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Learning Strategies

Polya's Problem Solving

George Polya was a famous Hungarian mathematician who developed a framework for problem-solving in mathematics in 1957. His problem-solving approach is still used widely today and can be applied to any problem-solving discipline (i.e. chemistry, statistics, computer science). Below you will find a description of each step along with strategies to help you accomplish each step. Having a specific strategy like this one may help to reduce anxiety around math tests.

 

Understand the Problem  

Understanding the problem is a crucial first step as this will help you identify what the question is asking and what you need to calculate. Strategies to help include: 

  1. Identify (i.e. highlight or circle) the unknowns in the problem or question.
  2. Draw or visualize a picture that can help you understand the problem. 

 

Devise a Plan  

Devising a plan is a process in which you find the connection between the data/information you are given and the unknown. However, you may not have been given enough data/information to find a connection immediately, so this process may involve calculating/finding additional variables before the final unknown can be solved. Strategies to help you devise a plan include:  

  1. List the unknowns and knowns. 
  2. Identify if a theorem would help you calculate the unknown (i.e. a2 + b2 = c2). 
  3. Decide what variables you need to know the value of to solve for the unknown. 
  4. Select which variable you will solve for first.

 

Carry Out the Plan  

This step involves calculating the steps identified in the “Devise a Plan” stage. Strategies to help you carry out the plan include:  

  1. Focus on solving one part of the problem at a time.
  2. Clearly write out each step. 
  3. Double check each variable or step as you solve.
  4. Repeat this process until you solve for the final unknown. 

 

Look Back 

This step involves reviewing your answer and steps to confirm that your final calculation is correct. Strategies to help you review your work include:  

  1. Recalculate each step to see if you get the same answer.
  2. Check if your final calculation has the appropriate units (i.e. m/s, N/m2). 
  3. Repeat steps to correct any errors found.