Titel Deelnemers "Korte inhoud" "Numerical magnitude understanding of natural and rational numbers in secondary-school students: a number line estimation study" "Wim Van Dooren, Koen Luwel" "Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students’ numerical magnitude understanding: number type (natural vs. rational) and structure of the notation system (place-value-based vs. non-placevalue-based). To do so, a 2 (number type) × 2 (structure of the notation system) within-subjects design was created in which 61 secondary-school students estimated the position of four notations on a number line: natural numbers (e.g., 214 on a 0–1000 number line), decimals (e.g., 0.214 on a 0–1 number line), fractions (e.g., 3/14 on a 0–1 number line), and separated fractions (3 on a 0–14 number line). In addition to response times and error rates, eye tracking captured students’ on-line solution process. Students had slower response times and higher error rates for fractions than the other notations. Eye tracking revealed that participants encoded fractions longer than the other notations. Also, the structure of the notation system influenced participants’ eye movement behavior in the endpoint of the number line more than number type. Overall, our findings suggest that when a notation contains both sources of difficulty (i.e., rational and non-place-value-based, like fractions), this contributes to a worse understanding of its numerical magnitude than when it contains only one (i.e., natural but non-place-value-based, like separated fractions, or place-valuebased but rational, like decimals) or neither (i.e., natural and place-value-based, like natural numbers) of these sources of difficulty." "Strategy flexibility in mathematics" "Lieven Verschaffel" "In this article we review the research on the flexible or adaptive use of solution strategies in school mathematics, with a focus on the most recent work in the field. After a short introduction, we provide an overview of the various ways in which strategy flexibility has been conceptualized and investigated in the research literature. Then we review the research that has looked at the relationship between strategy flexibility and task proficiency, followed by studies that analyzed the association of strategy flexibility and other learner variables, including learners’ age, general mathematical ability, prior knowledge, executive functions, gender, and affect. Studies addressing the socio-cultural and educational embeddedness of strategy flexibility are reviewed next, and, finally, we discuss the intervention studies that have tried to stimulate learners’ strategy flexibility by means of various instructional approaches. While this review reveals that strategy flexibility is increasingly recognized as an important and valuable construct in research and practice of mathematics education, and that recently substantial progress has been made in our understanding of this construct, there are many aspects of it that are still not well-understood and that need further investigation means of various instructional approaches. While this review reveals that strategy flexibility is increasingly recognized as an important and valuable construct in research and practice of mathematics education, and that recently substantial progress has been made in our understanding of this construct, there are many aspects of it that are still not well-understood and that need further investigation." "A teacher's choice: Preschool teachers’ selection and use of picture books for mathematics instruction" "Suzanne Splinter, Fien Depaepe, Lieven Verschaffel, Joke Torbeyns" "Children’s subtraction by addition strategy use and their subtraction-related conceptual knowledge" "Stijn Van Der Auwera, Bert De Smedt, Joke Torbeyns, Lieven Verschaffel" "A teacher's choice: Preschool teachers’ selection and use of picture books for mathematics instruction" "Suzanne Splinter, Fien Depaepe, Lieven Verschaffel, Joke Torbeyns" "Future preschool teachers' mathematical questions during shared book reading" "Emke Op 't Eynde, Fien Depaepe, Wim Van Den Noortgate, Lieven Verschaffel, Joke Torbeyns" "Recent studies demonstrated that the adult-preschooler interaction during shared book reading (SBR) contributes to its effectiveness (Mol et al., 2008). The level of abstraction, or complexity, of the mathematical questions adults formulate during SBR serves as an indicator of the interaction quality. We aimed to investigate the chance of spontaneously formulating a mathematical question and the level of abstraction of the mathematical questions future preschool teachers propose to formulate during SBR, and their association with teachers’ professional knowledge and beliefs, and type of picture book. Participants were 111 future preschool teachers. We investigated their chance of formulating a mathematical question and the level of abstraction of their mathematical questions using a video-based instrument, and distinguished between two types of picture books, namely mathematical and non-mathematical picture books. We additionally assessed their (1) mathematical content knowledge, (2) mathematical pedagogical content knowledge, and (3) beliefs about mathematics in general and about the teaching and learning of mathematics, with three online questionnaires. Data were analyzed using multilevel analyses. Results revealed that mathematical picture books increase the likelihood of formulating a mathematical question and provoked more abstract mathematical questions compared to non-mathematical picture books. There were no significant associations between teachers’ professional knowledge and beliefs and the dependent variables. Our findings point to the importance of adequately selecting picture books to stimulate mathematical preschoolers’ development via SBR, and also call for further investigations on the learning-supportive picture book characteristics and teacher characteristics." "The relationship between primary school children’s inhibition and the processing of rational numbers" "Karen De Keersmaeker, Jo Van Hoof, Wim Van Dooren" "Processing rational numbers is difficult for many children. The natural number bias is one possible explanation for why children struggle with rational numbers. It refers to the tendency to overgeneralize the properties of natural numbers. In this study, it is argued that in order to be successful in rational number tasks, individuals need to inhibit or suppress their unwanted impulses (in this case the tendency to apply natural number properties). It was investigated whether inhibition plays a role in the occurrence of the natural number bias among primary school children by administering two rational number tasks, two Stroop tasks and a questionnaire measuring inhibitory skills. The results indicated that primary school children were hampered by the natural number bias both in terms of accuracy rates and response times. Additionally, the results did not yield strong evidence for a relationship between inhibition and the occurrence of the natural number bias." "Shared picture book reading in early mathematics: A systematic literature review" "Emke Op 't Eynde, Fien Depaepe, Lieven Verschaffel, Joke Torbeyns" "Shared picture book reading (SPBR) refers to an activity in which the adult reads aloud a picture book to children and which often includes interactions about the picture book outside of the actual reading. In this systematic review, we analyzed the characteristics of the picture books that are used to stimulate early mathematics, and the frequency, quality, and effectiveness of SPBR in early mathematics. Additionally, we looked at the association between the frequency, quality, and effectiveness of this activity and the characteristics of the picture book, child, reader, and context. A systematic search in four databases yielded 49 articles that were eligible for inclusion. First, results showed that picture books contain characteristics that may both stimulate and hinder children’s mathematical development. Second, the frequency of SPBR was hardly studied, constraining current insights into this topic. Third, the quality of SPBR was mainly studied via the number and the type of mathematical utterances made by the child and/or the reader, with findings pointing to a rich variety of utterances in terms of both number and type. Fourth, SPBR was shown effective to stimulate children’s mathematical development. SPBR frequency, quality and effectiveness was hardly studied in association with picture book, child, reader, and context characteristics making it difficult to draw conclusions about their complex interplay. We end with gaps in the available research on SPBR in the domain of mathematics and offer suggestions for future research." "Incorrect ways of thinking about the size of fractions" "Jo Van Hoof, Wim Van Dooren" "The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing students’ accuracies in multiple-choice items. Evidence that supports that these incorrect ways of reasoning are indeed underlying is scarce. In the present work, we carried out interviews with 52 seventh grade students. The objective was to validate the existence of students’ incorrect ways of thinking about fraction size that were previously inferred from patterns of correct and incorrect answers to multiple-choice items, by looking at students’ verbalizations, and examine whether these ways of thinking are resistant to change. Students’ verbalizations support the existence of the different incorrect ways of thinking inferred from previous studies in fraction size. Furthermore, the high levels of confidence in their incorrect reasoning and the fact that they were reluctant to change their answer when they were confronted with other reasoning suggest that these ways of thinking may be resistant to change." "The development of computational estimation strategies: a longitudinal study with 6-to 7-year-olds" "Lieven Verschaffel, Koen Luwel"