Paul Drijvers

Paul Drijvers, Freudenthal Institute, Utrecht University and HU University of Applied Sciences Utrecht

Zooming in and zooming out: towards a realistic view on tool use in mathematics education

Since the origin of mankind, humans have been developing tools to extend their scope and to carry out tasks more easily and more efficiently. Also in the field of mathematics and mathematics education, tools have been widely used. Nowadays, the omnipresence of powerful digital mathematical tools raises important questions about their impact on mathematics teaching and learning, as is witnessed by CERME working groups on the topic over the years, and by recent publications (Ball et al., 2018; Monaghan, Trouche, & Borwein, 2016; Trgalová, Clark-Wilson, & Weigand, 2018). These questions not only concern the curriculum, but the relationship between tool use and learning in particular. To address the latter question, I will first zoom in on some specific examples of using digital tools in mathematics learning. Next, I will zoom out and present some overall findings on the effects this use is having. After a theoretical view on didactical functionalities of digital tools and on instrumental approaches to their use, I will address two relationships in some more detail: (1) the alignment of the use of digital tools with principles from the theory of Realistic Mathematics Education (RME, the domain-specific instruction theory for mathematics, developed in the Netherlands by Freudenthal, Treffers and colleagues), and (2) the relationship between tool use and embodied and extended views on cognition. As a conclusion, I will claim that both an RME lens and an embodied view on tool use may contribute to identifying criteria for a meaningful integration of tool use in mathematics education.

Ball, L., Drijvers, P., Ladel, S., Siller, H.-S., Tabach, M., & Vale, C. (Eds.) (2018). Uses of Technology in Primary and Secondary Mathematics Education; Tools, Topics and Trends. Cham, Switzerland: Springer International Publishing.

Monaghan, J., Trouche, L., & Borwein, J. (2016). Tools and Mathematics. Cham, Switzerland: Springer International Publishing.

Trgalová, J., Clark-Wilson, A., & Weigand, H.-G. (2018). Technology and resources in mathematics education. In T. Dreyfus, M. Artigue, D. Potari, S. Prediger, & K. Ruthven, Developing Research in Mathematics Education. Twenty Years of Communication and Collaboration in Europe (pp. 142–161). New York: Routledge.