From Raising the Floor to Raising the Ceiling

Whole Education 6th Annual Conference

Twitter | @WholeEducation #Seizingtheagenda

Establishing a shared vision for school improvement

Seizing the Agenda

Teaching for Mastery A strategy for closing the Gap

Whole Class Teaching the Shanghai Way

Debbie MorganDirector for Primary Mathematics

Points for consideration

• Can we really meet the needs and enable progress of all pupils in one lesson?

• Levels have gone, the door has opened. Please step out of the cell!

• Practice Makes Perfect!

Levels have goneThe door has

opened. Please step out of the cell!

The New Curriculum needs a New form of Assessment

The research for the review of the NationalCurriculum showed that it should focus on‘fewer things in greater depth’, in securelearning which persists, rather thanrelentless, “over-rapid progression”

Depth and sustainability is whatassessment should focus on (Living in a Levels-Free World, by Tim Oates published by DfE)

Next Steps

It should not be necessary to indicate next steps on a pupils’ work or to give individual targets for development. In a ‘teaching for mastery’ approach, each lesson is designed to address a key point which all pupils need to grasp. Therefore, the next key point or next step will be the next lesson.

AssessmentAssessment by questions is more reliable

than assessment by criteria.Can they do the maths?Do they evidence deep understanding of the

maths, such that learning is likely to be sustainable

However, the most important teacher activity is the designing and preparing of lessons and it is important that other activity is not too onerous or time-consuming.

Practice Makes Perfect!

Practice Makes Perfect !become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and are able to recall and apply their knowledge rapidly and accurately. (National Curriculum page 3)

How does this work?10

Repetition leads to Superficial Learning?

Many Western educators hold the viewthat students should be encouraged tounderstand rather than to memorise whatthey are learning (Purdie, Hattie &Douglas, 1996) as they believe thatunderstanding is more likely to lead to highquality outcomes than memorizing (Dahlin &Watkins, 2000).

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Are repetition and understanding in opposition to each other?

Chinese teachers do not see repetition and

understanding as separate but rather asinterlocking processes, complementary toeach other……….We argue that equating repetitive learningWith “surface learning withoutunderstanding” oversimplifies andmisinterprets the intrinsic meaning of theChinese notion of learning. (Lai et al 2012)

Practice Makes Perfect!

It depends on the nature of the practice.

We will consider the nature of intelligentpractice

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Purpose of Variation

Develop deep learning rather thansuperficial learning

Provide the necessary repetition to embedand sustain learning

Make connections between concepts

The central idea of teaching with variation is to highlight the essential features of the concepts through varying the non-essential features.Gu, Huang & Marton, 2004

Variation theory is posited on the view that “when certain aspects of a phenomenon vary while its other aspects are kept constant, those aspects that vary are discerned”.Lo, Chik & Pang, 2006

This practice also aims to provide opportunities for making connections, since comparison is considered thepre-condition to perceive the structures, dependencies, and relationships that may lead to mathematical abstraction. (Sun 2010

Teaching with Variation

Variety● ‘Pick and mix’● Most practice exercises contain variety

Variation● Careful choice of WHAT to vary● Careful choice of what the variation will

draw attention to

Variation versus Variety

Mike Askew 2015

Partitioning

Part whole relationships

7 is the whole and 3 is a part and 4 is a part

10

5

10

1 82

10

92

3

5

84

3

3

10

2

Drawing attention to structure

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Developing Depth/Simplicity/Clarity

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7 5.11.9

7.4 5.71.7

7 52

C

ba

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Ralph posts 40 letters, some of which are first class, and some are second.

He posts four times as many second class letters as first.

How many of each class of letter does he post?

He posts four times as many second class letters as first.How many of each class of letter does he post?

1st

402nd

Class

40 ÷ 5 = 88 x 4 = 321st Class 8 letters2nd Class 32 letters

8

8 8 8 8

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Ralph posts 40 letters, some of which are first class, and some are second.

He posts four times as many second class letters as first.

How many of each class of letter does he post?

GCSE higher

paper 2012!

Variation Theory in Practice

Consider how variation can both narrow and broaden the focusTaken from Mike Askew, Transforming Primary Mathematics, Chapter 6

Compare the two sets of calculationsWhat’s the same, what’s different?

Solve the following)

+ 17 = 15 + 2499 – = 90 – 59

Consider the strategies you used?

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Can we really meet the needs of all pupils in one lesson?

Identify the fraction

Ensure inclusion of challenge

True or False?

3 8

2 8+ = 5

16 3 9

2 9- = 1

9 214

1 7- = 1

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2 paper tapes were broken, can you guess which original paper tape is longer?

Why? How do you get your answer?

Looking at all aspects of the conceptTasks which challenge and provoke reasoning

15

15

13

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Second：

First

Think: Which line is longer?