Pits and piles, directions and debt: pre-service teachers' conceptions of negative numbers

Conference item

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.

Authors: Macmillan, E; Ingram, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: University of Heksinki
• Host title: Proceedings of the 49th Conference of the International Group for the Psychology of Mathematics Education: Research Report
• Publication date: 2026-08-01
• Acceptance date: 2026-04-01
• Event title: 49th Conference of the International Group for the Psychology of Mathematics Education
• Event location: Helsinki, Finland
• Event website: https://www.helsinki.fi/en/conferences/pme49
• Event start date: 2026-07-27
• Event end date: 2026-08-01
• ISSN: 3081- 0833
• Language: English