Designing aesthetic experiences for young mathematicians: a model for Mathematics Education reform

Autores

Palavras-chave:

Aesthetic Experience, Elementary Mathematics, Reform

Resumo

Although reform is typically associated with change on a grand, pervasive scale, our model is much less intrusive pedagogically. We are not seeking a revolution in mathematics education, but a strategic focus on mathematics worthy of attention, worthy of conversation, worthy of children's incredible minds, which thirst for knowledge and for opportunities to explore, question, flex their imagination, discover, discuss and share their learning. We believe that occasional, well-designed aesthetic mathematics experiences "that are immersive, infused with meaning, and felt as coherent and complete" (Parrish, 2009, p.511), and the associated experience of complex, surprising, emotionally engaging, and viscerally pleasing mathematics, can serve as "a process of enculturation" (Brown, Collins and Duguid, 1989, p. 33) with lasting impact on students' (and teachers') dispositions, living fruitfully in future experiences (Dewey, 1938), by raising expectation and anticipation of what mathematics can offer, and what the intellectual, emotional and visceral rewards might be when quenching a thirst for mathematics.

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Referências

Boorstin, J. (1990). The Hollywood eye: What makes movies work. NY: Harper Collins Publishers.

Borba, M. & Villarreal, M.E. (2005). Humans-with-media and the reorganization of mathematical thinking. New York: Springer.

Boyd, B. (2001a). Nabokov's Pale Fire: The magic of artistic discovery. Princeton, NJ: Princeton University Press.

Boyd, B. (2001b). The origin of stories: Horton hears a Who. Philosophy and Literature 25(2), 197-214.

Boyd, B. (2009). On the origin of stories: evolution, cognition, and fiction. Cambridge, MA: Harvard University Press.

Brown, J.S., Collins, A,, & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32-42.

Bruner, J. (1962). On Knowing: Essays for the Left Hand. Cambridge, MA: Harvard University Press.

Burton, L. (1999). The practices of mathematicians: what do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37, 121-143.

Cummins, J., Brown, K. & Sayers, D. (2007). Literacy, Technology, and Diversity: Teaching for Success in Changing Times. Boston: Pearson Education, Inc.

Daniels, H. (1983). Famous last words: The American language crisis reconsidered. Carbondale, IL: Southern Illinois University Press.

Davis, B. and Simmt, E. (2006). Mathematics-for-teaching: an ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematic,. 61(3), 293–319.

Dewey, J. (1938). Experience & education. NY: Collier Books.

De Saint-Exupery, A. (1943/1999). The little prince. Hertfordshire, UK: Wordsworth Editions.

Dissanakye, E. (1992). Homo aestheticus. New York, NY: Free Press.

Egan, K. (1997). The educated mind: how cognitive tools shape our understanding. Chicago: University of Chicago Press.

Egan, K. (2002). Getting it wrong from the beginning. Our progressive inheritance from Herbert Spencer, John Dewey, and Jean Piaget. New Haven: Yale University Press.

Eisner, E. (2002). What can education learn from the arts about the practice of education? The John Dewey Lecture. Stanford University. Retrieved 17 December 2014.

Elmore, R.F. (1990). Restructuring Schools: The Next Generation of Educational Reform. San Francisco, CA: Jossey-Bass Publishers.

Fernandez-Armesto, F. (1997). Truth: A history and a guide for the perplexed. London: Bartam.

Fisher, P. (1998). Wonder, the rainbow, and the aesthetics of rare experiences. Cambridge, MA: Harvard University Press.

Fullan, M. (2007). The New Meaning of Educational Change. NY: Teachers College Press.

Gadanidis, G. (2012). Why can't I be a mathematician? For the Learning of Mathematics, 32(2), 20-26.

Gadanidis, G. (2014). Young children, mathematics and coding: A low floor, high ceiling, wide walls learning environment. In D. Polly (Ed). Cases on Technology Integration in Mathematics Education (pp. 312-344). Hersey, PA: IGI Global.

Gadanidis, G. (2015). Coding as a Trojan Horse for mathematics education reform. Journal of Computers in Mathematics and Science Teaching, 34(2), 155-173.

Gadanidis, G. & Borba, M. (2008). Our lives as performance mathematicians. For the Learning of Mathematics, 28(1), 42-49.

Gadanidis, G. & Borba, M. (2013). New media and research dissemination: the case of performing mathematics education research. Journal of Educational Multimedia and Hypermedia, 21(1), 335-348.

Gadanidis, G., Hughes, J. & Borba, M. (2008). Students as performance mathematicians. Mathematics Teaching in the Middle School, 14(3), 168-175.

Gadanidis, G., Hughes, J. & Cordy, M. (2011). Mathematics for gifted students in an arts- and technology-rich setting. Journal for the Education of the Gifted, 34(3), 397-433.

Gattegno, C. (1974). The Common Sense of Teaching Mathematics. New York, NY: Educational Solutions.

Gattegno, C. (1987). The Science of Education. Part 1 - Theoretical Considerations. New York, NY: Educational Solutions.

Greene, M. (1978). Towards wide-awakeness: An argument for the arts and humanities in education. In Landscapes in learning (pp. 162-167). NY: Teachers College Press.

Greene, M. (1995). Releasing the imagination: Essays on education, the arts, and social change. San Francisco: Jossey-Bass.

Hemmings, R. & Tahta, D.G. (1984). Images of Infinity. Fredonia, NY: Leapfrog Press.

Hess, F.M. (1998). Spinning Wheels: The Politics of Urban School Reform. Washington, D.C.: Brookings Institution Press.

Hewitt, D. (1999). Arbitrary and Necessary Part 1: A Way of Viewing the Mathematics Curriculum. For the Learning of Mathematics, 19(3), 2-9.

Holt, J. (1964). How children fail. London, UK: Pitman Publishing Company.

Hughes, J. (2008). The performative pull of research with new media. International Journal of Qualitative Methods, 7(3), 16-34.

Hull, G.A. & Katz, M. (2006). Creating an agentive self: case studies of digital storytelling. Research in the Teaching of English, 41(1), 43-81.

Kierkegaard, S. (1947). Concluding unscientific postscript to the 'Philosophical Fragments'. In R. Bretall (Ed.). A Kierkegaard Anthology (p. 74). Princeton, NJ: Princeton University Press.

Kleiner, I. & Movshovitz-Hadar, N. (1994). The Role of Paradoxes in the Evolution of Mathematics. The American Mathematical Monthly, 101(10) 963-974.

Levy, P. (1993). Tecnologias da Inteligência: O futuro do pensamento na era da informática. [Technologies of Intelligence: the future of thinking in the informatics era]. Rio de Janeiro, Brazil: Editora 34.

Malmivuori, M. (2006). Affect and self-regulation. Educational Studies in Mathematics, 63, 149-164.

Maturana, H.R. (1988). Reality: The search for objectivity or the quest for a compelling argument. The Irish Journal of Psychology, 9(1), 25–82.

Movshovitz-Hadar, N. (1994). Mathematics Theorems: An Endless Source of Surprise. For the Learning of Mathematics, 8(3), 34-40.

Norman, D.A. (2004). Emotional Design: Why we Love (or Hate) Everyday Things. NY: Basic Books.

Nunn, T.P. (1920). Education: its data and first principles. London; Edward, Arnold. Op 'T Eynde, P., De Corte, E. and Vershaffel, L. (2006). "Accepting emotional complexity": a socio-constructivist perspective on the role of emotions in the mathematics classroom. Educational Studies in Mathematics, 63, 193-207.

Papert, S. (1978). The mathematical unconscious. In J. Weshsler (Ed.) On aesthetics in science. Cambridge, MA: MIT Press.

Papert, S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. Basic Books, New York, 1980.

Parrish, P.E. (2009). Aesthetic principles for instructional design. Educational Technology and Research Development, 57, 511-528.

Piaget, J. (2008). Intellectual evolution from adolescence to adulthood. Human Development, 51, 40-47. (Original work published 1972)

Rancière , J. (1991). The Ignorant Schoolmaster: Five Lessons in Intellectual Emancipation. Redwood City, CA: Stanford University Press.

Root-Bernstein, R. (1996). The sciences and arts share a common creative aesthetic. In The elusive synthesis: Aesthetics and science (pp.49-82). Netherlands: Kluwer Academic Publishers.

Rodd, M. (2003). Witness as participation: the lecture theatre as site for mathematical awe and wonder. For the Learning of Mathematics 23(1), 39-43.

Schmittau, J. (2005). The development of algebraic thinking - A Vygotskian perspective. ZDM , 37(1), 16-22.

Sriraman, B. & Lesh, R. (2007). A conversation with Zoltan P. Dienes. Mathematical Thinking and Learning 9(1), 57-75.

Sinclair, N. (2001). The aesthetic is relevant. For the Learning of Mathematics, 21(1): 25-32.

Sinclair, N. & Watson, A. (2001). Wonder, the rainbow, and the aesthetics of rare experiences. The aesthetic is relevant. For the Learning of Mathematics, 21(1): 25-32.

Snow, C.P. (Jan 2013), "The Two cultures", The New Statesman. Retrieved 10/07/2015.

Sullivan, A.M. (2000). Notes from a marine biologist's daughter: on the art and science of attention. Harvard Educational Review, 70(2), 211-227.

Taylor, P. (1997). A small napkin. Globe and Mail, Facts and Arguments. 6 February 1997.

Accessed 14 December 2014 from http://www.mast.queensu.ca/~peter/pdf/smallnapkin.pdf.

Taylor, P. (2009). Telescopes and paraboloids. Toronto, ON: The Fields Institute. Accessed 14 December 2014 from http://www.fields.utoronto.ca/mathwindows.

Watson, A. & Mason, J. (2007). Surprise and inspiration. Mathematics Teaching, 200, 4-7.

Whitehead, A.N. (1967), The Aims of Education and Other Essays. New York: The Free Press.

Whittin, D.J. & Gary, C.C. (1994). Promoting mathematical explorations through children’s literature. The Arithmetic Teacher, 41(7), 394-399.

Wubbels, T. Korthagen, F. & Broekman, H. (1997). Preparing teachers for realistic mathematics education. Educational Studies in Mathematics, 32, 1–28.

Zan, R., Brown, L., Evans, J. and Hannula, M.S. (2006). Affect in mathematics education: an introduction. Educational Studies in Mathematics, 63, 113-121.

Zaslavsky, O. (2005). Seizing the opportunity to create uncertainty in learning mathematics. Educational Studies in Mathematics, 60, 297-321.

Zwicky, J. (2003). Wisdom & metaphor. Kentville, Nova Scotia: Gaspereau Press.

Publicado

2016-07-01

Como Citar

GADANIDIS, G.; BORBA, M. DE C.; HUGHES, J.; LACERDA, H. D. Designing aesthetic experiences for young mathematicians: a model for Mathematics Education reform. Revista Internacional de Pesquisa em Educação Matemática, v. 6, n. 2, p. 225-244, 1 jul. 2016.

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