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Mathematical reasoning

We are interested in the ways students develop their mathematical reasoning skills. In one of our research projects we follow the way students develop their understanding of derivative in senior level secondary school over a period of several years. We are particularly interested in students’ use of graphical, numerical and symbolical representations of derivative and the factors that influence this development.

In a second project we explore the ways students develop their skills to solve integration problems in undergraduate calculus courses. We focus on the way students relate task properties and possible approaches.


Aldine Aaten, Gerrit Roorda, Martin Goedhart

In collaboration with: Johan Deprez (Leuven), Pauline Vos (Agder), Paul Drijvers (Utrecht)

Key publications:

Roorda, G., Vos, P. & Goedhart M.J. (2007). The concept of derivative in modelling and applications. In C. Haines, P. Galbraith, W. Blum & S. Khan S. (eds.), Mathematical Modelling (ICTMA 12): Education, Engineering and Economics (pp. 288 - 293).  Chichester, UK: Horwood Publishing.

Roorda, G., Vos, F.P., & Goedhart, M.J. (2014). An actor-oriented transfer perspective on high school students’ development of the use of procedures to solve problems on “rate of change”. International Journal of Science and Mathematics Education, 13(4), 863-889.

Roorda, G., Vos, P., Drijvers, P, & Goedhart, M. (2016). Solving rate of change tasks with a graphing calculator: A case study on instrumental genesis. Digital Experience in Mathematics Education 2(3), 228-252.

Aaten, A.B., Roorda, G., Deprez, J., & Goedhart, M. (2018). Evolution of undergraduate students’ mathematical reasoning . In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, p. 3). Umeå, Sweden: PME.

Full list of publications

Last modified:11 July 2023 11.41 a.m.