Marshall Cavendish Education Global Conference 2012

Equity for the Individual Learner Practices to Engage Learners & Build Learners’

Mathematical Knowledge

Yeap Ban Har

Marshall Cavendish Institute

Equity for Every Learner

• Struggling Learners

• Average Learners

• Advanced Learners

How does a teacher cater to them?

What role does school leaders play?

What are the implications on policy matters?

What role does school leaders play?

What role do school leaders play?

This lecture will discuss this from three perspectives.

• Curriculum Design

• Textbook Use

• Classroom Practices

The discussion on curriculum design was mostly

addressed in the lecture Improving Curriculum

Structures and Instruction.

This lecture will discuss this from three perspectives.

• Textbook Use

Part 1

• Textbook Use

The Use of Research to Improve Curriculum

This has been discussed in a lecture on the first day of

the conference

The Use of Data to Refine the Curriculum

Example: National Test Item in Singapore

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24

25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56

Source: Singapore Examination and Assessment Board

Table 1 consists of numbers from 1 to 56. Kay and Lin

are given a plastic frame that covers exactly 9 squares

of Table 1 with the centre square darkened.

(a) Kay puts the frame on 9 squares as shown in the

figure below.

19 20 21

What is the average of the 8

numbers that can be seen in the

frame?

(a) Kay puts the frame on 9 squares as shown in the

figure below.

19 20 21

What is the average of the 8

numbers that can be seen in the

frame?

Alternate

Method

4 x 24 = 96

96 ÷ 8 = 12

3+4+5+11+13+19+2

0 = 96

96 ÷ 8 = 12

(b) Lin puts the frame on some other 9 squares.

The sum of the 8 numbers that can be seen in the

frame is 272.

What is the largest number that can be seen in the

frame?

Method 1

272 ÷ 4 = 60 + 8 = 68

25 + 43 = 68

The largest number is 43.

Alternately, we can use guess-and-check.

Method 2

272 ÷ 8 = 34

The hidden number is 34.

The largest number is 43.

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24

25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24

25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56

Advanced

Intermediate

38 41 38

70 74 73

89 92 91

96 98 97

In Singapore, the general data from national tests

suggest that, by the end of primary school:

Level Proportion

Able to handle novel and

complex tasks most of

the time

Able to handle novel and

complex tasks half the

Able to handle only

familiar applications

Able to handle only

routine procedures

The Explication of What to Teach and How to Teach

Most curriculum documents includes

only what to teach.

G5.Mensuration Students should have

opportunities to

5.1 Area of parallelogram

and trapezium

make connections

between the area of a

parallelogram and that of

a rectangle and the area

of a trapezium and that of

a parallelogram.

Learning Experiences are made explicit

in the curriculum document so that

students have equal access to a

stimulating learning environment.

Part 2

• Textbook Use

Part 3

• Textbook Use

Classroom Practice

• Three-Part Lesson Structure

Singapore textbooks are written for a three-

part problem-based lesson structure:

Anchor Problem

This one task is discussed thoroughly for

about one third of the lesson time.

Guided Practice

This is when teachers provide differentiated

instruction.

Independent Practice

This can be done in class or at home. It may be

consolidation or extension.

Anchor Problem

Guided Practice

instruction.

Anchor Problem

Guided Practice

instruction.

At Marshall Cavendish Institute, we teach teachers to

use four questions to guide lesson planning and

lesson delivery

• What is it that I want students to learn?

• How do I know?

• What if some students cannot learn it?

• What if some students already learn it? (Du Four, 2004)

Singapore

The Netherlands

Anchor Task

Draw quadrilateral with

four dots. Find its area.

The Netherlands The Netherlands

Classroom Practice

• Board Writing

MCI advocates

Three Part Lesson Structure

Board Writing (teachers)

Journal Writing (students)

Singapore

Classroom Practice

• Journal Writing

Colorado

Anchor Task

Board Writing

Students who were already good in the skill of

multiplying two-digit number with a single-digit number

were asked to make observations. They were asked

“What do you notice? Are there some digits that cannot

be used ta all?”

Journal Writing

What competencies do teachers need

and how are these developed?

Singapore teachers learn what they need to learn through an

approach that balances content and pedagogy.

There is an

emphasis on

teachers

solving the

problems

themselves

during the

course.

We learn from the Japanese method to help teachers

develop better skills in observing students. This is lesson

study.

Teachers learn from the

textbooks and teachers’

guide.

The practice component is given emphasis – micro teaching,

practicum and lesson study.

TEDS-M Elementary Teachers

Content Knowledge TEDS-M Elementary Teachers

Pedagogical Content Knowledge

… mindsets are changed, knowledge is constructed and the capacity to learn is

enhanced.

Google learns from typos and spelling mistakes we all make when searching

to help give you quicker and more accurate search results. So if you type

‘grizzly pears’, we can guess that you probably meant ‘grizzly bears’.

Goggle does not have a degree in English. We can do this because over the

years we’ve studied how people search and learned what the most common

errors are. So it’s good to know that all those little mistakes aren’t made in

Conference for Teachers

Singapore Math Institute

26 – 27 November 2012

Singapore

Please contact yeapbanhar@gmail.com

Marshall Cavendish Education Global Conference 2012

Education

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