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Gender differences in TIMSS mathematics achievement of four Asian nations: a secondary analysis
Studies in Educational Evaluation Studies in Educational Evaluation 27 (2001) 33 I-340 www.elsevier.nl/stueduc
GENDER DIFFERENCES IN TIMSS MATHEMATICS ACHIEVEMENT OF FOUR ASIAN NATIONS: A SECONDARY ANALYSIS
Soh Kay Cheng and Quek Khiok Seng
National Institute of Education, Nanyang Technological University, Singapore
Introduction Gender differences in mathematics achievement are by now a well-known fact and research in this area has a long history dating back to the seventies (e.g., Fennema, 1974). This difference has been attributed to biological origins (Benbow, 1988), socialised preferences of males and females (Shearman, 1980), and an interaction between the biological and the social factors (McGuinness & Pribram, 1979). More recently, Geary (1996) has proposed an interactionist model that embraces biological, cognitive and psychosocial influences to account for such differences. Geary argues that sexual selection in humans, operating via “associated proximate mechanisms” such as sex hormones, indirectly provides the biological influences that lead to sex differences in the development of functional cognitive and affective systems, as well as to sex differences in social preferences and cognitive styles. These, in turn, influence the mathematical development of males and females differentially in certain areas of mathematics, especially in what Geary calls the biologically-secondary mathematics abilities (described below). The associated sex differences are by no means the direct result of evolutionary pressures. Geary differentiates between two sets of mathematical abilities which he calls biologically-primary and biologically-secondary. Both males and females possess an innate set of biologically-primary mathematical abilities. These abilities are believed to be pan-cultural and include at least four numerical abilities such as numerosity, ordinality, counting, and simple arithmetic. For these, little or no differences between
0191-491X/01/$ -see front matter 0 2001 Published by Elsevier Science Ltd PII: s0191-491x(01)00028-1
332
S. K. Cheng, Q. K. Seng / Studies in Educational Evaluation 27 (2001) 33 l-340
young boys and girls have been observed. The biologically-secondary mathematical abilities emerge only through interaction with the specific social-cultural practices (e.g., prolonged formal education) that provide the requisite experiences. This set of biologicallysecondary abilities would, because of formal education, include the more complex and abstract domains of mathematics such as algebra, geometry, and calculus. In Geary’s (1996) comprehensive review, three general findings with regard to male advantage in mathematics achievement stand out. First, male achievement scores are about half a standard deviation above those of females. Second, this difference is found almost exclusively in nations where mathematics achievement is high. And, third, male advantage shows up more clearly in areas involving spatial abilities, such as geometry and measurement. Male advantage in mathematics achievement seems to be a universal phenomenon and differential participation has been proposed to explain this. At the International Commission on Mathematics Instruction Conference in 1993, practically all the participating nations reported male advantage (Hanna, 1996). The only exception was the People’s Republic of China which reported an experiment carried out in Shanghai where secondary girls outperformed boys (Tang, Zheng, & Wu, 1996). In this experiment, the teachers adopted a non-sexist attitude in teaching mathematics to girls, cultivated the girls’ confidence in their ability to learn mathematics, provided girls with individual coaching, and stressed vigorously the foundations of learning mathematics. The Shanghai experiment might be an isolated case in the gamut of gender difference studies carried out in various nations but, nevertheless, it highlights the possibility of a reversal of the direction of such difference through attitudinal and instructional changes. That such a reversal might be effected in more places may not be totally unfounded. Already there is a decreasing gap in gender differences in mathematics performance in more places, as Hanna (2000) concludes from her examination of the findings of the three International Association for the Evaluation of Educational Achievement (IEA) studies - FIMS (1964), SIMS (1980-82) and TIMSS (1995). In her words, “the most significant contribution of the IEA international comparisons, in the context of gender studies, is to have revealed that several countries have in effect achieved gender equity in mathematics” (p. 16). It is noted here that Hanna’s findings may not be interpreted as a trend either in terms of more countries achieving gender equity in mathematics or toward a reversal in gender difference in mathematics. However, in the light of the Shanghai study and Hanna’s review, the better performance of the seventh and eighth grade girls of Singapore, as compared with the boys, in the TIMSS is worthy of research effort and its cultural and instructional implications need to be explored. Method Previous research (Geary, 1996) has indicated that sex differences in mathematics achievement are observed more often in nations in which formal mathematics education is in place and the level of student achievement is relatively high. The present study, therefore, restricts itself to comparing only the seventh and eighth grades in the four Asian nations that head the list of the nations involved in the TIMSS, namely, Singapore, Japan, Korea, and Hong Kong. Using the published TIMSS data (Beaton, Mullis, Martin,
S. K. Cheng, Q. K. Seng /Studies in Educational Evaluation 27 (2001) 331-340
333
Gonzalez, Kelly, & Smith, 1996), correlations were calculated to investigate the degree to which achievement profiles are similar between boys and girls within each nation and, also, across nations within sex. The effect sizes were then estimated, within the context of the nations compared, with the convention that a positive effect size indicates male advantage in mathematics achievement, a negative one indicates female advantage, and a zero difference indicates comparable performance between sexes within a nation. Results Table 1 shows the means and the percentages of passes for boys and girls of the four nations on the TIMSS mathematics test as a whole and the six sub-tests. These data were culled from Tables 2.1 and 2.2 of the TIMSS report (Beaton et al., 1996) Table 1:
Achievement of Seventh and Eighth Graders BOYS HK* KOR JAP SIN HK
Seventh Grade Overall mean 570 584 576 601 556 Overall % 66 68 68 73 64 Function and number sense 67 72 72 79 66 Geometry 69 71 64 68 66 Algebra 66 64 73 68 65 Data presentation, analysis & probability 69 75 73 72 67 Measurement 63 64 63 70 60 Proportionality 56 59 57 70 54 Eighth Grade Overall mean 597 615 609 642 577 Overall % 72 73 74 79 68 Function and number sense 74 76 76 83 70 Geometry 74 77 79 76 71 Algebra 71 70 72 75 69 Data presentation, analysis & probability 73 80 79 79 69 Measurement 68 69 68 77 62 Proportionality 63 62 62 75 60 *HK = Hong Kong, KOR = Korea, JAP = Japan, and SIN = Singapore
GIRLS KOR JAP
SIN
567 65 70 70 63 70 60 53
565 66 70 63 72 72 60 53
601 73 79 69 68 73 70 71
598 70 72 73 69 75 62 61
600 73 75 80 72 77 67 60
645 79 84 77 77 79 77 76
Before comparing the boys and girls on their performance, it is interesting, first of all, to find out (a) whether they have similar achievement profiles in terms of the six sub-areas tested by the TIMSS test and (b) whether nations are similar in their achievement profiles, controlled for sex. To answer these questions, Spearman’s rank difference correlations were calculated for the percentages of passes for the six sub-tests. As shown by the very high cross-sex correlations in Table 2, the achievement profiles of the boys and girls are very similar for all four nations at both the seventh and eighth grades. This suggests the effect of instruction since the boys and girls would have had undergone very similar national mathematics programmes of their respective nations.
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Cheng, Q. K. Seng /Studies in Educational Evaluation 27 (2001) 331-340
Table 2: Inter-Nation Spearman Correlations for Seventh and Eighth Grades HK
BOYS KOR JAP
SIN
HK
GIRLS KOR JAP
SIN
SeventhGrade Boys HongKong Korea Japan Singapore
1.oo
.88*
.62
I .oo
.66
.08 Sl
1.oo
.08
.96* .93* 1.oo*
.97*
1.oo
Girls
1.oo
Hong Kong Korea Japan Singapore
.96*
1.oo
.74 .65
1.oo
.34 .27 -.03 1.oo
Eighth Grade Boys Hong Kong Korea Japan Singapore Girls Hong Kong Korea Japan Singapore
1.oo
.81*
I .oo
.87* .99*
1.oo
.59 .55 .50
.97*
1.oo* .99*
I .oo
.89*
I .oo
.75 1.oo
.90* .94*
I .oo
.59 .70 .58
1.oo
* p .05
Cross-nation-within-sex correlations are significant for some pairs of nations but not the others. While Hong Kong, Korea, and Japan tend to have significant correlations among them, Singapore is obviously standing alone. These findings suggest that the mathematics programme and instruction in Singapore are somewhat distinct from those of the other three Asian nations. Table 3 shows the sex differences within each nation. The differences were obtained by subtracting the means and percentages of passes for boys from those for girls. Thus, positive differences denote boys’ superiority in achievement. As can be seen in Table 3, greater sex differences are found for Hong Kong and Korea, and to a lesser degree for Japan, but least in Singapore. In fact, in Singapore girls tended to perform better than boys. To ascertain the extent of such sex differences as observed in Table 3, the sex differences were converted to effect sizes by expressing the differences in standard deviation units as shown in Table 4. Applying the criteria suggested for evaluating effect sizes by Rosenthal and Rosnow (1984), it is observed that Korea has consistently shown high boys’ superiority while sex differences for Japan are lower. This is true for both seventh and eighth grades. As for Hong Kong, boys’ superiority is moderate at the seventh grade but increases to become large at the eighth grade. It is of worthy of note that, for Singapore, there is distinctly high girls’ superiority, as indicated by the negative effect sizes, at both grade levels.
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335
Table 3: Sex Differences of Seventh and Eighth Grades
Seventh Grade Overall mean Overall % Function and number sense Geometry Algebra Data presentation, analysis & probability Measurement Proportionality Eighth Grade Overall mean Overall % Function and number sense Geometry Algebra Data presentation, analysis & probability Measurement Proportionality
SD
Mean
HK
KOR
JAP
SIN
14 2
I
17 3 2
11 2 2
0 0 0
3
I
1
-1
1.0
I
I
1
0
2 3 2
5 4 6
1
-1
3 4
0 -1
0.8 1.8 2.5 2.8
7.4 1.3 1.0 1.6 0.5 2.5 1.7 3.0
20 4 4 3 2 4 6 3
17 3 4 4
9
-3
1
0
1 -1
-1 -1 -2 0
10.8 2.0 2.0 1.3 0.3 2.8 3.5 1.3
10.3 1.8 2.4 2.6 1.7 2.2 3.5 1.7
I
0
5 7
2 1
0
I
2
-1
10.5 1.8 1.3
Table 4: Effect Sizes of Seventh and Eighth Grades
Seventh Grade Overall mean Overall % Function and number sense Geometry Algebra Data presentation, analysis & probability Measurement Proportionality Mean Eighth Grade Overall mean Overall % Function and number sense Geometry Algebra Data presentation, analysis & probability Measurement Proportionality Mean SD
HK
KOR
0.5 0.2 -0.3 1.2 0.5 0.1 0.3 -0.3 0.3
0.9 1.0 0.8 0.0 0.5 1.3 0.9 1.1 0.8
0.1 0.2 0.8 0.0 0.5 -0.3 0.3 0.4 0.2
-1.4 -1.4 -1.3 -1.2 -1.5 -1.1 -1.4 -1.3 -1.3
0.9 1.1 0.8 0.7 1.0 0.6 0.7 1.0 0.9 0.2
0.6 0.5 0.8 1.0 0.4 1.0 1.0 -0.1 0.7 0.4
-0.2 -0.5 -0.4 -0.9 -0.1 -0.3 -0.7 0.4 -0.3 0.4
-1.3 -1.1 -1.2 -0.9 -1.3 -1.2 -1.0 -1.3 -1.2 0.2
JAP
SIN
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With reference to the six TIMSS sub-tests, at the seventh grade level, sex differences are more even across the subtests for Singapore (as indicated by the small standard deviation of 0.1) but erratic for the other three nations (with SDS varying from .3 for Japan to .5 for Hong Kong). At the eighth grade level, sex differences remain rather even for Singapore, now joined by Hong Kong, but still varying for Korea and Japan. Discussion and Conclusion In the TIMSS, Singapore came in at the top of the achievement list for mathematics. Various explanations have been suggested to account for this and a secondary analysis by Soh (1999) shows that mathematics-related social attitudes and out-of-class coaching are related to performance. Although the amount of homework has been evoked as a contributing factor to mathematics achievement in cross-nation studies (Stanley, Huang, & Zu, 1986), a negative correlation between homework and performance on TIMSS test has also been reported by Soh (1999). The findings of this secondary analysis of the TIMSS data supports Geary’s (1996) interactionist model, in which biologically-secondary mathematical abilities are posited to emerge only with prolonged exposure to certain specialised social-cultural practices. The female advantage in Singapore suggests there might be certain social-cultural practices here that influence the development of cognitive and affective systems supporting the biologically-secondary mathematical abilities in the boys and girls alike. The better performance of girls in Singapore weakens the claim of a wholly biological account (Benbow, 1985) of gender differences in terms of male dominance in mathematics. On the other hand, in the other three countries compared in this secondary analysis, there is still a male advantage in mathematical performance that takes hold in around the seventh and eighth grades, as compared to no gender difference in earlier grades. This is noticeably strongest in Korea followed by Hong Kong (Table 3). Thus, the argument for a biological account of male advantage in the development of mathematics ability cannot be totally precluded. Soh (1999) observes that where a particular country has performed well in TIMSS, there was also a good match between that country’s mathematics curriculum and the performance demands of the TIMSS assessment tasks. A separate secondary analysis of the TIMSS data by Soh (2000) highlights the substantial contributions of specific socialcultural expectations and instructional practices in Singapore to her performance in TIMSS. These two observations might be taken as indications of the influence of specific socialcultural practices in the development of the biologically-secondary mathematical abilities. In this case, the supported biologically-secondary mathematical abilities would be those measured by the TIMSS tests. Although the IEA assures quality in data collection (Martin & Mullis, 1996), formal testing of this nature is very much a form of cultural practice and the task of eliminating cultural nuances in the tests and the test items is still a major challenge. Indeed, the care which IEA took in crafting gender-fair test items in TIMSS could have enabled the girls to compete on equitable grounds with the boys. Table 4 shows that sex differences in favour of girls are relatively more even in Singapore than the other three countries. However, it is interesting to note that sex differences within Singapore are slightly more variable in the eighth grade than the seventh.
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A question raised here is whether this slightly greater variability is indicative of the gradual emergence of the cognitive systems that support habitat navigation which, Geary (1996) argues, favour males in mathematical problem solving and geometry. Evidence from two local studies (Kaur, 1990; Foong & Loy, 1998) endorses his argument. Kaur (1990) reported better achievement by the Singapore boys in mathematics taken at the GCE “0” level, with prominent male advantage in the compulsory questions that tested spatial ability and female advantage in questions that demand skills (e.g., application of an algorithm) that could be acquired with drill and practice. Foong and Loy (1998) also found male advantage in mathematical reasoning tasks in two comparable groups of boys and girls in the GCE “0” Level year. These Singapore students completed a validated version of the CollisRomberg Mathematical Profile (Collis, Romberg, & Jurdak, 1992) that was developed for assessing levels of mathematical reasoning based on the Structure of Observed Learning Outcome (SOLO) taxonomy (Biggs & Collis, 1982). That girls convincingly outperformed boys in Singapore in the TIMSS also places Singapore apart from the three countries compared in this secondary analysis. Across countries, judging by the high cross-nation-within-sex correlations in Table 2, the countrydifferences could have arisen because Singapore’s approach to mathematics instruction is distinct from those of the other three countries. However, within Singapore itself, what would account for the girls’ better performance over the boys? A non-sexist mathematics learning environment might be a crucial factor. The Shanghai study (Tang, Zheng, & Wu, 1996) found girls outperforming boys in a non-sexist learning environment and Soh (1999, 2000) suggests such a non-sexist learning environment is present in Singapore, where teachers as well as parents, peers and society, expect boys and girls alike to do well in mathematics. Moreover, in Singapore, mathematics is not seen as a male domain simply because there are many more female than male mathematics teachers here. The “reversed” result of better performance in geometry by the girls in Singapore at seventh and eighth grades is also worth mentioning since many studies (Geary, 1996) reported that males generally performed better than females in geometry. In his interactionist model, Geary (1996) argues that sexual selection directly shapes sex differences in cognitive systems that support habitat navigation and so favour the male especially in mathematical problem solving and geometry. He did not rule out the possibility of females co-opting these cognitive systems after prolonged exposure to the specific social-cultural practices supporting their development. Rather his model posits bidirectional influences between sex differences in mathematics-related activities and sex differences in cognitive systems that support habitat navigation. If Geary’s (1996) interactionist account were tenable, the better performance of girls in the Shanghai study and in Singapore in the TIMSS would suggest that sustained exposure to certain social and instructional endeavours and mathematics-related social attitudes might close the gender gap. Gazzaniga (1992) argues in support of this idea in his book Nature’s mind: The biological roots of thinking, emotions, sexuality, language, and intelligence. He claims that environmental pressures lead to selection of certain neural pathways and the atrophy of others. Thus, whereas both sexes are predisposed to acquiring certain mathematical abilities, environmental factors determine the specific abilities that develop.
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Evaluation 27 (2001) 331-340
A secondary analysis of this nature cannot preclude the possibility of females outperforming males in mathematics in other non-Asian countries. The better performance of girls in Singapore than those in Hong Kong and, to lesser extent, Korea and Japan, suggests that a gender-equitable education system is achievable and is therefore worthy of further study. In Singapore, for instance, is this female advantage related to the greater multicultural mix (race and ethnicity) of students as compared to students in the other countries? At a micro-level, where Singapore boys and girls performed equally well on the subtests, would knowing how they performed differentially in certain items (Holland & Wainer, 1993) shed light on the biologically-secondary mathematically ability differences? Finally, because highly-achieving formal schooling environments are considered favourable to the development of biologically-secondary mathematical abilities, the availability in Singapore of several top primary and secondary schools which are also single-sex offers opportunities for an in-depth study of an interactionist model of gender differences. References Beaton, A.E., Mullis, I.V.S., Martin, M.O., Gonzalez, E.J., Kelly, D.L., and Smith, T.A. (1996). achievement in the middle school years: IEA’s Third International Mathematics and Science Study. Chestnut Hill, MA: TIMSS International Study Centre, Boston College. Mathematics
Benbow, C.P. (1988). Sex differences in mathematical reasoning ability in intellectually talented preadolescents: Their nature, effects, and possible causes. Behavioral and Brain Sciences, II, 169-232. Biggs, J.B., & Collis, K.F. (1982). Evaluating the quality oflearning: York: Academic Press.
The SOLO taxonomy. New
Collis, K.F., Romberg, T.A., & Jurdak, M.E. (I 992). Collis-Romberg mathematical problem solving projiles. Hawthorn, Victoria: Australian Council for Educational Research. Fennema, E. (I 974). Mathematics Mathematics Education, 5 (3), l26- 139.
learning and the sexes: A review. Journal
of Research
in
Foong, P.Y. & Loy C.F. (1998). Mathematical reasoning: Do males and females think alike? In M.L. Quah, & W.K. Ho (Ed%), Thinking processes: Going beyond the surface curriculum: A selection of papers from the Concurrent Sessions of the 71hInternational Conference on Thinking. Singapore 1997, 19% , 204. Singapore: SprintPrint-Prentice Hall. Gazzaniga, M.S. (1992). Nature’s mind: The biological roots of thinking, emotions, sexuality, language, and intelligence. New York: Basic Books. Geary, D.C. (1996). Sexual selection and sex differences Brain Sciences, 19 (2) 229-284. Hanna, G. (Ed.). (1996). Towards Dordrecht: Kluwer.
in mathematical abilities. Behavioral and
gender equity in mathematics
Hanna, G. (2000). Declining gender differences Mathematical Education, 32 (I), 1 I - 17.
education:
An ICMI study.
from FIMS to TIMSS. International
Reviews on
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Collis, K.F., Romberg, T.A., & Jurdak, M.E. (1992). Collis-Romberg mathematical problem solving profiles. Hawthorn, Victoria: Australian Council for Educational Research. Fennema, E. (1974). Mathematics Mathematics Education, 5 (3), 126-139.
learning and the sexes: A review. Journal
of Research
in
Foong, P.Y. & Loy C.F. (1998). Mathematical reasoning: Do males and females think alike? In M.L. Quah, & W.K. Ho (Eds.), Thinkingprocesses: Going beyond the surface curriculum: A selection of papers from the Concurrent Sessions of the 71hInternational Conference on Thinking. Singapore 1997, 198204. Singapore: SprintPrint-Prentice Hall. Gazzaniga, M.S. (1992). Nature’s mind: The biological roots of thinking, emotions, sexuality, language, and intelligence. New York: Basic Books. Geary, DC. (I 996). Sexual selection and sex differences Brain Sciences, 19 (2), 229-284. Hanna, G. (Ed.). (1996). Towards Dordrecht: Kluwer.
in mathematical abilities. Behavioral and
gender equity in mathematics
Hanna, G. (2000). Declining gender differences Mathematical Education, 32 (I), 1 l-l 7.
education:
An ICMI study.
from FIMS to TIMSS. International Reviews on
Holland, P. W., & Wainer, H. (Ed.). (1993). Dtfjerential item functioning.
Hillsdale, NJ: Lawrence.
Kaur, B. (1990). Girls and mathematics in Singapore: The case of O-level mathematics. Burton (Ed.), Gender and mathematics: An internationalperspective (pp. 98112). London: Cassell.
In L.
Martin, M.O., & Mullis, V.S., (Eds.). (1996). Third International Mathematics and Science Study: Quality assurance in data collection. Chestnut Hill, MA: Center for the Study of Testing, Evaluation, and Educational Policy, Boston College. McGuinness, D. , & Pribram, H.K. (1979). The origins of sensory bias in the development of gender differences in perception and cognition. In M. Bortner (Ed.), Cognitive growth and development: Essays in memory of Herbert G. Birch. New York: BrunnerMazel. Rosenthal, R., & Rosnow, analysis. New York: McGraw-Hill.
R.L. (1984). Essentials
of behavioural research methods and data
Shearman, J. (1980). Mathematics, spatial visualisation, and related factors: Changes in girls and boys, grades 8-l I. Journal of Educational Psychology, 27, 476-82. Soh, K.C. (I 999). Three G7 and the Little Asian dragons in TIMMS mathematics grade. The Mathematics Educator, A (2) 126-37.
at the fourth
Soh, K.C. (2000). Why Singapore eighth graders did better among the Asians in the TIMSS mathematics: A secondary analysis. The Mathematics Educator, 5 (l/2), 169-179. Stanley, J.C., Huang, J., & Zu, X. (1986). SAT-M scores of highly selected students in Shanghai tested when less than 13 years old. College Board Review, 140, lo- 13,28-29.
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Tang, R.F., Zheng, Q.M., & Wu, S.Q. (1996). Gender and mathematics education: A snapshot of China. In G. Hanna, G. (Ed.), Towards gender equity in mathematics education: An ICMZ study (pp. 271276). Dordrecht: Kluwer.
The Authors SOH KAY CHENG is Senior Fellow at the National Institute of Education, Nanyang Technological University, Singapore. His research interests include measurement and evaluation in education and psychology, creativity, cultural studies, bilingualism, and school effectiveness. QUEK KHIOK SENG is Lecturer at the National Institute of Education, Nanyang Technological University, Singapore. His main research interests are in educational assessment, mathematics education, and context and cognition.
GENDER DIFFERENCES IN TIMSS MATHEMATICS ACHIEVEMENT OF FOUR ASIAN NATIONS: A SECONDARY ANALYSIS
Soh Kay Cheng and Quek Khiok Seng
National Institute of Education, Nanyang Technological University, Singapore
Introduction Gender differences in mathematics achievement are by now a well-known fact and research in this area has a long history dating back to the seventies (e.g., Fennema, 1974). This difference has been attributed to biological origins (Benbow, 1988), socialised preferences of males and females (Shearman, 1980), and an interaction between the biological and the social factors (McGuinness & Pribram, 1979). More recently, Geary (1996) has proposed an interactionist model that embraces biological, cognitive and psychosocial influences to account for such differences. Geary argues that sexual selection in humans, operating via “associated proximate mechanisms” such as sex hormones, indirectly provides the biological influences that lead to sex differences in the development of functional cognitive and affective systems, as well as to sex differences in social preferences and cognitive styles. These, in turn, influence the mathematical development of males and females differentially in certain areas of mathematics, especially in what Geary calls the biologically-secondary mathematics abilities (described below). The associated sex differences are by no means the direct result of evolutionary pressures. Geary differentiates between two sets of mathematical abilities which he calls biologically-primary and biologically-secondary. Both males and females possess an innate set of biologically-primary mathematical abilities. These abilities are believed to be pan-cultural and include at least four numerical abilities such as numerosity, ordinality, counting, and simple arithmetic. For these, little or no differences between
0191-491X/01/$ -see front matter 0 2001 Published by Elsevier Science Ltd PII: s0191-491x(01)00028-1
332
S. K. Cheng, Q. K. Seng / Studies in Educational Evaluation 27 (2001) 33 l-340
young boys and girls have been observed. The biologically-secondary mathematical abilities emerge only through interaction with the specific social-cultural practices (e.g., prolonged formal education) that provide the requisite experiences. This set of biologicallysecondary abilities would, because of formal education, include the more complex and abstract domains of mathematics such as algebra, geometry, and calculus. In Geary’s (1996) comprehensive review, three general findings with regard to male advantage in mathematics achievement stand out. First, male achievement scores are about half a standard deviation above those of females. Second, this difference is found almost exclusively in nations where mathematics achievement is high. And, third, male advantage shows up more clearly in areas involving spatial abilities, such as geometry and measurement. Male advantage in mathematics achievement seems to be a universal phenomenon and differential participation has been proposed to explain this. At the International Commission on Mathematics Instruction Conference in 1993, practically all the participating nations reported male advantage (Hanna, 1996). The only exception was the People’s Republic of China which reported an experiment carried out in Shanghai where secondary girls outperformed boys (Tang, Zheng, & Wu, 1996). In this experiment, the teachers adopted a non-sexist attitude in teaching mathematics to girls, cultivated the girls’ confidence in their ability to learn mathematics, provided girls with individual coaching, and stressed vigorously the foundations of learning mathematics. The Shanghai experiment might be an isolated case in the gamut of gender difference studies carried out in various nations but, nevertheless, it highlights the possibility of a reversal of the direction of such difference through attitudinal and instructional changes. That such a reversal might be effected in more places may not be totally unfounded. Already there is a decreasing gap in gender differences in mathematics performance in more places, as Hanna (2000) concludes from her examination of the findings of the three International Association for the Evaluation of Educational Achievement (IEA) studies - FIMS (1964), SIMS (1980-82) and TIMSS (1995). In her words, “the most significant contribution of the IEA international comparisons, in the context of gender studies, is to have revealed that several countries have in effect achieved gender equity in mathematics” (p. 16). It is noted here that Hanna’s findings may not be interpreted as a trend either in terms of more countries achieving gender equity in mathematics or toward a reversal in gender difference in mathematics. However, in the light of the Shanghai study and Hanna’s review, the better performance of the seventh and eighth grade girls of Singapore, as compared with the boys, in the TIMSS is worthy of research effort and its cultural and instructional implications need to be explored. Method Previous research (Geary, 1996) has indicated that sex differences in mathematics achievement are observed more often in nations in which formal mathematics education is in place and the level of student achievement is relatively high. The present study, therefore, restricts itself to comparing only the seventh and eighth grades in the four Asian nations that head the list of the nations involved in the TIMSS, namely, Singapore, Japan, Korea, and Hong Kong. Using the published TIMSS data (Beaton, Mullis, Martin,
S. K. Cheng, Q. K. Seng /Studies in Educational Evaluation 27 (2001) 331-340
333
Gonzalez, Kelly, & Smith, 1996), correlations were calculated to investigate the degree to which achievement profiles are similar between boys and girls within each nation and, also, across nations within sex. The effect sizes were then estimated, within the context of the nations compared, with the convention that a positive effect size indicates male advantage in mathematics achievement, a negative one indicates female advantage, and a zero difference indicates comparable performance between sexes within a nation. Results Table 1 shows the means and the percentages of passes for boys and girls of the four nations on the TIMSS mathematics test as a whole and the six sub-tests. These data were culled from Tables 2.1 and 2.2 of the TIMSS report (Beaton et al., 1996) Table 1:
Achievement of Seventh and Eighth Graders BOYS HK* KOR JAP SIN HK
Seventh Grade Overall mean 570 584 576 601 556 Overall % 66 68 68 73 64 Function and number sense 67 72 72 79 66 Geometry 69 71 64 68 66 Algebra 66 64 73 68 65 Data presentation, analysis & probability 69 75 73 72 67 Measurement 63 64 63 70 60 Proportionality 56 59 57 70 54 Eighth Grade Overall mean 597 615 609 642 577 Overall % 72 73 74 79 68 Function and number sense 74 76 76 83 70 Geometry 74 77 79 76 71 Algebra 71 70 72 75 69 Data presentation, analysis & probability 73 80 79 79 69 Measurement 68 69 68 77 62 Proportionality 63 62 62 75 60 *HK = Hong Kong, KOR = Korea, JAP = Japan, and SIN = Singapore
GIRLS KOR JAP
SIN
567 65 70 70 63 70 60 53
565 66 70 63 72 72 60 53
601 73 79 69 68 73 70 71
598 70 72 73 69 75 62 61
600 73 75 80 72 77 67 60
645 79 84 77 77 79 77 76
Before comparing the boys and girls on their performance, it is interesting, first of all, to find out (a) whether they have similar achievement profiles in terms of the six sub-areas tested by the TIMSS test and (b) whether nations are similar in their achievement profiles, controlled for sex. To answer these questions, Spearman’s rank difference correlations were calculated for the percentages of passes for the six sub-tests. As shown by the very high cross-sex correlations in Table 2, the achievement profiles of the boys and girls are very similar for all four nations at both the seventh and eighth grades. This suggests the effect of instruction since the boys and girls would have had undergone very similar national mathematics programmes of their respective nations.
334
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Cheng, Q. K. Seng /Studies in Educational Evaluation 27 (2001) 331-340
Table 2: Inter-Nation Spearman Correlations for Seventh and Eighth Grades HK
BOYS KOR JAP
SIN
HK
GIRLS KOR JAP
SIN
SeventhGrade Boys HongKong Korea Japan Singapore
1.oo
.88*
.62
I .oo
.66
.08 Sl
1.oo
.08
.96* .93* 1.oo*
.97*
1.oo
Girls
1.oo
Hong Kong Korea Japan Singapore
.96*
1.oo
.74 .65
1.oo
.34 .27 -.03 1.oo
Eighth Grade Boys Hong Kong Korea Japan Singapore Girls Hong Kong Korea Japan Singapore
1.oo
.81*
I .oo
.87* .99*
1.oo
.59 .55 .50
.97*
1.oo* .99*
I .oo
.89*
I .oo
.75 1.oo
.90* .94*
I .oo
.59 .70 .58
1.oo
* p .05
Cross-nation-within-sex correlations are significant for some pairs of nations but not the others. While Hong Kong, Korea, and Japan tend to have significant correlations among them, Singapore is obviously standing alone. These findings suggest that the mathematics programme and instruction in Singapore are somewhat distinct from those of the other three Asian nations. Table 3 shows the sex differences within each nation. The differences were obtained by subtracting the means and percentages of passes for boys from those for girls. Thus, positive differences denote boys’ superiority in achievement. As can be seen in Table 3, greater sex differences are found for Hong Kong and Korea, and to a lesser degree for Japan, but least in Singapore. In fact, in Singapore girls tended to perform better than boys. To ascertain the extent of such sex differences as observed in Table 3, the sex differences were converted to effect sizes by expressing the differences in standard deviation units as shown in Table 4. Applying the criteria suggested for evaluating effect sizes by Rosenthal and Rosnow (1984), it is observed that Korea has consistently shown high boys’ superiority while sex differences for Japan are lower. This is true for both seventh and eighth grades. As for Hong Kong, boys’ superiority is moderate at the seventh grade but increases to become large at the eighth grade. It is of worthy of note that, for Singapore, there is distinctly high girls’ superiority, as indicated by the negative effect sizes, at both grade levels.
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Table 3: Sex Differences of Seventh and Eighth Grades
Seventh Grade Overall mean Overall % Function and number sense Geometry Algebra Data presentation, analysis & probability Measurement Proportionality Eighth Grade Overall mean Overall % Function and number sense Geometry Algebra Data presentation, analysis & probability Measurement Proportionality
SD
Mean
HK
KOR
JAP
SIN
14 2
I
17 3 2
11 2 2
0 0 0
3
I
1
-1
1.0
I
I
1
0
2 3 2
5 4 6
1
-1
3 4
0 -1
0.8 1.8 2.5 2.8
7.4 1.3 1.0 1.6 0.5 2.5 1.7 3.0
20 4 4 3 2 4 6 3
17 3 4 4
9
-3
1
0
1 -1
-1 -1 -2 0
10.8 2.0 2.0 1.3 0.3 2.8 3.5 1.3
10.3 1.8 2.4 2.6 1.7 2.2 3.5 1.7
I
0
5 7
2 1
0
I
2
-1
10.5 1.8 1.3
Table 4: Effect Sizes of Seventh and Eighth Grades
Seventh Grade Overall mean Overall % Function and number sense Geometry Algebra Data presentation, analysis & probability Measurement Proportionality Mean Eighth Grade Overall mean Overall % Function and number sense Geometry Algebra Data presentation, analysis & probability Measurement Proportionality Mean SD
HK
KOR
0.5 0.2 -0.3 1.2 0.5 0.1 0.3 -0.3 0.3
0.9 1.0 0.8 0.0 0.5 1.3 0.9 1.1 0.8
0.1 0.2 0.8 0.0 0.5 -0.3 0.3 0.4 0.2
-1.4 -1.4 -1.3 -1.2 -1.5 -1.1 -1.4 -1.3 -1.3
0.9 1.1 0.8 0.7 1.0 0.6 0.7 1.0 0.9 0.2
0.6 0.5 0.8 1.0 0.4 1.0 1.0 -0.1 0.7 0.4
-0.2 -0.5 -0.4 -0.9 -0.1 -0.3 -0.7 0.4 -0.3 0.4
-1.3 -1.1 -1.2 -0.9 -1.3 -1.2 -1.0 -1.3 -1.2 0.2
JAP
SIN
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With reference to the six TIMSS sub-tests, at the seventh grade level, sex differences are more even across the subtests for Singapore (as indicated by the small standard deviation of 0.1) but erratic for the other three nations (with SDS varying from .3 for Japan to .5 for Hong Kong). At the eighth grade level, sex differences remain rather even for Singapore, now joined by Hong Kong, but still varying for Korea and Japan. Discussion and Conclusion In the TIMSS, Singapore came in at the top of the achievement list for mathematics. Various explanations have been suggested to account for this and a secondary analysis by Soh (1999) shows that mathematics-related social attitudes and out-of-class coaching are related to performance. Although the amount of homework has been evoked as a contributing factor to mathematics achievement in cross-nation studies (Stanley, Huang, & Zu, 1986), a negative correlation between homework and performance on TIMSS test has also been reported by Soh (1999). The findings of this secondary analysis of the TIMSS data supports Geary’s (1996) interactionist model, in which biologically-secondary mathematical abilities are posited to emerge only with prolonged exposure to certain specialised social-cultural practices. The female advantage in Singapore suggests there might be certain social-cultural practices here that influence the development of cognitive and affective systems supporting the biologically-secondary mathematical abilities in the boys and girls alike. The better performance of girls in Singapore weakens the claim of a wholly biological account (Benbow, 1985) of gender differences in terms of male dominance in mathematics. On the other hand, in the other three countries compared in this secondary analysis, there is still a male advantage in mathematical performance that takes hold in around the seventh and eighth grades, as compared to no gender difference in earlier grades. This is noticeably strongest in Korea followed by Hong Kong (Table 3). Thus, the argument for a biological account of male advantage in the development of mathematics ability cannot be totally precluded. Soh (1999) observes that where a particular country has performed well in TIMSS, there was also a good match between that country’s mathematics curriculum and the performance demands of the TIMSS assessment tasks. A separate secondary analysis of the TIMSS data by Soh (2000) highlights the substantial contributions of specific socialcultural expectations and instructional practices in Singapore to her performance in TIMSS. These two observations might be taken as indications of the influence of specific socialcultural practices in the development of the biologically-secondary mathematical abilities. In this case, the supported biologically-secondary mathematical abilities would be those measured by the TIMSS tests. Although the IEA assures quality in data collection (Martin & Mullis, 1996), formal testing of this nature is very much a form of cultural practice and the task of eliminating cultural nuances in the tests and the test items is still a major challenge. Indeed, the care which IEA took in crafting gender-fair test items in TIMSS could have enabled the girls to compete on equitable grounds with the boys. Table 4 shows that sex differences in favour of girls are relatively more even in Singapore than the other three countries. However, it is interesting to note that sex differences within Singapore are slightly more variable in the eighth grade than the seventh.
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A question raised here is whether this slightly greater variability is indicative of the gradual emergence of the cognitive systems that support habitat navigation which, Geary (1996) argues, favour males in mathematical problem solving and geometry. Evidence from two local studies (Kaur, 1990; Foong & Loy, 1998) endorses his argument. Kaur (1990) reported better achievement by the Singapore boys in mathematics taken at the GCE “0” level, with prominent male advantage in the compulsory questions that tested spatial ability and female advantage in questions that demand skills (e.g., application of an algorithm) that could be acquired with drill and practice. Foong and Loy (1998) also found male advantage in mathematical reasoning tasks in two comparable groups of boys and girls in the GCE “0” Level year. These Singapore students completed a validated version of the CollisRomberg Mathematical Profile (Collis, Romberg, & Jurdak, 1992) that was developed for assessing levels of mathematical reasoning based on the Structure of Observed Learning Outcome (SOLO) taxonomy (Biggs & Collis, 1982). That girls convincingly outperformed boys in Singapore in the TIMSS also places Singapore apart from the three countries compared in this secondary analysis. Across countries, judging by the high cross-nation-within-sex correlations in Table 2, the countrydifferences could have arisen because Singapore’s approach to mathematics instruction is distinct from those of the other three countries. However, within Singapore itself, what would account for the girls’ better performance over the boys? A non-sexist mathematics learning environment might be a crucial factor. The Shanghai study (Tang, Zheng, & Wu, 1996) found girls outperforming boys in a non-sexist learning environment and Soh (1999, 2000) suggests such a non-sexist learning environment is present in Singapore, where teachers as well as parents, peers and society, expect boys and girls alike to do well in mathematics. Moreover, in Singapore, mathematics is not seen as a male domain simply because there are many more female than male mathematics teachers here. The “reversed” result of better performance in geometry by the girls in Singapore at seventh and eighth grades is also worth mentioning since many studies (Geary, 1996) reported that males generally performed better than females in geometry. In his interactionist model, Geary (1996) argues that sexual selection directly shapes sex differences in cognitive systems that support habitat navigation and so favour the male especially in mathematical problem solving and geometry. He did not rule out the possibility of females co-opting these cognitive systems after prolonged exposure to the specific social-cultural practices supporting their development. Rather his model posits bidirectional influences between sex differences in mathematics-related activities and sex differences in cognitive systems that support habitat navigation. If Geary’s (1996) interactionist account were tenable, the better performance of girls in the Shanghai study and in Singapore in the TIMSS would suggest that sustained exposure to certain social and instructional endeavours and mathematics-related social attitudes might close the gender gap. Gazzaniga (1992) argues in support of this idea in his book Nature’s mind: The biological roots of thinking, emotions, sexuality, language, and intelligence. He claims that environmental pressures lead to selection of certain neural pathways and the atrophy of others. Thus, whereas both sexes are predisposed to acquiring certain mathematical abilities, environmental factors determine the specific abilities that develop.
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A secondary analysis of this nature cannot preclude the possibility of females outperforming males in mathematics in other non-Asian countries. The better performance of girls in Singapore than those in Hong Kong and, to lesser extent, Korea and Japan, suggests that a gender-equitable education system is achievable and is therefore worthy of further study. In Singapore, for instance, is this female advantage related to the greater multicultural mix (race and ethnicity) of students as compared to students in the other countries? At a micro-level, where Singapore boys and girls performed equally well on the subtests, would knowing how they performed differentially in certain items (Holland & Wainer, 1993) shed light on the biologically-secondary mathematically ability differences? Finally, because highly-achieving formal schooling environments are considered favourable to the development of biologically-secondary mathematical abilities, the availability in Singapore of several top primary and secondary schools which are also single-sex offers opportunities for an in-depth study of an interactionist model of gender differences. References Beaton, A.E., Mullis, I.V.S., Martin, M.O., Gonzalez, E.J., Kelly, D.L., and Smith, T.A. (1996). achievement in the middle school years: IEA’s Third International Mathematics and Science Study. Chestnut Hill, MA: TIMSS International Study Centre, Boston College. Mathematics
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The Authors SOH KAY CHENG is Senior Fellow at the National Institute of Education, Nanyang Technological University, Singapore. His research interests include measurement and evaluation in education and psychology, creativity, cultural studies, bilingualism, and school effectiveness. QUEK KHIOK SENG is Lecturer at the National Institute of Education, Nanyang Technological University, Singapore. His main research interests are in educational assessment, mathematics education, and context and cognition.