Mathematics Problem Posing Techniques

Choose a study mode

Play Quiz

Study Flashcards

Spaced Repetition

Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

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. (C)</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. (D)</p> Signup and view all the answers

Signup and view all the answers

Flashcards

Problem Posing

The act of creating new math problems based on a specific situation.

Problem Posing Stages

Problem posing can happen before you start solving a math problem to help you understand the situation better, during solving when you change things up, or after you solve it to create a new one based on your experience.

Writing Problems

Instead of giving students a pre-made problem, encourage them to write their own based on a real-world situation, like building a chicken coop.

Personalized Problems

Students are more likely to find a problem interesting and want to solve it if they can relate it to someone they know.

Signup and view all the flashcards

Problem Posing for a Friend

When students write problems for others to solve, they learn about their friend's math skills and have to consider what they might find challenging or easy.

Signup and view all the flashcards

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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

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.