Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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
  • html
  • text
  • asciidoc
  • rtf
An important part of the whole: The role of metaphors in the teaching and learning of mathematics
Stockholm University, Faculty of Humanities, Department of Teaching and Learning.ORCID iD: 0000-0001-6381-7534
2022 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This study aims to investigate the role of metaphor in the teaching and learning of mathematics. Two different studies help to fulfil this aim.

The first study involves a configurative literature review of empirical mathematics education research where two interpretations of the metaphor concept are applied: conceptual metaphor and extraneous metaphor, with the purpose of distinguishing patterns in metaphor concept use. The analysis found explicit, vague, or absent theoretical definitions of the metaphor concept as well as several metaphor examples, and generated three categories of concept use: 1) Conceptual metaphor, 2) Extraneous metaphor, and 3) Potentially conceptual/extraneous. The review stresses the need for a theoretical and empirical distinction between different types of metaphors, to sharpen the analytical tools available to researchers and, by extension, to more clearly highlight the specific function of metaphor in teachers’ classroom work.

The second study examines the presence of three conceptual metaphors as the basis for rational numbers as fractions in Swedish textbooks for years 1–3 and which aspects of fractions are distinguished in the student responses required in these books. The results are related to process-object theory (Sfard, 1991), intending to discern the different degrees of reification of the mathematical objects that hypothetically have the opportunity to develop with the help of these metaphors. The results show, in three of the book series, an abundance of labelling exercises related to the metaphor Arithmetic is object construction, mainly with images of geometric shapes. One book series reversely introduces fractions with The measuring stick metaphor and Arithmetic is motion along a path, with representations of number lines in focus. All in all, there is a significant variation between the textbooks, which could have consequences for instruction.

This thesis shows the importance of theoretically distinguishing conceptual metaphor from extraneous metaphor, and of understanding their different roles in a teaching and learning context. The thesis also shows how the conceptual metaphors underlying the mathematical concepts describe different aspects of these concepts and that several conceptual metaphors need to be taken into account, together with a consideration of different degrees of reification of the mathematical objects. In addition, the thesis shows that metaphors, as they are understood in Conceptual metaphor theory, point to similar conceptual and discursive processes that can be found in Sfard’s (1991, 2008) more established theories on mathematical conceptualisation.

Place, publisher, year, edition, pages
Institutionen för ämnesdidaktik , 2022.
National Category
Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:su:diva-209718OAI: oai:DiVA.org:su-209718DiVA, id: diva2:1698594
Presentation
2022-09-16, Svend Pedersen, Svante Arrheniusväg 20A, Stockholm, 15:31 (Swedish)
Opponent
Supervisors
Available from: 2022-09-26 Created: 2022-09-24 Last updated: 2022-09-27Bibliographically approved
List of papers
1. Some Conceptual Metaphors for Rational Numbers as Fractions in Swedish Mathematics Textbooks for Elementary Education
Open this publication in new window or tab >>Some Conceptual Metaphors for Rational Numbers as Fractions in Swedish Mathematics Textbooks for Elementary Education
2023 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 67, no 6, p. 914-927Article in journal (Refereed) Published
Abstract [en]

This study examines the presence of three conceptual metaphors for fractions – The measuring stick metaphor, Arithmetic is motion along a path, and Arithmetic is object construction – in four common and popular Swedish mathematics textbook series for years 1–3. I analyse the introduction of fractions and the kinds of tasks students are given in these books. The results show an abundance of labelling exercises related to Arithmetic is object construction, with representations of geometric shapes, in three of the book series. One book series reversely introduces fractions with The measuring stick metaphor and Arithmetic is motion along a path, with a focus on number line representations. The consequences of these variations in fraction introduction and treatment are discussed in relation to previous research and to process-object theories.

Keywords
Textbook analysis, fractions, metaphor, conceptual metaphor theory, process-object
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-209713 (URN)10.1080/00313831.2022.2114541 (DOI)000853484300001 ()2-s2.0-85138414685 (Scopus ID)
Available from: 2022-09-24 Created: 2022-09-24 Last updated: 2023-10-05Bibliographically approved
2. Conceptual, Extraneous or Other?: A Configurative Review Concerning Mathematical Metaphors in Empirical Education Research
Open this publication in new window or tab >>Conceptual, Extraneous or Other?: A Configurative Review Concerning Mathematical Metaphors in Empirical Education Research
2021 (English)In: Philosophy of Mathematics Education Journal, ISSN 1465-2978, Vol. 2021, no 38Article in journal (Refereed) Published
Abstract [en]

In this review, metaphor is seen as an essential phenomenon for conceptualisation in mathematical teaching and learning. The aim of this review is to discern some patterns in concept use concerning metaphor, within 25 empirical mathematics education research papers, guided by two perspectives on metaphor; conceptual metaphor and extraneous metaphor. The analysis found explicit, vague or absent theoretical definitions of the metaphor concept as well as several metaphor examples, generating three categories of concept use; conceptual metaphor, extraneous metaphor, and potentially conceptual/extraneous. The review stresses the need for a theoretical and empirical distinction between different types of metaphors, in order to sharpen the analytical tools available to researchers and, by extension, to more clearly highlight the specific function of metaphor in teachers’ classroom work.

National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-209714 (URN)
Available from: 2022-09-24 Created: 2022-09-24 Last updated: 2024-01-31Bibliographically approved

Open Access in DiVA

An important part of the whole. The role of metaphors in the teaching and learning of mathematics.(1304 kB)217 downloads
File information
File name FULLTEXT01.pdfFile size 1304 kBChecksum SHA-512
272a88e7f3de246d8bf30ae84d4d77c92187f0bce0ee1ac834ee8ed32760e80412c5e7f5eca8ac90246d998d0aadb77dc014ce002ec8425825bd7341eac1037b
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Berggren, Johannes
By organisation
Department of Teaching and Learning
Didactics

Search outside of DiVA

GoogleGoogle Scholar
Total: 218 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 501 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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
  • html
  • text
  • asciidoc
  • rtf