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The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning

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Abstract

This study explores interactions with diagrams that are involved in geometrical reasoning; more specifically, how students publicly make and justify conjectures through multimodal representations of diagrams. We describe how students interact with diagrams using both gestural and verbal modalities, and examine how such multimodal interactions with diagrams reveal their reasoning. We argue that when limited information is given in a diagram, students make use of gestural and verbal expressions to compensate for those limitations as they engage in making and proving conjectures. The constraints of a diagram, gestures and linguistic systems are semiotic resources that students may use to engage in geometrical reasoning.

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Notes

  1. The word modality is often used to refer to each of the semiotic systems used in communication; thus the expression “multimodal representation” used above. Modality is also used in linguistics with a different meaning. Particularly, in systemic linguistics, modality is used to name one of the systems with which speakers construct relationships with their audience. This is the sense with which it is used in this section. Elsewhere in the paper we may use modality in the first, semiotic, sense. The context will help clarify what is the usage alluded to.

  2. All the names of the teachers and students in this paper are pseudonyms.

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Author information

Authors and Affiliations

  1. The University of Michigan, Ann Arbor, MI, USA

    Chia-Ling Chen & Patricio Herbst

  2. 610 East University Ave, Room 4119 School of Education, Ann Arbor, MI, 48109-1259, USA

    Patricio Herbst

Authors
  1. Chia-Ling Chen
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  2. Patricio Herbst
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Corresponding author

Correspondence to Patricio Herbst.

Additional information

The research reported in this study was done with the support of a National Science Foundation CAREER grant, REC 0133619 to the second author. All opinions are those of the authors and do not necessarily represent the views of the Foundation.

Appendix: activity worksheet of the intervention lesson

Appendix: activity worksheet of the intervention lesson

figure a

There are six lines on the paper and some of their intersections are not visible.

  1. 1.

    Would it be possible for somebody to determine the measures of all the angles formed by those lines, considering that not all angles can be measured? Explain.

  2. 2.

    What is the total number of different angle measures that one would need to determine? Explain.

  3. 3.

    How many of those angle measures would be impossible to find unless one could extend the lines beyond the screen limits? Explain.

  4. 4.

    What is the minimum number of angles that one would have to measure before being able to say “I know all the angle measures”? Explain.

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Chen, CL., Herbst, P. The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning. Educ Stud Math 83, 285–307 (2013). https://doi.org/10.1007/s10649-012-9454-2

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