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Exploring the Integer Addition and Subtraction Landscape pp 143–166Cite as

Different Differences: Metaphorical Interpretations of “Difference” in Integer Addition and Subtraction

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Part of the book series: Research in Mathematics Education ((RME))

Abstract

Mathematically speaking, a difference is the result of a subtraction. However, when the number domain is extended from natural numbers to integers, the separation of the magnitude of a number from its value creates “different differences,” where the connection to subtraction is no longer straightforward. Based on video-recorded lessons and individual student interviews with 21 students in a Swedish year 8 class, a conceptual metaphor analysis of the discourse shows how ambiguous the term difference can be and how an implicit use of metaphors can create confusion in relation to addition and subtraction with integers.

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Notes

  1. 1.

    The vignette is a transcript of a classroom video that was recorded and distributed as part of a professional development program for teaching basic arithmetic (Dolk & Fosnot, 2006). The purpose of the video is to illustrate how teachers can introduce the number line model for subtraction to enhance mathematical reflection. This video is not part of the empirical data reported in the result section.

  2. 2.

    For a more thorough analysis of these metaphors, see Kilhamn (2011).

  3. 3.

    Carlsson, S., Hake, K. B., & Öberg, B. (2002). Matte direkt, år 8. Stockholm: Bonniers.

  4. 4.

    Transcript orthography: … means a short pause; […] indicates removed words or utterances; [word] indicates what the conversation is about; (word) clarifies an action/gesture; emphasis in bold writing is added by the author as part of the analysis.

  5. 5.

    In a Swedish school context, negative numbers are most commonly spoken of as minus-numbers. The distinction between “minus seven” meaning subtract seven and “minus-seven” meaning negative seven is very difficult to discern. To make this clearer in the excerpts, negative numbers such as (−7) are expressed in words: minus-seven.

  6. 6.

    In a Swedish school mathematics context, the verbs adding and subtracting are often spoken of as “plussing” and “minusing.”

  7. 7.

    Two test versions were used: one had the numbers −12 and + 20 and the other −14 and + 20. For comparison reasons they are all referred to here as though they were − 14 and + 20.

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Authors and Affiliations

  1. Gothenburg University, Gothenburg, Sweden

    Cecilia Kilhamn

  2. Uppsala University, Uppsala, Sweden

    Cecilia Kilhamn

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  1. Cecilia Kilhamn
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Correspondence to Cecilia Kilhamn .

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Editors and Affiliations

  1. Department of Curriculum and Instruction, Purdue University, West Lafayette, Indiana, USA

    Laura Bofferding

  2. School of Education, George Fox University, Newberg, Oregon, USA

    Nicole M. Wessman-Enzinger

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Kilhamn, C. (2018). Different Differences: Metaphorical Interpretations of “Difference” in Integer Addition and Subtraction. In: Bofferding, L., Wessman-Enzinger, N. (eds) Exploring the Integer Addition and Subtraction Landscape. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-90692-8_6

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  • DOI: https://doi.org/10.1007/978-3-319-90692-8_6

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