Taiwan’s Mathematics and Science Education in TIMSS 2015 · In a nutshell, students in Taiwan...

EXECUTIVE SUMMARY - 1 -

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015

Taiwan’s Mathematics and Science Education in TIMSS 2015:

Summary of the National Report for Taiwan1

Chun-Yeng Chang2, Che-Di Lee2*, Tsung-Hau Jen2, Pi-Jen Lin3, Mei-Yu Chang4, Po-Son Tsao5, Wen-Jin Yang6, Wei-Ning Chang2

1. Introduction

The Trends in International Mathematics and Science Study (TIMSS) is an international

assessment for students’ achievement in mathematics and science in the fourth and eighth grade.

TIMSS has been conducted every four years by the International Association for the Evaluation

of Educational Achievement (IEA), and TIMSS 2015 is the sixth cycle since 1995. TIMSS is

designed to help participating countries to improve teaching and learning in mathematics and science

(IEA, 2015). There were 57 countries and 7 benchmarking entities that participated in TIMSS

2015.

Taiwan has participated in TIMSS since 1999, with 4,291 fourth-graders and 5,711 eighth-

graders in TIMSS 2015. In a nutshell, students in Taiwan performed excellently in TIMSS 2015

as previous cycles of TIMSS. However, there are four well known issues from previous cycles

and still remained in this cycle of TIMSS study. The first one is that comparing to other

participating countries, students in Taiwan had less positive attitude and self-confidence and

valued less about their science and mathematics learning. The second one is that comparing to

other participating countries in East Asia (i.e., Hong Kong, Japan, South Korea, and Singapore),

there were more students with low achievement in Taiwan. The last two issues are large

mathematics and science achievement gap between rural and urban eighth graders, and large

discrepancy of mathematics achievement between high and low eighth-grade performers. In

addition to the above four issues, in this cycle, we identify more issues in school environment

and teaching practice for mathematics and science in Taiwan.

This report will first highlight the overall performance of students in Taiwan relative to

their peers in other countries, and the changes in their achievement in mathematics and science

since 1999. Then, the report will highlight other contexts related to Taiwanese students’

achievement in TIMSS 2015. Taiwan’s detailed results of TIMSS 2015 are documented in

“TIMSS 2015: Taiwan’s Mathematics and Science Education” (Chang, 2018).

1 Recommended citation:

Chang, C-Y., Lee, C-D., Jen, T-H., Lin, P-J.,Chang, M-Y., Tsao, P.-S, Yang, W-J.,& Chang, W-N. (2018).

Taiwan’s mathematics and science education in TIMSS 2015: Summary of the national report for Taiwan.

Retrieved from http://www.sec.ntnu.edu.tw/timss2015/downloads/T15TWNexecutive.pdf 2 Science Education Center, National Taiwan Normal University, Taipei, Taiwan 3 Graduate Institute of Mathematics and Science Education, National Tsing Hua University, Hsinchu, Taiwan 4 Department of Education and Learning Technology, National Tsing Hua University, Hsinchu, Taiwan 5 Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan 6 Graduate Institute of Science Education , National Taiwan Normal University, Taipei, Taiwan

* Corresponding author: Che-Di Lee, [email protected]

- 2 - EXECUTIVE SUMMARY


2. Mathematics and Science Achievement

2.1 Overall Achievement

Similar to other East Asia countries ( i.e. Singapore, Japan, South Korea and Hong Kong),

both fourth- grade and eighth- grade -students in Taiwan performed well and had outstanding results

for TIMSS 2015 as usual. Figure 1 presents the ranking of international mathematics achievements

and Figure 2 presents the ranking of international science achievements at both grade four and eight.

Figure 1. The ranking of international mathematics achievement in TIMSS 2015.

Source: “TIMSS 2015 International Results in Mathematics,” by Mullis, I. V. S., Martin, M. O., Foy, P., &

Hooper, M.,2016, retrieve from Boston College, TIMSS & PIRLS International Study Center website:

http://timssandpirls.bc.edu/timss2015/international-results Copyright 2016 by IEA.

http://timssandpirls.bc.edu/timss2015/international-results



As Figure 1 shows, the fourth - grade - students’ average score (597) in mathematics was ranked

fourth out of the 49 countries, and listed in the top five with other East Asia countries. Their

average score (555) in science was ranked sixth out of the 47 countries (see Figure 2). Their

science achievement were not significantly different than fourth graders in Hong Kong, who

ranked the fifth in TIMSS 2015 ( In this article, all statistical significant level at alpha level .05).

Figure 2. The ranking of international science in TIMSS 2015.

Source: “TIMSS 2015 International Results in Science, ”by Martin, M. O., Mullis, I. V. S., Foy, P., & Hooper,

M.,2016, retrieve from Boston College, TIMSS & PIRLS International Study Center website: http://tims-

sandpirls.bc.edu/timss2015/international-results Copyright 2016 by IEA.





The eighth grade students’ average scores in both mathematics (599; see Figure 1) and

science (569; see Figure 2) ranked third out of the 39 countries. Both their mathematics and

science achievement were not statistically different than the countries which ranked the second

(Mathematics: South Korea; Science: Japan) in TIMSS 2015.

In comparison to TIMSS 2011, students’ achievement in Taiwan has changed in mathematics,

but not in science. Table 1 shows the students’ achievement of every TIMSS cycle at both grade

eight and grade four in Taiwan. While fourth graders showed improvement, eighth graders

actually showed retrogression in mathematics. However, there was no significant difference

between 2007 and 2015 in terms of the students’ mathematics achievement at grade eight.

While Taiwanese students’ achievements in science at grade four and grade eight have not

changed significantly since 1995, the science achievements at both grade four and grade eight in

Singapore, Hong-Kong, Japan, and South Korea have significantly improved. The future studies

should investigate the underneath reasons why science achievements remain the same in

Taiwan while other countries have made more progress in science.

Table 1

Students’ achievement at both grade eight and grade four in Taiwan

Cycle

Mathematics Science

Grade 4 Grade 8 Grade 4 Grade 8

M Rank N

M Rank N

M Rank N

M Rank N

1999 -- -- -- 585 (4.2) 3 38 -- -- -- 569 (4.2) 1 38

2003 564 (1.8) 4 25 585 (4.6) 4 46 551 (1.8) 2 25 571 (3.5) 2 46

2007 576 (1.8) ▲ 3 36 598 (4.6) ▲ 1 49 557 (2.0) ▲ 2 36 561 (3.6) ▼ 2 49

2011 591 (2.0) ▲ 4 53 609 (3.2) ▲ 3 45 552 (2.2) 6 53 564 (2.3) 2 45

2015 597 (1.9) ▲ 4 49 599 (2.4) ▼ 3 39 555 (1.8) 6 47 569 (2.1) 3 39

Note. Only eighth grade students participated in TIMSS 1999; Standard error is highlight by ( );▼= the

achievement is significantly lower than previous year;▲ = the achievement is significantly higher than previous

year; N = total number of participated countries in TIMSS 2015. Adapted from Achievement in Mathematics

Content Domain, by Mullis, I.V.S., Martin, M.O., Foy, P. & Hooper, M.,2016, retrieve from Boston College,

TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/timss2015/international-results

Copyright 2016 by IEA.

2.2 Achievement by Content Domains

The achievement defined by TIMSS is composed of two dimensions—content and cognitive

domains. The content domain assesses subject matters, whereas the cognitive domain assesses

students’ thinking processes (Mullis & Martin, 2013). The highlights of students’ achievement in

Taiwan within content and cognitive domains are listed in the following.

Grade four. The content domains of TIMSS 2015 mathematics at grade four include

Number, Geometric Shapes and Measures, and Data Display (Martin et al., 2016). Table 2

displays the international ranking for mathematics achievement by content domains at grade

four in TIMSS 2015. As Table 2 shows, fourth-graders in Taiwan ranked above fifth in all




three subjects (Mullis et al., 2016). While comparing the achievement among the three sub-

jects, students in Taiwan performed better in the Number domain than in Geometric Shapes

and Measures, and Data Display.

Table 2

Top 10 Ranking for Mathematics Achievement by Content Domains at Grade 4 in TIMSS 2015

Rank

Number Geometric

Shapes & Measures

Data Display

Country M

Country M

Country M

1 Singapore 630 (4.2) Hong Kong 617 (3.4) Hong Kong 611 (3.8)

2 Hong Kong 616 (3.1) South Korea 610 (2.3) South Korea 607 (2.6)

3 South Korea 610 (2.6) Singapore 607 (4.2) Singapore 600 (4.1)

4 Taiwan 599 (1.8) Japan 601 (2.5) Japan 593 (2.6)

5 Japan 592 (1.9) Taiwan 597 (3.0) Taiwan 591 (2.2)

6 Northern Ireland 574 (3.1) Northern Ireland 566 (3.3) Russia 573 (3.6)

7 Russia 567 (3.3) Belgium 564 (2.3) Northern Ireland 567 (3.8)

8 Kazakhstan 552 (4.0) Norway

(Grade 5) 559 (3.5)

Norway (Grade 5)

566 (3.0)

9 Ireland 551 (2.2) Russia 557 (4.4) England 552 (3.2)

10 England 547 (3.2) Demark 555 (3.2) Ireland 548 (3.8)

Note. Standard error is listed in ( ). 49 countries participated in international ranking. Adapted from TIMSS 2015

International Results in Mathematics, by Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M, 2016 retrieve

from Boston College, TIMSS & PIRLS International Study Center website: http://tims-

sandpirls.bc.edu/timss2015/international-results Copyright 2016 by IEA.

Table 3

Top 10 Ranking for Science Achievement by Content Domains at Grade 4 in TIMSS 2015

Rank

Life Science Physical Science Earth Science

Country M

Country M

Country M

1 Singapore 607 (4.4) Singapore 603 (3.7) South Korea 591 (4.1)

2 South Korea 581 (1.9) South Korea 597 (2.0) Hong Kong 574 (3.1)

3 Russia 569 (3.1) Japan 587 (2.6) Japan 563 (2.5)

4 Poland 557 (2.5) Taiwan 568 (2.0) Russia 562 (4.7)

5 Japan 556 (2.2) Russia 567 (3.6) Finland 560 (2.6)

6 Finland 556 (2.6) Kazakhstan 559 (5.0) Taiwan 555 (2.5)

7 USA 555 (2.3) Hong Kong 555 (3.5) Sweden 552 (4.1)

8 Hungary 550 (3.4)

Finland 547 (2.3) Norway

(Grade 5) 549 (3.8)

9 Hong Kong 550 (3.7) Slovenia 546 (2.4) Singapore 546 (3.7)

10 Norway (Grade 5）

546 (2.6)

Poland 540 (2.1)

Kazakhstan 542 (5.4)

Note. Standard error is listed in ( ). 47 countries participated in ranking. Taiwan ranked 11th of Life Science, and

the mean of Life Science achievement was 545 (2.0). Adapted from TIMSS 2015 International Results in Science,

by Martin, Mullis, Foy & Hooper, retrieve from Boston College, TIMSS & PIRLS International Study Center

website:http://timssandpirls.bc.edu/timss2015/international-results Copyright 2016 by IEA.






The content domains of TIMSS 2015 science at the fourth grade include Life Science,

Physical Science, and Earth Science (Martin et al., 2016). Table 3 displays the international

ranking for science achievement by content domains at grade four in TIMSS 2015. As Table 3

shows, Taiwanese students ranked fourth in Physical Science, sixth in Earth Science and 11th

in Life Science internationally in TIMSS 2015 (Mullis et al., 2016). The fourth graders in

Taiwan performed weaker in Life Science than the other two subjects. Unlike other participating

countries in which Life Science has an adequate portion in science curriculum before grade

four (Mullis, Martin, Goh, & Cotter, 2016), many topics of Life Science in science assessment

has been planned in the curriculum above grade four in Taiwan. Hence, Taiwanese students’

achievement in Life Science at grade four is lower than the other two science subjects because

they have not yet developed Life Science competencies to succeed in the TIMSS fourth grade

assessment. Taiwan could reevaluate the curriculum design of science based on the percentage

of TIMSS science assessment devoted to the content at grade four (45% Life Science, 35%

Physics and 20% Earth Science; Mullis & Martin, 2013),

Grade eight. The content domains of TIMSS 2015 mathematics at grade eight include

Number, Algebra, Geometric, and Data and Chance (Mullis & Martin, 2013). Table 4 displays

the international ranking for mathematics achievement by content domains at grade eight in

TIMSS 2015. According to Table 4, the achievement of Taiwanese eighth-grade students was

ranked top five in all four subjects ( Mullis et al., 2016). While comparing within the achievement

in these four domains, the eighth grade students in Taiwan performed the best in Algebra, but

the worst in Data and Chance.

Table 4

Top 10 Ranking for Mathematics Achievement by Content Domains at Grade 8 in TIMSS 2015

Rank

Number Algebra Geometry Data & Chance

Country M Country M Country M Country M

1 Singapore 629 (3.2) Singapore 623 (3.4) Singapore 617 (3.5) Singapore 617 (3.4)

2 South Korea 601 (2.4) Taiwan 613 (2.8) South Korea 612 (3.4) South Korea 600 (2.4)

3 Hong Kong 594 (4.9) South Korea 612 (2.9) Taiwan 607 (2.6) Hong Kong 597 (5.9)

4 Taiwan 590 (2.4) Japan 596 (2.8) Hong Kong 602 (5.1) Japan 589 (2.3)

5 Japan 572 (2.4) Hong Kong 593 (4.7) Japan 598 (2.6) Taiwan 588 (2.5)

6 Ireland 544 (3.3) Russia 558 (5.2) Russia 536 (5.6) Norway (Grade 9)

542 (3.2)

7 Canada 537 (2.4) Kazakhstan 555 (5.6) Kazakhstan 529 (6.4) England 541 (4.7)

8 Russian 533 (4.5) USA 525 (3.1) Canada 527 (2.5) Canada 534 (2.9)

9 Norway (Grade 9)

529 (2.6) Israel 517 (4.7) Slovenia 522 (2.8) Ireland 534 (3.8)

10 England 528 (4.5) Canada 513 (2.2) Hungary 518 (4.2) Slovenia 525 (2.7)

Note. Standard error is listed in ( ). Total 39 countries participated in ranking. Adapted from Achievement in

Mathematics Content Domain, by Mullis, Martin, Foy & Hooper, retrieve from Boston College, TIMSS & PIRLS

International Study Center website: http://timssandpirls.bc.edu/timss2015/international-results Copyright 2016 by

IEA.

The content domains of TIMSS 2015 science at grade eight include Biology, Chemistry,

Physics and Earth Science (Mullis & Martin, 2013). Table 5 displays the international ranking




for science achievement by content domains at grade eight in TIMSS 2015. According to Table

5, Taiwanese eighth graders’ achievement in the four contents of science all ranked above fourth

internationally (Martin et al., 2016). While comparing the eighth graders’ science achievement

by content in Taiwan, the students performed better in Earth Science and Chemistry than in

Biology and Physics.

Table 5

Top 10 Ranking for Science Achievement by Content Domains at Grade 8 in TIMSS 2015

Rank

Biology Chemistry Physics Earth Science

Country M Country M Country M Country M

1 Singapore 609 (3.5) Singapore 593 (3.6) Singapore 608 (3.1) Taiwan 581 (2.7)

2 Japan 570 (2.9) Taiwan 579 (2.7) Japan 570 (2.3) Japan 574 (2.0)

3 Taiwan 565 (2.2) Japan 570 (2.4) South Korea 564 (2.8) Singapore 565 (3.6)

4 South Korea 554 (2.2) Russia 558 (4.9) Taiwan 560 (3.0) Slovenia 564 (2.9)

5 Hong Kong 549 (4.7) Kazakhstan 554 (5.2) Russia 548 (4.2) Hong Kong 558 (4.3)

6 Slovenia 548 (2.8) Slovenia 552 (2.6) Slovenia 545 (2.9) South Korea 554 (2.7)

7 England 542 (4.0) South Korea 550 (2.5) Kazakhstan 543 (5.0) Ireland 542 (3.1)

8 USA 540 (2.9) Hong Kong 536 (4.1) Hong Kong 540 (4.1) England 536 (4.0)

9 Russia 539 (4.4) Hungary 534 (3.6) England 535 (3.9) USA 535 (3.1)

10 Ireland 534 (2.9) England 529 (4.5) Hungary 531 (4.0) Russia 532 (4.7)

Note. Standard Error is listed in ( ). 39 countries participated in ranking. Adapted from TIMSS 2015 Interna-

tional Results in Science, by Martin, Mullis, Foy & Hooper, retrieve from Boston College, TIMSS & PIRLS In-

ternational Study Center website:http://timssandpirls.bc.edu/timss2015/international-results Copyright 2016 by

IEA.

2.3 Achievement by Cognitive Domains

Regarding to mathematics and science achievements of both the fourth and eighth grade

students TIMSS assessed three cognitive domains: knowing, applying, and reasoning (Martin

& Mullis, 2013). In this section, we further highlight students’ achievement of each domain

in Taiwan.

Grade four. Similar to TIMSS 2007, fourth graders in Taiwan had relatively higher

mathematics achievement in knowing and applying than reasoning in TIMSS 2015. From

TIMSS 2007 to 2011, fourth graders’ applying skills in mathematics in Taiwan improved

significantly, from 574 to 593 points and reasoning skills remained the same. From TIMSS

2011 to 2015, both applying and reasoning skills of fourth graders in Taiwan did not improve.

On the other hand, fourth graders in Taiwan performed equally well across cognitive

domains in TIMSS 2015 science achievement. In comparison to TIMSS 2007 and 2011 science

achievement, fourth graders in Taiwan had relative improvement in the knowing domain, but

regressed in the reasoning domain in TIMSS 2015.

Grade eight. Like the results of TIMSS 2007 and 2011, students in Taiwan had balanced

achievement across all three cognitive domains in mathematics at grade eight. However, it is

worth to note that comparing to TIMSS 2011, eighth graders performed relatively weaker in




knowing and applying domains of mathematics. For science achievement, Taiwanese students

significantly improved their science achievement in the reasoning domain in comparison to

2011. Yet, Taiwanese students performed relatively weaker in the applying or reasoning domains

than in the knowing domain.

Table 6 displays student’s mathematics and science achievements by domains in Taiwan.

Table 6

Student’s mathematics and science achievement by domains in Taiwan

6

Mathematics Science


M MD M MD M MD M MD

Knowing 620 (2.3) 21* 598 (2.9) -13* 557 (2.5) 13* 569 (4.2) 20*

Applying 593 (2.1) 0 602 (2.5) -12* 553 (2.6) 1 571 (3.5) -5

Reasoning 576 (3.1) -1 602 (2.5) -7 558 (3.1) -10* 561 (3.6) 9*

Note. M= Mean; MD= mean difference between 2011and 2015; Standard error is listed in ( ); * p<.05.

2.4 Gap between High and Low Performers

TIMSS has identified four international benchmarks—advanced (625 points),

high (550 points), intermediate (475 points) and low (400 points) (Mullis, Cotter,

Centurino, Fishbein & Liu, 2015), and the standard deviation of achievement refers to the

gap between the students with high achievement and with low achievement. Table 7 presents

the standard deviation of Taiwanese students’ achievements and their international ranking in

the previous and current TIMSS cycles.

Table 7

Standard Deviation and International Ranking of Taiwanese Students’ Achievements

The standard deviation has been an indicator of inequality of education, and it has been a

well-known issue for mathematics at grade eight in Taiwan. According to the Table 7, the

standard deviation of the eighth graders’ mathematics achievement in Taiwan has been wider

than most of other countries since 1991. The standard deviation of students’ mathematics

achievements at eight grade in Taiwan was both 106 points in TIMSS 2007 and 2011, and it

narrowed down to 97 points in TIMSS 2015. Ideally, the shrinkage of standard deviation may

Cycle

Mathematics Science


SD Rank N SD Rank N SD Rank N SD Rank N

1999 -- -- -- 104 (1.8) 2 38 -- -- -- 89 (2.2) 15 38

2003 63 (1.1) 22 25 100 (2.2) 2 46 69 (1.3) 20 25 79 (1.7) 18 46

2007 69 (0.9) 31 36 106 (2.2) 2 49 77 (1.3) 23 36 89 (1.6) 15 49

2011 73 (0.9) 35 53 106 (2.0) 5 45 74 (1.3) 35 53 84 (1.4) 24 45

2015 71 (1.2) 34 49 97 (1.7) 6 39 68 (1.1) 38 47 83 (1.2) 24 39

Note. Standard error is listed in ( ); N=total participated countries.



suggest more equality of education when there were less students with low achievement.

Nevertheless, the cause of shrinkage of the standard deviation is the decreasing percentage of

students with advanced achievements. This result contradicts to the assumption that shrinkage of

the standard deviation indicates the enhancement of equality in education.

As a matter of fact, the percentage of lagging students is a more critical indicator than

wide standard deviation for inequality of education for Taiwan. Hypothetically, if all students

perform above intermediate benchmark, a wide standard deviation indicates that there are high

percentage of students who can reach advanced benchmark and develop their potentials. As a

result, a wide standard deviation is not problematic when all students reach intermediate benchmark.

In reality, most of the eighth-graders (88%) in Taiwan performed above intermediate

benchmark in TIMSS 2015 (Tsao, 2018), and this suggests that reducing the percentage of

lagging students is more urgent than reducing the standard deviation in Taiwan.

Although the standard deviation of science achievement has not been wider than the

mathematics achievement at grade eight, its trend is also worthy of attention. From TIMSS

2007 to TIMSS 2015, the standard deviation of science achievement at grade eight in Taiwan

has been narrowing down. However, when comparing with the five countries in East Asia for

TMSS 2015’s results, the standard deviation of science achievement at grade eight in Taiwan

was close to Singapore’s standard deviation which is the largest among the five countries. This

result is due to the fact that Singapore’s standard deviation of science achievement has

dramatically drop down in TIMSS 2015. According to TIMSS 2011, the standard deviation of

science achievement in Taiwan, Singapore, South Korea, Japan and Hong Kong were 84, 97,

77, 76, and 75 respectively (Martin, Mullis, Foy, & Stanco, 2012). In TIMSS 2015, the standard

deviation of science achievement in Taiwan, Singapore, South Korea, Japan and Hong Kong

were 83, 86, 78, 75, and 72 respectively (Martin et al., 2016). Through the trend of standard

deviation of science achievement among the five countries in East Asia, we call for future

research to investigate why the standard deviation of science achievement in Taiwan has been

detained.

2.5 Degree of Lagging in Achievement

According to the distribution of students’ achievement in mathematics and science in Taiwan,

“lagging students” is defined as students with achievement below the international intermediate

benchmark. Figure 3 presents the trend of lagging students among five countries in East Asia. In

Taiwan, there was 5% of lagging students in fourth-grade mathematics, 12% in eighth-grade

mathematics, 12% in fourth-grade science and 14% in eighth-grade science in TIMSS 2015.

On the one hand, compared to other countries in East Asia (i.e., Hong Kong, Japan, Singapore,

and South Korea), Taiwan had the highest percentage of lagging students in eighth-grade

mathematics and in fourth-grade science in the latest cycle of TIMSS, and the second highest



percentage of lagging students in eighth-grade science (only one percent lower than the highest

percentage).

Figure 3. The percentage of lagging students among five countries in East Asia for each TIMSS cycle.

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The percentage of lagging fourth graders in Taiwan has significantly decreased since 2011,

mathematics and science, but not for eighth-graders (see Figure 3). More specific, the

percentage of Taiwanese lagging fourth-grade students has decreased from 7% to 5% in

mathematics and from 15% to 12% in science. However, there was no significant change in

the percentage of eighth graders lagging in mathematics and science, while other countries in

East Asia have been gradually reducing their percentage of lagging students for both fourth-

grade and eighth-grade. The percentage of Hong Kong’s lagging eighth-grade students has

decreased from 15% to 8 % in mathematics and from 23% to 15% in science. In a similar way,

the percentage of lagging eighth-grade students in Singapore has decreased from 12% to 6%

in mathematics and from 20% to 10% in science. While other countries in East Asia has been

significantly reducing lagging students, future researchers should explore further on reducing

lagging students at grade eight in Taiwan.

2.6 Rural-Urban Gap in Achievement

Figure 4 displays the trend of percentage of lagging students in Taiwan by rural-urban categories.

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Figure 4. The percentage of lagging students by rural-urban categories.



As Figure 4 shows, the rural-urban gap in Taiwan has been narrowing among fourth graders’

mathematics and science achievement, and it has been slightly increasing among eighth graders’

mathematics and science achievement from 2011 to 2015. According to TIMSS 2015, the gap

between students’ achievement in urban areas (i.e., populations over .5 billion) and in rural

areas (i.e., population under 50,000) was 25 points for fourth-grade mathematics, 64 points for

eighth-grade mathematics, 25 points for fourth-grade science, and 52 points for eighth-grade

science. In 2011, the gap between students’ achievement in urban areas and in rural areas was

34 points for fourth-grade mathematics, 61 points for eighth-grade mathematics, 35 points for

fourth-grade science, and 46 points for eighth-grade science.

The rural-urban gaps in mathematics and science achievement for fourth-grade students

have narrowed by about 29% between 2011 and 2015. On the other hand, urban gap is more

severe in eighth graders’ mathematics and science achievement than among fourth graders.

Furthermore, from the viewpoint of lagging students in TIMSS 2011 and 2015, the percentage

of fourth-grade rural students lagging in mathematics and science has decreased. Yet, the

percentage of eighth-grade students lagging in mathematics continues to be two to three times

higher in rural areas than in urban areas since 2003.

3. Students’ Attitudes toward Learning Mathematics and Sciences

Other than assessing mathematics and science achievement, TIMSS 2015 also examined

students’ attitudes toward learning mathematics and science. The attitudes include students’

enjoyment, confidence, and values toward mathematics and science. Overall, except for fourth-

grade science, Taiwanese students reported that they disliked, had low confidence in, and did

not value learning science and mathematics.

3.1 Students Like Learning Mathematics and Science

Similar to the international average of all participating countries (56%), 58 % of fourth

graders in Taiwan expressed that they like learning science very much In contrast,

proportions of fourth graders who like math very much (23% ), and eighth graders who like

math very much (11%), and who like science very much (18%) were far below the

international average, which were 46%, 22%, and 37% correspondingly. Regarding TIMSS

2015 international ranking of students’ level of liking to learn mathematics, Taiwanese fourth

graders ranked 20 out of 47, and Taiwanese eighth graders ranked 35 out of 39. For

TIMSS2015 international ranking of students’ level of liking to learn science, Taiwanese

fourth graders ranked 20 out of 47 and the eight graders ranked 27 out of 29.

Figure 5 presents the relationship between students’ level of liking to learn mathematics

and science and achievements in TIMSS 2015



3.2 Students’ Confidence in Mathematics and Science

Similar to the international average (40%), 38% of fourth graders in Taiwan had a high

level of confidence in learning science. Except for fourth-grade science, the percentage of

students with high levels of confidence in learning fourth-grade mathematics or eighth-grade

Figure 5. The relationship between students’ level of liking mathematics or sciences and achievements at grade 4

and grade 8 in TIMSS 2015.

Singapore, 24

South Korea,8 Taiwan, 11

Hong Kong, 15

Japan, 90

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ics

(%)

Mathematics Achievement at grade 8

Singapore, 56

South Korea,42Japan,53

Hong Kong, 57Taiwan,58

0

20

40

60

80

100

350 400 450 500 550 600 650Per

cen

tage

of

stu

den

ts w

ho

lik

e sc

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%)

Science achievement at grade 4

Singapore,38

Japan,15 Taiwan,18

Sourth Korea,10

Hong Kong, 30

0

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350 400 450 500 550 600 650

Per

cen

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%)


Singapore,39

Hong Kong, 35

South Korea,19Taiwan, 23

Japan,26

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Per

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Mathematics achievement at grade 4



mathematics and science were all far below the international average, which were 32%, 14%,

and 22% respectively. In particular, 15% of Taiwanese students at grade four had high level of

confidence in mathematics, and 9% of Taiwanese students at grade eight had a high level of

confidence in science and mathematics. Figure 6 presents the relationship between confidence

and achievements at grade four and grade eight.

Singapore, 13

South Korea, 8

Taiwan, 9

Hong Kong, 10

Japan, 50

20

40

60

80

100

350 400 450 500 550 600 650

Per

cen

tage

of

stsu

den

ts w

ith

co

nfi

den

ce in

mat

hem

atic

s (%

)

Mathematics achievement at grade 8

Singapore, 17

Japan, 5Taiwan, 9

South Korea, 7

Hong Kong , 13

0

20

40

60

80

100

350 400 450 500 550 600 650

Per

cen

tage

of

stu

den

ts

wit

h c

on

fid

ence

in s

cien

ce

(%)


Singapore, 26

South Korea, 20Japan, 24

Hong Kong , …

Taiwan, 38

0

20

40

60

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350 400 450 500 550 600 650

Per

cen

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of

sstu

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ith

con

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%)


Singapore, 19Hong Kong, 19

South Korea, 13

Taiwan, 15

Japan, 15

0

20

40

60

80

100

350 400 450 500 550 600 650

Per

cen

tage

of

stu

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ith

co

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hem

aati

cs

(%)

Mathematics Achievement at grade 4

Figure 6. The relationship between students’ confidence level and achievement in TIMSS 2015



As for the international ranking of the confidence in learning mathematics and science,

Taiwanese students ranked 48 out of 49 at fourth-grade mathematics, 33 out of 39 at eighth-

grade mathematics, 28 out of 47 at fourth-grade science and 25 out of 29 at eighth-grade science.

Figure 6 presents the relationship between students’ confidence and their performance in TIMSS

2015.

3.3 Students Value Mathematics and Science

TIMSS 2015 only assessed students’ value toward science and mathematics in grade

eight. Figure 7 displays the percentage of students who value science and mathematics at grade

eight internationally. Only 10% of students in Taiwan highly valued learning mathematics, and

11% highly valued learning science. Both the percentages of students highly valuing learning

mathematics and science were lower than the international average (42% and 40%

respectively). In fact, Taiwanese students’ values toward mathematics ranked last internationally,

and their values toward science ranked the second from the last internationally.

In general, TIMSS results show that there is a negative correlation between students’

achievement and students’ attitudes toward learning mathematics and science (Martin et al.,

2016; Mullis et al., 2016). However, some countries (e.g. Singapore) can still maintain both

high achievement and positive attitudes toward learning mathematics and science.

4. Instructional Time

About the mathematics and science curriculum, we are also concerned the instructional

time spent on mathematics at grade four in addition to the above mentioned issue of Life

Science curriculum at grade four in Taiwan. Figure 8 presents the instructional time spent on

Singapore, 34

South Korea, 13Taiwan, 10

Hong Kong, 19

Japan, 110

20

40

60

80

100

350 400 450 500 550 600 650

Per

cen

tage

of

stu

den

ts

wh

o v

alu

e m

ath

emat

ics

(%)

Mathematics achievement

Singapore, 37

Japan, 9Taiwan, 11

South Korea, 13

Hong Kong, 24

0

20

40

60

80

100

350 400 450 500 550 600 650

Per

cen

tage

of

stu

den

ts

wh

o v

alu

e sc

ien

ce (

%)

Science achievement

Figure 7. The relationship between students’ value and achievement at grade 8.



mathematics at grade four and grade eight. Compared to other countries, there was relatively

less instructional time spent on mathematics in grade four. The instructional hours of mathematics

curriculum at grade four in Taiwan was ranked 36 out of 48 internationally. On average, the

instructional time spent on mathematics at grade four in Taiwan was 128 hours. On the other

hand, the hours of mathematics curriculum at eighth grade in Taiwan ranked fifth out of 39.

On average, the instructional time spent on mathematics at grade eight was 160 hours.

Taken together, the total instructional time spent on mathematics for eighth graders was more

than fourth graders in Taiwan. In contrast, Hong Kong, Japan and Singapore spent more hours

on mathematics in grade four than in grade eight. For examples, the total instructional hours

spent on mathematics curriculum in grade four in Singapore is about 201 hours, which is 57%

more than in Taiwan.

It is worth noting that students with slower cognitive development may benefit from

having more hours of mathematics curriculum. At elementary school, children differ in cognitive

development, and some students may take more time to process and learn mathematics. It would be

beneficial for elementary students to foster their own learning interests and build self-confidence

in mathematics by spending more time on thinking, experiencing, and exploring mathematics as

well as building relationship with mathematics.

5. Home Environment

Both home and school contexts have significant influences on students’ achievement in

mathematics and science (Hooper, Mullis & Martin, 2013). Students who receive abundant

South Korea, 100

Taiwan, 128

Japan, 151

Hong Kong, 159

Singapore, 201

0 50 100 150 200 250 300

Avg. of hours at grade 4

Co

un

trie

s

Taiwan, 160

Hong Kong ,

139

Singapore, 129

South Korea ,

114

Japan, 106

0 50 100 150 200 250 300

Avg. of hours at grade 8

Co

un

trie

s

Figure 8. Instruction time spent on mathematics at grade four and grade eight.



home support resources, use the same language as TIMSS assessment, and have high parental

educational expectations may have higher achievement in mathematics and science (Hooper et

al., 2013). Moreover, early literacy, numeracy, and science activity may predict fourth graders’

TIMSS achievement (Gustafsson, Hansen, & Rosén, 2013).

Regarding to the home context in Taiwan, the findings of TIMSS 2015 are listed in the

following:

1. Seventeen percent of fourth graders and 15% of eighth graders came from homes

with abundant resources for learning mathematics and science.

2. Sixty percent of fourth-grade students and 91% of eighth-grade students reported

“always” or “almost always” using the same language as used in TIMSS assessment

(i.e., Mandarin).

3. Twenty-three percent of fourth graders frequently experienced early literacy and

numeracy activities before receiving elementary education, and 52% of fourth graders

had preschool education for at least three years. Although the percentage of

frequently experiencing early literacy and numeracy activities in Taiwan was lower

than the international average (43%), the percentage of fourth graders acquiring

“great” numeracy and literacy skills by the time they started the first grade (33%)

was higher than the international average (21%).

4. Forty-nine percent of fourth graders’ parents had “very positive” attitudes toward

mathematics and science, which is lower than the international average (66%).

5. Taiwanese fourth graders’ TIMSS achievement was positively associated with home

resources for learning, early literacy and numeracy activities, and proficiency in

numeracy and literacy.

6. Taiwanese eighth graders’ TIMSS achievement had a positive correlation with home

resource and language used at home as well.

6. School Environment

TIMSS collected information related school contexts such as school location, principal

leadership, teacher availability, etc. (Hooper et al., 2013). School contexts can be indicators not

only for school quality, but also for the effectiveness of reaching curricular goals (Hooper et

al., 2013). For example, students’ achievement can be associated with schools’ emphasis on

academic success (Hoy, Tarter, & Hoy, 2006; McGuigan & Hoy, 2006; Wu, Hoy, & Tarter,

2013); A positive school climate may also lead to students’ high achievement (Greenberg,

Skidmore, & Rhodes, 2004). Overall, school contexts play an important role in students’

achievement, especially at grade eight in Taiwan. According to the results from TIMSS 2007

to 2015 in Taiwan, the variation of achievement in mathematics and science among junior high

schools was greater than it among elementary schools. In TIMSS 2015, school factors can

explain 32% and 26% variance in students’ achievement of mathematics and science



respectively at the eighth grade, but they only explain 12% and 11% variances at the fourth

grade. Additionally, the trend shows that the percentages of variances in eighth-grade

mathematics and science achievement explained by school and class factors were growing

higher.

More key findings related to school context in Taiwan are listed in the following:

1. In Taiwan, TIMSS was assessed in Mandarin. Not surprisingly, the schools with 90%

of students’ mother tongue is Mandarin had higher achievement scores than the

schools with only 50% of students whose mother tongue is Mandarin. The differences

between the two types of schools in fourth-grade mathematics and science, and

eighth-grade mathematics and science are 22, 16, 64, and 52 points respectively. As

we mentioned earlier, the gap of achievement between school compositions by students’

language use became more apparent and significant at grade eight.

2. In comparison to South Korea and Singapore, the amount of school resources still

needs to be improved for instructing mathematics and science. On average, principals

from Taiwan reported that instruction has been somewhat affected by mathematics

or science resource shortages.

3. In comparison to the international average, schools in Taiwan did not overly emphasize

academic success. According to principals’ reports, the average score of school

emphasis on academic success for elementary schools in Taiwan was 10.6, which is

slightly higher than the international average (10.0), and for junior high schools in

Taiwan, it is 10.0. According to teachers’ reports, both average scores of school

emphasis on academic success for elementary schools and for junior high schools in

Taiwan are not significantly different from the international average.

4. Compared to all participating countries, the sense of school belonging among Taiwanese

fourth graders and eighth graders was low—with both ranked third from last. In other

words, only 46% of fourth graders and 27% eighth graders in Taiwan had high sense

of school belonging (for the international average, 66% for the fourth-grade and 44%

for the eighth-grade).

5. Relating to school climate, the issue of student bullying is more sever in grade four

than in grade eight. In Taiwan, 58% of fourth graders and 86% of eighth graders

reported that they almost never experienced student bullying.

7. Teachers and Teaching Practice

In order to assess how teachers implement the curriculum goals effectively, TIMSS 2015

also collected information related to teacher preparation and experience (Hooper et al., 2013).

The key findings about teachers and teaching practice in Taiwan are listed in the following:

1. Regarding teacher availability and retention, most mathematics and science teachers

in Taiwan are well-prepared. Compared to other countries in East Asia, there was a



higher percentage of students in Taiwan who were taught by teachers with a

postgraduate university degree (39%, 36%, 51%, and 50% for fourth-grade

mathematics and science, and eighth-grade mathematics and science respectively).

Moreover, Taiwanese mathematics and science teachers’ years of teaching were

slightly above the international averages. The percentages of students in Taiwan who

were taught by teachers teaching above ten years in fourth-grade mathematics and

science were 82% and 72% (71% and 69% for the international average); the

percentages in eighth-grade mathematics and science were 66% and 62% (64% and

62% for the international average). However, in grade eight, the percentages of

Taiwanese students having teachers that majored neither in mathematics or science,

nor in mathematics or science education, increased; from TIMSS 2011 to 2015, for

mathematics, it changed from 8% to 15%, and for science, it changed from 1% to

6%. Students with teachers who neither majored in mathematics or science, nor in

mathematics or science education, presented a lower level of liking learning and self-

confidence in mathematics and science (Chang et al., 2018).

2. In-service teachers’ professional development may enhance teaching effectiveness

(Blank & de las Alas, 2009; Yoon, Duncan, Lee, Scarloss, & Shapley, 2007). Overall,

both fourth-grade and eighth-grade teachers teaching mathematics and science in

Taiwan valued their professional development in three areas: subject content,

pedagogy/instruction, and curriculum. In addition, the percentage of fourth-grade

students with mathematics teachers participating in the field of addressing individual

students’ needs was the highest among all areas of professional development (Chang

et al., 2018).

3. Regarding teachers’ perception about their work, compared to the international

averages, there were fewer mathematics and science teachers in Taiwan that reported

facing challenges or pressure at work. The proportion of Taiwanese mathematics and

science teachers “very satisfied” with their job is similar to the international average

(46%, 49%, 48%, and 42% for fourth-grade mathematics and science teachers, and

eighth-grade mathematics and science teachers respectively; 52%, 52%, 50%, and

49% correspondingly for the international average). Nevertheless, the ranking of the

job satisfaction for teachers in Taiwan is at the bottom internationally. The ranking

of job satisfaction for the fourth-grade mathematic teachers was 35, for the fourth-

grade science teachers was 27, for eight-grade mathematic teachers was 21 and for

eighth-grade science teachers was 26.

4. In consideration of learning readiness at the level of class, Taiwan had an issue that

comparing to Hong Kong, Japan and Singapore, the percentages of Taiwanese stu-

dents with teachers reporting their mathematics and science teaching “very limited”

by students’ psychological and physical needs is the highest (Chang et al., 2018).

5. There was a low frequency of student absences in Taiwan. About 83% of fourth

graders and 89% of eighth graders reported that they were “never or almost never”

absent from school. On the other hand, about 67% of fourth graders and 61% of



eighth graders across all countries reported that they were “never or almost never”

absent from school.

6. The use of Internet may encourage students to explore their interest and deepen

their knowledge in mathematics and science (Hooper et al., 2013). In Taiwan, the

majority of the eighth graders use the Internet for accessing their textbook or other

course materials (74%) and collaborating with classmates on assignments/projects

(72%) and fewer eighth graders reported using the Internet for information, articles,

or tutorials to aid in understanding mathematics (38%) or science (46%).

7. The percentages of Taiwanese students with available computers in a lesson for stu-

dents to use were only close to the international average; The percentages for

fourth-grade mathematics and science lesson, and eighth-grade mathematics and

science lesson are 30%, 47%, 28%, and 44%. In addition, whether in mathematics

or science class, eighth graders have fewer computer activities during lessons than

fourth graders. Moreover, the number of computer activities during fourth-grade

mathematics, and eighth-grade mathematics and science, is less than the interna-

tional average.

Some factors are left to the next section because of relating to the issue of cultivating

students’ attitudes toward mathematics and science, which was found since TIMSS 1999.

8. Cultivating Students’ Attitudes toward Mathematics and Science

In this section, we address the issues of Taiwanese students’ attitudes toward learning

mathematics and science, because their attitudes have remained the same as previous TIMSS

cycles. Therefore, how to cultivate students’ attitudes toward learning mathematics and science

is especially important for us to discuss. In particular, we look into teaching strategies with the

aspect of promoting students’ learning interest and confidence, because instructional

engagement may foster students’ positive attitudes in learning mathematics and science

(Savelsbergh et al., 2016). According to TIMSS 2015, it seems that engaging teaching, inquiry

teaching and collaborative learning are associated with promoting Taiwanese students’ learning

interests and confidence in mathematics and science. However, we are concerned that these

teaching strategies for promoting students’ learning interests and confidence are less

implemented in grade eight than grade four in Taiwan.

As we found in TIMSS 2015, the percentage of students who perceived having high level

of engaging teaching, inquiry teaching, or a collaborative learning atmosphere is decreasing

from fourth grade to eighth grade in Taiwan. While 51% of fourth-grade students in Taiwan

agreed that their teachers provided very engaging teaching in mathematics, only 23% of eighth-

grade students held the same opinion. Likewise, 58% of fourth-grade students in Taiwan agreed

that their teachers provide very engaging teaching in science, whereas only 21% of eighth-

grade students held this opinion. According to these data, Taiwanese students viewed that their

teachers paid less attention to inquiry activities at the eighth-grade level than the fourth-grade

level. Furthermore, Taiwanese students also viewed that their teachers may put less emphasis



on collaborative learning activities in science course at the eighth-grade level than at the fourth-

grade level in Taiwan. In comparison to 82% of fourth graders, only 34% of eighth graders in

Taiwan perceived having a good collaborative atmosphere in their science course. Regarding

to the aspect of increasing students’ learning interest and confidence in mathematics and

science, there is still improving area for teaching strategies regarding to promote students’

learning interests and confidence.

In addition, for the purpose of promoting students’ learning interest and confidence in

mathematics and science, assigning appropriate amount of homework might be helpful. TIMSS

results suggest an association between the amount of homework and students’ learning

achievement as well as interests in science and mathematics at grade eight. In the eighth grade,

Taiwanese students who spend between 45 minutes to three hours on mathematics or science

homework had higher achievement in TIMSS. Students who spend less than 45 minutes on

their homework had lower achievement in science and/or mathematics. Interestingly, students

who spend over 3 hours on their homework presented lowest interest and self-confidence in

learning mathematics and science. These results could be a reference in teaching practice and

training teachers.

9. Summary of TIMSS 2015 for Taiwan

From TIMSS 1999 to 2015, the overall students’ mathematics and science achievement in

Taiwan has been steady and outstanding. However, mathematics and science education in

Taiwan have two issues based on the previous and the current findings of TIMSS. First,

mathematics and science education in Taiwan is effective for students to maintain high

achievement, but it attenuates students’ positive attitudes in learning mathematics and science.

In other words, students in Taiwan paid more attention to the cognitive domain than affective

domain. Except for fourth-grade science, most of the students in Taiwan have continually

presented negative attitudes including “dislike,” “lack of confidence,” and “disregard the

importance” in regard to learning mathematics and science in comparison to other countries.

To promote students’ positive attitudes, we suggest that teachers take inquiry teaching approach,

establish collaborative learning atmosphere and assign appropriate amount of homework.

Second, the rural-urban gap in mathematics and science achievement at grade eight is a

rising issue in Taiwan. The issue of rural-urban gap is also associate with high percentage of

lagging students (below the international intermediate benchmark) in Taiwan, because most of

lagging students in TIMSS 2015 resided in rural areas. This indicates that there might be

educational inequity regarding mathematics and science achievement in Taiwan. According to

the data from TIMSS 2003 to TIMSS 2015, the highest rate of Taiwanese lagging students in

metropolitan area is 10%, except for eighth-grade science in TIMSS 2007. In the near future,

we hope to cut down the rate of Taiwanese lagging students to less than 10 % in both urban

and rural area.

In addition to the above two issues, we found several critical issues related to elementary

and middle school education in Taiwan through cross-countries comparisons. We encourage

that future researchers and educators in Taiwan to explore and examine in the following issue:



1. Students have low sense of belonging in school.

2. Bullying at schools is a serious issue in grade four.

3. Mathematics and science teachers indicate low satisfaction at work.

4. The teaching of mathematics and science at grade eight does not foster student

engagement.

5. Inquiry learning and collaborative learning are emphasized in eighth-grade science less

than in fourth-grade science.

6. Fourth-graders’ achievement in Life Science is relatively lower than other content do-

mains in science achievement.



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