solution to our conceptual prediction - that's  what we are supposed to do, anyhow, but since most  

students skip the conceptual prediction step, they  get to their answer at the end and if they stop to  

evaluate it they're probably doing so in a pretty  superficial way like, "hey my answer is supposed  

to be positive. Is it positive? Yes. Okay, that's  great, I'm going to move on." Checking your answer  

in this way is fine but solving the problem and  then checking to see if your answer makes sense  

is a completely different cognitive process than  making a conceptual prediction and then comparing  

your numerical solution with the prediction that  you made earlier. When you skip the conceptual  

prediction step and you only evaluate your  answer after you've gotten a numerical solution,  

you are looking for a justification for  why that solution might make sense. But  

when you make a conceptual prediction you  are pitting two models against each other.  

One is an idealized conceptual model that's  based on your physics intuition and the other  

is a mathematical model based on the math that  your teacher told you to use. In situations  

like this, when these two models are in  conflict, you end up learning something.

Either the conceptual prediction is  wrong and there's something about the  

mathematics - something going on with the  mathematics that you don't understand. Or  

the conceptual prediction is right and something  went wrong with your mathematics. Either you're  

applying the wrong equations or maybe you made a  mistake in the arithmetic somewhere along the way.  

In either case, you get to improve either your  conceptual understanding of what's going on or  

your procedural skill at executing the mathematics  involved. As you solve more problems in this way,  

you end up knitting your conceptual  predictions and your mathematical skills  

together. That way, you don't end up like the  students I talked about in the other video who  

learn how to solve basic physics problems  without ever understanding physics concepts

I get into more detail about the nature of problem  

solving in this video over here. Thanks  for watching, I'll see you next time.