Addressing dualism in mathematical abstraction: An argument for the role of Construal Level Theory in mathematics education

Torr, Stuart; Craig, Tracy S

Addressing dualism in mathematical abstraction: An argument for the role of Construal Level Theory in mathematics education

Conference Paper

2013-11

Publisher

School of Computing, Engineering and Mathematics, University of Western Sydney

Publisher

University of Cape Town

Series

The Ninth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics, 24 - 29 November, KIAMA, Australia

Abstract

Learners of mathematics often struggle to balance the apparently conflicting demands for abstract thinking as well as (often simultaneous) concrete cognitive engagement. Conflicting demands of successful mathematical engagement have been addressed in the literature pertaining to procedural versus conceptual approaches to mathematical learning as well as in the literature on cognitive and meta-cognitive mathematical demands. Construal Level Theory offers an opportunity to understand both these dualities as aspects of the same psychological response to contextual priming. In addition, Construal Level Theory can be understood to illuminate student difficulties with heuristic strategies in mathematical problem-solving. The focus of Construal Level Theory on abstract and concrete cognitive construals as a consequence of psychological distance provides a useful lens for teaching and learning opportunities. We argue that Construal Level Theory offers an opportunity to draw together several strands of mathematics education theory and to help educators address learning challenges in the classroom.