Diverse yet consistent: How mathematicians position computational thinking across research and teaching

TL;DR

This study explores how mathematicians integrate computational thinking into research and teaching, revealing diverse perspectives influenced by their views on mathematics' purpose and real-world impact.

Contribution

It introduces a three-perspectives model explaining mathematicians' positioning of computational thinking in relation to mathematical theory and practice.

Findings

Mathematicians' views on real-world impact influence their use of programming in teaching.

The perceived clash between mathematical thinking and computational thinking is partly ontological.

Authentic learning goals external to mathematics can facilitate meaningful integration of computational thinking.

Abstract

Recent research in mathematics education points to an "epistemic clash" when programming and computational thinking (CT) are leveraged alongside more established forms of mathematical thinking (MT). The emergence of generative AI emphasises the need to understand the mechanisms shaping relations between CT and MT. We address this need by analysing interviews with 15 mathematicians on their use of computations across their teaching and research activities. The interviews were conducted at a critical site with a history of integrating computations across its science and mathematics programs for more than 20 years. Drawing on Cultural Historical Activity Theory and Communities of Practice theory, we consider MT and CT as methodologies grounded in practice. We identify three perspectives shaping how mathematicians position CT: mathematical theory considered as a source of control, computations as a source of pragmatic reach, and real-world impact as a source of legitimacy. This three-perspectives model explains why mathematicians who emphasise real-world impact are most likely to carry programming into teaching, whereas those who position theoretical mathematics as authoritative are least likely to do so. Mathematicians working on numerical algorithms occupy an uneasy intermediate position. Our findings suggest that the perceived clash between MT and CT is not purely epistemic, but also ontological, as it depends on how computations are positioned within the goal of doing mathematics. For mathematics education, this implies that perceived meaningful integration with CT is mediated by context, and that more extensive use can be stabilised by leveraging authentic learning goals external to mathematics.