MATMOD: 4 - Mathematical Problem-solving

Paul Zeitz

Who created the lecture entitled “The Art and Craft of Problem Solving”?

Problem

defined in “The Art and Craft of Problem Solving” as an inquiry that demands much thought and resourcefulness before the right approach is found.

Exercise

defined in “The Art and Craft of Problem Solving” as a question that you know how to resolve immediately. It depends on how expertly you apply specific techniques, but you don’t need to puzzle out what techniques to use.

Problem-solving

defined by the National Council of Teachers of Mathematics as the ways in which problems are represented, the meanings of the language of mathematics, and the ways in which one conjectures and reason.

Heuristics

defined by the National Council of Teachers of Mathematics as the systematic search strategies for problem analysis and transformation. It does not guarantee that one will find a solution, they just increase one’s probability of success in solving a problem.

George Polya

born in December 13, 1887, he was a teacher and mathematician and considered the Father of problem-solving.

How to Solve It

What was the book that the “Father of Problem-solving” published in 1945?

Deductive Reasoning

A type of mathematical reasoning that takes general principles and makes a specific conclusion. It ensures the truth of the conclusion at all times.

Inductive Reasoning

A type of mathematical reasoning that takes premises of specific cases and makes a general conclusion. It does not guarantee the truth of the conclusion.

1. Understand the problem

2. Make a plan

3. Carry out the plan

4. Look back & Review

5. Answer the question

What are the 4 steps of Polya’s Problem-solving Strategy?