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Intra-Cohort Growth in the Inequality of Mathematics Performance

Intra-Cohort Growth in the Inequality of Mathematics Performance

average performance was

average performance was significantly heightened. As a result, Taiwanese eighth gradersperformed as well as those in Singapore and South Korea, which ranked top in eighth-grademathematics performance in TIMSS 2011. These three top-performing countries did notdiffer significantly from one another in average performance in Grade 8 mathematics.Table 3 indicates that fourth-graders in Massachusetts perform equally well withfourth-graders in Taiwan and Japan. As these students progressed to Grade 8, however,students in Massachusetts and Japan perform significantly more poorly, compared to theircounterparts in Taiwan. Students in Taiwan and Massachusetts have almost the samedistribution in mathematics performance in Grade 4. By Grade 8, however, high-performingTaiwanese students perform much better than high-performing students in Massachusetts.While the U.S., as a whole, is not among the high-performing countries in mathematics,students in Massachusetts do very well from an international perspective. This suggests thatbetween-state differences in average performance in mathematics can be very significant inthe U.S., and calls for future research into whether state-differences in mathematicsperformance in the U.S. are attributable to demographic differences in student population,or differences in state and local policies.For fourth-graders in 2007, who had progressed to Grade 8 in 2011, Table 4 reportsbetween-grade changes in the percentage of students reaching the advanced internationalbenchmark and in the percentage of students failing to reach the low internationalbenchmark. Like the previous TIMSS cohort, which was four years older, students of thisTIMSS cohort also made remarkable improvement in the percentage reaching the advancedinternational benchmark, from 24% to 49%, as they progressed from Grade 4 to Grade 8.Such a dramatic improvement is not seen in other countries, as demonstrated in Table 4.While there was a significant increase in the proportion of students reaching the advancedbenchmark, there was also an increase in the percentage of students failing to reach the lowinternational benchmark, from 1% to 4%, as these Taiwanese students progressed from12

Grade 4 to Grade 8.4.1.3. Grade 7 of 2001 and Grade 9 of 2003As indicated in Tables 1 and 3, the widening gap in mathematics performance in Taiwanis exceptionally large compared with that seen in other countries, and it occurred acrossmultiple birth cohorts covered by the TIMSS. To shed additional light upon thephenomenon, I use data from a national educational longitudinal survey in Taiwan, theTEPS, which covered junior high school students born around 1989. Table 5 reports thosefindings. The standard deviation in student mathematics performance expanded from 1 inGrade 7, to 1.25 in Grade 9, for those who born around 1989. Such an expansion invariation is also apparent in Figure 2, which compares the mathematics test scoredistribution in Grade 7 with that of Grade 9. As shown in Figure 2, after students progressfrom Grade 7 to Grade 9, they perform more unequally in math. The expansion in variationexists because low-performing ninth-graders do as poorly as low-performingseventh-graders, but high-performing ninth-graders do much better than high-performingseventh-graders.This increase in variation in performance is smaller than that reported by Huang (2007,p. 180), who also used data from the TEPS and suggested an expansion in the standarddeviation from 1 to 1.4 as students moved from Grade 7 in 2001, to Grade 9 in 2003. Theinconsistency may due to the fact that Huang (2007) used a data set released to the public,which contained only 70% of the total TEPS sample. In addition, Huang did not applysample weights in his analysis. In the Appendix, Table A1 reports the TEPS findingswithout applying sample weights. When sample weights are not applied, the widening-gapphenomenon is slightly more significant, suggesting an expansion in the standard deviationof mathematics performance from 1 to 1.3 as students progressed over time from Grade 7 toGrade 9.Until the final year of lower-secondary schooling (Grade 9), the widening-gap13

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