Volume 17, Issue 1
  • ISSN 1568-1475
  • E-ISSN: 1569-9773
Buy:$35.00 + Taxes



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.


Article metrics loading...

Loading full text...

Full text loading...


  1. Adámek, Jiri
    (1983) Theory of mathematical structures. Dordrecht: D. Reidel Publishing Company.
    [Google Scholar]
  2. 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), 210–233.10.1075/gest.13.2.05ali
    https://doi.org/10.1075/gest.13.2.05ali [Google Scholar]
  3. 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, 45, 425–440.10.1007/s11858‑012‑0476‑0
    https://doi.org/10.1007/s11858-012-0476-0 [Google Scholar]
  4. 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), 65–100.10.1080/07370008.2013.858161
    https://doi.org/10.1080/07370008.2013.858161 [Google Scholar]
  5. Baker, J. E. , Maxim Bruckheimer , & H. Graham Flegg
    (1971) A pedagogic approach to morphisms. Educational Studies in Mathematics, 4 (2), 252–263.10.1007/BF00303390
    https://doi.org/10.1007/BF00303390 [Google Scholar]
  6. 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, 136, 539–550.10.1037/0096‑3445.136.4.539
    https://doi.org/10.1037/0096-3445.136.4.539 [Google Scholar]
  7. Calbris, Geneviève
    (2011) Elements of meaning in gesture. Amsterdam & Philadelphia: John Benjamins Publishing Company.10.1075/gs.5
    https://doi.org/10.1075/gs.5 [Google Scholar]
  8. 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, 7, 303–319.10.1080/13670050408667815
    https://doi.org/10.1080/13670050408667815 [Google Scholar]
  9. 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.10.1007/978‑3‑642‑04793‑0_4
    https://doi.org/10.1007/978-3-642-04793-0_4 [Google Scholar]
  10. Cook, Susan W. , Ryan G. Duffy , & Kimberly M. Fenn
    (2013) Consolidation and transfer of learning after observing hand gesture. Child Development, 84 (6), 1863–1871.10.1111/cdev.12097
    https://doi.org/10.1111/cdev.12097 [Google Scholar]
  11. 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, 7, 211–232.10.1207/s15327647jcd0702_4
    https://doi.org/10.1207/s15327647jcd0702_4 [Google Scholar]
  12. Gallistel, Charles R. & Adam P. King
    (2009) Memory and the computational brain: Why cognitive science will transform neuroscience. Chichester: Wiley-Blackwell.10.1002/9781444310498
    https://doi.org/10.1002/9781444310498 [Google Scholar]
  13. Gerofsky, Susan
    (2010) Mathematical learning and gesture: Character viewpoint and observer viewpoint in students’ gestured graphs of functions. Gesture, 10 (2/3), 321–343.10.1075/gest.10.2‑3.10ger
    https://doi.org/10.1075/gest.10.2-3.10ger [Google Scholar]
  14. Goldin-Meadow, Susan
    (2009) How gesture promotes learning throughout childhood. Child Development Perspectives, 3, 106–111.10.1111/j.1750‑8606.2009.00088.x
    https://doi.org/10.1111/j.1750-8606.2009.00088.x [Google Scholar]
  15. 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]
  16. Gullberg, Marianne
    (2006) Some reasons for studying gesture and second language acquisition (Hommage à Adam Kendon). International Review of Applied Linguistics, 44, 103–124.10.1515/IRAL.2006.004
    https://doi.org/10.1515/IRAL.2006.004 [Google Scholar]
  17. Krause, Eugene F.
    (1969) Homomorphism: A unifying concept, Mathematics Teacher, 62 (8), 617–622.
    [Google Scholar]
  18. Lakoff, George & Raphael Núñez
    (2000) Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
    [Google Scholar]
  19. McNeill, David
    (1992) Hand and mind: What gestures reveal about thought. Chicago, IL: University of Chicago Press.
    [Google Scholar]
  20. Ping, Raedy & Susan Goldin-Meadow
    (2008) Hands in the air: Using ungrounded iconic gestures to teach children conservation of quantity. Developmental Psychology, 44 (5), 1277–1287.10.1037/0012‑1649.44.5.1277
    https://doi.org/10.1037/0012-1649.44.5.1277 [Google Scholar]
  21. Richland, Lindsey Engle
    (2015) Linking gestures: Cross-cultural variation during instructional analogies. Cognition and Instruction, 33 (4), 295–321.10.1080/07370008.2015.1091459
    https://doi.org/10.1080/07370008.2015.1091459 [Google Scholar]
  22. Roth, Wolff-Michael
    (2001) Their role in teaching and learning. Review of Educational Research, 71 (3), 365–392.10.3102/00346543071003365
    https://doi.org/10.3102/00346543071003365 [Google Scholar]
  23. Sime, Daniela
    (2006) What do learners make of teachers’ gestures in the classroom?International Review of Applied Linguistics in Language Teaching, 44 (2), 211–230.10.1515/IRAL.2006.009
    https://doi.org/10.1515/IRAL.2006.009 [Google Scholar]
  24. Singer, Melissa A. & Susan Goldin-Meadow
    (2005) Children learn when their teachers’ gestures and speech differ. Psychological Science, 16, 85–89.10.1111/j.0956‑7976.2005.00786.x
    https://doi.org/10.1111/j.0956-7976.2005.00786.x [Google Scholar]
  25. 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]
  26. Valenzeno, Laura , Martha W. Alibali , & Roberta L. Klatzky
    (2003) Teachers’ gestures facilitate students’ learning: A lesson in symmetry. Contemporary Educational Psychology, 28, 187–204.10.1016/S0361‑476X(02)00007‑3
    https://doi.org/10.1016/S0361-476X(02)00007-3 [Google Scholar]

Data & Media loading...

  • Article Type: Research Article
Keyword(s): gesture; gesture sequence; learning; mathematics; polysign
This is a required field
Please enter a valid email address
Approval was successful
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error