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# Ame sms conference 2013 problem solving and posing as context for development (for students)

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### Ame sms conference 2013 problem solving and posing as context for development (for students)

1. 1. Problem Solving and Posing as Context for Developing Mathematical Habits of Mind Adapted from Dr Hang Kim Hoo
2. 2. Problem Solving and Posing as Context for Developing Mathematical Habits of Mind “Using Geometry to demonstrate how problem solving and problem posing can be integrated naturally to explicate mathematical reasoning and develop productive habits of mind in learning and doing mathematics…”
3. 3. Hierarchy of Developmental Stages Problem Solving and Posing as Context for Developing Mathematical Habits of Mind LEVEL 4 • Formal Deduction • Proving and confirming results LEVEL 3 Third Concept LEVEL 1 LEVEL 2 • Informal Deduction • Looking for and establishing relationships, conjecturing • Recognition • Concrete experiences • Analysis • Describing and making sense of experiences
4. 4. Problem Generating Strategies Strengthen/weaken Hypothesis(Conclusion) Generalise (Specialize) Consider the Converse Problem Solving and Posing as Context for Developing Mathematical Habits of Mind
5. 5. Problem Solving and Posing as Context for Developing Mathematical Habits of Mind A B C DE Given AB = AC = 4 cm and BCDE is a square, find the area of triangle ABE.
6. 6. Problem Solving and Posing as Context for Developing Mathematical Habits of Mind A B C DE Given AB = 3cm, AC = 4 cm and BCDE is a square, find the area of triangle ABE.
7. 7. Problem Solving and Posing as Context for Developing Mathematical Habits of Mind A B C DE The figure shows an equilateral triangle ABC and a square BCDE. Find…
8. 8. Problem Solving and Posing as Context for Developing Mathematical Habits of Mind A B C DE The figure shows two equilateral triangles ABC and CDG and a square BCDE. Show that the points E, A and G are on the same line. G
9. 9. Problem Solving and Posing as Context for Developing Mathematical Habits of Mind A B C DE The figure shows two equilateral triangles ABC and CDG and a rectangle BCDE. Show that the triangles BCD and ACG are congruent. G
10. 10. Problem Solving and Posing as Context for Developing Mathematical Habits of Mind • Focus on the generative nature in the engagement with Mathematics… • Through generating “new questions, students are able to connect the contents together and spur further exploration…