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Problem Solving and Posing as Context for Developing Mathematical
Habits of Mind
Adapted from Dr Hang Kim Hoo
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…”
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 3Third Concept
LEVEL 1
LEVEL 2
• Informal Deduction• Looking for and establishing
relationships, conjecturing
• Recognition• Concrete experiences
• Analysis • Describing and making sense of
experiences
Problem Generating Strategies
Strengthen/weaken Hypothesis(Conclusion)
Generalise (Specialize)
Consider the Converse
Problem Solving and Posing as Context for Developing Mathematical Habits of
Mind
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.
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.
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…
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
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
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…
