The Importance of Seeing in Mathematics Communication

Isabel Vale, Ana Barbosa

Abstract

This paper discusses the difficulties, reactions and conceptions of future teachers in relation to tasks that privilege different forms of communication in visual contexts. The tasks proposed focus on seeing the information directly or listening to the information without seeing. This research is of qualitative nature and was developed with forty-five future teachers of basic education. Data emerged from classroom observations, a questionnaire, written productions and photographic registers of students solving the tasks. The results show that students reacted positively to the proposed tasks, manifesting interest and motivation despite of some difficulties revealed in communication. They recognized the potential of the tasks to develop/improve mathematical knowledge.

Keywords

Teacher training, mathematical communication, visual context

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References

Bishop, A., & Goffree, F. (1986). Classroom organization and dynamics. In B. Christiansen, A.G. Howson & M. Otte (Eds.), Perspectives on mathematics education (pp. 309-365). Dordrecht: Reidel.

Boavida, A. M., Paiva, A. L., Cebola, G. Vale, I. & Pimentel, T. (2008). A experiência matemática no ensino básico. Lisboa: ME/DGIDC

Borromeo Ferri, R. (2012). Mathematical Thinking styles and their influence on teaching and learning mathematics. Paper presented at the 12th International Congress on Mathematical Education, Seul, Korea. Retrieved in march, 5, 2015 from: http://www.icme12.org/upload/submission/1905_F.pdf

Cuevas, G. J. (1984). Mathematics Learning in English as a Second Language. Journal of Research in Mathematics Education, 15, 135-44.

Doyle, W. (1988). Work in mathematics classes: The context of students’ thinking during instruction. Educational Psycologist, 23, 167-80.

Franke, M.L., Kazemi, E., & Battey, D. (2007). Understanding teaching and classroom practice in mathematics. In F. Lester (Ed.), Second handbook of mathematics teaching and learning (pp. 225-256). Greenwich, CT: Information Age.

Gardner, H. (1983). Frames of mind: the theory of multiple intelligences. New York: Basic Books.

Goldin, G. (2008). Perspectives on representation in mathematical learning and problem solving. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed). NY: Routledge.

Goldin-Meadow, S., Kim, S. & Singer, M. (1999). What the teacher’s hands tell the student’s mind about Math. Journal of Educational Psychology, 91(4), 720-730.

Goldin-Meadow, S. & Wagner, S. (2005). How our hands help us learn. TRENDS in Cognitive Sciences, 9(5), 234-241.

Holton, D., Cheung, K., Kesianye, S., Losada, M., Leikin, R., Makrides, G., Meissner, H., Sheffield, L. & Yeap, B. (2009). Teacher development and mathematical challenge. In Edward J., Barbeau & Peter J. Taylor (Eds.), Challenging Mathematics In and Beyond the Classroom – New ICMI Study Series 12 (pp. 205-242). New York: Springer.

Hwang, S., Herzig, M. & Padden, C. (2013). Different ways of thinking: The importance of gesture in child development. Visual language & Visual learning: research brief. Retrieved in june, 11, 2016, from: http://vl2.gallaudet.edu/files/2913/9216/6292/research-brief-10-different-ways-of-thinking.pdf

Kessler, C., Quinn, M.E. & Hayes, C.W. (1985). Processing Mathematics in a Second Language: Problems for LEP Children. Paper presented at the Delaware Symposium VII on Language Studies. University of Delaware, Newark, DE.

Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.

Martinho, M. H., e Ponte, J. P. (2005). Comunicação na sala de aula de Matemática: Práticas e reflexão de uma professora de Matemática. In J. Brocardo, F. Mendes, e A. M. Boavida (Eds.), Actas do XVI Seminário de Investigação em Educação Matemática (pp. 273-293). Setúbal: APM.

National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.

Neill, S. (1991). Classroom nonverbal communication. London: Routledge.

Ontario Ministry of Education. (2005). The Ontario Curriculum, Grades 1 to 8: Mathematics. Toronto, ON: Queen’s Printer for Ontario.

Ponte, J. P. (2005). Gestão curricular em Matemática. In GTI (Ed.), O professor e o desenvolvimento curricular (pp. 11-34). Lisboa: APM.

Presmeg, N. (2014). Creative advantages of visual solutions to some non-routine mathematical problems. In S. Carreira, N. Amado, K. Jones & H. Jacinto, (Eds.), Proceedings of the Problem@Web International Conference: Technology, Creativity and Affect in mathematical problem solving (pp. 156-167). Faro, Portugal: Universidade do Algarve.

Rivera, F. (2011). Toward a Visually-Oriented School Mathematics Curriculum: Research, Theory, Practice, and Issues. Dordrecht, Netherlands: Springer.

Stein, M. & Smith, M. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268-275.

Tripathi, P. N. (2008). Developing mathematical understanding through multiple representations. Mathematics Teaching in Middle School, 13(89), 438-445.

Vale, I. (2009). Das tarefas com padrões visuais à generalização. XX SIEM. in J. Fernandes, H. Martinho & F. Viseu (Orgs), Actas do Seminário de Investigação em Educação Matemática (p. 35-63). Viana do Castelo: APM.

Vale, I. & Barbosa, A. (2015). Mathematics Creativity in Elementary Teacher Training. Journal of the European Teacher Education Network, 10, 101-109.

Vygotsky, L.S. (1997). Collected works, vol4, (R. Rieber, Ed). New York: Plenum.

Wood, L. (2012). Practice And Conceptions: Communicating Mathematics In The Workplace. Educational Studies In Mathematics, 79(1), pp. 109-125.

Zimmermann, W., & Cunningham, S. (1991). Visualization in teaching and learning Mathematics. Washington, DC: Mathematical Association of America.



Categories: 2017, Articles, Mathematics Education

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