Taiwan's Mathematics and Science Education in TIMSS 2015

Home , 2015 in Taiwan, Fourth grade

EXECUTIVE SUMMARY - 1 -

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]

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 - 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.

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015

EXECUTIVE SUMMARY - 3 -

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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 - 4 - EXECUTIVE SUMMARY

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 Mathematics Science Grade 4 Grade 8 Grade 4 Grade 8

Cycle 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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 5 - three subjects (Mullis et al., 2016). While comparing the achievement among the three subjects, 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 Geometric Number Data Display Shapes & Measures

Rank 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) Norway Norway 8 Kazakhstan 552 (4.0) 559 (3.5) 566 (3.0) (Grade 5) (Grade 5) 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://timssandpirls.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 Life Science Physical Science Earth Science

Rank 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) Norway 8 Hungary 550 (3.4) Finland 547 (2.3) 549 (3.8) (Grade 5) 9 Hong Kong 550 (3.7) Slovenia 546 (2.4) Singapore 546 (3.7) Norway 10 546 (2.6) Poland 540 (2.1) Kazakhstan 542 (5.4) (Grade 5） 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.

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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 Number Algebra Geometry Data & Chance

Rank 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) Norway 6 Ireland 544 (3.3) Russia 558 (5.2) Russia 536 (5.6) 542 (3.2) (Grade 9) 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) Norway 9 529 (2.6) Israel 517 (4.7) Slovenia 522 (2.8) Ireland 534 (3.8) (Grade 9) 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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 7 - 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 Biology Chemistry Physics Earth Science

Rank 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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 - 8 - EXECUTIVE SUMMARY 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 Mathematics Science Grade 4 Grade 8 Grade 4 Grade 8 6 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 Mathematics Science Grade 4 Grade 8 Grade 4 Grade 8

Cycle 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.

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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 9 - 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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 - 10 - EXECUTIVE SUMMARY percentage of lagging students in eighth-grade science (only one percent lower than the highest percentage).

15 Mathematics:Grade 4 11 11 10 9 8 8 7 7 6

students (%) 6 5 4 5

Percentage Percentage of lagging 3 3 3 2 0 2003 2007 2011 2015 TIMSS Cycle Mathematics: Grade 8 15 15 15 15 14 13 12 13 12 12 12 10 10 11 11 9 10 10 8 8 8 7

students (%) 6 7 7 6

5 Percentage Percentage of lagging

0 1999 2003 2007 2011 2015 TIMSS Cycle

Science: Grade 4 20 18 16 14 15 15 14 13 11 12 10 12 10 10 students (%) 7 5 5

Percentage Percentage of lagging 4 0 2003 2007 2011 2015 TIMSS Cycle

25 Science: Grade 8 23 20 20

） 20 20 % 19 17 （ 16 15 15 15 15 14 14 15 14 14 12 13 11 students 10 11

Percentage Percentage of lagging 10

5 1999 2003 2007 2011 2015 TIMSS Cycle

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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 11 -

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.

Mathematics: Grade 4 Mathematic:Grade 8

24 22 21

25 25 16 13 20 12 11 20 15 12 13 12 7 15 15 8 7 6 5 10 10 10 9 7 5 5 5 4 4 3 5 0 0 2003 2007 2011 2015

Percentage Percentage of laggingstudents (%) 2003 2007 2011 2015 Percentage Percentage of laggingstudents (%) TIMSS Cycle TIMSS Cycle

Science: Grade 4 Science : Grade 8 26 22 22 19 20 19 25 16 25 16 16 16 20 14 20 13 13 12 13 11 15 15 12 10 10 8 9 9 8 8 8 7 5 5

0 0

Percentage Percentage of laggingstudents (%) 2003 2007 2011 2015 2003 2007 2011 2015 Percentage Percentage of laggingstudents (%) TIMSS Cycle TIMSS Cycle

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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 - 12 - EXECUTIVE SUMMARY

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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 13 -

100

40 Singapore,39 Hong Kong, 35 Japan,26 20 South Korea,19

like mathematics (%)like mathematics Taiwan, 23

0 Percentage of students ofwho students Percentage 350 400 450 500 550 600 650 Mathematics achievement at grade 4

100

40 Singapore, 24 Hong Kong, 15 20

like mathematics (%)like mathematics Taiwan, 11 Japan, 9 South Korea,8

Percentage of students ofwho students Percentage 0 350 400 450 500 550 600 650 Mathematics Achievement at grade 8 100

80 Taiwan,58 Hong Kong, 57 60 Singapore, 56 Japan,53 40 South Korea,42

20 like science (%)like science 0

Percentage of students ofwho students Percentage 350 400 450 500 550 600 650 Science achievement at grade 4

100

40 Singapore,38 Hong Kong, 30 like science (%)like science 20 Taiwan,18 Japan,15 Sourth Korea,10 Percentage of students ofwho students Percentage 0 350 400 450 500 550 600 650 Science achievement at grade 8 Figure 5. The relationship between students’ level of liking mathematics or sciences and achievements at grade 4 and grade 8 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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 - 14 - EXECUTIVE SUMMARY 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. 100

(%) 40 Hong Kong, 19 20 Taiwan, 15 Singapore, 19 Japan, 15

South Korea, 13 Percentage of students with ofstudents Percentage confidence in mathemaatics mathemaatics in confidence 0 350 400 450 500 550 600 650 Mathematics Achievement at grade 4

100

(%) 40 Taiwan, 9 20 Hong Kong, 10 Singapore, 13 Japan, 5

0 South Korea, 8 confidence in mathematics mathematics in confidence Percentage of stsudents with ofstsudents Percentage 350 400 450 500 550 600 650 Mathematics achievement at grade 8 100

(%) 80

60 Taiwan, 38 40 Singapore, 26 20 Hong Kong , … South Korea, 20

Japan, 24 confidence in science science in confidence Percentage of sstudents with ofsstudents Percentage 0 350 400 450 500 550 600 650 Science achievement at grade 4

100

(%) 40 Hong Kong , 13 20 Singapore, 17 Taiwan, 9

Percentage Percentage of students Japan, 5

0 South Korea, 7 withconfidence inscience 350 400 450 500 550 600 650 Science achievement at grade 8

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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 15 -

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.

100

40 (%) Singapore, 34 Hong Kong, 19 20

Japan, 11 South Korea, 13 Percentage Percentage of students who value mathematics 0 Taiwan, 10 350 400 450 500 550 600 650 Mathematics achievement

100

40 Singapore, 37 Hong Kong, 24 20

Taiwan, 11 who value science (%) Percentage Percentage of students South Korea, 13 Japan, 9 0 350 400 450 500 550 600 650 Science achievement Figure 7. The relationship between students’ value and achievement at grade 8.

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

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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.

Taiwan, 160 Singapore, 201

Hong Kong, 159 Hong Kong ,

Japan, 151 139

Countries Countries Countries

Singapore , 129 Taiwan, 128

South Korea , 114 Japan, 106 South Korea, 100 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Avg. of hours at grade 4 Avg. of hours at grade 8 Figure 8. Instruction time spent on mathematics at grade four and grade eight.

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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 17 - 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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 - 18 - EXECUTIVE SUMMARY 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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 19 -

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 students 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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 - 20 - EXECUTIVE SUMMARY

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 students 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 international 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

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 21 - 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:

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 - 22 - EXECUTIVE SUMMARY

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 domains in science achievement.

TAIWAN’S MATHEMATICS AND SCIENCE EDUCATION IN TIMSS 2015 EXECUTIVE SUMMARY - 23 -

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