1. Problem Solving and Posing as
Context for Developing
Mathematical Habits of Mind
Adapted from Dr Hang Kim Hoo

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. 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. 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. 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. 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. 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. 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. 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. 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…