Designing an APOS Theory : technoscience framework to understand mathematical thinking

Abstract

The understanding of mathematical thinking is fundamental cognitive and neuroscience phenomenon in mathematics education that can enhance both instructional and pedagogical practice for improved learning outcomes in mathematics. Several studies for the past decades have been thriving to bring out both operational and structural nature of mathematical thinking. This paper presents the novel theoretical framework as a build on to the APOS theory. The APOS theory has managed to successfully explain the mathematics thinking processes involved in the construction of a mathematics concept based on the premises of limited technology integration into mathematics education. Technology and science artefacts are now ubiquitous and constantly advancing and affecting our philosophical assumptions in mathematics education. We carried out a quasi-experiment in a mathematics laboratory involving two groups of 80 students apiece per study year taking Calculus course with differentiated teaching and learning at the University of Zimbabwe. This novel framework, APOS Theory-Technoscience, factored in technological and scientific oriented actions and processes led us to suggest an APOS-T framework as a didactic model for teaching Mathematics in Higher Education. The model could be an emerging digital pedagogy for face to face and remote mathematics instruction.