Everything you do in mathematics should make sense to you

(Sense making and the effective teaching practices)

Linda GojakImmediate Past President, NCTM

Effective Mathematics Teaching Practices

1. Establish mathematics goals to focus learning.

2. Implement tasks that promote reasoning and problem solving.

3. Use and connect mathematical representations.

4. Facilitate meaningful mathematical discourse.

5. Pose purposeful questions.

6. Build procedural fluency from conceptual understanding.

7. Support productive struggle in learning mathematics.

8. Elicit and use evidence of student thinking.

Effective Mathematics Teaching Practices

1. Establish mathematics goals to focus learning.

2. Implement tasks that promote reasoning and problem solving.

3. Use and connect mathematical representations.

4. Facilitate meaningful mathematical discourse.

5. Pose purposeful questions.

6. Build procedural fluency from conceptual understanding.

7. Support productive struggle in learning mathematics.

8. Elicit and use evidence of student thinking.

Whole Numbers

$ 40.00- 31.28

3 9 9 9

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8. Elicit and use evidence of student thinking

1. Establish mathematics goals to focus learning

The “No Purpose” Zero

207x 106 1242 00002070021942

393x 30 0001179011790

6. Build procedural fluency from conceptual understanding

Watch your language...

3. Use and connectmathematical representations

“Reducing” Fractions

15 25

35

8. Elicit and use evidence of student thinking

=

1. Establish mathematics goals to focus learning

Adding Fractions

35

5. Pose purposeful questions

Adding Fractions

35

3. Use and connectmathematical representations

Mixed Numbers

5 - 2 3

2. Implement tasks that promote reasoning and problem solving

Division of Fractions

7. Support productive struggle in learning mathematics

Division of Fractions

6. Build procedural fluency from conceptual understanding

Decimals

6. Build procedural fluency from conceptual understanding

4. Facilitate meaningful mathematical discourse

Communication

8. Elicit and use evidence of student thinking

Using Formulas……2l +2w

l x w

πr2

2πr ½a

b

½(a+b)h

r x t = d

p r t = ia2+b2=c2

L x W x H

l x w

πr22πr½ab

½(a+b)hUsing Formulas…… r x t = d

3. Use and connectmathematical representations

Everything you do in mathematics should make sense to you….

…except trapezoids!