Mathematical Problem Solving

Mathematical Problem Solving

• MPS is a process of engaging in seeking a solution to math problems.

• It requires a mathematical skill but the solver has no direct means or knowledge on how to solve the problem.

Mathematical Problem Solving

• MPS also involves expanding a task or finding other solutions to a problem.

• It helps nurture one’s mental abilities, practical know-how, analysis and critical thinking.

PROBLEM:

• In how many ways can the word ALGEBRA be spelled, given the diagram below?

Polya’s Stages

1. Understanding the Problem

a. Write down your feelings about the problem.

b. Write down the things you don’t understand in the problem.

c. Write down some attempts to understand the problem.

Polya’s Stages

2. Devise a Plan

a. Write the key concepts that might be involved in solving the problem.

b. Do you think you have enough knowledge to implement a plan?

c. Write out each plan concisely and clearly.

Polya’s Stages

3. Carry out the Plan

a. Use the labels Plan 1, Plan 2, etc. as you carry out one plan at a time.

b. Articulate your thoughts on each plan by filling in the “control” part.

Polya’s Stages

4. Check and Expand

a. Check your solution. Write down how you did it.

b. Write down your level of satisfaction.

c. Identify possible generalizations based from the problem. Try to expand the problem by formulating a parallel problem.