School mathematics performance: a longitudinal case study
In South African schooling, two sectors exist in which 75% of schools achieve significantly lower than the upper 25% of schools, resulting in a bimodal education system. However, the level of mathematics performance of South African learners from schools of all quintiles is far below international standards. There is a dearth of longitudinal studies investigating mathematics performance and it appears as though none have been done on South African learner performance in mathematics from Grade 1 to 12. The aim of this study was to investigate the mathematics performance from Grade 1 to 12 of boys attending a South African ex-Model C, single-gender school. A two-pronged approach was used. Firstly, the mathematics performance of learners who took Mathematics up to Grade 12 was compared to that of those who opted for Grade 12 Mathematical Literacy instead. Secondly, the effectiveness of mathematics performance in lower grades in predicting that in subsequent grades was investigated. In order to do so, the promotion marks of learners in eight consecutive cohorts (Grades 1 to 12) at the same school were used. Archived data were retrieved from SA-SAMS and the school’s hardcopies of learners’ results. Learners matriculating at the school in either Mathematics or Mathematical Literacy were separated into a Mathematics-set (M-set) (n=302) or a Mathematical Literacy set (ML-set) (n=160) respectively. The “Proc Mixed” procedure was used to analyse the data. The Mixed Model for Repeated Measures (MMRM) with an unstructured covariance matrix for repeated measures within learners was fitted, using Restricted Maximum Likelihood (REML), fitting fixed effects of cohort, grade and grade within a cohort. Regression analysis was performed to establish correlations and thus the precision with which current grade marks predict future grade marks. Ryan and Deci’s Self-Determination Theory and Piaget’s Cognitive Theory were useful in providing possible explanations for the results. The mathematics performance of the two sets from Grade 1 to 7 followed a similar trend, but on average, the M-set performed 10% better than the ML-set. Mathematics performance was stable in the Foundation Phase. While national results generally reflect a decrease in marks from Grade 3 to 4, the learners in the current study showed an increase in mean marks. There was a decline in mean marks in Grade 6, which had the weakest correlations with those in other grades than any other grades with one another. The highest mean mark for Mathematics (across all grades) was in Grade 7. The steepest decline in mean marks was from Grade 7 to 9; however, the ML-set experienced a much greater decline, causing the gap between the two sets to widen to 22%. The implications arising from these results are numerous. For instance, the ML-set achieved mean marks that were below those of the M-set. The set that started out lower in Grade 1 ended lower in Grade 7. This underscores the importance of learners starting formal education in the strongest position possible as this trajectory is generally maintained throughout their schooling. Contrary to national averages, the mean marks increased from Grade 3 to 4. The learners’ minimum of four years’ exposure to English, as the LOLT, prior to Grade 4 could account for this. The decline in mean marks from Grade 7 to 9 coincides with other simultaneously occurring factors, namely puberty, the transition to high school and the introduction of more abstract concepts such as algebra. Learners in the Senior Phase face many difficulties and adjustments. It is in the interest of the learners’ education that they are supported and guided, especially during these changes.