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Exploring students’ conceptual understanding through mathematical problem solving: students’ use of and shift between different representations of rational numbers
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Mathematics, and Science Education (2023-).ORCID iD: 0000-0002-8498-8014
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Mathematics, and Science Education (2023-).ORCID iD: 0000-0002-5981-3722
2025 (English)In: Research in Mathematics Education, ISSN 1479-4802, E-ISSN 1754-0178Article in journal (Refereed) Epub ahead of print
Abstract [en]

One way to stimulate conceptual considerations is through mathematical problem solving, which requires students to construct new solution methods, potentially including new representations. Hence, this study focuses on students’ use of and shift between representations during problem solving, specifically regarding the fundamental and often challenging concept of rational numbers. Swedish elementary school students were observed when tackling mathematical problems in pairs. The findings revealed that the students’ considerations concerned several conceptual properties of rational numbers through the use of different representations. However, students tended to use the representations presented in the problem, favouring the most familiar representation rather than constructing their own. As a result, they may have overlooked opportunities to explore a wider range of representations which could have deepened their understanding of the concept. This suggests a potential opportunity to design problems that require students to transfer between representations and grapple with unfamiliar ones.

Place, publisher, year, edition, pages
Informa UK Limited , 2025.
Keywords [en]
Conceptual understanding, problem solving, representations
National Category
Educational Sciences Didactics
Identifiers
URN: urn:nbn:se:miun:diva-53781DOI: 10.1080/14794802.2025.2456840ISI: 001413006500001Scopus ID: 2-s2.0-85216766115OAI: oai:DiVA.org:miun-53781DiVA, id: diva2:1936444
Funder
Mid Sweden University, MIUN 2022/970Mid Sweden University, MIUN 2022/970Available from: 2025-02-11 Created: 2025-02-11 Last updated: 2025-02-14

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Jäder, JonasJohansson, Helena

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Citation style
  • apa
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Output format
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