1. Big Ideas: From within-topic to across-topics
Leong Yew Hoong

2. What is a “BIG idea”
In the current rhetoric, it is about mathematical big ideas, NOT pedagogical big ideas (but they are related)
Big idea comes in various sizes – don’t be dogmatic!
Teaching for big ideas is nice because it highlights connections in mathematics
When planning for “big” idea, can start with ‘small’ observations
Official curriculum and operational curriculum.
How do teachers implement curriculum during mathematics lessons?
What factors influence the teacher-intended curriculum? Our definition of “teacher-intended” curriculum is a plan of the teacher about what and how to teach.
What teaching / learning resources do they use in their lessons? How close is the match of the “teacher-intended” curriculum to the official curriculum prescribed by the Ministry of Education.

3. Topic 1: Algebraic fractions

4. Topic 1: Algebraic fractions

5. Topic 1: Algebraic fractions

6. Topic 1: Algebraic fractions
The big ideas?

7. Topic 1: Algebraic fractions
The big ideas? Big ideas extendable to ‘neighbouring’ topics?

8. Topic 1: Algebraic fractions

9. Topic 2: Equation of line
From textbook: Given equation, find coordinates of points Given point and gradient, find equation Given two points, find equation

10. Topic 2: Equation of line
From textbook: Given equation, find coordinates of points Given point and gradient, find equation Given two points, find equation
The big ideas?

11. Topic 2: Equation of line
From textbook: Given equation, find coordinates of points Given point and gradient, find equation Given two points, find equation
The big ideas? Big ideas extendable to ‘neighbouring’ topics? Why define gradient this way? Coordinate geometry

12. Topic 3: Basic trigo
Pythagoras theorem Definition of Tangent Definition of Sine Definition of Cosine
The big ideas?

13. Topic 3: Basic trigo
Pythagoras theorem Definition of Tangent Definition of Sine Definition of Cosine
The big ideas? Big ideas extendable to ‘neighbouring’ topics? Non just right-angled triangles; Definition of Sine, Cosine, and Tangent of obtuse angles

14. Topic 4: Indices
The big ideas?

15. Topic 4: Indices
The big ideas? Big ideas extendable to ‘neighbouring’ topics? Look back and compare “repeated addition” Rational indices Irrational indices?

16. Reflections To study Big ideas, can start with ‘small’ observations
Mathematical big ideas not enough; need to complement with pedagogical big ideas
Replacement Units