A framework for the design of adaptive curriculum focused on the development of mathematical thinking

Abstract

The objective of this research was to design a methodology for the design of adaptive curricula that favor the development of mathematical thinking, taking into account the learning conditions of the students. In this work, the learning conditions related to the modes of thought proposed by Sierpinska (2000) were especially considered, since these modes are related to linear algebra, which was the field of mathematics where this research was applied. For this, the design-based research method was used, within the qualitative research approach. Following this method, a test for the characterization of ways of thinking (geometric and arithmetic) was elaborated and an adaptable learning system (ALMS) was built for the management of the , of which two iterations were carried out in its implementation. with students of courses related to linear algebra. From this, it was possible to identify essential characteristics that adaptive curricula must contain to favor the development of mathematical thinking, thus surpassing the current state in the design of this type of curricula, fundamentally focused on learning outcomes and not in the thought processes involved.