Recent Reforms in
Singapore School Math
Curriculum
WONG Khoon Yoong 黄冠麒
National Institute of Education
Nanyang Technological University
Singapore
khoonyoong.wong@nie.edu.sg
12 June 2009
Sole teacher
training institute in
Singapore
NIE
新加坡国立教育学院
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
2
Books: Singapore Math Education



World Scientific: Series on Mathematics
Education
Vol. 1: How Chinese learn mathematics:
Perspectives from Insiders (2004).
Vol. 2: Mathematics Education: The
Singapore Journey (Feb 2009).
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
3
Books: Resources for Math Teachers


Produce locally relevant materials.
McGraw-Hill Education (Asia):



Teaching Primary School
Mathematics: A Resource Book.
Teaching Secondary School
Mathematics: A Resource Book.
World Scientific: Mathematical
problem solving. Inaugural
Yearbook of the Association of
Mathematics Educators; cf. Hong
Kong Association for Math Ed.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
4
Books: Singapore Model Drawing

Kho Tek Hong, Yeo Shu Mei, & James Lim
(2009). The Singapore model method for
learning mathematics. Singapore:
Curriculum Planning & Development
Division, Ministry of Education. (Panpac
Education)
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
5
TIMSS 2007: Hong Kong vs Singapore

Learn from Hong Kong. 取 经
G4 (Math)
G8 (Math)
2007
Change
from
1995
2007
Change
from
1995
Hong Kong
607 (1)
+ 50
572 (4)
+3
Singapore
599 (2)
+9
593 (3)
-16
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
6
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
7
Scenario

Child born in 2009.




Enter school in 2015.
Start work in 2030.
What Mathematics will All of them need?
How to prepare for it?
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
8
Major Reforms
Year
1966
1978
1996
1997
1997
2003
2004
2006
2008
2015?
•
•
•
•
•
•
•
•
•
•
Reforms
Bilingual policy; English as first language.
Ability-based streaming.
National Education (Singapore values).
Thinking Schools Learning Nation (TSLN).
IT Masterplan 1.
Compulsory education (10 years)
Teaching Less Learn More (TLLM)
Pre-university curriculum; special schools.
Subject-based banding.
C2015
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
9
Reforms: Considerations
1. National goals (C2015):


To prepare Singapore youths to face the future.
To inculcate Singapore rootedness (social
cohesion in multi-racial nation) and universal
values.
2. Reforms of individual subjects must support
national goals.
3. International trends in math education and
research: ICT, cooperative learning, etc.
 Relate to Mathematics for All theme.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
10
Three Main Themes
1.
2.
3.

Math for All according to Abilities;
core and differentiated curriculum
and instruction. #1
Math Tools for All; calculators and
ICT. #2
Math by All; enhance learning
experiences. #3
Wrapping Up. #4
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
11
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
12
Math for All according to Abilities



John Perry (1902): Ruin all boys just to
catch in our net the one demigod in
pure math?
Opposite: Starve the talented just to
teach math to a few mathematically
challenged pupils?
Solution: Core and Differentiated
Curriculum and Instruction.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
13
Core Math Curriculum

Encapsulated by the Singapore Math
Curriculum Framework (“Pentagon”).
Mathematics
Problem
Solving

An extended version (Wong, 2008).
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
14
Differentiated Curriculum
• Differentiated
based on
ability;
streaming
(tracking).
• Diversity and
complexity of
the national
system.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
15
Differentiated Curriculum: 4 Cases
1. Primary 5 & Primary 6: Foundation or
Standard.
2. A-Level (Pre-University): H1, H2, H3.
3. Integrated Programmes (IP).
4. Special Schools.
 Different curricula require different
instructional techniques.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
16
P5 & P6

Streaming at Primary 5 & 6:







(1980s) Normal (6 years), Extended (8 years),
Monolingual (8 years).
(1990) Standardised to 6 years (age differences):
EM1, EM2, EM3.
2008: Subject-based banding replaces
streaming, P5: Foundation or Standard versions.
Reduce social division through academic elitism.
Math P1 to P4: Same contents.
P5 & P6: Foundation: slower pace, more
hands-on activities, repeat some P1-P4 topics.
Different exam papers at PSLE; 2009 first
batch. Foundation papers: simpler language
and no long answer questions.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
17
A-Level (Pre-University)






2006. 2 years; thinking skills, greater breadth
of learning, and different pathways.
95% of A-level students take Math.
H2: “Standard”, by science-oriented students.
H1: half of H2 (functions and graphs,
calculus, and statistics) but similar rigour;
change quantity but maintain quality.
H3: (i) choose from Differential Equations
and any two of Plane Geometry, Graph
Theory, or Combinatorics, or (ii) projects.
They must take H2 also.
Can use non-programmable graphic
calculators (international trend).
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
18
Integrated Programmes (IP)






2004.
For those who aim for university.
Start at Secondary 1 (6-year) or Secondary
3 (4-year).
End with A-Level or the International
Baccalaureate.
Bypass O-Level (4th year); “save” time to
allow for more active learning, real-life
experience, raise intellectual curiosity.
Curriculum designed by schools or Junior
Colleges (11).
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
19
IP: Raffles Institution




Adopted: Understanding By Design
Model (Wriggins and McTighe) and
NCTM.
Standard math contents.
Enriched activities: Math seminars,
workshops, competitions, research
studies.
http://www.raffles.sg/family.html
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
20
Special Schools

1.
2.
3.
4.
High plateau but few peaks. Help students
to “climb new peaks … of excellence”
(Minister Tharman, 2006).
Singapore Sports School (2004).
National University of Singapore Math and
Science High School (2005).
Arts School (2008).
School of Science and Technology (2010).
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
21
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
22


1.
2.
3.
Math Tools for All
Low budget tools available to all.
High tech tools: System must
make available to all.
Scientific calculators at P5 & P6:
From 2008.
Non-programmable graphic
calculators at A-level: From 2006.
ICT Master Plans.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
23
Calculator part of Mathematician?
By a Singapore pupil. Misperception about
math?
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
24
Multiplication Skills: 13  17
1.
2.
3.
4.
Paper and pencil (P&P) computation.
Mental strategies (MS); exact or estimate;
different ways.
•
15  15 = 225
•
10  20 = 200
Calculator: Punch keys, read output, write
down answer.
Excel: = 13*17
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
25
Calculator and Learning
Learning
Understand how algorithms
work.
Recall numerical facts.
Develop number sense.
Higher order thinking.
Use messy, real-life data.
Reduce computation anxiety.
Strengthen mental discipline.
Wong Khoon Yoong (12 June 2009, Hong Kong)
P&P
MS Cal
IT
















Themes
26
Generation Effect
Manually do the steps; better understanding, improve recall.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
27
Calculators at P5 & P6

Rationale:
1.
2.
3.



Balance between computation and problem
solving in teaching and assessment.
Widen repertoire of teaching and learning.
Help pupils who have difficulty with mastering
complex computational skills.
Scientific calculator with fraction features.
Basic computation still important, mental
calculation, estimation. No calculator from
P1 to P4.
Teacher training: Guides, workshops.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
28
Calculators at PSLE



PSLE Paper 1: No calculator.
PSLE Paper 2: Allows calculator use.
First batch in 2009.
US National Mathematics Advisory
Panel (2008): “calculators should not
be used on test items designed to
assess computational facility” (p. xxv).
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
29
Graphic Calculators at A-Level


From 2006.
Rationale:



Explore properties (e.g., non-standard
functions), test ideas individually or in
groups.
Reduce routine and tedious computations
and graphing.
Teacher training: In-service courses,
workshops, teacher guide, meetings.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
30
Graphic Calculators: Exam


Non-supported answers are accepted
unless otherwise stated.
GC item:


Not GC item:


Use GC to graph a quartic function, use
analytic method to find its stationary
points.
Given that lnp = 4000, evaluate ln(pe8).
[Value too big]
Assessment and teaching should align.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
31
ICT Master Plans






Pioneer Years: 1980 – 1996. Computer appreciation clubs,
computer science at A-level, School Link Project.
Foundation Years: IT Masterplan 1, mp1: 1997 – 2002 ($2
billions): Infrastructure, basic ICT skills for teachers.
Engaging Years: IT Masterplan 2, mp2: 2003 – 2008 ($470
millions): Baseline ICT standards for pupils, higher ICT use
through pedagogy prototype, school’s ownership of ICT plan,
partnership.
Future Years: IT Masterplan 3, mp3: 2009 – 2014: Strengthen
integration of ICT into curriculum, pedagogy and assessment,
competencies for the 21st century; FutureSchools@Singapore.
http://www.moe.gov.sg/media/press/2008/08/moe-launchesthird-masterplan.php
Part of Intelligent Nation (iN2015) Masterplan
(http://www.in2015.sg)
(Koh & Lee, 2008)
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
32
ICT & Math




Develop interest in math, enrich learning
experience, become independent
thinkers and learners (MOE, 2000).
Popular: Sketchpad, graphing.
Teacher demonstration rather than pupil
hands-on.
“Not Knowing is not seeing”:


Do not “see” the math.
“See” the obvious”.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
33
Not Knowing is Not Seeing

“Obvious” features?
What feedback to help
pupils improve?
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
34
Graph Example


Popular graphing activity: Zoom in and
zoom out.
Graphs of y = x2 and y = |x|.
(a) Normal scales. (b) Zoom in.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
35
Challenge: Digital Natives





Pupils are digital natives; Clickerati
kids (Harel, 1999).
Visual, short attention span, multitasking; SMS short forms (b4, icu).
Young teachers are ICT savvy but not
clear how to integrate ICT with
teaching?
Older teachers are digital immigrants;
keen to learn; more pedagogical ideas.
Get teachers of different ages to work
in teams.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
36
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
37
Mathematics by All




Math for All: Entitlement curriculum (Burton,
1994). Perspective of curriculum designers,
teachers.
Math by All: Volmink (1994). What do
students do with the math?
Bertrand Russell (1907/1994): “One of the
chief ends served by mathematics, when
rightly taught, is to awaken the learner’s
belief in reason, his confidence in the truth
of what has been demonstrated, and in the
value of demonstration” (p. 64).
Pupils must be able to apply math;
applications and math modelling.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
38
Help Students to Ask Questions
Meaning
M1: What do you mean by ….
M2:What is the difference
between …. and ….
M3: Can you use a diagram to
show ….
M4: (Your own question)*
Method
Md1: Can you show us how to
do this problem in another way?
Md2: Can you explain/show us
this step (….) again?
Md3: What will you do next?
Md4: (Your own question)*
Reasoning
R1: Why do you do that ….?
R2: What happens if you change
…. to ….?
R3: (Your own question)*
Application
A1: Why do we study this topic
(….)?
A2: How do we use this (….) in
everyday life?
A3: (Your own question)*
* for students who wished to ask their own questions
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
39
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
40
Wrapping Up (1)
1.
2.
Subject-System alignment: Reforms of
specific subject must be aligned with
national goals.
Provide resources and teacher training.
What teachers don’t want is to be thrown into
something they have not had the opportunity to
learn about and become comfortable with. Bill
Gates (1999)
3.
4.
Focus on student experiences; pupils
brought up by maids, one parent families,
traditional values vs. “critical skills”, etc.
Pace of reforms will accelerate. Keep
abreast and keep ahead!
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
41
Wrapping Up (2)

April 2009: Review primary education.





Replace year-end examinations with mini-tests.
Measure pupils’ social and emotional
development.
Increase floor space to enable schools to carry
out experiential forms of learning in arts and
sports.
Research about reforms still lacking.
We can learn from Hong Kong reforms.
Thank you for your attention.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
42
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
43



Culturally Relevant Pedagogy
Apply math to immediate
environment.
Develop cultural competence by
taking a math lens about daily
events.
Critical: Promote social justice.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
44
request
And we hope you can
say something about the differentiation at both
primary and secondary levels
(e.g. Standard and Foundation Programme at
Primary 5-6, and differentiation
at Junior Secondary levels). Also, we hope you
can say something about
calculator and ICT use (including their use in
school-based assessment and
public examinations). Furthermore, we also want
to know the preliminary
effects of such attempts, especially on students
with different ability and
attitude.
Wong Khoon Yoong (12 June 2009, Hong Kong)
Themes
45