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Intra-Cohort Growth in the Inequality of Mathematics Performance

Intra-Cohort Growth in the Inequality of Mathematics Performance

4.5. Do Those Who Do

4.5. Do Those Who Do Better Initially Progress More Rapidly Over Time?A possible explanation for the widening-gap phenomenon in Taiwan is that those whoperform better in mathematics initially may progress more rapidly over time. To test thishypothesis, I use data derived solely from the TEPS. This is because the TEPS is alongitudinal study and its mathematical IRT scores are suitable for between-gradecomparisons. I divided the sample from an earlier data collection wave into 10 decile groupsaccording to students’ mathematics IRT scores, then estimated the average growth inmathematics scores for each of these ten groups in a later follow-up survey. The results ofthis exercise are found in Table 9. For Taiwanese students who attended Grade 7 in 2001,and Grade 9 in 2003, those who performed better in mathematics in Grade 7 tended toimprove more in terms of their test scores two years later. This is particularly evident whenthe highest-performing and the lowest-performing decile groups are excluded. The growthof the top-performing group may have been suppressed by a ceiling effect, while thelowest-performing group may have had more room to grow than other groups.4.6. Does the Widening-Gap Phenomenon Occur Between or Within SocioeconomicGroups?I use data from the TEPS to address the question whether the widening-gap phenomenonoccur between or within socioeconomic groups. I took the father’s level of education toindicate a student’s socioeconomic background. The father’s level of education describedaccording to one of five categories: less than high school, high school, some college, college,and having a graduate degree.Table 10 presents the results for the analysis using data from the TEPS. For those whoattended Grade 7 in 2001 and Grade 9 in 2003, the widening-gap phenomenon occurred toall students, but the phenomenon was twice as significant among students with lessfavorable family backgrounds than among students with more favorable backgrounds.Furthermore, students from more favorable family backgrounds progressed more rapidly in16

mathematics performance as they moved through the grades.5. Discussions and ConclusionsThe widening-gap phenomenon in mathematics performance, which occurred prior toGrade 9 in Taiwan, is unique from an international perspective. It is unique because no othercountry has as large a widening gap as that found in Taiwan. The phenomenon is uniquealso because that it accompanies a significant increase in average performance and aremarkable increase in the percentage of students reaching advanced internationalbenchmark. Hong Kong, for example, also had a widening-gap phenomenon in mathematicsperformance, but mathematics performance did not improve significantly.Both male and female Taiwanese students in elementary and junior high schoolsexperienced the widening-gap phenomenon in mathematics performance. The widening-gapphenomenon is common to all residential areas, whether they are cities, towns, or thecountry side, and it occurred mainly within classrooms. No other country showed such ahigh level of within-classroom variation, moving from a very low level of within-classroomvariation in Grade 4, to extremely heterogeneous classrooms in Grade 8. This dramaticchange in within-classroom variation between grade levels is distinctive from aninternational perspective.The widening-gap phenomenon in Taiwan is associated with findings that those whoperformed better initially progressed more rapidly over time. Additionally, students withmore favorable family backgrounds improved more significantly over time, and theydisplayed a less significant widening-gap phenomenon amongst themselves.In Taiwanese elementary and junior high schools, most variation in student performanceoccurs within classrooms. In Grade 8, most Taiwanese schools and classrooms areextremely heterogeneous internally in terms of mathematics performance. Thus, rather thanbeing concentrated on a few classrooms or schools, poorly-performing students in Taiwanare dispersed widely across classrooms. Therefore, a policy targeting low-performing17

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