Differentiation in primary mathematics education

Abstract

Adapting education to the diverse needs of students with a broad range of academic achievement levels is a challenge for teachers. The goals of this dissertation were (1) to specify what readiness-based differentiation entails in primary mathematics education (2) to investigate the degree to which teachers implement the various recommended strategies (3) to develop and evaluate a teacher professional development (PD) programme about differentiation in primary school mathematics and (4) to investigate the reciprocal relations between achievement and several aspects of motivation for mathematics both in general and for subsamples of low-achieving, average-achieving, and high-achieving students. In the first stage of the project, experts reached consensus on the cycle of differentiation, a prescriptive model for differentiation consisting of the following five steps: diagnosing educational needs, differentiated goals, differentiated instruction, differentiated practice, and evaluation of progress and process. Specific strategies were recommended for each step. In the second stage of the project, a PD programme was developed and evaluated in a large-scale study involving thirty whole primary schools divided over three cohorts. Cohort 1 received the PD in Year 1, Cohort 2 received the PD in Year 2 and Cohort 3 was the control condition during two years. At baseline, most teachers already implemented some aspects of differentiation, including ability grouping and differentiation of the practice tasks. Refined, qualitative diagnosis and adaptations to students’ educational needs, as well as instructional attention for the specific needs of high-achieving students were implemented relatively infrequently. Effects of the PD programme on teachers’ observed instructional behaviour could not be unequivocally demonstrated, although there were indications for long-term effects on the implementation of differentiation in Cohort 1 in Year 2. Effects of the PD programme on student achievement differed between the cohorts. In Cohort 1, the PD had a small positive effect on mathematics achievement growth and this applied to low-achieving, average-achieving and high-achieving students. However, these effects could not be replicated in Cohort 2 in Year 2. Regarding the relations between motivation and achievement, it was found that the effects of previous achievement were generally stronger for high-achieving students, whereas the effects of motivation on subsequent achievement were similar across achievement groups. For students of all achievement levels, perceived competence was the only motivational variable which was not only influenced by previous achievement, but also predicted subsequent achievement after controlling for previous achievement and working memory. These findings have the following implications. The cycle of differentiation provides teachers and teacher educators with concrete guidelines for implementing differentiation in primary mathematics education. Moreover, specific areas for improvement were identified. The results of the PD programme show that PD about differentiation has the potential to improve student achievement growth in mathematics. Importantly, students of all achievement levels could profit equally. However, such effects are not guaranteed, indicating that enhancing differentiation is not straightforward. The bidirectional relation between perceived competence and achievement raises new questions regarding the effects of differentiated instruction on the perceived competence of low-achieving, average-achieving and high-achieving students.