Scheiner, T. & Pinto, MM. (2016). Images of abstraction in mathematics education: Contradictions, controversies, and convergences (Vol. 4). C. Csíkos, A. Rausch, J. Szitányi. Proceedings of the 40th Conference of the International Group for Psychology of Mathematics Education 155-162. Szeged, Hungary: International Group for the Psychology of Mathematics.
In this paper we offer a critical reflection of the mathematics education literature on abstraction. We explore several explicit or implicit basic orientations, or what we call images, about abstraction in knowing and learning mathematics. Our reflection is intended to provide readers with an organized way to discern the contradictions, controversies, and convergences concerning the many images of abstraction. Given the complexity and multidimensionality of the notion of abstraction, we argue that seemingly conflicting views become alternatives to be explored rather than competitors to be eliminated. We suggest considering abstraction as a constructive process that characterizes the development of mathematical thinking and learning and accounts for the contextuality of students’ ideas by acknowledging knowledge as a complex system.
Institute for Learning Sciences and Teacher Education
Open Access Conference Paper