Gesture as a Cognitive Support to Solve Mathematical Problems

Mauro Francaviglia, Rocco Servidio

.

DOI: 10.4236/psych.2011.22015                

Abstract

The aim of this study was to investigate the relationships between gestures and mathematical problem solving. It concentrates on the idea that gestures can improve the student’s mathematical conceptual abilities. The educational aim of the current study was to understand whether Penelope sewing the cloth every day will be eventually able to finish it in 50 days, before Ulysses returns in his home-town. To analyse children’s gestures we applied the McNeill classification. The participants were five children aged between 9 and 10 years, attending the fifth-grade class of a primary school in Turin, Italy. We used the observational method to analyse the children’s gestures behaviour. At the end of the analysis, we collected a corpus of 538 gestures. Results show that children use different gesture patterns to communicate their own mathematical ideas. Overall, these findings suggest that gestures facilitate children’ learning of mathematical concepts and improve their cognitive strategies to the problem solution.

Keywords

Gestures, Mathematical Problem Solving, Mathematical Learning, Cognitive Processing

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Alibali, M. W., Bassok, M., Solomon, K. O. S., Syc, E., & Goldin- Meadow, S. (1999). Illuminating mental representations through speech and gesture. Psychological Science, 10, 327-333. doi:10.1111/1467-9280.00163
[2]	Arzarello, F., Bazzini, L., Ferrara, F., Robutti, O., Sabena, C., & Villa, B. (2006). Will Penelope choose another bridegroom? Looking for an answer through signs. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 73-80). Prague: Charles University.
[3]	Arzarello, F., Francaviglia, M., & Servidio, R. (2006). Gesture and body-tactile experience in the learning of mathematical concepts. In Proceedings of the International Conference on Applied Mathematics-APLIMAT (pp. 253-259). Bratislava, SL: University of Slovenia.
[4]	Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70, 97-109. doi:10.1007/s10649-008-9163-z
[5]	Bazzini, L. (2001). From grounding metaphors to technological devices: A call for legitimacy in school mathematics. Educational Studies in Mathematics, 47, 259-271. doi:10.1023/A:1015143318759
[6]	Church, R. B., Ayman-Nolley, S., & Alibali, M. W. (2001). Cross- modal representation and deep learning. Annual meeting of the cognitive development society. Virginia Beach, VA.
[7]	Cook, S. W., & Goldin-Meadow, S. (2006). The role of gesture in learning: Do children use their hands to change their minds? Journal of Cognition and Development, 7, 211-232. doi:10.1207/s15327647jcd0702_4
[8]	Edwards, L. (2009). Gesture, conceptual integration and mathematical talk. International Journal for Studies in Mathematics Education, 1, 33-46.
[9]	Gallese, V., & Lakoff, G. (2005). The brain’s concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22, 455-479. doi:10.1080/02643290442000310
[10]	Goldin-Meadow, S. (1999). The role of gesture in communication and thinking. Trends in Cognitive Sciences, 3, 419-429. doi:10.1016/S1364-6613(99)01397-2
[11]	Goldin-Meadow, S. (2003). Hearing gestures: How our hands help us think. Chicago: University Press.
[12]	Goldin-Meadow, S., Nusbaum, H., Kelly, S. D., & Wagner, S. (2001). Explaining math: Gesturing lightens the load. Psychological Science, 12, 516-522. doi:10.1111/1467-9280.00395
[13]	Kelly, S. D., Singer, M., Hicks, M. J. & Goldin-Meadow, S. (2002). A helping hand in assessing children’s knowledge: Instructing adults to attend to gesture. Cognition and Instruction, 20, pp. 1-26. doi:10.1207/S1532690XCI2001_1
[14]	Kendon, A. (2004). Gesture: Visible action as utterance. Cambridge, UK: University Press.
[15]	Kita, S. (2000). How representational gestures help speaking. In D. McNeill (Ed.), Language and gesture (pp. 162-185). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511620850.011
[16]	Kita, S. (2003). Pointing: A foundational building block of human communication. In S. Kita (Ed.), Pointing: Where language, culture and cognition meet (pp. 1-9). Mahwah: Lawrence Erlbaum.
[17]	Lakoff, G., & Nú?ez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.
[18]	Lim, K. V., Wilson, J. A., Hamm, J. P., Phillips, N., Iwabuchi, J. S., Corballis, C. M., Arzarello, F. & Thomas O. M. (2009). Semantic processing of mathematical gestures. Brain and Cognition, 71, 306- 312. doi:10.1016/j.bandc.2009.07.004
[19]	McNeill, D. (1996). Hand and mind: What gestures reveal about thought. Chicago: The Uni-versity of Chicago Press.
[20]	Nemirovsky, R., & Ferrara, F. (2009). Mathematical imagination and embodied cognition. Educational Studies in Mathematics, 70, 159- 174. doi:10.1007/s10649-008-9150-4
[21]	Parrill, F., & Sweetser, E. (2004). What we mean by meaning. Gesture, 4, 197-219. doi:10.1075/gest.4.2.05par
[22]	Perfect, T. J., & Schwartz, B. L. (2002). Applied metacognition. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511489976
[23]	Radford, L., Edwards, L., & Arzarello, F. (2009). Introduction: Beyond words. Educational Stud-ies in Mathematics, 70, 91-95. doi:10.1007/s10649-008-9172-y
[24]	Rasmussen, C., Stephan, M., & Allen, K. (2004). Classroom mathematical practices and gesturing. Journal of Mathematical Behavior, 23, 301-323. doi:10.1016/j.jmathb.2004.06.003
[25]	Reynolds, F. J., & Reeve, R. A. (2002). Gesture in collaborative mathematics problem-solving. Journal of Mathematical Behavior, 20, 447-460. doi:10.1016/S0732-3123(02)00091-3
[26]	Singer, M. A., & Goldin-Meadow, S. (2005). Children learn when their teacher’s ges-tures and speech differ. Psychological Science, 16, 85- 89. doi:10.1111/j.0956-7976.2005.00786.x
[27]	Vygotskij, L. S. (1962). Thought and language. Chicago: MIT Press. doi:10.1037/11193-000