Timss 2

Title TIMSS-R mathematics achievement of eighth graders from South East
Asian countries
Author(s) Berinderjeet Kaur
Source Journal of Science and Mathematics Education in Southeast Asia, XXV(2),
66-92
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JOURNAL OF SCIENCE AND MATHEMATICS EDUCATION IN S.E. ASIA Vol. 25, No. 2
66
TIMSS -R
MATHEMATICS ACHIEVEMENT OF EIGHTH GRADERS
FROM SOUTH EAST
ASIAN COUNTRIES
Berinderjeet Kaur
National Institute of Education
Nanyang Technological University
Singapore
In 1999, the Third International Mathematics and Science Study
(TIMSS) was replicated at the eighth grade. This study known as
TIMSS–R or TIMSS-1999 was designed to provide trends in eighth
grade mathematics and science achievement in an international context.
This paper reviews the mathematics achievement of Eighth graders from
five South East Asian countries (Indonesia, Malaysia, Philippines,
Singapore and Thailand) that participated in TIMSS-1999. The
achievement data show significant differences amongst eighth graders
from South East Asia. The paper also reviews the intended mathematics
curriculum of these countries and attempts to explore factors that may
have contributed towards high achievement.
WHAT IS TIMSS-R?
The Third International Mathematics and Science Study, TIMSS, (Beaton,
Mullis, Martin, Gonzalez, Kelly, & Smith, 1996) was conducted in 1995.
Forty-one countries participated and testing was carried out at five grade
levels. The aim of TIMSS, also known as TIMSS-1995, was to provide a
base from which policy makers, curriculum specialists and researchers could
better understand the performance of their educational systems. The two
South East Asian countries that participated in TIMSS were Singapore and
Thailand.
In 1999, TIMSS was replicated at the eighth grade. This study known as
TIMSS–R or TIMSS-1999 (Mullis, Martin, Gonzalez, Gregory, Garden,
O’Conner, Chrostowski, & Smith, 2000) was designed to provide trends in
eighth grade mathematics and science achievement in an international
context. Thirty-eighth countries including Indonesia, Malaysia, Philippines,

67
Singapore and Thailand participated in TIMSS-99. As Singapore and
Thailand were the only two South East Asian countries that participated in
both TIMSS and TIMSS-1999, this paper only discusses data related to
TIMSS-1999 for the five South East Asian Countries: Indonesia, Malaysia,
Philippines, Singapore and Thailand.
THE PARTICIPANTS
Table 1 gives some background data about the students from South East
Asia (SEA) who participated in TIMSS-1999. In all the countries, except for
Singapore, 150 schools participated in the study. In Singapore 145 schools
participated in the study. The number of students (eighth graders) who
took the tests varied from country to country as this was determined by the
sampling requirements. The number of students ranged from 4966 to 6601.
In all the countries with the exception of Philippines, students were in their
eighth year of formal schooling. In the Philippines, the students were in
their seventh year of formal schooling. The average age of the students
from SEA ranged from 14.1 to 14.6 years.
Table 1
Background data of the students from SEA in TIMSS-1999
Country Number of Number of Number of years Average age of
Schools Students of formal schooling students (years)
Indonesia 150 5848 8 14.6
Malaysia 150 5577 8 14.4
Philippines 150 6601 7 14.1
Singapore 145 4966 8 14.4
Thailand 150 5732 8 14.5
THE TESTS
The TIMSS–1999 tests (Research & Evaluation Branch, MOE; 2000) included
more than 300 multiple-choice and open-ended test items, covering a range
of mathematics and science topics and skills. About one-third of these items
were identical to those in TIMSS –1995. Eighth different booklets containing
a selection of the 162 mathematics and 146 science items were administered
to the sampled students. Each student completed the test in one booklet.
Testing time was 90 minutes. In accordance with IEApolicy (TIMSS, 2000),

68
about one-half of the TIMSS-1999 items was not released to the public but
kept secure for future use to measure international trends in mathematics
and science achievement. Eighty-two of the mathematics items used in
TIMSS-1999 were released. The mathematics items were classified by
content category and performance expectation.
CONTENT CATEGORY
The mathematics items were reported according to five content areas (Mullis,
et al., 2000). These areas, with their main topics were:
• Fractions and number sense
Includes whole numbers, fractions and decimals, integers, exponents,
estimation and approximation, proportionality;
• Measurement
Includes standard and non-standard units, common measures,
perimeter, area, volume, estimation of measures;
• Data representation, analysis, and probability
Includes representing and interpreting tables, charts, and graphs;
range, mean; likelihood, simple numerical probability;
• Geometry
Includes points, lines, planes, angles, visualization, triangles,
polygons, circles, transformations, symmetry, congruence, similarity,
and constructions; and
• Algebra
Includes number patterns, representation of numerical situations,
solving of linear equations, operations with expressions,
representations of relations and functions.
Table 2, shows the distribution of the test items by content area and type.
A total of 162 items were used in TIMSS-1999 and 82 of these items are
released. Almost 40 % of the items were in the content area Fractions and
number sense. About 20 % of the items were in the content area Algebra,
15 % in the content area Measurement, and 13 % each in the content areas
Geometry and Data representation, analysis and probability. The Majority
of the items (i.e. 77 %) were multiple choice in type. Only about a quarter
of the items had short answers (13 %) and extended responses (10 %).

69
Table 2
Distribution of the test items by content area and type
Type of Item
Content Area Number of Multiple Choice Short Answer Extended
items (MC) (SA) Response (ER)
Fractions &
number sense 61 (35) 47 (27) 11(6) 3(2)
Measurement 24 (8) 15 (7) 4 (1) 5 (0)
Data
representation,
analysis, &
probability 21(10) 19 (8) 1 (1) 1 (1)
Geometry 21 (9) 20 (9) 1 (0) 0 (0)
Algebra 35 (20) 24 (14) 4 (2) 7 (4)
Total 162 (82) 125 (65) 21 (10) 16 (7)
The numbers within the ( ) give the number of items released
PERFORMANCE EXPECTATION
The mathematics items were classified into the following performance
expectations:
Knowing (K).
Using Routine Procedures (URP).
Using Complex Procedures (UCP).
Investigating & Problem Solving (I and SP).
Mathematical Reasoning & Communicating (MR and C).
Table 3 shows the distribution of the 82 released items by content area
and performance expectation. About a third (31.7 % to be exact) of these
items belonged to the Investigating and Problem Solving category which
may be considered a high level of mathematical performance i.e. applying
mathematical knowledge to solve problems while almost a quarter (25.6 %
to be exact) of them belonged to the Knowing category which may be
considered the lowest level of mathematical performance, i.e. mere recall
of mathematical facts and knowledge. About 40 % of these items belonged

70
to the Using Routine Procedures (18.3 % to be exact) and Using Complex
Procedures (22 % to be exact) categories. These items mainly tested
mathematical skills in simple and complex situations. Only a very small
percentage (2.4 % to be exact) of the items released belonged to the category
Mathematical Reasoning and Communication that may be considered as
the highest level of mathematical performance tested in the TIMSS 1999
tests.
Table 3
Distribution of released test items by content area and performance expectation
Content Area Performance Expectation Total
K URP UCP I & SP MR & C
Fractions &
number sense 7 7 9 12 0 35
Measurement 3 0 1 4 0 8
Data
representation,
analysis, &
probability 1 0 6 2 1 10
Geometry 2 3 2 2 0 9
Algebra 8 5 0 6 1 20
Total 21 15 18 26 2 82
MATHEMATICS ACHIEVEMENT OF EIGHTH GRADERS FROM
SOUTH EAST ASIA
Thirty-eight countries participated in TIMSS-1999. The countries ranked
in order of achievement were Singapore, Republic of Korea, Chinese Taipei,
Hong Kong SAR, Japan, Belgium (Flemish), Netherlands, Slovak Republic,
Hungary, Canada, Slovenia, Russian Federation, Australia, Finland, Czech
Republic, Malaysia, Bulgaria, Latvia (LSS), United States, England, New
Zealand, Lithuania, Italy, Cyprus, Romania, Moldova, Thailand, Israel,
Tunisia, Republic of Macedonia, Turkey, Jordan, Islamic Republic of Iran,
Indonesia, Chile, Philippines, Morocco and South Africa. Table 4 shows the
ranking and average scale scores of the South East Asian countries that
participated in TIMSS-1999. Singapore and Malaysia had average scale
scores above the International average while Thailand, Indonesia and the

71
Philippines had average scores below the International average. In TIMSS-
1995 (Beaton et al., 1996), Singapore was also ranked top for the achievement
for the eighth graders. The mean score was 643 for Singapore. Thailand
failed to meet the approved sampling procedures at classroom level for
TIMSS-1995 and was not ranked but the mean score of their eighth graders
was 522.
From Table 4 it is obvious that the performance of students from
Singapore was significantly better than that of students from the other South
East Asian countries. The performance of the students from Malaysia was
also commendable as their average scale scores were significantly higher
than the international average. It is also worthy to note that the average
scale scores of the other three countries, Thailand, Indonesia and the
Philippines were significantly lower than the International average.
Table 4
Rank and Average Scale Scores of Eighth Graders
from SEA
Country Rank Average Scale Score
Singapore 1 604 (6.3)
Malaysia 16 519 (4.4)
International
Average - 487 (0.7)
Thailand 27 467 (5.1)
Indonesia 34 403 (4.9)
Philippines 36 345 (6.0)
Numbers within ( ) give the standard errors
AVERAGE ACHIEVEMENT ACROSS MATHEMATICS CONTENT
AREAS
As the TIMSS-1999 tests covered five content areas in mathematics, Tables
5A and 5B show the average achievement of participants from SEA in the
mathematics content areas. From Tables 5A and 5B, it is evident that
performance in the five content areas for all countries was consistent with
their overall performance in the tests. However, focusing on the relative
performance of individual countries across the five content areas, certain

72
trends are evident. Singapore’s eighth graders performed best on items in
the content area Fractions and number sense, followed by Measurement,
Algebra, Data representation, analysis and probability; and Geometry in
decreasing order of performance. Malaysia’s eighth graders also performed
best on items in the content area Fractions and number sense followed by
Measurement and Algebra like Singapore students. However their weakest
content area was Data representation, analysis and probability Thailand’s
and Indonesia’s eighth graders performed best on items in the content area
Geometry but differed in their relative performance for the other content
areas. Thailand’s and Philippines eighth graders’ weakest content area was
Algebra while that of Indonesia’s eighth graders was Measurement.
Table 5A
Average achievement in mathematics content areas
Country Average Scale Score
Fractions & Measurement Data Representation,
Number Sense Analysis, & Probability
(61 items) (24 items) (21 items)
Singapore 608 (5.6) 599 (6.3) 562 (6.2)
Malaysia 532 (4.7) 514 (4.6) 491 (4.0)
International Average 487 (0.7) 487 (0.7) 487 (0.7)
Thailand 471 (5.3) 463 (6.2) 476 (4.0)
Indonesia 406 (4.1) 395 (5.1) 423 (4.4)
Philippines 378 (6.3) 355 (6.2) 406 (3.5)

73
Table 5B
Average achievement in mathematics content areas – continued
Country Average Scale Score
Geometry Algebra
(21 items) (35 items)
Singapore 560 (6.7) 576 (6.2)
Malaysia 497 (4.4) 505 (4.8)
International Average 487 (0.7) 487 (0.7)
Thailand 484 (4.4) 456 (4.9)
Indonesia 441 (5.1) 424 (5.7)
Philippines 383 (3.4) 345 (5.8)
TIMSS-1999 INTERNATIONAL BENCHMARKS OF
MATHEMATICS ACHIEVEMENT
The International benchmarks presented as part of the TIMSS-1999 data
(Mullis et al., 2000) help to provide participating countries with a distribution
of the performance of their eighth graders in an international setting. For
the participating countries the proportions of their students reaching these
benchmarks perhaps speak for certain strengths and weaknesses of
mathematics education programs in their countries. The benchmarks
delineate performance of the top 10%, top quarter, top half, and lower
quarter of students in the countries participating in TIMSS-1999. The analysis
of performance at these benchmarks in mathematics suggests that three
primary factors appeared to differentiate performance among the four levels:
• the mathematical operation required
• the complexity of the numbers or number system
• the nature of the problem situation.
Table 6 shows the percentage of students from SEA reaching TIMSS-
1999 International benchmarks of mathematics achievement. It is interesting
to note that for Singapore almost half of their eighth graders were among
the top 10% and nearly all of them were amongst the top 75% of the
participants in TIMSS-1999. More than a third of the eighth graders from

74
Malaysia were amongst the top 25% of the participants, though only 12 %
were amongst the top 10%. About four fifths of the eighth graders from
Thailand were among the top 75% of the participants, though only 4 % and
16 % were amongst the top 10 % and top 25 % respectively. Only about a
half of the eighth graders from Indonesia and a third of the eighth graders
from Philippines were among the top 75 % of the participants in TIMSS-
1999. For both Indonesia and Philippines the percentages of eighth graders
at all benchmarks were significantly low and merit attention.
Table 6
Percentages of Students Reaching TIMSS 1999 International Benchmarks of Mathematics
Achievement
Country Top 10% Upper Quarter Median Lower Quarter
(90th
percentile) (75th
percentile) (50th
percentile) (25th
percentile)
Singapore 46 (3.5) 75 (2.7) 93 (1.3) 99 (0.3)
Malaysia 12 (1.4) 34 (2.4) 69 (2.2) 94 (0.8)
Thailand 4 (0.8) 16 (1.8) 44 (2.6) 81 (1.6)
Indonesia 2 (0.4) 7 (0.9) 22 (1.4) 52 (2.2)
Philippines 0 (0.1) 1 (0.5) 8 (1.4) 31 (2.5)
What do these benchmarks mean? To make them more meaningful, the
profiles of the students reaching these International benchmarks and
examples of items they are mostly likely to answer correctly are explained
as follows:
Top 10 % International benchmark
These students can organize information, make generalizations, and explain
solution strategies in non-routine problem solving situations. They can
organize information and make generalizations to solve problems; apply
knowledge of numeric, geometric, and algebraic relationships to solve
problems (e.g., among fractions, decimals, and percents; geometric
properties; and algebraic rules); and find the equivalent forms of algebraic
expressions. Examples 1 and 2 are representative items of this benchmark
that students reaching the benchmark are likely to answer correctly.

75
Example 1
Content area: Data representation, Analysis and Probability
Performance Expectation: Communicating & Reasoning
Description: Selects relevant information from two advertisements to solve
a complex word problem involving decimals.
Chris plans to order 24 issues of a magazine. He reads the following
advertisements for two magazines. Ceds are the units of currency in Chris’
country.
Which magazine is the least expensive for 24 issues? How much less
expensive?
Show your work.
Percent correct:
Singapore - 57; Thailand - 21;
Malaysia - 19; Indonesia - 5;
Philippines - 3; International - 24.
Teen Life
Magazine
24 issues
First four issues FREE
The rest
3 ceds each
Teen News
Magazine
24 issues
First six issues FREE
The rest
3.5 ceds each

76
Example 2
Content Area: Algebra
Performance Expectation: Investigating & Solving Problems
Description: Given the initial terms in a sequence and, for example, the 50th
term of that sequence, generalizes to find the next term.
The figures show four sets consisting of circles.
Figure 1 Figure 2 Figure 3 Figure 4
a) Complete the table below. First fill in how many circles make up Figure
4. Then, find the number of circles that would be needed for the 5th
figure if the sequence of figures is extended.
Figure Number of
circles
1 1
2 3
3 6
4
5
b) The sequence of figures is extended to the 7th figure. How many circles
would be needed for Figure 7?
Answer:______________________
c) The 50th figure in the sequence contains 1275 circles. Determine the
number of circles in the 51st figure. Without drawing the 51st
figure,
explain or show how you arrived at your answer.

77
Percent correct:
Singapore - 65; Malaysia - 37;
Thailand - 25; Indonesia - 24;
Upper Quarter International benchmark
These students can apply their understanding and knowledge in a wide
variety of relatively complex situations. They can order, relate and compute
with fractions and decimals to solve word problems; solve multi-step word
problems involving proportions with whole numbers; solve probability
problems; use knowledge of geometric properties to solve problems; identify
and evaluate algebraic expressions and solve equations with one variable.
Examples 3 and 4 are representative items of this benchmark that students
reaching the benchmark are likely to answer correctly.
Example 3
Content Area: Fractions and Number Sense
Description: Solves a multi-step word problem that involves dividing a
quantity in a given ratio.
John sold 60 magazines and Mark sold 80 magazines. The magazines
were all sold for the same price. The total amount of money received for
the magazines was $700. How much money did Mark receive?
Answer:_______________________
Percent correct:

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Example 4
Content Area: Measurement
Description: Find the area of a rectangle contained in a parallelogram of
given dimensions.
The figure shows a shaded rectangle inside a parallelogram.
What is the area of the shaded rectangle?
Answer:____________________
Percent correct:
MEDIAN INTERNATIONAL BENCHMARK
These students can apply basic mathematical knowledge in straightforward
situations. They can add or subtract to solve one-step word problems
involving whole numbers and decimals; identify representations of common
fractions and relative sizes of fractions; solve for missing terms in
proportions; recognize basic notions of percents and probability; use basic
properties of geometric figures; read and interpret graphs, tables, and scales;
and understand simple algebraic relationships. Examples 5 and 6 are
representative items of this benchmark that students reaching the
benchmark are likely to answer correctly.
8 cm
3 cm

79
Example 5
Content Area: Geometry
Performance Expectation: Using Routine Procedures
Description: Locates the point on a grid with 5-unit divisions when the
point lies between the grid lines.
Which point on the graph could have coordinates (7,16)?
A. Point P
B. Point Q
C. Point R
D. Point S
Percent correct:
Indonesia - 50; Thailand - 37;
20
15
10
5
0
5 10 15 20
x
y
S
P
R
Q

80
Example 6
Content Area: Algebra
Performance Expectation: Knowing
Description: Identifies the linear equation corresponding to a given verbal
statement involving a variable.
n is a number. When n is multiplied by 7, and 6 is then added, the result is
41.
Which of these equations represents this relation?
A. 7n + 6 = 41
B. 7n – 6 = 41
C. 7n x 6 = 41
D. 7(n + 6) = 41
Percent correct:
Singapore - 89; Thailand - 67;
Malaysia - 57; Indonesia - 37;
Lower Quarter International benchmark
These students can do basic computations with whole numbers. The few
items that anchor at this level provide some evidence that students can
add, subtract, and round with whole numbers. With decimals of the same
order i.e. the same number of decimal places, they can subtract with multiple
regrouping. Students can round whole numbers to the nearest hundred.
They recognize some basic notation and terminology. Examples 7 and 8 are
representative items of this benchmark that students reaching the
benchmark are likely to answer correctly.

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Example 7
Performance Expectation: Using Routine Procedures
Description: Subtracts a three-decimal number from another with multiple
regrouping.
Subtract: 4.722 – 1.935 =
A. 2.787
B. 2.797
C. 2.887
D. 2.897
Percent correct:
Malaysia - 92; Singapore - 90;
Example 8
Performance Expectation: Using Complex Procedures
Description: Rounds to estimate the sum of two three-digit numbers.
The sum 691 + 208 is closest to the sum
A. 600 + 200
B. 700 + 200
C. 700 + 300
D. 900 + 200
Percent correct:

82
The Mathematics Curriculum
In comparing achievement across countries, it is important to consider
differences in students’ curricular experiences and how these may affect
the mathematics they have studied. TIMSS-1999 database (Mullis, et al.,
2000) provides information concerning the intended mathematics
curriculum (Robitaille, & Dirks, 1982) of the participating countries.
Type of Intended Curriculum
For all the five South EastAsian countries (Indonesia, Malaysia, Philippines,
Singapore and Thailand) that participated in TIMSS-1999, the intended
mathematics curriculum was a National curriculum often having the
ministry of education being exclusively responsible for the major decisions
governing the direction of education.
Methods for Supporting and Monitoring Curriculum Implementation
Different education systems may use different ways to achieve the best
match between their intended and implemented curriculum (Robitaille, &
Dirks, 1982). In Malaysia, Singapore and Thailand the methods used to
support or monitor curriculum implementation were:
• pre-service teacher education,
• in-service teacher education,
• mandated or recommended textbook(s),
• instructional or pedagogical guide,
• ministry notes and directives,
• system of school inspection or audit.
In Indonesia and the Philippines, the methods were all of the above except
pre-service teacher education.
Examinations and Assessments in Mathematics
Public examinations help to select students for university or academic tracks
in secondary school, while system-wide assessments in mathematics
primarily inform policy makers about matters such as national standards
of achievement of the intended curriculum objectives, strengths and

83
weaknesses in the curriculum and how it is being implemented, and whether
educational achievement is improving or deteriorating. Table 7 shows the
grade levels at which students in SEA take public examinations and system-
wide assessments in mathematics. Indonesia appears to be the only SEA
country that participated in TIMSS-1999 that does not seem to have a robust
system-wide assessment agenda.
Table 7
Grades at which Public Examinations & System-wide Assessments are
conducted for students in SEA
Country Public Examinations System-wide Assessments
Indonesia 6, 9, 12 -
Malaysia 6, 9, 11, 13 6, 9, 11, 13
Philippines 6, 10 6, 10
Singapore 6, 10, 12 6, 10, 12
Thailand 12 6, 9, 12
Instructional Time for Mathematics
The percentage of time recommended for the study of mathematics at any
grade reflects the importance attached to the learning of mathematics in
the school curriculum. Table 8 shows the percentages of time recommended
for the subject mathematics at three different grade levels for a country.
This data shows some trend as regards to the importance of mathematics
in the school curriculum of a particular country. From Table 8, it appears
that in both Singapore and Malaysia, there appears to be a strong emphasis
on the learning of mathematics in the primary school years. For both
Indonesia (14 %) and Thailand (8 %), the percentage of instructional time
recommended for mathematics appears to be constant across the grade
levels. In the Philippines the instructional time recommended decreases
(from 12 % to 10 %) gradually as the grade levels increase. At grade 8,
Singapore appears to have the highest percentage (15%) of time
recommended for mathematics, when compared with the other South East
Asian countries that participated in TIMSS-1999.

84
Table 8
Instructional time recommended for Mathematics in SEA
Country Grade 4 Grade 6 Grade 8 Comments
Indonesia 14 % 14 % 14 % -
Malaysia 20 % 20 % 3 % From Grade 8 through
secondary school, the
instructional time specified
for mathematics remains
about the same. The math-
ematics curriculum empha-
sizes understanding concepts
and mastering processes.
Emphasis for the higher-level
processes increases as
students progress through
school.
Philippines 12 % 11 % 10 % To supplement the regular
mathematics program,
enrichment topics and
activities are included in
mathematics for Grade 7,
especially in the special
science classes/schools.
Singapore 22 % 20 % 15 % Students are required to
study mathematics, English
and the mother tongue
language throughout
primary and secondary
school. Pupils who are
planning to pursue further
study in mathematics or a
related discipline are offered
an additional mathematics
subject in Grade 9.
Thailand 8 % 8 % 8 % There is no change in
content, but there is change
in depth.

85
Individual Differences and Mathematics Instruction
It is a fact that not all persons have the same ability or aptitude for any
cognitive activity or skill. So, similarly not all students have the same ability
or aptitude for the study of mathematics. In Malaysia, Philippines, Singapore
and Thailand there was differentiation of instruction for students with
different abilities or interests. In Singapore different curricula were used
for different ability groups of students. In Malaysia, Philippines and
Thailand the same curricula were available for all students but teachers
adapted the curricula to meet the needs of different ability groups of
students. In Indonesia it appears that the same curricula were used for all
ability groups of students with little or no adaptations.
Emphasis on Approaches and Processes
The major characteristics of any intended curriculum are often presented
in the form of emphasis placed on approaches and processes by which the
content matter is to be transmitted. Table 9 shows the relative emphasis
given to various aspects of mathematics instruction in the intended
curriculum by the five countries in SEA that participated in TIMSS-1999.
All five countries placed major emphasis on mastering basic skills and
understanding concepts. Malaysia, Philippines and Singapore also placed
major emphasis on real-life applications of mathematics while Indonesia and
Thailand placed only moderate emphasis on it. The Philippines and
Singapore placed major emphasis on communicating mathematically while
Indonesia, Malaysia and Thailand placed only moderate emphasis on it.
Indonesia and Singapore placed major emphasis on solving non-routine
problems while Malaysia and Philippines placed only moderate emphasis
on it only. None of the five countries placed major emphasis on deriving
formal proofs, working on mathematics projects, integrating of mathematics with
other school subjects, thematic approach and multicultural approach. Indonesia,
The Philippines and Singapore placed major emphasis on assessing student
learning, while Malaysia and Thailand only placed moderate emphasis on
it.

86
Table 9
Emphasis on Approaches and Processes of the Mathematics Curriculum in SEA
Indonesia Malaysia Philippines S’pore Thailand
Mastering Basic Skills xxx xxx xxx xxx xxx
Understanding Concepts xxx xxx xxx xxx xxx
Real-life Applications of
Mathematics xx xxx xxx xxx xx
Communicating
Mathematically xx xx xxx xxx xx
Solving Non-Routine
Problems xxx xx xx xxx x
Deriving Formal Proofs x x xx xx x
Working on Mathematics
Projects xx x xx x x
Integrating of Mathematics
with Other School Subjects xx xx x x xx
Thematic Approach xx xx x x x
Multicultural Approach x x x x x
Assessing Student Learning xxx xx xxx xxx xx
xxx – Major Emphasis; xx – Moderate Emphasis; x – Minor/No Emphasis
Have Students been Taught the Topics tested by TIMSS –1999?
Although the Intended curricula of the participating countries do confirm
that students at the eighth grade would have been taught most of the topics
in the five content areas tested, to get a better picture of the implemented
curriculum teachers of the students who participated in TIMSS-1999 were
asked to provide information about the topics again. With the help of a
questionnaire they were asked to indicate against the topics that were being
tested if their students had been taught the topic in grade 8, at an earlier
grade or not at all. This data is presented in Exhibits 5.12 – 5.16 in Mullis et
al., (2000). Table 10 shows a summary of this data. The average of the
percentages for all topics within a particular content area was found for the
respective countries.

87
Table 10
Average of Percentage of students taught topics tested in the content areas
Average percentages across topics in content areas
Country Fractions & Measurement Data Geometry Algebra
Number Representation,
Sense Analysis &
Probability
Indonesia 99 94 94 74 87
Malaysia 98 93 42 76 93
Philippines 94 78 41 48 66
Singapore 100 99 67 89 98
Thailand 97 89 64 81 84
From Table 10, it is clear that for all the five countries, the content area
Fractions and Number Sense was their forte, and rightfully in the TIMSS-
1999 tests the abundance of items were on this particular content area. It is
also clear from the data in Table 10 that some countries may have been at a
disadvantage with regards to certain content areas. However, based on
the data in Table 10 alone, it is not possible to justify the rankings of the five
South East Asian countries that participated in TIMSS-1999.
DISCUSSION
The TIMSS-1999, data show that the performance of eighth graders in
mathematics from SEA differ significantly. Eighth graders from Singapore
were at the top of the ranking table while their counterparts from Indonesia
and the Philippines were almost at the opposite end of the table. A review
of their intended mathematics curriculum does not suggest any reasonable
correlation between any aspect of the intended curriculum and the average
scale scores of the countries.
However, it appears that introducing the intended mathematics
curriculum to teachers during their pre-service teacher education, having a
robust system-wide assessment agenda to monitor the implementation of
the curriculum, adequate emphasis on the learning of mathematics (in terms
of percentage of instructional time), providing for individual differences
by way of different curriculum and approaches, and emphasizing certain
approaches and processes during the implementation of the curriculum

88
may amongst other factors provide possible leads to good performance of
students in mathematics.
From the national reports on TIMSS (Research & Testing Division, MOE;
1966), TIMSS-1999 (Research & Evaluation Branch, MOE; 2000) and an
analysis by Kaur (2002) the following are the possible factors that may have
contributed to the high performance of Singapore’s eighth graders in
mathematics.
• The education system
Singapore has a centralized education system. The Ministry of
Education is the national authority that provides guidelines in the
areas of curriculum and assessment. This ensures a high degree of
homogeneity and coherence in curriculum coverage. The streaming
of pupils according to ability and the availability of suitable
curriculum enables teachers to be focused in their teaching and also
provide for individual needs of the students.
• School organization and environment
Schools in Singapore appear to be well organized in terms of high
availability of resources (e.g. computers, space and materials) for
instruction, despite having very large enrolments. The school
atmosphere appeared to be conducive to teaching and learning as
relatively few school principals reported absenteeism, late-coming
and discipline as serious problems in their schools compared with
their counterparts in other countries that participated in TIMSS and
TIMSS-1999. Principals of Singapore schools also reported working
long hours performing various school activities, thereby indicating
their high level of commitment to their role.
• Mathematics curricula implementation
The mathematics syllabuses developed by the Ministry of Education
in Singapore, which were revised in 1990 and again in 2000, place
emphasis on the development of mathematical concepts and skills,
and the ability to apply them to solve problems. The syllabuses are
embedded in a framework, shown in figure 1 (MOE, 2000a; 2000b),
that enables students to develop thinking processes as well as attitudes
and metacognition necessary for problem-solving.

89
Figure 1: Framework of the Mathematics Curriculum
(MOE, 2000a; 2000b)
Heads of mathematics departments and mathematics teachers are
familiarized with the framework of the mathematics syllabuses periodically
through school-based, pre-service, in-service and national level briefings
and workshops. In Singapore, the gap between the intended and
implemented curriculum is very narrow. This is so as the Ministry of
Education closely regulates and monitors the implementation of the
mathematics curriculum in all schools. It provides schools with titles of
recommended texts, pedagogical / instructional guides for teachers,
assessment guides and set achievement standards. The Ministry also
supports schools with a system of directives and notes, as well as school
inspection. Teachers place major emphasis on mastering basic skills,
understanding mathematical concepts, applying mathematics to real life
situations, communicating mathematically, solving non-routine problems
and assessing student learning during mathematics lessons.
• Qualifications and working ethos of teachers
Most of the teachers in schools are certified and have the relevant
mathematics qualifications. Compared to their international
counterparts, mathematics teachers in Singapore put in the highest
number of hours (ten hours per week) in marking and grading
students’ work, and in lesson planning. In addition to their scheduled
Appreciation
Interest
Confidence
Perseverance
Monitoring one’s own
thinking
Estimation and
Approximation
Mental calculation
Communication
Use of mathematical
tools
Arithmetic
manipulation
handling data
Thinking skills
Heuristics
Numerical
Geometrical
Algebraic
Statistical
Attitudes
M
etacognition
Processes
Skills
Mathematical
Problem
Solving
Concepts

90
teaching and extra-curricular duties, they spent on the average another
three hours per week on keeping student records and doing other
administrative tasks. The dedication and effort on the part of
Singapore teachers would have contributed in no small way to the
outstanding mathematics achievement of all Singapore students.
• Training and professional development of teachers
Professional upgrading of mathematics teachers is an ongoing process
in Singapore. Teachers are entitled to 100 hours of in-service training
each year. The Ministry of Education continually organizes
workshops, in-service courses and seminars to upgrade teachers’
knowledge and skills, to equip them with effective teaching strategies,
and to keep them abreast of recent developments in mathematics
education. Teachers are encouraged to engage in lifelong learning
and at the school and national level many initiatives are in place to
facilitate sharing of teaching ideas and good practices. The National
Institute of Education is actively engaged in the constant upgrading
of mathematics teachers via the Diploma level and the Master Degree
level courses. The Association of Mathematics Educators and the
Singapore Mathematical Society also have an active role in the
professional development of mathematics teachers in Singapore.
• Home environment and support
In Singapore, society as a whole places a high premium on success at
school. The virtue of hard work and the need to strive for excellence
are ingrained in students from an early age. Parents have high
expectations of their children and are willing to invest in their
children’s education in terms of resources and ‘out-of-school’ help.
The TIMSS findings showed that, compared to their counterparts in
other countries, Singapore students were amongst the most
hardworking in the world in terms of the amount of time spent
studying or doing homework in mathematics. They had good access
to educational resources (e.g. study table, dictionary, relevant books)
for study at home generally. TIMSS-1999 data show that 80 % of the
students reported that they had a computer at home and this is 30%
more than that reported in TIMSS. It appears that society as a whole

91
is well informed of educational initiatives and prepared to support
them.
• Students’ attitude and expectations
The majority of Singapore students liked mathematics. They regarded
doing well in mathematics as important. Nearly 60 % of the eighth
graders indicated that they expected to finish university education.
Almost 90 % of the students in TIMSS-1999 indicated that they had a
reasonable self-concept in mathematics.
CONCLUSION
Having speculated what may contribute towards high achievement in
mathematics based on the data in the paper and from the review of the
factors that may have contributed towards the high achievement of Eighth
Graders in Singapore, it appears that central to high achievement in
mathematics are:
• People
Good teachers, keen students, dedicated school leaders, enthusiastic
parents, and definitely society as a whole with a vision.
• Environment
Learning environments must be supportive and conducive both at
home and in school
• Mathematics curriculum
Relevant with sufficient depth and breadth
• Systems
Good and efficient monitoring and assessment methods.
TIMSS and TIMSS-1999 have provided the participating countries with
a wealth of data and also an objective measure of its mathematics education
against world benchmarks. For some countries these studies have affirmed
that their mathematics education programs are sound, while for others they
have provided an impetus to re-look at some aspects of their mathematics
curriculum.

92
REFERENCES
Beaton, A. E., Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., Kelly, D. L. & Smith,
T.A. (1996). Mathematics Achievement in the Middle School Years: IEA’s Third
International Mathematics and Science Study (TIMSS). MA: Boston College, TIMSS
International Study Center.
Kaur, B. (2002). Reflections on the curriculum – TIMSS & TIMSS-R: Performance
of Grade Eighth Singaporean Students. Reflections, Journal of the Mathematical
Association of New South Wales, Australia, 27(2), 7-12.
Ministry of Education (MOE). 2000a. Mathematics Syllabus – Primary. Singapore:
Curriculum Planning and Development Division, Ministry of Education.
Ministry of Education (MOE). 2000b. Mathematics Syllabus – Lower Secondary.
Singapore: Curriculum Planning and Development Division, Ministry of
Education.
Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., Gregory, K. D., Garden, R. A.,
O’Conner, K. M., Chrostowski, S. J. & Smith, T. A.(2000). TIMSS 1999: –
International Mathematics Report – Findings from IEA’s Repeat of the Third
International Mathematics and Science Study at the Eighth Grade. MA: Boston
College – Lynch School of Education, The International Study Center.
Research & Evaluation Branch, MOE. (2000). Third International Mathematics and
Science Study 1999 (TIMSS 1999) – National Report for Singapore. Singapore:
Ministry of Education.
Research & Testing Division, MOE. (1996). Third International Mathematics and
Science Study (TIMSS) – National Report for Singapore (Population 2). Singapore:
Ministry of Education.
Robitaille, D. & Dirks, M. (1982). Models for Mathematics Curriculum. For the
Learning of Mathematics, 2(3), 3 – 21.
TIMSS. (2000). TIMSS- 1999 Mathematics Items – Released Set for Eighth Grade.
MA: Boston College - Lynch School of Education, The International Study
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