1. Principles to actions Chapter: Effective Teaching and Learning
USA
Book title:
Principles to actions
Ensuring mathematical success for all
Chapter: Effective Teaching and Learning
Establish mathematic goals to focus learning
Implement tasks that promote reasoning and problem solving
Use and connect mathematical representations
Facilitate meaningful mathematical discourse
Pose purposeful questions
Build procedural fluency from conceptual understanding
Support productive strugle in learning mathematics
Elicit and use evidence of student thinking

2. Build Procedural Fluency from Conceptual understanding
Effective mathematics teaching focuses on the development of both conceptual understanding and procedural fluency
First Conceptual understanding, then Procedural Fluency

3. Build Procedural Fluency from Conceptual understanding
Being fluent means being able to choose flexibly among methods and strategies to solve contextual and mathematical problems.
… to be able to explain their approaches, and being able to produce accurate answers effenciently.

4. In moving to fluency, learners also need opportunities to practice strategies and procedures to solidify their knowledge
Standard algorithms are to be understood and explained and related to visual models before there is any focus on fluency.

5. Standard algorithms
Do standard algorithms exist?

6. 48 : 6 =
92 : 5 =
189 : 21 =
288 : 0.6 =
4308 : 12 =

9. First Conceptual understanding, then Procedural Fluency
First: x + 3 = 5
Subtract 3 on both sides of the equation
x + 3 − 3 = 5 – 3
x = 2
Then: x + 3 = 5
Move 3 to the other side and change the sign from pluss to minus
x = 5 – 3

10. 3 8 = 6 𝑥 First Conceptual understanding, then Procedural Fluency
3 8 = 6 𝑥
Først: Multiply both sides by 8
Multiply both sides by x
Divide both side by 3
x = 16

11. 3 8 = 6 𝑥 Først: Multiply both sides by 8 Multiply both sides by x
3 8 = 6 𝑥
Først: Multiply both sides by 8
Multiply both sides by x
Divide both side by 3
x = 16
Then: Cross multiply
3x = 48
etc

12. 3 8 = 6 𝑥
3 8 =
48 = 48

13. 3 8 = 6 𝑥

14. 3 8 = 6 𝑥 𝑎 𝑏 = 𝑐 𝑑 ad = bc Multiply by b on both sides
3 8 = 6 𝑥
𝑎 𝑏 = 𝑐 𝑑
Multiply by b on both sides
Multiply by d on both sides
ad = bc

15. Principles to actions Chapter: Effective Teaching and Learning
USA
Book title:
Principles to actions
Ensuring mathematical success for all
Chapter: Effective Teaching and Learning
Establish mathematic goals to focus learning
Implement tasks that promote reasoning and problem solving
Use and connect mathematical representations
Facilitate meaningful mathematical discourse
Pose purposeful questions
Build procedural fluency from conceptual understanding
Support productive struggle in learning mathematics
Elicit and use evidence of student thinking

16. Support productive struggle in learning mathematics
«If you don’t struggle, you don’t learn»
Example: Ann and Joan

18. Find all possible combinations , such as 1-2; 1-3; 1-4; 2-1; 2-3; etc
How many same colour, how many different colour?