Question

Describe the general model of problem solving presented in the text. What are the three main phases and the different analysis step involved?

Answer 1

There are three main phases for solving any problem. These are:

The Three Stages

• Understanding the Problem: The most important part of solving any problem is understanding it. Ask yourself or guide others to ask themselves the following questions:
  1. What am I looking for?
  2. What is the unknown?
  3. Do I understand every word and concept in the problem?
  4. Am I familiar with the units in which measurements are given?
  5. Is there information that seems missing?
  6. Is there information that seems superfluous?
  7. Is the source of information bona fide? (Think about those instances when a friend gives you a puzzle to solve and you suspect there’s something wrong with the way the puzzle is posed.)

• Strategizing: Now that we think we understand the problem, we choose a strategy or a set of strategies to try to solve the problem. Ten general strategies[1] are:
  1. Logical reasoning
  2. Pattern recognition
  3. Working backwards
  4. Adopting a different point of view
  5. Considering extreme cases
  6. Solving a simpler analogous problem
  7. Organizing data
  8. Making a visual representation
  9. Accounting for all possibilities
  10. Intelligent guessing and testing

I have produced videos explaining each one of these strategies individually using problems we have solved at the Chapel Hill Math Circle.

• Implementing: We now implement our strategy or set of strategies. As we progress, we check our reasoning and computations (if any). Many novice problem-solvers make the mistake of “doing something” before understanding (or at least thinking they understand) the problem. For instance, if you ask them “What are you looking for?”, they might not be able to answer. Certainly, it is possible to have an incorrect understanding of the problem, but that is different from not even realizing that we have to understand the problem before we attempt to solve it!

Finally Reviewing the solution basically aims at analysis of final output with respect to objective or goal. It aims at finding out how effectively the goal has been met.