1. Math for Elementary Teachers - Kinholt 1 Math for Elementary Teachers Chapter 1: Problem-Solving

2. 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.

3. Math for Elementary Teachers - Kinholt 3 Exercise vs. Problem 4 EXERCISE  apply a “routine” procedure  helps you learn concepts, properties, procedures which will be needed for...... 4 PROBLEM  pause, reflect, be creative  you must WANT to solve a problem  there must be a question  No given procedure

4. Math for Elementary Teachers - Kinholt 4 Polya’s 4-Steps 1. Understand the Problem 2. Devise a Plan 3. Carry Out the Plan 4. Look Back

5. Math for Elementary Teachers - Kinholt 5 Strategies from Chapter 1 Guess and Check Use a Variable Draw a Picture Look for a Pattern Make a List Solve a Simpler Problem

6. Math for Elementary Teachers - Kinholt 6 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”!

7. Math for Elementary Teachers - Kinholt 7 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?

8. Math for Elementary Teachers - Kinholt 8 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