Emilie Prast en Marian Hickendorff van de Universiteit Leiden verdiepen in hun keynote het thema differentiatie vanuit een meer vakdidactische insteek. Vertrekkend vanuit algemene principes van... Show moreEmilie Prast en Marian Hickendorff van de Universiteit Leiden verdiepen in hun keynote het thema differentiatie vanuit een meer vakdidactische insteek. Vertrekkend vanuit algemene principes van differentiatie voor verschillende doelgroepen zoomen zij in op differentiatie voor sterke rekenaars. Je krijgt inzicht in het belang van differentiatie voor sterke rekenaars, manieren waarop in de praktijk al wordt gedifferentieerd voor deze groep, en kansen om differentiatie voor sterke rekenaars te verbeteren. Daarbij krijg je tips om je rekenonderwijs systematisch af te stemmen op de onderwijsbehoeften van deze groep leerlingen. Show less
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... Show moreAdapting 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. Show less
Hickendorff, M.; Torbeyns, J.; Verschaffel, L. 2019
This chapter provides an overview of the current findings about (the obstacles in) primary school children’s strategy use in the domain of multi-digit arithmetic. This involves addition,... Show moreThis chapter provides an overview of the current findings about (the obstacles in) primary school children’s strategy use in the domain of multi-digit arithmetic. This involves addition, subtraction, multiplication, and division tasks in which at least one of the operands contains two or more digits. For both the additive and multiplicative domains, we provide a comprehensive framework for the classification of strategies, with two dimensions: (1) the operation that underlies the solution process and (2) the way the numbers are dealt with in computing the outcome (manipulating whole numbers or single digits). Empirical findings of children’s strategy use in the additive and multiplicative domain show that children use a variety of number-based strategies efficiently and adaptively before the introduction of the digit-based algorithms. The introduction of the digit-based algorithms seems a critical instructional event: children show a large tendency to use the digit-based algorithms once they are instructed, and they do so rather efficiently. The major obstacles children encounter in developing, selecting, or executing these strategies are their conceptual understanding, procedural fluency, and adaptive/flexible strategy selection. Show less
Hickendorff, M.; Mostert, T.M.M.; Van, Dijk C.J.; Jansen, L.L.M.; Van, der Zee L.L.; Fagginger, Auer M.F. 2017
This thesis focuses on primary school students’ mathematical ability in the Netherlands. Starting with a systematic research synthesis of performance outcomes of different mathematics programs in... Show moreThis thesis focuses on primary school students’ mathematical ability in the Netherlands. Starting with a systematic research synthesis of performance outcomes of different mathematics programs in Chapter 1, the remaining Chapters 2 to 7 report the results of six empirical studies. These studies address the determinants of students’ ability in the domain of arithmetic (addition, subtraction, multiplication, and division). Moreover, they can be said to cross the border between the academic fields of substantive (educational and cognitive) psychology on the one hand, and psychometrics on the other. Chapters 2 and 3 report on the results of secondary analyses on data collected for CITO’s national mathematics assessment in grade six (12-year-olds) focusing on the strategies students used to solve the problems. Chapters 4 and 5 aimed to more systematically investigate the distinction between mental and written solution strategies for solving division problems. Finally, Chapters 6 and 7 address the role of realistic contexts in mathematics problems, both for students in early grades as well as in grade six. The data analyzed in the empirical studies are complex, requiring advanced psychometric modeling. It is argued that latent variable models incorporating explanatory variables are appropriate to analyze data on solution strategies and performance. Show less
