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Mathematics students talking past each other: emergence of ambiguities in linear algebra proof constructions involving the uniqueness quantification

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Abstract

This paper examines proof constructions in group work in the field of linear algebra teaching at the university level. Studies have shown that students at tertiary level have difficulties in understanding different kinds of quantifiers, which are fundamental in linear algebra proof constructions. This study investigates how two student groups, with a tutor involved in one of the groups, construed meaning in the context of proving unique existence of the adjoint endomorphism. The students and the tutor used certain words and phrases in the context of mathematical uniqueness differently. The study analyses from an interactionist standpoint how these ambiguities emerged. The results indicate that due to different background understandings of mathematical uniqueness students attributed different meanings to certain words and expressions, which prevented the students from negotiating a consensus during the proving process.

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Notes

  1. In the interactionist perspective one speaks of taken-to-be-shared-meanings to be more precise.

  2. If we extend the notions of the word element beyond the strictly linear algebra setting, elements could mean variables, symbols, chemical substances and much more.

  3. Conventional character of the framing means that this way of interpreting the situation is established and therefore usually fits the interpretations of other interaction participants.

  4. Under the interactionist assumption that the interpretations of the interlocutors cannot be congruent, it must be expected that ambiguities of certain words and phrases occur permanently in interactions. Here, ambiguities are considered that prevent the state of intersubjectivity.

  5. The students’ names are pseudonyms.

  6. The students’ names are pseudonyms.

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  1. Universität Hamburg, Hamburg, Germany

    Ann Sophie Stuhlmann

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  1. Ann Sophie Stuhlmann
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Correspondence to Ann Sophie Stuhlmann.

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Appendix

Appendix

<:

Overlapping/simultaneous speech

#:

Interrupting, seamless transition between speakers

(.)/(..)/(…):

Pause for 1–3 s

?:

Rising intonation

.:

Lowering intonation

THEN:

Speaking up

[Laughs]:

Actions, paralinguistic utterances

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Stuhlmann, A.S. Mathematics students talking past each other: emergence of ambiguities in linear algebra proof constructions involving the uniqueness quantification. ZDM Mathematics Education 51, 1083–1095 (2019). https://doi.org/10.1007/s11858-019-01099-9

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