International Group for the Psychology of Mathematics Education (PME)

Proceedings of the International Group for the Psychology of Mathematics Education · Volume 1

Pits and Piles, Directions, and Debt: Pre-service Teachers' Conceptions of Negative Numbers

Emily Macmillan, Jenni Ingram

University of Oxford

49th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2026Helsinki27 July 2026 - 1 August 2026pp. 963–970ISSN 2790-36482026Scopus conference code 336559
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Abstract

Children naturally use fingers or objects to count whole numbers, but there is no similarly intuitive way of representing negative numbers. Using scripting as a proxy for practice, we investigated the conceptions pre-service teachers drew on through the representations they used and the structures they highlighted when explaining how to calculate with negative numbers. We categorised the conceptions into quantity (debt, counterbalance, and relativity), movement (translation and rotation), position (order and symmetry), and symbolic (removed from context). The pre-service teachers used multiple conceptions and representations between and within explanations, rarely overtly drawing attention to mathematical structures.

Keywords

Pre-service teachersnegative numbersconceptionsrepresentationsscripting

Recommended citation

Macmillan, E., & Ingram, J. (2026). Pits and Piles, Directions, and Debt: Pre-service Teachers' Conceptions of Negative Numbers. In Krzywacki H., Hähkiöniemi M., Haataja E., Hannula M.S., Hästö P. (Eds.), Proceedings of the International Group for the Psychology of Mathematics Education, Volume 1 (pp. 963–970). Psychology of Mathematics Education (PME). ISSN 2790-3648.

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