Making every maths lesson count

#rEDDurrington #MEMLC @MccreaEmma

Source: https://www.olicav.com/#/posters/

The Curse of Knowledge:

when we are given

knowledge, it is impossible

to imagine what it’s like to

LACK that knowledge

Chip Heath, Made to Stick

Is 2𝑥 + 3𝑦 = 5 a …

1 formula only2 function only3 equation only4 all of the above

The Curse of

Knowledge is blinding

A worked example is a

step-by-step demonstration

of how to perform a task or

solve a problem

Ken Koedinger

Calculate the length of the circumference Calculate the length of the circumference

6 cm4 cm

Worked example pairs

© Making every maths lesson count, 2019

• Teacher models example, students complete theirs

• Student question is minimally different

• Withhold student question until worked example is completed

• Get students to answer on mwbs as check for understanding

• Respond accordingly

• Use earlier in the learning episode

Worked example pairs

3 1 7 120 5

Calculate 171 ÷ 3 Solve 2x + 1 > 7

2x + 1 > 72x > 6

Solve x2 + 3 = -4x

x2 + 3 = -4x

x2 + 4x + 3 = 0

(x + 1)(x + 3) = 0

x = -1 and x = -3

Find the mean of3, 5, 6, 6, 7, 8 and 8

43 7 = 6.1 (to 1 decimal place)

Incomplete worked examples

© Making every maths lesson count, 2019

• Scaffold practice (inc retrieval practice)

• Backwards fading more effective for far transfer

• Use early in the learning episode

Incomplete worked examples

Incorrect worked examples

© Making every maths lesson count, 2019

• Expose misconceptions

• No more than one misconception per worked example

• Use later in the learning episode

• Perfect for exit tickets

• Most effective when paired with student self-explanation prompts

Incorrect worked examples

Emma solved this problem incorrectly.

What did Emma do wrong when adding the fractions?

Is Emma’s answer bigger or smaller than the correct answer? How can you tell?

Incorrect worked examples

© Making every maths lesson count, 2019

Emma solved this problem incorrectly.

What did Emma do wrong when adding the fractions?

Is Emma’s answer bigger or smaller than the correct answer? How can you tell?

Your turn

5

2−3

4

Incorrect worked examples

© Making every maths lesson count, 2019

Incorrect worked examples

© Making every maths lesson count, 2019

Incorrect worked examples

Whose strategy is better and why?

Strategy comparison worked examples

© Making every maths lesson count, 2019

Calculate 24 x 16

What is the same and what is different?

Strategy comparison worked examples

200 40

120 24

20 4

10

6

2 4 0

1 4 4

3 8 4

© Making every maths lesson count, 2019

Solve 3(𝑥 + 1) = 15

Give an example of an equation that it would be better to use Mullen’s strategy.What makes one strategy better than another?

Strategy comparison worked examples

© Making every maths lesson count, 2019

Increase £16 by 15%

Strategy comparison worked examples

Whose strategy is better and why?Can you think of a scenario when Louise’s strategy might be better?

© Making every maths lesson count, 2019

1. Worked example pairs

2. Incomplete worked examples

3. Incorrect worked examples

4. Strategy comparison worked examples

The versatility of worked examples

Praise for Making every maths lesson count

#rEDDurrington #MEMLC @MccreaEmma