# Mathematics Education Seminar Online

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## The 4S model for selecting, analyzing and designing tasks

The history of mathematics (HoM) can be used in mathematics education in many ways. Both Tzanakis et al. (2000) and Jankvist (2009) have written important texts on how this can be done and reasons for doing so.  In a recent article (Agterberg et al., 2021) we describe a categorization of ways how HoM can be presented in curriculum materials or classroom activities. This categorization is meant to be used as a tool in what we call a design-oriented approach. With the help of this tool, teachers should be enabled to select and adjust curriculum materials that use HoM or even design classroom activities themselves. We called this tool the 4S-model. We distinguish between four formats for presenting HoM in curriculum materials. We chose format names that all start with the letter S: speck, stamp, snippet and story. The term speck was chosen to indicate the smallest format. The word stamp refers to the notion of a small, separate box of information, alongside the main text. The term snippet is used for the average size piece of historical information with substantial relation to the text in which it is incorporated. The fourth and last format story relates to larger historical packages that transfer a story of mathematics. A complete description of the formats can be found in the article (Agterberg et al., 2021).

In the seminar I will explain the 4S-model and give examples of the four formats from Dutch curriculum materials. Furthermore, I will describe how these formats can be used to raise the cognitive level of existing tasks and design new tasks. The 4S-model was used in a teacher-training program at the Amsterdam University of Applied Sciences in the spring of 2021. An article on the results of this empirical study is in preparation. In the second part of the presentation I will share some of the outcomes.

References

Agterberg, D.A., Oostdam, R.J. & Janssen, F.J.J.M. (2021). From speck to story: relating history of mathematics to the cognitive demand level of tasks. Educational Studies in Mathematics  https://doi.org/10.1007/s10649-021-10093-6

Jankvist, U.T. (2009). A categorization of the “whys” and “hows” of using history in mathematics education. Educational Studies in Mathematics, 71, 235–261. https://doi.org/10.1007/s10649-008-9174-9

Tzanakis, C., Arcavi, A., Correia de Sa, C., Isoda, M., Lit, C.-K., Niss, M., et al. (2000). Integrating history of mathematics in the classroom: An analytic survey. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: The ICMI study. New ICMI Study Series (Vol. 6, pp. 201–240). Kluwer.

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Online in Microsoft Teams