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Teaching and learning the multiplication table by using multiplicative structures: Variation and crutial patterns
Södertörn University, Teacher Education, Mathematics Education.ORCID iD: 0000-0003-0417-2574
University of Gothenburg, Sweden.
2022 (English)In: Education and New Developments 2022: Volyme 1 / [ed] Mafalda Carmo, Lisboa: inScience Press, 2022, Vol. 1, p. 45-49Conference paper, Published paper (Refereed)
Abstract [en]

This paper examines and analyzes how students learn multiplication tables, specifically the role of multiplicative structures and how these are used as students learn to master the tables. The analysis is performed in the context of the generalization process related to the teaching activity focusing students’ perception of concepts. The theoretical approach applies Davydov’s concept of theoretical generalization as perception-conception-elementary concept (PCE model) and Vergnaud’s theory of multiplicative structures in three classes: mapping rule (MR), multiplicative comparison (MC), and Cartesian product (CP). For the methodological design, Marton’s variation theory has been chosen.

This study includes two teachers and 40 students in two Year 3 classes, followed two years later by one teacher and 25 students in one Year 5 class. The analysis of the outcome is based on documented classroom observations, one-on-one interviews with students and teachers’ reflections on students’ learning outcomes. The conclusion of the study is that the generalization of multiplication is a difficult process for students, especially in the classes MC and PC, and one that sometimes results in challenges to identifying multiplicative situations and relating these to the multiplication tables. This illustrates that teaching activities and teachers’ support are necessary conditions for students’ learning. The study also shows that multiplicative structures can help students to find and systematize crucial patterns in the multiplication table, allowing them to learn the multiplication table in a more efficient and structured manner. During the one-on-one interviews, students actively searched for and found structures and solutions that did not come up during lessons. This shows that multiplicative structures are a suitable didactic tool for identifying patterns in multiplication tables, thereby facilitating learning other than by rote.

Place, publisher, year, edition, pages
Lisboa: inScience Press, 2022. Vol. 1, p. 45-49
Series
Education and new developments, ISSN 2184-044X, E-ISSN 2184-1489
Keywords [en]
Multiplicative structures, multiplication table, generalization, student’s perception, elementary basic concepts.
National Category
Mathematics Didactics Pedagogy
Identifiers
URN: urn:nbn:se:sh:diva-49209DOI: 10.36315/2022v1end010ISBN: 978-989-53614-3-4 (print)OAI: oai:DiVA.org:sh-49209DiVA, id: diva2:1668340
Conference
Education and New Developments 2022, Madeira island, June 18-20, 2022.
Note

The project has been funded by School of Natural Sciences, Technology and Environmental Studies, Södertörn university 

Available from: 2022-06-13 Created: 2022-06-13 Last updated: 2024-05-21Bibliographically approved

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Karlsson, Natalia

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • harvard-anglia-ruskin-university
  • apa-old-doi-prefix.csl
  • sodertorns-hogskola-harvard.csl
  • sodertorns-hogskola-oxford.csl
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • text
  • asciidoc
  • rtf