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Adapting education to students’ diverse educational needs is widely recognised as an important, but also complex aspect of effective teaching. In this chapter, we provide insight into how Dutch primary school teachers implement differentiation based on students’ current mathematics achievement level. We review evidence from four independent samples in which the same teacher self-assessment questionnaire was administered (N = 907 teachers in total), supplemented with qualitative data from various perspectives: external observers, students, and teachers. Based on these sources of information, we identify the following general patterns. Teachers generally implement achievement-based differentiation at least to some extent. That is, student achievement is monitored, and efforts are taken to adapt instruction or practice to students’ current achievement level. This is often organised using within-class homogeneous achievement groups. While low-achieving students regularly receive additional instruction, specific instruction for high-achieving students is uncommon. Refined, qualitative strategies to diagnose students’ individual educational needs and to adapt education to these individual needs are also used relatively infrequently. These relatively infrequently used strategies point to areas for improvement. Furthermore, the flexibility of within-class achievement groups seems to vary and deserves more attention in future research and practice.

De rekenmethode geeft vaak suggesties voor verwerking op meerdere niveaus, maar wat kun je als leerkracht zelf doen om je onderwijs beter af te stemmen op de onderwijsbehoefte van de kinderen? Hoe pak je differentiatie aan?

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.

Item does not contain fulltext Motivation and achievement are known to be related, but the nature of this relation is complex. This study investigated the relations between achievement and several core aspects of motivation for mathematics in primary school: self-efficacy, self-concept, task value, and mathematics anxiety (N = 4306 students of grade 2 - 6). Moreover, it was investigated whether these relations were similar or different for low-achieving, average-achieving, and high-achieving students. Students completed a standardised mathematics achievement test at T1 and T3 and a mathematics motivation questionnaire at T2. Working memory was measured as a covariate. Self-efficacy and self-concept were combined into a single perceived competence variable due to their high intercorrelation. T1 achievement positively predicted perceived competence and task value and negatively predicted mathematics anxiety. Only perceived competence had a significant effect on T3 achievement after controlling for T1 achievement and working memory, and significantly mediated between previous and subsequent achievement. This pattern of effects was largely similar across achievement groups, although the effects of previous achievement on task value and perceived competence were stronger for high-achieving students. In each achievement group, perceived competence was the only motivational variable with a significant effect on subsequent achievement over and above the effects of previous achievement. 13 p.

The diversity of students’ achievement levels within classrooms has made it essential forteachers to adapt their lessons to the varying educational needs of their students(‘differentiation’). However, the term differentiation has been interpreted in diverse waysand there is a need to specify what effective differentiation entails. Previous reports oflow to moderate application of differentiation underscore the importance of practicalguidelines for implementing differentiation. In two studies, we investigated how teachersshould differentiate according to experts, as well as the degree to which teachers alreadyapply the recommended strategies. Study 1 employed the Delphi technique and focusgroup discussions to achieve consensus among eleven mathematics experts regarding afeasible model for differentiation in primary mathematics. The experts agreed on a fivestepcycle of differentiation: (1) identification of educational needs, (2) differentiatedgoals, (3) differentiated instruction, (4) differentiated practice, and (5) evaluation ofprogress and process. For each step, strategies were specified. In Study 2, theDifferentiation Self-Assessment Questionnaire (DSAQ) was developed to investigate howteachers self-assess their use of the strategies recommended by the experts. Whileteachers (N = 268) were moderately positive about their application of the strategiesoverall, we also identified areas of relatively low usage (including differentiation forhigh-achieving students) which require attention in teacher professional development.Together, these two studies provide a model and strategies for differentiation in primarymathematics based on expert consensus, the DSAQ which can be employed in futurestudies, and insights into teachers’ self-assessed application of specific aspects ofdifferentiation.

Working memory is an important predictor of academic performance, and of math performance in particular. Most working memory tasks depend on one-to-one administration by a testing assistant, which makes the use of such tasks in large-scale studies time-consuming and costly. Therefore, an online, self-reliant visual–spatial working memory task (the Lion game) was developed for primary school children (6–12 years of age). In two studies, the validity and reliability of the Lion game were investigated. The results from Study 1 (n = 442) indicated satisfactory six-week test–retest reliability, excellent internal consistency, and good concurrent and predictive validity. The results from Study 2 (n = 5,059) confirmed the results on the internal consistency and predictive validity of the Lion game. In addition, multilevel analysis revealed that classroom membership influenced Lion game scores.We concluded that the Lion game is a valid and reliable instrument for the online computerized and self-reliant measurement of visual– spatial working memory (i.e., updating).