Problem Solving Fall 2016

Carol Dweck, Ph.D. has conducted extensive research in regards to learning. A most important feature in her work is her research on Mindsets. You can either have a fixed mindset or a growth mindset in how you see yourself. A fixed mindset deals with beliefs about yourself that can be quite limiting. Do you say about yourself, “ I am not good at ( _______ ).” Well, this phrase is heard a lot in classes like math, chemistry, … So, if you think you can’t, you won’t.

Reset Your Thinking to a Growth Mindset The homework, quiz or test grade is a reflection of your study strategies and previous experience with the material. It has nothing to do with innate intelligence. It has nothing to do with the amount of time you have spent studying. (A factor which is often irrelevant to academic performance.) How you approach problem solving can affect your success.

Let’s try an exercise to explore Problem Solving

Put the numbers 2, 3, 4, 5, and 6 in the hexagons to make the sum across and the sum down equal to 12. Are other solutions possible? List at least two, if possible.

What do you know. What types of strategies might help What do you know? What types of strategies might help? Have you tried all of your strategies? What did you do to solve it? Have you written down the steps?

approaching any kind of Problem Solving Steps to consider when approaching any kind of Problem Solving George Polya was the first individual to look into the steps essential to good problem solving. Understand the problem. Devise a plan. Carryout the plan. Look back and evaluate.

1 Understand the problem: Things to consider….. Draw a picture. Look to see if it has a pattern. Is there a similarity to another problem you have seen or solved? Can you give the information structure by using a table? Make sure you understand what the question is asking of you.

2 Devise a plan: Are there any formulas you think are relevant 2 Devise a plan: Are there any formulas you think are relevant? Does the problem need more than one step to solve? Do you need to find out more information? As you devise a plan, revisit the step for understanding the problem.

Yea! We are finally able to 3 Carryout the plan. Yea! We are finally able to Make sure to write down the steps you followed to solve the problem.

4 Look back and evaluate. Did you answer the original question? Did you label your answer? Was there a different way it could have been solved? Any steps not essential to the solution?

Here is another model to find solutions.

Other Approaches to Problem Solving

Most every class that addresses problem solving will say at some time, “Don’t memorize the problem, I want you to understand the problem.” Students will still need to memorize FACTS. To understand the problem, it is helpful to already know some of the basic facts. Create flashcards

It is helpful to create procedural templates for different types of problems. For example, ICE problems in General Chemistry.

Richard Feynman was a Nobel prize winning physicist. He used the following technique to learn new material in order to solve problems. Step One: Choose Your Concept Step Two: Pretend You’re Teaching the Idea to a New Student Step Three: Whenever You Get Stuck, Go Back to the Book Step Four: Simplify and Create Analogies There is power when you try to teach something to another person. It helps you focus your words and thoughts to convey a concept.

Summary: things to think about Part of the growth mindset is using your mistakes to refine how you approach problem solving. What worked? More importantly, what didn’t work and why? Once you figure it out, go back and explain what worked and the reasoning that went into the solution. If you are not struggling, you are not learning. So take struggling as a good thing in that it is a sign of growth.