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
Jul 11, 2015
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
Marshall Cavendish Education Global Conference 2012
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?
Marshall Cavendish Education Global Conference 2012
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?
Marshall Cavendish Education Global Conference 2012
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?
Marshall Cavendish Education Global Conference 2012
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?
Marshall Cavendish Education Global Conference 2012
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.
Marshall Cavendish Education Global Conference 2012
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.
Marshall Cavendish Education Global Conference 2012
Part 1
• Curriculum Design
• Textbook Use
• Classroom Practices
The discussion on curriculum design was mostly
addressed in the lecture Improving Curriculum
Structures and Instruction.
Marshall Cavendish Education Global Conference 2012
The Use of Research to Improve Curriculum
This has been discussed in a lecture on the first day of
the conference
Marshall Cavendish Education Global Conference 2012
The Use of Data to Refine the Curriculum
Marshall Cavendish Education Global Conference 2012
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
Marshall Cavendish Education Global Conference 2012
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.
Marshall Cavendish Education Global Conference 2012
(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?
Marshall Cavendish Education Global Conference 2012
(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?
Alternate
Method
4 x 24 = 96
96 ÷ 8 = 12
3+4+5+11+13+19+2
0 = 96
96 ÷ 8 = 12
Marshall Cavendish Education Global Conference 2012
(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.
Marshall Cavendish Education Global Conference 2012
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
Marshall Cavendish Education Global Conference 2012
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
Marshall Cavendish Education Global Conference 2012
TIMSS
Advanced
Intermediate
Low
High
19
95
20
03
20
07
38 41 38
70 74 73
89 92 91
96 98 97
Gra
de
4
Inte
rna
tio
na
l
5
26
67
90
Marshall Cavendish Education Global Conference 2012
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
20
Able to handle novel and
complex tasks half the
time
20
Able to handle only
familiar applications
45
Able to handle only
routine procedures
10
Marshall Cavendish Education Global Conference 2012
The Explication of What to Teach and How to Teach
Most curriculum documents includes
only what to teach.
Marshall Cavendish Education Global Conference 2012
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.
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Part 2
• Curriculum Design
• Textbook Use
• Classroom Practices
The discussion on curriculum design was mostly
addressed in the lecture Improving Curriculum
Structures and Instruction.
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Part 3
• Curriculum Design
• Textbook Use
• Classroom Practices
The discussion on curriculum design was mostly
addressed in the lecture Improving Curriculum
Structures and Instruction.
Marshall Cavendish Education Global Conference 2012
Classroom Practice
• Three-Part Lesson Structure
Marshall Cavendish Education Global Conference 2012
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.
Marshall Cavendish Education Global Conference 2012
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.
Marshall Cavendish Education Global Conference 2012
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.
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
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)
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Singapore
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
The Netherlands
Anchor Task
Draw quadrilateral with
four dots. Find its area.
Marshall Cavendish Education Global Conference 2012
The Netherlands The Netherlands
Marshall Cavendish Education Global Conference 2012
Classroom Practice
• Board Writing
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
MCI advocates
Three Part Lesson Structure
Board Writing (teachers)
Journal Writing (students)
Singapore
Marshall Cavendish Education Global Conference 2012
Classroom Practice
• Journal Writing
Marshall Cavendish Education Global Conference 2012
Colorado
Anchor Task
Marshall Cavendish Education Global Conference 2012
Board Writing
Marshall Cavendish Education Global Conference 2012
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
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
What competencies do teachers need
and how are these developed?
Marshall Cavendish Education Global Conference 2012
Singapore teachers learn what they need to learn through an
approach that balances content and pedagogy.
Marshall Cavendish Education Global Conference 2012
There is an
emphasis on
teachers
solving the
problems
themselves
during the
course.
Marshall Cavendish Education Global Conference 2012
We learn from the Japanese method to help teachers
develop better skills in observing students. This is lesson
study.
Marshall Cavendish Education Global Conference 2012
Teachers learn from the
textbooks and teachers’
guide.
Marshall Cavendish Education Global Conference 2012
The practice component is given emphasis – micro teaching,
practicum and lesson study.
Marshall Cavendish Education Global Conference 2012
TEDS-M Elementary Teachers
Content Knowledge TEDS-M Elementary Teachers
Pedagogical Content Knowledge
Marshall Cavendish Education Global Conference 2012
… mindsets are changed, knowledge is constructed and the capacity to learn is
enhanced.
Marshall Cavendish Education Global Conference 2012
Marshall Cavendish Education Global Conference 2012
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.
Marshall Cavendish Education Global Conference 2012
Conference for Teachers
Singapore Math Institute
26 – 27 November 2012
Singapore
Please contact [email protected]