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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.
Math for Elementary Teachers - Kinholt 3
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
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
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
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”!
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?
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