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
Van der Ven, S.H.G.; Prast, E.J.; Van de Weijer-Bergsma, E. 2023
Individual variation in mathematical skills can be ascribed to differences in cognitive ability, but also to students’ emotional experiences of mathematics, such as enjoyment and anxiety. The... Show moreIndividual variation in mathematical skills can be ascribed to differences in cognitive ability, but also to students’ emotional experiences of mathematics, such as enjoyment and anxiety. The current study investigated how the interplay of working memory with math anxiety and enjoyment explains mathematical performance in primary school students. We also explored whether these relations differed with the type of math test and students’ age. Using mixed effect models, we reanalyzed data from 4471 Dutch primary school students (grades 2–6) who had completed two computerized working memory tasks, had filled out a questionnaire on math emotions, and had completed two math tests: story problems and speeded arithmetic. Findings showed that working memory, anxiety, and enjoyment were linear (but not curvilinear) predictors of performance on both tests, while some relations were stronger for the math (story)-problem-solving test. Higher math anxiety negatively impacted performance more strongly for students with stronger working memory skills, but only on the arithmetic test. No interaction between working memory and enjoyment was found. The relation between math anxiety and math performance increased with grade level, but no other age-related changes were found. Interpretations and recommendations focus on situated views on learning and emotion. Show less
Fagginger Auer, M.F.; Hickendorff, M.; Putten, C.M. van 2018
National large-scale assessments have demonstrated a decrease in Dutch primary school students' performance on multidigit multiplication and division problems (e.g., 56x23 and 544:34) in the... Show moreNational large-scale assessments have demonstrated a decrease in Dutch primary school students' performance on multidigit multiplication and division problems (e.g., 56x23 and 544:34) in the past two decades. This performance decrease appears to be related to changes in students' use of mathematical strategies: the use of relatively accurate strategies for which calculations are written down has decreased, while the use of inaccurate mental strategies has increased. To gain more insight into these developments and how to possibly turn them around, factors that affect students' mathematical strategy use and performance were investigated. New applications of latent variable models to national large-scale assessment data were used to relate teachers' reports of their mathematics teaching to students' problem solving. Follow-up experiments were conducted at primary schools for a more controlled investigation of students' strategy choices and of how to influence those choices (and thereby, performance) favorably. It was found that teachers mainly influence students' choices between strategies with written work, and that they have less influence on choices for the inaccurate mental strategies (made more frequently by boys and weaker students). Extra instruction targeted at the latter was found to increase weaker students' choices for writing down calculations, and this improved students' performance. Show less
Anicius Manlius Severinus Boethius (480-525 A.D.) is regarded as a great thinker of the early Middle Ages. Indeed, Boethius is a man of immense erudition and his works touch upon many philosophical... Show moreAnicius Manlius Severinus Boethius (480-525 A.D.) is regarded as a great thinker of the early Middle Ages. Indeed, Boethius is a man of immense erudition and his works touch upon many philosophical fields, including mathematics, logic and theology. In Boethius’ classification system, mathematics and theology belong to speculative philosophy, and logic is both a part of philosophy and an instrument of philosophy. However, scholars from different fields tend to focus only on the part of Boethius’ thoughts that relate to their own disciplines. The result is a lack of understanding Boethius as a whole. In my dissertation, I will reassess Boethius’ mathematics and logic, and their roles in philosophy, and on the basis of these, I will explore the connections between mathematics and logic in Boethius and their applications to theological or philosophical topics. However, I will not focus on the applications of al l his mathematical and logical knowledge but only on his basic ideas of arithmetic and music, and basic logic including knowledge of categories, theories of division and definition Show less
The thesis deals with certain aspects of Katz modular forms over finite fields, in particular of weight one. A special case of Serre's conjecture is proved and the faithfulness of the Hecke module... Show moreThe thesis deals with certain aspects of Katz modular forms over finite fields, in particular of weight one. A special case of Serre's conjecture is proved and the faithfulness of the Hecke module of modular symbols is studied. Show less
