Math for Elementary Teachers Chapter 1 ProblemSolving Math

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

Polya’s 10 Commandments 1. 2. 3. 4. 5. 6. 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. • • Math for Elementary Teachers - Kinholt 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. 2

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

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

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

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 problemsolving? Where does problem-solving occur? Consider having your students place a problem “in their pocket”! Math for Elementary Teachers - Kinholt 6

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? Math for Elementary Teachers - Kinholt 7

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 Math for Elementary Teachers - Kinholt 8