Polya's Problem Solving Strategies: Introduction

Which mathematician is prominently associated with the development of problem-solving heuristics in mathematics education?

• Isaac Newton

• George Pólya

• Leonhard Euler

• Carl Gauss

Select all areas to which George Pólya made fundamental contributions, according to the introduction.

• Combinatorics

• Number theory

• Numerical analysis

• Topology

• Probability theory

Fill in the blank: George Pólya’s influential 1945 book is titled (a)   .

Explain why George Pólya is sometimes called “the father of problem solving,” based on the introduction.

Which option lists Polya’s four steps in the correct order?

• Understand the problem → Devise a plan → Carry out the plan → Review the solution

• Devise a plan → Understand the problem → Review the solution → Carry out the plan

• Understand the problem → Carry out the plan → Devise a plan → Review the solution

• Review the solution → Carry out the plan → Devise a plan → Understand the problem

Select all statements that align with Polya’s strategy.

• Begin by clarifying what is being asked before choosing methods.

• Formulate a method of attack after understanding the task.

• Execute the chosen approach and compute results.

• Skip reflection once an answer is found to save time.

Which prompt best aligns with Polya’s step “Understand the problem”?

• Write an equation and define variables.

• Work backwards from the desired result.

• Identify whether there is extraneous information not needed to solve the problem.

• Perform an experiment to test a conjecture.

Select ALL actions that belong to the “Devise a plan” stage of Polya’s method.

• Make a list of the known information.

• Ask, “Can you restate the problem in your own words?”

• Draw a diagram.

• Look for a pattern.

• Determine what is known about these types of problems.

In one or two sentences, explain why drawing a diagram fits within the “Devise a plan” step, and describe how it can support solving a problem.

According to the guidance for carrying out a plan, which action is explicitly recommended when your initial approach fails?

• Abandon the problem entirely

• Devise another plan or modify the existing plan

• Retry the same steps repeatedly without changes

• Ask someone else to solve it