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The co-construction of learning difficulties in mathematics—teacher–student interactions and their role in the development of a disabled mathematical identity

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Abstract

Leaning on a communicational framework for studying social, affective, and cognitive aspects of learning, the present study offers a new look at the construction of an identity of failure in mathematics as it occurs through teaching–learning interactions. Using the case of Dana, an extremely low-achieving student in 7th grade mathematics, I attempt to unearth the mechanisms of interaction between Dana and myself, her teacher, that instead of advancing Dana, perpetuated her failure. Through examining the interactional routines followed by Dana and me, I show how Dana’s deviations from normative routines resulted in my identification of Dana as “clueless” in mathematics. This identification, shared both by Dana and by me, was accompanied by adherence to ritual rule following that did not enable Dana’s advancement in mathematical discourse. This case points to the need to re-examine permanent difficulties in mathematics in light of the reciprocal nature of such difficulties’ (re)construction in teaching-and-learning interactions.

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Notes

  1. Heb: “Tavniot mispar”; “Number formula” is the Hebrew term that refers to algebraic expressions. I chose here to use the literary form because the students refer specifically to the word “formula”.

  2. All the students articulated the English pronunciation of the capitalized letters

  3. “The eights” was a popular Israeli T.V. series in that year.

  4. Heb: “Keta”, Lit: a section. The word “Keta” is very common in Hebrew slang for denoting some piece of information. The closest translation would be something between “a thing” and “stuff”.

  5. For technical reasons, I did not get straight access to Dana’s psychological diagnosis.

  6. Heb: “Az pakhot ekhad” Lit: so subtract one. “Pakhot” is the word for the subtraction sign, and is not used in this context as “minus” which might signify the number (−1).

  7. Legend: ^high pitch^; .hhh: audible inhale; >accelerated talk<

  8. Heb: “Dai”, Lit: enough, stop it

  9. Heb: “Tedamyenu lachem, Da-mu lachem”; Dana is changing slightly the verb of “imagine” to be in the correct form, which is only used in literary Hebrew, thus exaggerating a “high” form of speech.

  10. Heb: “Damu-na”—a literary form of saying “imagine please”, hardly ever used in today’s spoken Hebrew.

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Acknowledgments

I am grateful to Prof. Anna Sfard, my advisor for the present study. In addition, I wish to express my thanks to the Mandel Scholars program for PhD students and the Golda-Meir foundation of the Hebrew University for having provided financial support for the writing process. Finally, I wish to thank Dr. Adam Lefstein and the anonymous reviewers for their useful comments on the first drafts of this manuscript.

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  1. The Technion - Israel Institute of Technology, Hagalil St. 14, Lapid, Israel

    Einat Heyd-Metzuyanim

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  1. Einat Heyd-Metzuyanim
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Correspondence to Einat Heyd-Metzuyanim.

Appendix

Appendix

Table 4 Dana’s first assessment—10/2/08
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Table 5 Dana’s final assessment—24/6/08
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Heyd-Metzuyanim, E. The co-construction of learning difficulties in mathematics—teacher–student interactions and their role in the development of a disabled mathematical identity. Educ Stud Math 83, 341–368 (2013). https://doi.org/10.1007/s10649-012-9457-z

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