The Development of Mathematics Achievement in Secondary School

The present study focuses on the effect of students’ own characteristics on the their mathematics performance and progress. School context and climate characteristics, as well as the cluster effect of school are considered. Using the Longitudinal Study of American Youth (LSAY), where students were repeatedly measured and clustered within schools, a 3-level multilevel model is applied. Given that some demographic information, such as parent academic push, does not remain constant, the variations of these variables between the waves of the longitudinal study are taken into account. The relationship between student initial mathematics achievement and growth trajectory are also examined. The results provide a frame of reference to compare changes over time given more recent national panel studies. The Development of Math Achievement 2 The Development of Mathematics Achievement in Secondary School Individual Differences and School Effects Students’ mathematical achievements in secondary school have an influential effect on their performance in college and their future careers. Having a solid background in mathematics helps students develop sophisticated perspectives and offers more career options. The importance of mathematical learning has repeatedly been emphasized by educators and politicians (Wilkins & Ma, 2002). Both teachers and parents have paid attention to students’ performance in mathematics and their progress every year. Politicians have also called for improving students’ overall performances and closing students’ achievement gaps. Until teachers and parents recognize what factors influence their students’ mathematics achievement and improvement, they will be unable to help them make substantial academic progress. Educators have relied on many sources of information and focused on various factors that might affect students’ mathematical achievements, including students’ own backgrounds, peer environment, and parental involvement (Young, Reynolds & Walberg, 1996). In Ma and Klinger (2000), student individual characteristics, gender, age, ethnicity, and their family characteristics, marital status, socioeconomic status, were investigated. Some interaction effect was considered by Muller, Stage and Kinzie (2001) where they looked at the interaction of race-ethnicity and gender. More than a decade ago, it was criticized by Willms and Raudenbush (1989) that lacking of adequate statistical control over school characteristics had been a chief limitation for research on school effects. Still, the influence of school on students’ mathematics progress has often been The Development of Math Achievement 3 overlooked. School characteristics can often be classified into two sets of variables. One set describes the context of a school: school enrollment size, school location, and percentage of freelunch students. The other set of school level variables, often referred to as ”evaluative variables,” are associated with school climate, attempting to describe the inner working of school life, for example, school organization and expectations of students, parents, and teachers. Previous studies (Ma, 1999; Wilkins and Ma, 2002) have neglected to address this in detail. Muller et al. (2001) points out that a more dynamic approach to experiences in academic achievement is needed. Wilkins and Ma (2002) called for further detailed longitudinal studies. Cross-sectional data considering achievement have been a main source of information. Regardless of the cost, a panel study could “show the precise patterns of persistence and change in intentions” and “eliminate the confusion by showing the change of the sample in cross section study” (Babbie, 2002. p. 98-99). A panel study should be used in order to increase the explanatory and predictable power. Wilkins and Ma (2002) studied students’ initial mathematics achievement, annual progress and their relationship in the middle schools and high schools separately and reported that students who had higher initial status tended to grow faster than those from a lower starting point. Still, the cluster effect associated with schools was neglected. It is essential to explore the relationship when other environmental factors are considered. OBJECTIVES This study examines students’ initial mathematics performance and their annual progress in the secondary school. By studying the relationship of initial mathematics status and the students’ growth rates, the pattern of change is reported. This study emphasized the impact of student and school on mathematics achievement. Students’ individual, peer and family The Development of Math Achievement 4 characteristics are used to explain both initial math achievement and growth trajectories. School context variables and school climate variables are included in this study, and variances of student’s motivation and attitude will be taken into account. This research focuses on the students’ mathematics performance in secondary school. Specifically, the following research questions will be answered: 1. What are students’ initial status and the rate of growth during secondary school? 2. Do the initial status and the growth trajectory differ by student or school characteristics? Will the interactions affect students’ mathematics performances? Will the variation within students as related to motivation and attitude influence their academic progress? Will the variation within schools influence students’ academic performance? 3. Is there an existing pattern between the initial status and growth trajectory? In educational effectiveness research, multilevel models have become popular since these models take account of the hierarchical structure of the data. In the social sciences, hierarchical structured data arise routinely where the students are nested within the schools (Young et al., 1996). The multilevel structure could not be ignored, as the independent assumption of many traditional statistical analyses is violated (Muller et al., 2001). Multilevel modeling was used as the method of analysis to solve the dilemma. Though it is a relatively new approach to the analysis of hierarchically structured data, it is a refined version of multiple regression. Similar to multiple regression, it can be used to look at potentially interesting differences. The multilevel modeling can also be used to explore differences in mathematical growth trajectories (Ma, 1999). Less obvious applications of multilevel models are longitudinal research and growth research where several distinct observations are nested within individuals (Hox, 1995). In The Development of Math Achievement 5 this study, the same students were measured more than once in the longitudinal studies and the students were nested in schools. Therefore, a three-level hierarchical linear growth model is applied. The first level is to model the students’ mathematics scores on their grade levels. At the second level, student-level variables are added to model the initial status and the rate of growth. The third level of the model includes two between school equations that regressed the average initial status and average rate of growth in mathematics on several school-level covariates. MLwin is a windows-based statistical software package developed by the Multilevel Models Project for the analysis of multilevel models. It is used to analyze the three level model in this study. METHODS Data The data for the present study came from the second cohort of the stratified national probability sample of 52 schools in the Longitudinal Study of American Youth (LSAY). Beginning in the fall of 1987, the LSAY was a longitudinal panel study of public middle and high school students. About 60 seventh graders were randomly selected in each of the 52 schools, and the total sample size was 3116 students. Students were tracked from Grade 7 to Grade 12, taking mathematics and science achievement tests and completing student questionnaires annually. With a focus on mathematics and science education, background information from parents, peers and teachers was also included in the study (Miller & Hoffer, 1994). This LSAY project guaranteed anonymity, providing aggregated data. These LSAY data are available on a CD-ROM. After selecting the variables needed, the raw data could be converted into a SPSS formatted data file by the electronic codebook system. The SPSS file was then exported into an MLwin worksheet for analyses. The Development of Math Achievement 6 Variables Measurement of student mathematics achievement refers to student mathematical test scores from Grade 7 to Grade 12, using as dependent variables. The mathematics test contained questions drawn from the fields of basic mathematics, Algebra, Geometry, Quantitative literacy. Those scores were imputed scores, which were non-aberrant observed scores. They were stored as continuous variables and were comparable across grade levels within each school subject. Some data were missing because some students were absent during testing or they dropped out. Nevertheless, all the available data could be used for hierarchical linear modeling. The difference in student academic achievement could be typically explained by students’ individual characteristics and their family characteristics. For this reason, gender, race-ethnicity, the interaction of gender and race-ethnicity, age, number of parents, parents’ socioeconomic status, number of siblings, parent push and students’ attitudes are used in this study as explanatory variables at the student level. Considering students’ mathematics achievements could be influenced by their peer academic push, therefore, peer push is also included as an explanatory variable. Gender came from student self-reports obtained in the fall of 1987. Female was recoded as a dichotomous variable comparing females with males, with 0=male and 1=female. Using the recorded month and year of birth, age was calculated as the number of months since birth. The LSAY identi