Pólya's problem-solving methods

Pólya's problem-solving methods are widely applicable and can be used not only in mathematics but also in various problem-solving situations. 

Polya four main steps to Solve Problems:

1. Understand the Problem:

   • Read and reread the problem carefully to ensure a clear understanding.
   • Identify what is given and what needs to be found.
   • Devise a plan by breaking down the problem into smaller, more manageable parts.

2. Devise a Plan:

   • Choose a strategy or method to solve the problem. Common strategies include:
     • Guess and Check: Make an initial attempt and adjust based on the outcome.
     • Draw a Diagram: Visualize the problem to gain insights.
     • Use Logical Reasoning: Apply reasoning and deduction to derive a solution.
     • Solve a Simpler Problem: Begin with a simpler version of the problem to build understanding.
     • Look for a Pattern: Identify patterns or trends within the problem.
     • Work Backwards: Start from the desired solution and determine the steps backward.

3. Carry Out the Plan:

   • Implement the chosen strategy or method.
   • Perform calculations or take steps to arrive at a solution.
   • Be flexible and open to adjusting the plan if necessary.

4. Review and Reflect:

   • Examine the solution critically.
   • Check for errors and ensure the solution makes sense.
   • Consider alternative approaches or methods.
   • Reflect on the problem-solving process and what could be learned from it.

 

Pólya's problem-solving methods emphasize the importance of understanding the problem deeply, being creative in devising a plan, and reflecting on the solution.