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README.md

Problem Solving

What is Problem?

  • Math in not a Problem
  • Reading assessment = Word problem
  • Translating it into arithmetic
  • Doing computations
  • Getting the correct answer

What is a Good Problem?

  • engage students' intellect
  • stimulate students to make connections and develop a coherent framework for mathematical reasoning
  • based on knowledge of the range of ways that diverse students learn mathematics

Phases of Problem Solving

  1. Entry Phase
  • What do I know?

    • Reading the question
    • Past experience
  • What do I want?

    • Write the problem in your own words.
    • Watch out for possible ambiguities.
    • Don't make assumption
  • What can I introduce?

    • Make a diagram
    • Write in mathematical notation
    • Think outside box
  1. Attack Phase
  • Brute Force

    • Four color theorem
  • Clever Strategy

    • Pattern recognition
  1. Review Phase
  • Check

    • Make sure your solution actually works.
  • Reflect

    • What were the big realizations?
  • Extend

    • Generalization
  • Caution!

    • Patterns can be misleading

Resources

  • Book

Thinking Mathematically by J.Mason