Abstract:

How Systems Thinking enriches the learning of mathematics?
What are the components of holistic thinking needed by future citizens of a changing and globalized world today?
What does allows the graphical representations of Systems Thinking to the deeper understanding of key mathematical concepts?
What elements of critical thinking can be enriched by the construction of simulators and experiences of students in a math class?

The world with complex systems in which we live today requires of the future citizens of the XXI century a new thinking that in other dynamics of years ago did not need. The Education Community must rethink teaching of several disciplines as soon as possible including Science and particularly Mathematics in all educational levels. This is the origin of this work which part of an academic and interdisciplinary initiative between two Professors (a mathematician and a engineer) in a private University in Northeast Mexico.

The idea in this paper is to show, in a first moment, the basic ideas of a systems thinking some basic mathematical notions that we want to share and transfer to students and finally emphasizes the strengths, weaknesses and, mainly the common points in both disciplines: the Mathematics and Systems Thinking.

For the first stage of the work a qualitative analysis methodology has been developed and implemented with the analysis of official documents and textbooks and also classroom observations complemented with in-depth interviews that took place during 11 months. Initial findings indicate the great wealth that a synergy between the two disciplines, which allows to play in the learner modeling and computer simulation of complex systems often involve phenomena of social and economical nature, where the human factor is highly valuable and essential in the dynamics of the system in question.

Moreover, results on the upper level in two courses (undergraduate level, second year of college for first year for engineers; and postgraduate level, first year in a master programme) during 12 weeks with regular work in 3 different groups are also reported with detail. In this second phase, through a mixte (primarily qualitative) study allowed us -through the design and implementation of learning activities and building simulators- observe and identify student difficulties around mathematical concepts as differential equations, converting verbal to mathematical language and the difficulties encountered in the modeling of many complex phenomena. As part of the found results, we report that the teaching of systems thinking in students allows a more meaningful learning of mathematics on the one hand but also to acquire a technique that allows the understanding of issues and negotiate in groups how to deal with complex phenomena in a globalized and changing world in which we now live. The use of technology (to build simulators in our case through the use of free software called Vensim) helps students to enrich their vision about the long-term effects of decisions that they make in many situations that we confront day by day.

Keywords:

Systems Thinking, Teaching, Mathematics, future citizen, globalized world.