Problem Solving Processes and Heuristics

Mathematician, George Polya (1887-1985) developed a 4-step problem solving process to help us become good problem solvers:

Step 1: Understanding the Problem
(a) Can you restate the problem in your own words?
(b) What do you need to find out, or what is the goal?
(c) What are the information given - What is known and what is unknown?
(d) Is there sufficient information, or redundant information?

Step 2: Devising a Plan
(a) Find the connection between the given information, unknowns and the goal.
(b) Consider some possible actions or heuristics.

Here are some simple and efficient strategies:
(i) Use guess and check
(ii) Draw a diagram
(iii) Look for a pattern
(iv) Make a table
(v) Work backward
(vi) Use a variable
(vii) Write an equation
(viii) Think of a simpler problem
(ix) Examine a simpler problem
(x) Identify sub-goals

Step 3: Carrying out the Plan
(a) Implement the strategy or strategies that you have chosen
(b) Carry out the necessary actions or computations
(c) Modify your plan and choose a new strategy if necessary until the problem is solved.

Step 4: Looking Back
(a) Check that the solution is reasonable and satisfies the original problem
(b) Examine whether there is another easier method to find the solution
(c) Extend the solution to solve other problems or more general problems

Source: Discovering Mathematics 1 (p201)

The following worksheet (CHALLENGE) was given to you when we started the topic ALGEBRA. Look at how Algebra is used, when we generalise the pattern into something that can be applied beyond the given scope.