How to Solve It

How to Solve It (Polya & Conway, 2014) is a classic book on problem-solving. It provides a structured approach to tackling mathematical problems, which can also be applied to general problem-solving. Pólya outlines a four-step method:

• Understand the problem: Identify what’s given, unknown, and the conditions.
• Devise a plan: Consider possible strategies, like looking for patterns or working backward.
• Carry out the plan: Implement the chosen strategy carefully.
• Look back: Review the solution, check for errors, and see if it can be applied to other problems.

The book emphasizes logical reasoning, creativity, and persistence. It’s an essential resource for students, educators, and anyone interested in improving problem-solving skills.

Here are notable excerpts:

• On problem-solving: The first step is understanding the problem. It’s not enough to read or understand the words; you must grasp the meaning.
• On asking questions: If you’re unsure, ask yourself what you’re looking for, the conditions, the type of problem, and if there are applicable theorems or methods.
• On reviewing the solution: Reflect on the steps taken. Was the approach useful? Can it solve other problems? Can the solution be simplified?

These excerpts highlight Pólya’s emphasis on the thought process behind problem-solving, which is more important than just knowing formulas or techniques. He encourages critical thinking, curiosity, and continuous learning.

Reference