Abstract:

Nowadays, collaborative learning is a key element of distance education, and computer supported collaborative working has a pivotal role in working life: it is thus important to instill these ideas since the school years, involving both the problem solving competences and the remote collaboration (Bjørn et al., 2014).

The use of digital platforms for e-learning in Mathematics has been constantly increasing; in online courses, it is important to include both assessment and collaboration, which are also fundamental factors for engagement (Ng et al., 2018).

Indeed, in distance learning, the social aspect is very important, it being a core element of constructive learning environments, just as much as the use of realistic problem solving and the assessment for learning (Honebein, 1996).

In this paper we discuss how, through a collaborative virtual learning environment and online activities of problem solving and formative assessment, high school students are able to “construct” mathematics, meaning that they are able to experience how actual work concerning computations and mathematical procedures is carried out.
This is developed through a project, called DMT (Digital Math Training), designed and experimented by the University of Turin as an original way to develop competences relative to Mathematics, problem solving, and collaborative working.

Within DMT, 350 students use an Advanced Computer Environment (ACE), which is a powerful system for doing Mathematics (Barana et al., 2017), in order to solve mathematical problems contextualized in the reality.

They are also able to communicate between peers through a forum provided by a Learning Management System (LMS), that has also to be used for interacting with a group of expert tutors, which help them with the use of the ACE, and analyze the files with their solutions to the problems, in order to assess them.

We analyzed more than 5000 students’ interventions in the forum, and how they contributed to build progressively the context we were looking for: that is, we devised a classification for the interventions, based on their aim, and we applied it to the discussions relative to the solutions given to the problems during the training, in order to show that, once the students became familiar with the problem solving and the ACE, they were able, through the forums, to elaborate collaborative solutions, and to construct mathematical concepts.

This has been consistent with supporting the construction of a practice community, capable of constructing Mathematics with problem solving activities.

References:

Barana, A., Fioravera, M., & Marchisio, M. (2017). Developing problem solving competences through the resolution of contextualized problems with an Advanced Computing Environment. Proceedings of the 3rd International Conference on Higher Education Advances, 1015–1023.

Bjørn, P., Esbensen, M., Jensen, R.E., & Matthiesen, S. (2014). Does Distance Still Matter? Revisiting the CSCW Fundamentals on Distributed Collaboration. ACM Transactions on Computer-Human Interaction, 21(5), 1–26. doi:10.1145/2670534

Honebein, P.C. (1996). Seven Goals for the Design of Constructivist Learning Environments. In B. Wilson, Constructivist Learning Environments (pp. 11–24). New York: Educational Technology Publications

Ng, C., Bartlett, B., & Elliott, S.N. (2018). Empowering engagement: Creating learning opportunities for students from challenging backgrounds. New York, NY: Springer Science+Business Media.

Keywords:

Collaborative Learning, e-learning, Mathematics, Learning Management System, Problem Solving, Virtual Learning Environment.