Maria Antonietta Lepellere, Francesco Zucconi, Nizar Salahi Al Asbahi, Alberto Carminati


GeoUniud is a user-friendly platform built-in interactive tutors which allow students to investigate specific tasks by selecting their own input values and working through a problem in a step-by-step fashion together with immediate feedback at each step.  Lessons and exercises are stored and organized with a careful use of randomized controlled contents as exercises, geometrical pictures and abstract reasoning. The lessons are augmented by a virtually infinite collection of examples, and by interactive representations of concepts. As example we show the design of two interactive tools about linear transformation and change of basis in order to develop students’ sense-making in a dynamic geometry environment (DGE) within the perspective of semiotic mediation.



dynamic geometry environment; linear algebra; semiotic mediation; technology

Full Text:



Albano, G., & Ferrari, P.L. (2008). Integrating technology and research in mathematics education: the case of e-learning. In: Garcia Penalvo, F.J. (ed.) Advances in E-learning: Experiences and Methodologies (132-148). Information Science Reference (IGI Global), Hershey (PA-USA).

Bagley, S., Rasmussen, C., & Zandieh, M. (2015). Inverse, composition, and identity: the case of function and linear transformation. The Journal of Mathematical Behavior, 37, 36-47.

Beltran-Meneu, M.J., Murillo-Arcila, M., & Albarracin, L. (2016). Emphasizing visualization and physical applications in the study of eigenvectors and eigenvalues. Teaching Mathematics and Its Applications: An International Journal of the IMA, 36(3), 123-135.

Bartolini Bussi, M.G., & Mariotti, M.A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, Bartolini Bussi, M., Jones, G., Lesh, R., & Tirosh, D. (Eds.), Handbook of international research in mathematics education (Vol. 2, pp. 746–783). Mahwah: Erlbaum.

Caglayan, G. (2015). Making sense of eigenvalue–eigenvector relationships: Math majors’ linear algebra–geometry connections in a dynamic environment. The Journal of Mathematical Behavior, 40, 131–153.

Cooley, L., Vidakovic, D., Martin, W. O., Dexter, S., Suzuki, J., & Loch, S. (2014). Modules as learning tools in linear algebra. PRIMUS, 24(3), 257–278.

Dogan, H. (2018). Differing instructional modalities and cognitive structures: Linear algebra. Linear Algebra and Its Applications, 542, 464–483.

Dominguez-Garcia, S., Garcia-Plana, M. I., & Taberna, J. (2016). Mathematical modelling in engineering: An alternative way to teach linear algebra. International Journal of Mathematical Education in Science and Technology, 47(7), 1076–1086.

Dorier, J.L., Sierpinska, A. (2001). Research into the teaching and learning of linear algebra', in D. Holton (ed.), The Teaching and Learning of Mathematics at University Level (255-274). An ICMI Study, Kluwer Academic Publishers, Dortrecht/Boston/London.

Dorier, J.L., Robert, A., Robinet, J., & Rogalski, M. (2000). The obstacle of formalism in linear algebra. In Dorier, J.L. (Ed.), On the teaching of linear algebra (85-124). Dordrecht, the Netherlands: Kluwer Academic Publishers.

Ertmer, P.A., & Ottenbreit-Leftwich, A. (2013). Removing obstacles to the pedagogical changes required by Jonassen’s vision of authentic technology-enabled learning. Computers & Education, 64, 175-182.

European Commission (2009). Directorate-General for Education and Cultures. ECTS users’ guide. Retrieved from:

Gol Tabaghi, S. (2014). How dragging changes students’ awareness: Developing meanings for eigenvector and eigenvalue. Canadian Journal of Science, Mathematics and Technology Education, 14(3), 223–237.

Hillel, J. (2000). Modes of description and the problem of representation in linear algebra. In J.L. Dorier (Ed.), On the Teaching of Linear Algebra ( 91–207). New York: Springer.

Lepellere, M.A., Zucconi F., Salahi Al Asbahi, N., Carminati, A. (2020). MatUniud: Tools for Linear Algebra, INTED2020 Proceedings, In Press.

Leung, A., Chan, Y. C., & Lopez-Real, F. (2006). Instrumental genesis in dynamic geometry environments. In L.H. Son, N. Sinclair, J.B. Lagrange, & C. Hoyles (Eds.), Proceedings of the ICMI 17 Study Conference: Part 2, 346–353.

Mariotti, M.A. (2014). Transforming images in a DGS: The semiotic potential of the dragging tool for introducing the notion of conditional statement. In S. Rezat, M. Hattermann & A. Peter-Koop (Eds.), Transformation a fundamental idea of mathematics education (155–172). New York: Springer.

Martin, W., Loch, S., Cooley, L., Dexter, S., & Vidakovic, D. (2010). Integrating learning theories and application-based modules in teaching linear algebra. Linear Algebra and Its Applications, 432(8), 2089-2099.

Kolman, B., & Hill, D. (1999). Linear Algebra with Applications. New York: Kluwer Academic Publishers.

Turgut, M. (2019). Sense-making regarding matrix representation of geometric transformations in R2: a semiotic mediation perspective in a dynamic geometry environment. ZDM, 1-16.



  • There are currently no refbacks.