Approaches to Investigating Complex Dynamical Systems

Abstract

This chapter reports on a short experiment conducted in Canada to explore the potential, and feasibility, of introducing complex dynamical systems into mathematics curricula, both in schools and in university undergraduate programs. In particular it aimed to identify those mathematical habits of mind that are (or could be) developed in schools, universities and outside these traditional learning environments through exploring complex systems when approaching real life situations. The use of game design to engage members of the Canadian mathematics education community in the modelling of a real-life ecosystem brought to light different mathematical habits of mind and provided a snapshot of where we are with respect to modelling in mathematics education. Put in perspective with current lines of inquiry in the modelling of complex dynamical systems, in integrating modelling in mathematics education, and in developing computational thinking, the experiment opened a reflection on the possibilities and feasibility of helping tackle the complexity of our world's most pressing challenges through mathematics education.

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

“…They found out that the use of digital tools took place mainly within the phases of mathematising and mathematical work. In the context of a short experiment to investigate the potential of introducing complex dynamical systems into curricula, it was shown that the transition to working with a computer simulation system would require one or more types of processes of discretisation, for example, referring to time or space (Caron, 2019). Already as early as in the 1980s, Ziegenbalg (1984) emphasised the usage of discrete models in the context of computer simulation in mathematics education.…”

Teaching and learning discrete mathematics

“…In the context of a short Canadian experiment to explore the potential of introducing complex dynamical systems into curricula, it was discussed that the transition to a computer treatment involves as a fundamental element one or more types of discretization, for example of time, of space or of matter. Overall, computer simulation played an important role here (Caron, 2019). Ziegenbalg (1984) sees discrete models in the context of computer use in mathematics education.…”

Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education

“…His intention was to allow modelling as both vehicle and content and the contexts used were very familiar to the task solvers. For the Yellowstone Game Task, Canadian educators and mathematicians worked on modelling a real-life ecosystem (Caron 2019). Groups worked together to try to represent the situations and or solve the problem as to why a recent significant increase in the bear population had occurred.…”