Explain the four steps of Polya’s problem solving model and state how the model is important in teaching mathematics in the foundation phase? Give one mathematical example in each case.

Answer 1

Polya's problem-solving model is a four-step approach that helps individuals systematically tackle mathematical problems. The steps are:

1. Understanding the Problem: This step involves comprehending the problem's requirements and identifying the data given. It is crucial to rephrase the problem in simpler terms and determine what is being asked.

   Example: In a problem that states, "Jessica has 12 apples. She gives 3 apples to her friend. How many apples does she have left?", a student should identify that they need to find out how many apples remain after some are given away.

2. Devising a Plan: In this step, students brainstorm various strategies to solve the problem. This may involve drawing diagrams, looking for patterns, breaking the problem into smaller parts, or using known mathematical principles.

   Example: For the apple problem, a student might decide to use subtraction as a strategy since they're being asked to find a remainder after giving away items. The plan would be to subtract 3 from 12.

3. Carrying Out the Plan: Here, the student implements the chosen strategy step by step, performing any necessary calculations or operations.

   Example: Continuing with the apple problem: The student carries out the calculation: \(12 - 3 = 9\). They would verify their subtraction and ensure the calculation is done correctly.

4. Looking Back: The final step encourages students to reflect on their solution. They should check if their answer is reasonable and if it addresses the original question. Students can also explore alternative strategies or consider how similar problems could be approached in the future.

   Example: After finding that Jessica has 9 apples left, the student checks the original question to ensure it was answered. They might also reflect on whether they could have approached the problem differently or simplified their steps further.

Importance in Teaching Mathematics in the Foundation Phase

Polya's model is crucial in the foundation phase for several reasons:

• Encourages Critical Thinking: It fosters analytical skills by guiding learners through a structured approach to problem-solving, making them more independent thinkers.

• Promotes Understanding: By emphasizing the importance of understanding a problem, students learn to read and interpret mathematical language better, which is essential for their future studies.

• Builds Confidence: As students successfully solve problems using this structured approach, their confidence in tackling challenges increases, motivating them to engage further with mathematics.

• Facilitates Communication: Discussing their thought process during each stage helps students articulate their reasoning, enhancing their communication skills.

Overall, these skills not only contribute to mathematical proficiency but also prepare students for complex problem-solving in real-life scenarios.

Summary Example

• Understanding the Problem: Identify how many apples Jessica has and how many she gives away.
• Devising a Plan: Decide to use subtraction to find the remainder of apples.
• Carrying Out the Plan: Perform the calculation \(12 - 3 = 9\).
• Looking Back: Confirm that 9 is a reasonable answer to how many apples Jessica has left and reflect on the subtraction process.