Everyone misses this problem solving step
Summary
TLDRThe 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
- š The script discusses the problem-solving advice from a physics book that can be applied to various types of problems beyond physics.
- š§ It emphasizes the importance of learning both procedural skills and conceptual knowledge simultaneously to avoid misconceptions.
- š The four-step problem-solving process outlined in the book includes identifying concepts, setting up the problem, executing the solution, and evaluating the answer.
- š A crucial part of the 'set up the problem' step is to make an estimate or conceptual prediction before doing any calculations.
- š¤ The conceptual prediction is meant to be based on an understanding of the problem and applicable physics principles, not just symbolic manipulation.
- š The 'evaluate' step involves comparing the numerical solution to the conceptual prediction to check for consistency and logical sense.
- š« Skipping the conceptual prediction leads to superficial evaluation and a lack of deep understanding of the problem-solving process.
- š¤ Making a conceptual prediction and comparing it to the numerical solution is a cognitive process that helps in learning and understanding physics concepts better.
- š 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.
- š§ The process of making and comparing predictions can reveal misunderstandings in either the conceptual model or the mathematical application.
- š By consistently following this problem-solving approach, students can integrate their conceptual understanding with their mathematical abilities.
- š 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
š 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.
š 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.
Mindmap
Keywords
š”Problem Solving
š”Physics Principles
š”Conceptual Knowledge
š”Procedural Skills
š”Standardized Test
š”Misconceptions
š”Conceptual Prediction
š”Numerical Solution
š”Evaluate
š”Cognitive Process
š”Physics Intuition
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 someĀ extremely good advice about problem solvingĀ Ā
which students rarely follow. And it appliesĀ to all kinds of different problems - not justĀ Ā
physics problems. If you're longtime viewer, youĀ may have seen an old video of mine talking aboutĀ Ā
how students can learn to solve physics problemsĀ without actually learning physics. So studentsĀ Ā
will solve thousands of problems in preparationĀ for a standardized test, but they will walk awayĀ Ā
with fundamental misconceptions about basicĀ physics principles. I didn't really answerĀ Ā
the important question in that video, which wasĀ how can we avoid this result? How can we learnĀ Ā
procedural skills and conceptual knowledge atĀ the same time? This physics book has a prettyĀ Ā
good answer. Let's take a look at the book'sĀ description of the problem solving process.
Now, I'm not going to read everything here, I'mĀ going to simplify the process that they giveĀ Ā
and then we're going to focus on the importantĀ sentence. Step one is to identify the concepts.Ā Ā
What are the known quantities, what are theĀ implied quantities, and what are you trying toĀ Ā
figure out? Step two is to set up the problem. SoĀ you might draw a little picture that explains theĀ Ā
situation in the problem and choose equations thatĀ you are going to use. Step three is to execute.Ā Ā
That is, to do the math to get to the solution,Ā based on how you set up the problem. And stepĀ Ā
four is to evaluate the answer. That is,Ā to see if your answer makes some sense.
This seems like the usual problem-solving advice.Ā It's good, but so far there is nothing here thatĀ Ā
is going to knit your conceptual knowledgeĀ and your procedural skills together. TheĀ Ā
important sentence is in the "set up theĀ problem" step. So I'm going to read thatĀ Ā
right now. "As best you can, estimate what yourĀ results will be and, as appropriate, predict whatĀ Ā
the physical behavior of a system will be." ThisĀ is the key sentence. Notice that it happens afterĀ Ā
you set up the problem, but before you executeĀ your plan for a solution - before you do anyĀ Ā
mathematics. What is this direction telling us toĀ do? It's telling us to come up with a conceptualĀ Ā
prediction - one that's not based on symbolicĀ manipulation - one that's just based on ourĀ Ā
understanding of the problem and our understandingĀ of the applicable physics principles.
The conceptual prediction comes up again in theĀ last step, the "evaluate" step. So we're supposedĀ Ā
to check to see if our answer makes sense. Well,Ā what is it that we do? We compare our numericalĀ Ā
solution to our conceptual prediction - that'sĀ what we are supposed to do, anyhow, but since mostĀ Ā
students skip the conceptual prediction step, theyĀ get to their answer at the end and if they stop toĀ Ā
evaluate it they're probably doing so in a prettyĀ superficial way like, "hey my answer is supposedĀ Ā
to be positive. Is it positive? Yes. Okay, that'sĀ great, I'm going to move on." Checking your answerĀ Ā
in this way is fine but solving the problem andĀ then checking to see if your answer makes senseĀ Ā
is a completely different cognitive process thanĀ making a conceptual prediction and then comparingĀ Ā
your numerical solution with the prediction thatĀ you made earlier. When you skip the conceptualĀ Ā
prediction step and you only evaluate yourĀ answer after you've gotten a numerical solution,Ā Ā
you are looking for a justification forĀ why that solution might make sense. ButĀ Ā
when you make a conceptual prediction youĀ are pitting two models against each other.Ā Ā
One is an idealized conceptual model that'sĀ based on your physics intuition and the otherĀ Ā
is a mathematical model based on the math thatĀ your teacher told you to use. In situationsĀ Ā
like this, when these two models are inĀ conflict, you end up learning something.
Either the conceptual prediction isĀ wrong and there's something about theĀ Ā
mathematics - something going on with theĀ mathematics that you don't understand. OrĀ Ā
the conceptual prediction is right and somethingĀ went wrong with your mathematics. Either you'reĀ Ā
applying the wrong equations or maybe you made aĀ mistake in the arithmetic somewhere along the way.Ā Ā
In either case, you get to improve either yourĀ conceptual understanding of what's going on orĀ Ā
your procedural skill at executing the mathematicsĀ involved. As you solve more problems in this way,Ā Ā
you end up knitting your conceptualĀ predictions and your mathematical skillsĀ Ā
together. That way, you don't end up like theĀ students I talked about in the other video whoĀ Ā
learn how to solve basic physics problemsĀ without ever understanding physics concepts
I get into more detail about the nature of problemĀ Ā
solving in this video over here. ThanksĀ for watching, I'll see you next time.
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