This activity introduces a graph of sine function as built from the unit circle model. Starting with the input of the function, students move one point along the unit circle and another along the x-axis, keeping them equidistant from the starting point. In the sequence for the classroom, the circumference is introduced connecting the two points virtually to allow students measuring the arc in the unit circle via the sine graph using the radius, providing an embodied experience for radian measurement. For the output of the sine function, a student aligns the value of the function on the graph with sine value on the unit circle. Finally, a sine graph carves out from the students’ sensory-motor activity.

Main publications:

Shvarts, A., Bos, R., Doorman, M., & Drijvers, P. (2024). Reifying actions into artifacts: process–object duality from an embodied perspective on mathematics learning. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-024-10310-y

Shvarts, A., van Helden, G. (2023) Embodied learning at a distance: from sensory-motor experience to constructing and understanding a sine graph Mathematical Thinking and Learning, 25(4), 409–437, DOI: 10.1080/10986065.2021.1983691

Alberto, R., Shvarts, A., Drijvers, P., & Bakker, A. (2022). Action-based embodied design for mathematics learning: A decade of variations on a theme. International Journal of Child-Computer Interaction, 32, 1-23. Article 100419. https://doi.org/10.1016/j.ijcci.2021.100419

Shvarts, A., Alberto, R., Bakker, A., Doorman, M., & Drijvers, P. (2021). Embodied instrumentation in learning mathematics as the genesis of a body-artifact functional system. Educational Studies in Mathematics, 107(3), 447-469. https://doi.org/10.1007/s10649-021-10053-0

Shvarts A., Alberto A., (2021) Melting cultural artifacts back to personal actions: embodied design for a sine graph, In Inprasitha, M, Changsri, N., & Boonsena, N. (Eds.). Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 38-46. Khon Kaen, Thailand: PME.

Alberto, R. A., Bakker, A., Walker-van Aalst, O., Boon, P. B. J., & Drijvers, P. H. M. (2019). Networking theories in design research: an embodied instrumentation case study in trigonometry. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 3088-3095). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. https://www.mathematik.uni-dortmund.de/~erme/index.php?slab=proceedings

Other / Conference publications:

Drijvers, P. H. M. (2019). Embodied instrumentation: combining different views on using digital technology in mathematics education. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 8-28). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. https://hal.archives-ouvertes.fr/hal-02436279/

Shvarts, A. Y., Alberto, R. A., Bakker, A., Doorman, L. M., & Drijvers, P. H. M. (2020). Embodied instrumentation: Reification of sensorimotor activity into a mathematical artifact. In Proceedings of the 14th International Conference on Technology in Mathematics Teaching – ICTMT 14: Essen, Germany, 22nd to 25th of July 2019 Universität Duisburg-Essen. https://doi.org/10.17185/duepublico/70749

Shvarts, A., van Helden, G. (2021) Embodied design versus dynamic visualization: Benefits for a far transfer problem solving in trigonometry. In Reflecting the Past and Embracing the Future. Proceedings of ISLS Annual Meeting on Learning Sciences, 7-11^th of of June, 2021, Bochum, Germany. (link)

Professional publication:

Alberto R., Bos R. (2019) Het FIzier gericht op… Embodied cognition in wiskundeonderwijs Euclides,  95(5), 4–6. (link)