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Mathematics Problem Posing Techniques

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Questions and Answers

What is an essential characteristic of a well-structured problem?

The problem must inspire interest in the solver. (correct)

The solution method must be obvious.

The problem should evoke a sense of confusion.

The problem should be solvable without effort.

When can problem posing occur during the problem-solving process?

Only after the problem has been solved.

Only when the conditions of a problem are unchanged.

Before the problem is defined or while solving. (correct)

During any stage of solving without modification.

Why might it be beneficial for students to create problems for their friends to solve?

It guarantees an easier problem for the creator.

It encourages competition among peers.

It helps understand the friend's mathematical ability. (correct)

It allows one to demonstrate superiority in math skills.

Which of the following examples represents problem posing occurring during problem solving?

<p>Adjusting the amount of chicken wire needed for a project.</p> Signup and view all the answers

What is a key outcome of students posing problems effectively?

<p>Students enhance their engagement with mathematical concepts.</p> Signup and view all the answers

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Study Notes

Characteristics of Good Problems

Problems should not have immediately obvious solutions.
Students should feel capable of finding a solution.
Problems should be interesting to students.

Problem Posing in Mathematics

Problem posing is an essential part of mathematical activity, working alongside problem solving.
Silver (1995) identified three types of problem-posing opportunities:
- Before problem solving: Generate mathematical problems based on a situation. (Example: Designing a chicken coop)
- During problem solving: Intentionally change the problem's goals or conditions. (Example: Changing materials or measurements)
- After problem solving: Adapt experiences from a solved problem to a new scenario. (Example: Designing a fence for a garden)

Encouraging Problem Posing

Asking students to write problems for a friend can be motivating.
Researchers (e.g., Ellerton, 1986; Mamona-Downs, 1993) found that thinking of a specific person helps in creating relevant problems.
Designing problems for a friend helps problem-posers consider the intended recipient's understanding.

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Description

This quiz explores the characteristics of good mathematical problems and the importance of problem posing in mathematics. It emphasizes the various opportunities for problem posing, including generating problems and adapting experiences post-solving. Dive into the methods that encourage students to engage creatively with mathematical challenges.