Pixel International Conferences

The well-known Van Hiele model of geometric reasoning establishes five levels of development, from level 1 (visual) to level 5 (rigor). This theoretical framework describes in some detail the competences displayed by students through their progress in the Geometrical thinking. On the other hand, the Pirie/Kieren model describes the importance of folding back processes in the learning of mathematics.

This paper presents an activity implemented with mathematics teachers in training, concretelly, students enrolled in a Master’s degree program to become Secondary school Mathematics teachers. The activities presented promote folding back processes through the use of Van Hiele's level 5 and 4 tasks. Our results show how working with Van Hiele level 5 tasks favors reflection on similar level 4 tasks, leading to a greater depth in the reasoning of the latter. We consider that this type of activities can be especially useful in the case of students at a certain level showing some weaknesses typical of previous levels.    

Keywords: Van Hiele model, Geometric Reasoning, folding back, Preservice Mathematics Teachers

References:

[1] Arnal-Bailera & Manero, 2023. A Characterisation of Van Hiele’s level 5 of geometric reasoning using the Delphi methodology.

International Journal of Science and Mathematics Education.

https://doi.org/10.1007/s10763-023-10380-z">https://doi.org/10.1007/s10763-023-10380-z

[2] Blair, S. 2004. Describing undergraduates’ reasoning within and across Euclidean, taxicab and spherical geometries [PhD thesis, Portland State University].

[3] Kemp, A., & Vidakovic, D. 2021. Ways secondary mathematics teachers apply definitions in Taxicab geometry for a real-life situation: Midset.

The Journal of Mathematical Behavior, 62, 100848

https://doi.org/10.1016/j.jmathb.2021.100848">https://doi.org/10.1016/j.jmathb.2021.100848

[4] Manero, V., & Arnal-Bailera, A. 2021. Understanding Proof Practices of pre-Service Mathematics Teachers in Geometry. MTRJ 13(3), 99-130.

[5] Pirie, S., & Kieren, T. 1991. Folding back: Dynamics in the growth of mathematical understanding. In F. Furinghetti (Ed.), Proceedings of the fifteenth annual meeting of the International Group for the Psychology of Mathematics Education, Vol. 3 (pp. 169–176).

[6] Van Hiele, P. M. 1986. Structure and insight. A theory of mathematics education. Academic Press.