Impressies uit Japan

In augustus 2000 werd in Tokyo de ICME-9 (International Conference on Mathematics Education) gehouden. Dit is een vierjaarlijks congres waar wereldwijd de balans wordt opgemaakt over de stand van zaken in het wiskundeonderwijs

Task Contexts in Dutch Mathematics Education

This chapter offers a description of task contexts in mathematics education in the Netherlands. International comparative studies show that the Dutch average percentage of mathematics tasks with real-life connections per lesson exceeds any other country by far. This tradition goes back more than 500 years, when the earliest mathematics textbooks in the Dutch language consisted entirely of tasks, in which mathematics was put to use in commercial contexts. In this chapter characteristics of contexts in mathematics tasks in the Netherlands are studied. Underlying frame is the notion of usefulness, which is a perception by students on future practices outside school. A distinction is made between bare tasks (without contexts), tasks with mathematical contexts (e.g. matchstick pattern problems), dressed-up tasks (hiding a mathematical question), tasks with realistic contexts and questions that are useful within the context, and tasks with authentic contexts. The empirical part of this chapter is an analysis of a mathematics textbook chapter and a sample of examination papers. The analysis shows that Dutch mathematics education contains many links to real-life, which is not just verbally presented, but also visually with drawings, photos, diagrams and other visualisations. The contexts are drawn from a wide spectrum of areas in real-life, reflecting that mathematics can be found anywhere in society. The examinations contain more authentic aspects than the textbook, and the higher level examinations have more authentic aspects than the lower level examinations. Nevertheless contexts can be artificial and the posed questions would not be asked by actors within the context. Task contexts often come from recreational or professional practices, demonstrating to students the usefulness of mathematics in their future lives beyond school.publishedVersio

The spirit of mathematical modeling – a philosophical study on the occasion of 50 years of mathematical modeling education

We mark the 50th anniversary of mathematical modeling education by reviving the term the spirit of mathematical modeling (SoMM), which idealistically reflects core aspects of mathematical modeling. The basis of our analysis is the notion of bildung, which is an educational philosophy that strives for harmonizing heart, mind, social life and culture. We built SoMM on five descriptions of mathematical modeling: two research studies from the 1970s, two studies about the work of professional modelers, and one about an environmental school project. We captured SoMM as a collection of aspects at the micro, meso and macro level: at the micro level, we found aspects such as agency, anticipating, scrutiny and critique as part of SoMM; at the meso level, we found collaborating, consulting and navigating social norms; and at the macro level, interdisciplinarity, relevance and social justice. Through the lens of bildung-based educational philosophies, we see that instruction and assessment traditions have transposed mathematical modeling into ‘teachable’ practices that drift away from SoMM. We recommend focusing more on fostering mathematical modeling and to assess students through alternative formats (e.g., group projects)

Making sense of journalistic COVID-19 data visualizations: An in-depth study of two adults’ visual-numeric literacy

In 2020, the COVID-19 pandemic urged authorities to share quantitative information such as infection and death rates. One way of disseminating was through graphs, maps, and diagrams. Such data visualizations communicate numeric data in compact ways, but also require a particular mathematical literacy from readers. We conceptualized this particular mathematical literacy as visual-numeric literacy. To study it, we interviewed two young adults with higher education but low confidence in mathematics and asked them to make sense of COVID-19 data visualizations from journalistic digital media. An in-depth analysis of their visual-numeric literacy revealed that the two participants had developed various sense-making strategies. Their lived experience in the pandemic assisted them to overcome obstacles in mathematical sense-making, and gain insights from the data visualizations. We discuss out-of-school mathematics learning and provide recommendations for improving adults’ visual-numeric literacy.publishedVersio

The object-tool duality in mathematical modelling: a framework to analyze students’ appropriation of Sankey diagrams to model dynamic processes

Students often do not experience the relevance of learning mathematics. This paper reports on an exploratory case study, in which a class of grade 8 students (n=35) was introduced to Sankey diagrams. The aim was to explore to what extent these students could appropriate Sankey diagrams, meaning: they could describe these as objects in themselves and they could use them to model and visualize phenomena relevant to them. Based on Cultural-Historical Activity Theory, we developed an analytical construct defined as the object-tool duality, coordinating mathematics as a set of objects and as a set of tools. The analysis of students’ answers showed that they could use these diagrams as tools to visualize phenomena. When asked to describe the object, all mentioned the tool-side. So, in their appropriation the tool-side came before the object-side. Our contribution is that teaching the tool-side of mathematics before the object-side may increase students’ sense of the relevance of mathematics, which is a topic to develop for future research

Grade 8 students appropriating Sankey diagrams: The first cycle in an educational design research

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Interpreting teaching for conceptual and for procedural knowledge in a teaching video about linear algebra

Source at http://matematikdidaktik.org/wp-content/uploads/2019/05/NORMA-17-2018-papers-SMDF-skriftserie-f.pdf. Journal home page http://matematikdidaktik.org/index.php/madifs-skriftserie/.The aim of this study is to investigate teaching videos about mathematics, seeking to uncover research-based foundations for their quality. By drawing on the notions of procedural and conceptual knowledge, the research was operationalized by asking professionals in undergraduate mathematics education (n=18) to interpret sections of a teaching video. The video dealt with a topic in linear algebra. The results indicate rather divergent interpretations of conceptual knowledge. This can hinder a reliable evaluation of teaching in terms of aiming for conceptual or procedural knowledge. It is recommended that the notions should be carefully used, defined and explained when used to evaluate the quality of teaching videos in particular, or of teacher’s explanations in classrooms in general