Mathematical thinking

Question 1

What is problem solving?

Answer 1

the process of accepting a challenge and striving to resolve it

Question 2

Does problem solving apply to all questions posed?

Answer 2

No, only to those for which there are no immediate answers or obvious answers

Question 3

Problem solving applies to…

Answer 3

all 5 mathematical content areas

Question 4

Learners need to feel comfortable with ____ for problem solving.

Why?

Answer 4

Learners need to feel comfortable with making mistakes.

Mistakes provide learning opportunities.

Question 5

Why use problem solving?

Answer 5

• focusses learners on ideas and sense making
• develops learners’ believe that they can do mathematics
• develops learners’ understanding that maths makes sense
• provides ongoing assessment data
• engages learners
• develops the understanding that there are many ways of arriving at an answer

Question 6

What are the three stages included in solving problems which teachers should model?

Answer 6

• getting started (understanding the problem)
• working through the problem
• looking back (evaluating the reasonableness of your answer)

Question 6

What should the teacher do in problem-based lessons?

Answer 6

• get learners motivated and mentally ready to work on the problem
• set clear expectations
• listen carefully and observe
• provide hints
• accept solutions with evaluation
• conduct discussions for learners to justify and evaluate their choices

Question 7

Mathematical thinking

Answer 7

a way of looking at things, stripping them down to their essentials and analysing underlying patterns

Question 8

Steps involved in mathematical thinking

Answer 8

• breaking a task down into components
• identifying similar tasks that may help
• look for a pattern or connection
• consider alternative approaches

Question 9

Thinking mathematically involves…

Answer 9

• analysing how and evaluating why mathematical concepts, practices, and processes are used to address math problems
• creating new ideas, procedures, and ways of thinking about math

Question 10

The core of mathematical thinking is ….

Answer 10

problem solving

Question 11

Processes involved in mathematical thinking

Answer 11

• problem solving
• reasoning and proof
• communication
• connections
• representation

Question 12

What can teachers do to develop learners’ mathematical thinking?

Answer 12

• Use problems as a guide to create mathematical experiences that encourage students to think critically, creatively, and deeply.
• Connect each mathematical concept or idea to a real world issue, problem, or situation