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

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

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.

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.

Standard algorithms Do standard algorithms exist?

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

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

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

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

3 8 = 6 𝑥 3 8 = 6 16 48 = 48

3 8 = 6 𝑥

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

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

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

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?