Math for Elementary Teachers - Kinholt 1

Math for Elementary Teachers

Chapter 1: Problem-Solving

Math for Elementary Teachers - Kinholt 2

Polya’s 10 Commandments

• Be interested in your subject.• Know your subject.• Try to read the faces of your

students: try to see their expectations and difficulties; put yourself in their place.

• Realize that the best way to learn anything is to discover it by yourself.

• Give your students not only information, but also know-how, mental attitudes, the habit of methodical work.

• Let them learn guessing.

• Let them learn proving.• Look out for such features of the

problem at hand as may be useful in solving the problems to come – try to disclose the general pattern that lies behind the present concrete situation.

• Do not give away your whole secret at once – let the students guess before you tell it – let them find out by themselves as much as is feasible.

• Suggest it; do not force it down their throats.

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Exercise vs. Problem

EXERCISE apply a “routine” procedure helps you learn concepts, properties, procedures

which will be needed for......

PROBLEM pause, reflect, be creative you must WANT to solve a problem there must be a question No given procedure

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Polya’s 4-Steps

1. Understand the Problem

2. Devise a Plan

3. Carry Out the Plan

4. Look Back

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Strategies from Chapter 1

Guess and Check Use a Variable Draw a Picture Look for a Pattern Make a List Solve a Simpler Problem

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Things to Think About

• How can you make problem-solving come alive? Can you think of ways to animate a problem?

• What will parents think of problem-solving?

• Where does problem-solving occur? Consider having your students place a problem “in their pocket”!

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Things to Think About

• Would you ever give your students a problem that you don’t know how to solve?

• Are all problems appropriate for tests? If not, how would you evaluate your student’s problem-solving abilities?

• How much time should you give your students to solve a problem?

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Problem-Solving Games

• Dice Games• Come Into My Circle• This is a Kibbit. Is this a Kibbit?• Want to Come to My Picnic?• Hula Hoop Sorting• Linear Patterns With Buttons