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Sense making and reasoning in algebra
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0001-5753-444X
Linnaeus University, Faculty of Technology, Department of Mathematics.
2022 (English)In: Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education: Alicante, Spain, July 18 – 23, 2022 / [ed] Ceneida Fernández, Salvador Llinares, Ángel Gutiérrez, Núria Planas, Alicante: Universidad de Alicante, 2022, Vol. 4, p. 270-270Conference paper, Oral presentation with published abstract (Refereed)
Sustainable development
SDG 4: Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all
Abstract [en]

Researchers note that algebraic reasoning and sense making is essential for buildingconceptual knowledge in school mathematics. Consequently, pre-service teachers’own reasoning and sense making are useful in fostering and developing students’algebraic reasoning and sense making. We report here the features of pre-serviceteachers’ reasoning and sense making in algebra, specifically in the process ofanalysing problem posing, with a focus on first-degree equations. The followingresearch questions served as a guide in the analysis of data: What are the characteristicsof the problem-posing tasks used for reasoning and sense making of first-degreeequations? What are the characteristics of pre-service teachers’ reasoning and sensemaking in problem-posing tasks?This study is part of ongoing research carried out with pre-service teachers enrolled inthe abovementioned mathematics teacher education course. All the pre-serviceteachers were older than 19, from diverse socio-economic backgrounds and attendedclass for all 10 weeks of the semester, including the seven weeks in which data wascollected. Sixty-six pre-service primary teachers participated in an anonymous writtenexam and were informed about our research (characteristics, aim, confidentialityissues, etc.). The data analysis adopted a qualitative/interpretative approach, and theunit of analysis has three dimensions: reasoning, sense making and critical aspects.According to Olteanu (2020), reasoning and sense making are closely related to eachother and to these dimensions in the manner of a ‘rhizome’ (Deleuze & Guattari, 1987).Results revealed that the pre-service teachers create a rhizomatic reasoning and sensemaking that is characterized by lines of rupture. Those lines interconnect and arise fromincorrect translations of rhizomatic problem-posing task (RPPT) into mathematicalnotations and the failure to discern the difference between variables and variables asunknown numbers; i.e., between algebraic expression and equation. The characteristicsof reasoning in RPPT and of pre-service teachers are selecting, exploring,reconfiguring, encoding, abstracting, and connecting to highlight associations andrelationships between different content, and the characteristics of sense making arerecognition, relationships, profiling, comparing, laddering, and verifying.  

Place, publisher, year, edition, pages
Alicante: Universidad de Alicante, 2022. Vol. 4, p. 270-270
Series
Proceedings of the International Groups for the Psychology of Mathematics Education, ISSN 0771-100X ; 4
Keywords [en]
first-degree equations, problem-posing, reasoning, sense making, critical aspects
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
URN: urn:nbn:se:lnu:diva-115721Scopus ID: 2-s2.0-85181214828ISBN: 9788413021782 (print)OAI: oai:DiVA.org:lnu-115721DiVA, id: diva2:1686780
Conference
45th Conference of the International Group for the Psychology of Mathematics Education.
Available from: 2022-08-11 Created: 2022-08-11 Last updated: 2024-06-05Bibliographically approved

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Olteanu, ConstantaOlteanu, Lucian

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CiteExportLink to record
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Citation style
  • apa
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