3 years ago

Intra-Cohort Growth in the Inequality of Mathematics Performance

Intra-Cohort Growth in the Inequality of Mathematics Performance


students of different birth cohorts. If the Matthew effect operates in every successive birthcohort, this would imply that some institutional force, not the characteristics of a specificbirth cohort, is responsible for both reproducing and accelerating performance inequalitybetween students of different educational and socioeconomic origins. Fourth, I estimate themagnitude, and identify the characteristics, of the widening-gap phenomenon. Such ananalysis is important because the attributes of the widening-gap phenomenon may haveimplications for identifying its causes. Fifth, I investigate whether the widening gapphenomenon is associated with initial achievement levels, family background, gender, therural-urban gap, as well as between- and within-classroom differences. Specifically, Iaddress several questions in the fifth section: (a) Do those who perform better initiallyprogress more rapidly over time? (b) Does the Matthew effect occur within or betweenlevels of student socioeconomic background? (c) Does the Matthew effect operate within orbetween gender groups? (d) Does the Matthew effect broaden the urban-rural gap inmathematics performance? (e) Does the widening-gap phenomenon occur within orbetween classrooms? The sixth and final section concludes research findings. Some of theresearch questions in this study are addressed through international comparisons.2. DataThe investigate the widening-gap phenomenon, it is necessary to have data fromstudents who born around the same year and whose math performance were assessed inmultiple grade levels. This study, therefore, uses data from the TIMSS and the TEPS. TheTIMSS allows for an international comparison, so it is possible to examine thewidening-gap phenomenon in Taiwan in an international context.2.1. TIMSSThe use of the TIMSS data in this study is confined to those collected in 2003, 2007, and2011 when Taiwan was a participating country. The TIMSS 2003, 2007, and 2011 targetedstudents of two populations: those at the end of the fourth year of formal schooling, and4

those at the end of the eighth year, the equivalents of the fourth and eighth grades in mostcountries. The TIMSS adopted a two-stage clustered sample design within each country,with schools sampled in the first stage, and classrooms sampled in the second stage (Foy &Joncas, 2000). In most countries, only one classroom was randomly selected from asampled school, and when that classroom was sampled, all of the students in the classroomwere surveyed.The TIMSS achievement test was designed to reflect as many curricula as possible in allparticipating countries. To ensure that test items were appropriate and reflected differentcurricula among countries, the construction of math and science tests were based on theTIMSS curriculum frameworks, which were set by consensus and endorsed by allparticipating countries.The TIMSS test was composed of a series of multiple-choice test items and open-endedresponse questions requiring short, or more elaborate, explanations. Not all students weregiven the same test questions. To minimize the response burden on individual students,matrix-sampling techniques were used to divide the test item pool so that each sampledstudent responded to only a portion of the test questions, but a portion which nonethelesscovered all subject areas (Garden, 2000). Therefore, students answered different test itemsdepending upon which test booklets they received. On the basis of Item Response Theory,student responses were scaled to provide accurate estimates of achievement that could becompared across countries (Yamamoto, 2000). In addition, a “plausible values” method wasused to produce proficiency scores in mathematics and science. The achievement scores,therefore, are available as a set of five plausible values for every individual student in eachsubject. Country-specific statistics used in this study, such as mean, standard deviation, andscores at various percentiles of the performance distribution, were estimated five times,each time using a different plausible value. The final statistic used for analysis is theaverage of the five estimates. In the base year of TIMSS, 1995, the international proficiency5

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