Marshall Cavendish Education Global Conference 2012

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?


Equity for Every Learner
• Struggling Learners
• Average Learners
• Advanced Learners
How does a teacher cater to them?
What role do school leaders play?
What are the implications on policy matters?


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.


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.

3 4 5

11 13

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.
3+4+5+11+13+19+2
3 4 5
0 = 96
11 13 96 ÷ 8 = 12

19 20 21 Alternate
Method
What is the average of the 8 4 x 24 = 96
numbers that can be seen in the 96 ÷ 8 = 12
frame?


(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 Method 2
272 ÷ 4 = 60 + 8 = 68 272 ÷ 8 = 34
25 + 43 = 68 The hidden number is 34.
The largest number is 43. The largest number is 43.

Alternately, we can use guess-and-check.


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


International
1995

2003

2007
TIMSS

Advanced 38 38 41 5
Grade 4

High 70 73 74 26

Intermediate 89 91 92 67

Low 96 97 98 90


In Singapore, the general data from national tests
suggest that, by the end of primary school:

Level Proportion
Able to handle novel and 20
complex tasks most of
the time
Able to handle novel and 20
complex tasks half the
time
Able to handle only 45
familiar applications
Able to handle only 10
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 make connections
and trapezium 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.


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


Singapore

MCI advocates
 Three Part Lesson Structure
 Board Writing (teachers)
 Journal Writing (students)


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 TEDS-M Elementary Teachers
Content Knowledge 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
vain.


Conference for Teachers
Singapore Math Institute
26 – 27 November 2012
Singapore
Please contact yeapbanhar@gmail.com

Marshall Cavendish Education Global Conference 2012

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