The present study aims to provide a systematic understanding of how perspective-taking ability contributes to primary-school students’ cooperative behaviours and learning outcomes. The present... Show moreThe present study aims to provide a systematic understanding of how perspective-taking ability contributes to primary-school students’ cooperative behaviours and learning outcomes. The present study is frontline as we combined person-oriented (e.g., describing patterns of behaviours based on individual characteristics), process-oriented (e.g., examining factors affecting the quality of cooperative behaviours), and effect-oriented (e.g., examining the effect of cooperative learning on individual learning outcomes) analytical approaches within one research framework. In addition, we adhered to the multi-dimensional nature of perspective-taking ability and differentiated between social and cognitive perspective-taking ability while taking into account the contribution of perspective-taking ability at both the individual level and group level (i.e., heterogeneous and homogeneous perspective-taking ability groups) to cooperative behaviour profiles and learning outcomes of primary-school children. Based on transcribed episodes of interaction of 115 fifth-grade students, four different profiles of cooperative behaviours were discerned: captains, hard workers, switchers, and passive participants. We found that these profiles are related to perspective taking conceptualized at the group level, but not to individual-level perspective-taking ability. Profile membership, cognitive perspective-taking ability, and group-level perspective-taking ability could not predict students’ learning outcomes. Social perspective-taking ability and reading comprehension did positively predict learning outcomes. Our findings add to existing knowledge as they suggest that the influence of perspective-taking ability on cooperative behaviours and learning outcomes is susceptible to the conceptualization (i.e., cognitive vs. social) and measurement level (i.e., individual vs. group level) of perspective-taking ability. Show less
sing the choice/no-choice methodology we investigated Dutch fourth graders’ (N = 124) adaptive use of the indirect addition strategy to solve subtraction problems. Children solved multidigit... Show moresing the choice/no-choice methodology we investigated Dutch fourth graders’ (N = 124) adaptive use of the indirect addition strategy to solve subtraction problems. Children solved multidigit subtraction problems in one choice condition, in which they were free to choose between direct subtraction and indirect addition, and in two no-choice conditions, in which they had to use either direct subtraction or indirect addition. Furthermore, children were randomly assigned to mental computation, written computation, or free choice between mental and written computation. One third of the children adaptively switched their strategy according to the number characteristics of the problems, whereas the remaining children consistently used the same strategy. The likelihood to adaptively switch strategies decreased when written computation was allowed or required, compared to mandatory mental computation. On average, children were adaptive to their own speed differences but not to the accuracy differences between the strategies. 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.; Dijk, C.J. van; Jansen, L.L.M.; Van der Zee, L.L.; Fagginger Auer, M.F. 2019
Welke factoren in het onderwijsleerproces hangen samen met de rekenwiskundeprestaties van leerlingen in het basisonderwijs? Deze vraag stond centraal in een review-studie die op verzoek van de... Show moreWelke factoren in het onderwijsleerproces hangen samen met de rekenwiskundeprestaties van leerlingen in het basisonderwijs? Deze vraag stond centraal in een review-studie die op verzoek van de Inspectie van het Onderwijs en NRO is uitgevoerd. De focus lag op factoren in het onderwijsleerproces die beïnvloedbaar zijn: knoppen waaraan gedraaid zou kunnen worden. Allereerst schetsen we een beeld van de rekenwiskundeprestaties van Nederlandse basisschoolleerlingen aan de hand van de meest recente peilingsonderzoeken in groep 6 en 8 en de eindtoetsen. Uit deze gegevens blijkt ook dat de verschillen in rekenwiskundeprestaties tussen leerlingen maar voor een klein deel, hooguit 10 procent, toe te schrijven zijn aan verschillen in het rekenonderwijs dat zij krijgen op school. Vervolgens zijn de resultaten uit internationaal en Nederlands onderzoek in kaart gebracht om de vraag te beantwoorden welke factoren van het onderwijsleerproces effectief zijn. Dit leverde een grote verzameling op van kenmerken van de les die positief samenhangen met reken-wiskundeprestaties, zoals een verscheidenheid aan interventies met specifieke instructie- en werkvormen, het toepassen van technologische en niet-technologische hulpmiddelen en formatieve toetsing. Het is opvallend dat er geen robuuste onderzoeksresultaten zijn gevonden over de samenhang van leerstofaanbod of rekenmethode met reken-wiskundeprestaties. Verder vonden we een aantal kenmerken van de leerkracht, zoals vakinhoudelijke kennis over rekenen, en van de leerling, zoals rekenangst, die samenhangen met reken-wiskundeprestaties. Over de rol van kenmerken van de klas en van de school, zoals aanwezigheid van een rekencoördinator, zijn weinig onderzoeksresultaten gevonden. Alles bij elkaar genomen lijkt de leerkracht de cruciale rol te vervullen in het vormgeven van goed reken-wiskundeonderwijs. Show less
Fagginger Auer, M.F.; Hickendorff, M.; Putten, C.M. van 2018
We aimed to investigate upper elementary children's strategy use in the domain of multidigit division in two instructional settings: the Netherlands and Flanders (Belgium). A cross‐sectional sample... Show moreWe aimed to investigate upper elementary children's strategy use in the domain of multidigit division in two instructional settings: the Netherlands and Flanders (Belgium). A cross‐sectional sample of 119 Dutch and 122 Flemish fourth to sixth graders solved a varied set of multidigit division problems. With latent class analysis, three distinct strategy profiles were identified: children consistently using number‐based strategies, children combining the use of column‐based and number‐based strategies, and children combining the use of digit‐based and number‐based strategies. The relation between children's strategy profiles and their instructional setting (country) and grade were generally in line with instructional differences, but large individual differences remained. Furthermore, Dutch children more frequently made adaptive strategy choices and realistic solutions than their Flemish peers. These results complement and refine previous findings on children's strategy use in relation to mathematics instruction. Show less
Hickendorff, M.; Edelsbrunner, P.A.; McMullen, J.; Schneider, M.; Tresize, K. 2017
This article gives an introduction to latent class, latent profile, and latent transition models for researchers interested in investigating individual differences in learning and development. The... Show moreThis article gives an introduction to latent class, latent profile, and latent transition models for researchers interested in investigating individual differences in learning and development. The models allow analyzing how the observed heterogeneity in a group (e.g., individual differences in conceptual knowledge) can be traced back to underlying homogeneous subgroups (e.g., learners differing systematically in their developmental phases). The estimated parameters include a characteristic response pattern for each subgroup, and, in the case of longitudinal data, the probabilities of transitioning from one subgroup to another over time. This article describes the steps involved in using the models, gives practical examples, and discusses limitations and extensions. Overall, the models help to characterize heterogeneous learner populations, multidimensional learning outcomes, non-linear learning pathways, and changing relations between learning processes. The application of these models can therefore make a substantial contribution to our understanding of learning and individual differences. Show less
Inferring mathematical strategy use from primary school students' written work Verbal reports of mathematical strategy use can be inaccurate and can influence students' spontaneous strategy choices... Show moreInferring mathematical strategy use from primary school students' written work Verbal reports of mathematical strategy use can be inaccurate and can influence students' spontaneous strategy choices, and the effort involved in collecting them limits sample sizes. These disadvantages can be overcome with a straightforward non-verbal method: students' strategy use can often be inferred from the calculation steps that they write down as a natural part of their solution process. In this study, results of verbal and written strategy identification are compared in a recent large-scale mathematics assessment. In addition, the application of written strategy identification is illustrated with two examples. The first application is a study in which students' strategy use on a large-scale assessment was related to their teachers' mathematics instruction. The second application is a study which compared the strategy use of a large group of students on problems presented with and without a realistic context. Finally, the possibilities and limitations of written strategy identification are discussed. Show less
Mathematics education and assessments increasingly involve arithmetic problems presented in context: a realistic situation that requires mathematical modeling. This study assessed the effects of... Show moreMathematics education and assessments increasingly involve arithmetic problems presented in context: a realistic situation that requires mathematical modeling. This study assessed the effects of such typical school mathematics contexts on two aspects of problem solving: performance and strategy use. Multidigit arithmetic problems presented in two conditions-with and without a realistic context-were solved by 685 sixth graders from The Netherlands. Regarding performance, the same (latent) ability dimension was involved in solving both types of problems, and the presence of a context increased the difficulty level of the division problems but not of other operations. Regarding strategy use, strategy choice and strategy accuracy were not affected by the presence of a problem context. In sum, the presence of a typical context in multidigit arithmetic problems had no marked effects on students' problem-solving behavior, which held for different subgroups of students with respect to language ability and gender. Show less
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
Hickendorff, M.; Heiser, W.J.; Putten, C.M. van; Verhelst, N.D. 2009
