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Article published In:
Gesture
Vol. 17:1 (2018) ► pp.128–157

The role of gestural polysigns and gestural sequences in teaching mathematical concepts

The case of halving

| University of Johannesburg
| University of Cape Town
| University of Grenoble-Alpes
| University of Cape Town

In this paper, we examine the conceptual pedagogical value of representational gestures in the context of teaching halving to first graders. We use the concept of the ‘polysign’ as an analytical tool and introduce the notion of a ‘mathematics gesture sequence’ to assess the conceptual role gestures play in explicating mathematical concepts. In our study of four teachers each teaching a lesson on halving, they produced representational polysign gestures that provided multiple layers of information, and chained these gestures in mathematical gestural sequences to spatially represent the operation of halving. Their use of gestures and their ability to use gestures accurately to convey mathematical concepts varied. During the lesson, learners, whose teachers used few representational gestures or used gestures that were conceptually incongruent with the mathematical concept, expressed more confusion than learners whose teachers used conceptually appropriate gestures. While confusion can be a productive part of the learning process, our analysis shows that producing conceptually appropriate gestures may be important in mediating concepts and the transition from concrete and personal symbolic processes to institutional mathematical signs.

Keywords: gesture, learning, polysign, gesture sequence, mathematics
Article outline
  • Introduction
  • The role of gesture in mathematics classes
    • The polysign gesture: An analytical tool
  • Methodology
  • Teachers’ overall patterns of gesture use
  • Representing the mathematical concept of halving in gesture
    • The halving operation represented by polysigns being chained together
    • From doubling to halving, using a MGS
    • Halving using ambiguous polysign gestures
  • Children’s responses to instructional input
  • Conclusion
  • Acknowledgements
  • References
Published online: 19 October 2018
DOI logo
https://doi.org/10.1075/gest.00013.ove
References
Adámek, Jiri
(1983) Theory of mathematical structures. Dordrecht: D. Reidel Publishing Company.Google Scholar
Alibali, Martha W., Andrew G. Young, Noelle M. Crooks, Amelia Yeo, Matthew S. Wolfgram, Iasmine M. Ledesma, Mitchell J. Nathan, Ruth Breckinridge Church, & Eric J. Knuth
(2013a) Students learn more when their teacher has learned to gesture effectively. Gesture, 13 (2), 210–233. DOI logoGoogle Scholar
Alibali, Martha W., Mitchell J. Nathan, Ruth Breckinridge Church, Matthew S. Wolfgram, Suyeon Kim, & Eric J. Knuth
(2013b) Teachers’ gestures and speech in mathematics lessons: Forging common ground by resolving trouble spots. ZDM: The International Journal on Mathematics Education, 451, 425–440. DOI logoGoogle Scholar
Alibali, Martha W., Mitchell J. Nathan, Matthew S. Wolfgram, Ruth Breckinridge Church, Steven A. Jacobs, Chelsea Johnson Martinez, & Eric J. Knuth
(2014) How teachers link ideas in mathematics instruction using speech and gesture: A corpus analysis. Cognition and Instruction, 32 (1), 65–100. DOI logoGoogle Scholar
Baker, J. E., Maxim Bruckheimer, & H. Graham Flegg
(1971) A pedagogic approach to morphisms. Educational Studies in Mathematics, 4 (2), 252–263. DOI logoGoogle Scholar
Broaders, Sara C., Susan W. Cook, Zachary Mitchell, & Susan Goldin-Meadow
(2007) Making children gesture brings out implicit knowledge and leads to learning. Journal of Experimental Psychology: General, 1361, 539–550. DOI logoGoogle Scholar
Calbris, Geneviève
(2011) Elements of meaning in gesture. Amsterdam & Philadelphia: John Benjamins Publishing Company. DOI logoGoogle Scholar
Church, Ruth Breckinridge, Saba Ayman-Nolley, & Shahrzad Mahootian
(2004) The role of gesture in bilingual education: Does gesture enhance learning? International Journal of Bilingual Education and Bilingualism, 71, 303–319. DOI logoGoogle Scholar
Colletta, Jean-Marc, Ramona Nkosinathi Kunene, Aurélie Venouil, Virginie Kaufmann, & Jean-Pascal Simon
(2009) Multi-track annotation of child language and gestures. In Michael Kipp, Jean-Claude Martin, Patricia Paggio, & Dirk Heylen (Eds.), Multimodal corpora: From models of natural interactions to systems and applications (pp. 54–72). Berlin: Springer. DOI logoGoogle Scholar
Cook, Susan W., Ryan G. Duffy, & Kimberly M. Fenn
(2013) Consolidation and transfer of learning after observing hand gesture. Child Development, 84 (6), 1863–1871. DOI logoGoogle Scholar
Cook, Susan W. & Susan Goldin-Meadow
(2006) The role of gesture in learning: Do children use their hands to change their minds? Journal of Cognition and Development, 71, 211–232. DOI logoGoogle Scholar
Gallistel, Charles R. & Adam P. King
(2009) Memory and the computational brain: Why cognitive science will transform neuroscience. Chichester: Wiley-Blackwell. DOI logoGoogle Scholar
Goldin-Meadow, Susan
(2009) How gesture promotes learning throughout childhood. Child Development Perspectives, 31, 106–111. DOI logoGoogle Scholar
Goldin-Meadow, Susan, Susan W. Cook, & Zachary P. Mitchell
(2009) Gesturing gives children new ideas about math. Pyschological Science, 20 (3), 267–272.Google Scholar
Gullberg, Marianne
(2006) Some reasons for studying gesture and second language acquisition (Hommage à Adam Kendon). International Review of Applied Linguistics, 441, 103–124. DOI logoGoogle Scholar
Krause, Eugene F.
(1969) Homomorphism: A unifying concept, Mathematics Teacher, 62 (8), 617–622.Google Scholar
Lakoff, George & Raphael Núñez
(2000) Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
McNeill, David
(1992) Hand and mind: What gestures reveal about thought. Chicago, IL: University of Chicago Press.Google Scholar
Ping, Raedy & Susan Goldin-Meadow
(2008) Hands in the air: Using ungrounded iconic gestures to teach children conservation of quantity. Developmental Psychology, 44 (5), 1277–1287. DOI logoGoogle Scholar
Richland, Lindsey Engle
(2015) Linking gestures: Cross-cultural variation during instructional analogies. Cognition and Instruction, 33 (4), 295–321. DOI logoGoogle Scholar
Roth, Wolff-Michael
(2001) Their role in teaching and learning. Review of Educational Research, 71 (3), 365–392. DOI logoGoogle Scholar
Sime, Daniela
(2006) What do learners make of teachers’ gestures in the classroom? International Review of Applied Linguistics in Language Teaching, 44 (2), 211–230. DOI logoGoogle Scholar
Singer, Melissa A. & Susan Goldin-Meadow
(2005) Children learn when their teachers’ gestures and speech differ. Psychological Science, 161, 85–89. DOI logoGoogle Scholar
Tellier, Marion
(2008) The effect of gestures on second language memorization by young children. In Marianne Gullberg & Kees de Bot (Eds.), Special Issue: Gestures in language development. Gesture, 8 (2), 219–235.Google Scholar
Valenzeno, Laura, Martha W. Alibali, & Roberta L. Klatzky
(2003) Teachers’ gestures facilitate students’ learning: A lesson in symmetry. Contemporary Educational Psychology, 281, 187–204. DOI logoGoogle Scholar
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Nathan, Mitchell J., Amelia Yeo, Rebecca Boncoddo, Autumn B. Hostetter & Martha W. Alibali
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