Transitioning from “it looks like” to “it has to be” in geometrical workspaces: affect and near-to-me attention
Tipo de documento
Autores
Lista de autores
Rodd, Melissa
Resumen
Within a practitioner researcher framework, this paper draws on a particular mathematics education theory and aspects of neuroscience to show that, from a learner’s perspective, moving to a deductive reasoning style appropriate to basic Euclidean geometry, can be facilitated, or impeded, by emotion and/or directed attention. This shows that the issue of a person’s deductive reasoning is not a merely cognitive one, but can involve affective aspects related to perception – particularly perception of nearby sense data – and emotion. The mathematics education theory that has been used is that of the Espace de Travail Mathématique, the English translation of which is known as Mathematical Working Spaces (MWS). The aspects of neuroscience that have been used pertain to the distinct processing streams known as top-down and bottom-up attention. The practitioner research perspective is aligned with Mason’s teaching-practice-based ‘noticing’; qualitative data analysed in this report include individual interviews with school teachers on in-service courses and reflective notes from teaching. Basic Euclidean geometry is used as the medium for investigating transition from ‘it looks like’ to a reasoned ‘it has to be’.
Fecha
2016
Tipo de fecha
Estado publicación
Términos clave
Enfoque
Idioma
Revisado por pares
Formato del archivo
Volumen
30
Número
54
Rango páginas (artículo)
142-164
ISSN
19804415
Referencias
AUSTIN, J. H. Selfless Insight: Zen and the meditative transformation of consciousness. Cambridge MA: The MIT Press, 2009. AUSTIN, J. H. Zen and the brain: mutually illuminating topics. Frontiers in psychology, Lausanne Switzerland, v. 4, 784, p.1-9, oct. 2013. BARRANTES, M.; BLANCO, L. A study of prospective primary teachers’ conceptions of teaching and learning school geometry. Journal of Mathematics Teacher Education, Dordrecht, v. 9, issue 5, p.411-436, oct. 2006. BLACK, L.; MENDICK, H.; SOLOMON, Y. (Ed.). Mathematical Relationships: identities and Participation. Routledge: London, 2009. BLAKEMORE, S-J; FRITH, U. The Learning Brain. Oxford: Blackwell, 2005. BRITISH EDUCATIONAL RESEARCH ASSOCIATION-BERA. Ethical Guidelines for Educational research. 2014. Available at: Accessed: 11 Nov. 2015 DUBINSKY, J. M.; ROEHRIG, G.; VARMA, S. Infusing neuroscience into teacher professional development. Educational Researcher, Washington, v. 42, n. 6, p. 317-329, aug./sep. 2013. GAL, H.; LINCHEVSKI, L. To see or not to see: analyzing difficulties in geometry from the perspective of visual perception. Educational Studies in Mathematics, Dordrecht , v. 74, issue 2, p.163-183, jun. 2010. GARDNER, M. Aha! Insight. New York: W.H. Freeman & Company, 1978. GEOGEBRA. Dísponivel em: . Accessed 11 Nov. 2015. GOLDIN, G. A. Perspectives on emotion in mathematical engagement, learning and problem solving. In: PEKRUN, R.;LINNENBRINK-GARCIA, L. (Ed.). International handbook of emotions in education. Abingdon: Routledge, 2014. p. 391-414. GÓMEZ-CHACÓN I. M. Affective influences in the knowledge of mathematics. Educational Studies in Mathematics, Dordrecht v. 43, issue 2, p.149-168, sep. 2000. GÓMEZ-CHACÓN I. M.; KUZNIAK, A. Les espaces de travail géométrique de futurs professeurs en contexte de connaissances technologiques et professionnelles. Annales de Didactique et de Sciences Cognitives, Paris, v. 16, p. 187-216, 2011. GÓMEZ-CHACÓN I. M.; KUZNIAK, A. Spaces for geometric work: figural, instrumental, and discursive geneses of reasoning in a technological environment. International Journal of Science and Mathematics Education, Dordrecht v.13, n.1, p. 201-226, feb. 2015. GÓMEZ-CHACÓN, I. M. et al. (Ed.). Mathematical Working Space. Proceedings fourth etm symposium/espace de travail mathématique, actes quatrième symposium ETM. Madrid: Publicaciones del Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid. 2015. HATCH, G.; SHIU, C. Practitioner research and the construction of knowledge in mathematics education. 1998. In: SIERPINSKA, A.; KILPATRICK, J. (Ed.). Mathematics education as a research domain: a search for identity. An ICMI study. Netherlands: Springer Science & Business Media, 2012. v.4. p 297-315. HEATH, T. L. The thirteen books of euclid’s elements. Cambridge University Press, 1908. HODKINSON, P.; HODKINSON, H. The Strengths and Limitations of Case Study Research. Paper presented to the “Learning and Skills Development Agency conference Making an Impact on Policy and Practice”, Cambridge. 2001. p. 5–7. INGRAM, H. A. et al.. The role of proprioception and attention in a visuomotor adaptation task. Experimental Brain Research, Dordrecht v. 132, n.1, p. 114-126, may. 2000. KRAVITZ, D. J. et al.. A new neural framework for visuospatial processing. Nature Reviews Neuroscience, London, v. 12, issue 4, p. 217-230, apr. 2011. KÜCHEMANN, D.; RODD, M. On learning geometry for teaching, Mathematics Teaching, Derby,n. 229, p. 16-19, jul. 2012. KUZNIAK, A. Paradigmes et espaces de travail géométriques. Éléments d'un cadre théorique pour l'enseignement et la formation des enseignants en géométrie. Canadian Journal of Math, Science & Technology Education, Toronto, v. 6, n. 2, p. 167-187, 2006. KUZNIAK, A.; RAUSCHER, J-C. How do teachers’ approaches to geometric work relate to geometry students’ learning difficulties? Educational Studies in Mathematics, Dordrecht v. 77, issue 1, p.129-147, may. 2011. LILJEDAHL, P. Mathematical discovery and affect: The effect of AHA! experiences on undergraduate mathematics students. International Journal of Mathematical Education in Science and Technology, Abingdon v. 36, n.2-3, p. 219-236, 2005. MARESCHAL, D.; BUTTERWORTH, B.; TOLMIE, A. (Ed.). Educational Neuroscience. Oxford: Wiley-Blackwell, 2013. MASON, J.; PIMM, D. Stimulating Action Research on Teaching Mathematics through the use of explicit frameworks’. In: UNDERHILL, R.G. (Ed.). Proceedings of the 13th annual meeting of the north american chapter of the international group for the psychology of mathematics education. Blacksburg Virginia: Division of Curriculum and Instruction VPI & SU, 1991. p. 181-183,MASON, J.H. Researching your own practice: the discipline of noticing. Abingdon, Routledge, 2002. MOORE, C.; BARESSI, J. Imagination and the self. In: TAYLOR, M. (Ed.). The oxford handbook of the development of imagination. Oxford: Oxford University Press, 2013. p.288-301. NEMIROVSKY, R.; BORBA, M. Bodily activity and imagination in mathematics learning.Educational Studies in Mathematics, Dordrecht v. 57, issue 3, p. 303-305, nov. 2004. PINTO, Y. et al. Bottom-up and top-down attention are independent. Journal of vision, Rockville, v. 13, n.3, p. 16, jul. 2013. PRESMEG, N. C.; BALDERAS-CAÑAS, P. E. Visualization and affect in nonroutine problem solving. Mathematical Thinking and Learning, Philadelphia, v. 3, n. 4, p. 289 – 313, 2001. PROOF PROJECT. Longitudinal Proof project. 2003. Disponível em Accessed 13 Nov 2015. RESNICK, M. D. Mathematics as a science of patterns. Oxford: Clarendon Press. 1999. RODD, M. M. On Mathematical Warrants: proof does not always warrant, and a warrant may be other than a proof, Mathematical Thinking and Learning, Philadelphia, v. 2, n.3, p. 221-244, 2000. RODD, M. M. Teaching geometry interactively: communication, affect and visualization. In: HANNULA, M. et al. Current state of research on mathematical beliefs XVIII. Helsinki: Editora University of Helsinki., 2013.p. 341-357. RODD, M. Space for Geometric Work: points of affect. In: GÓMEZ-CHACÓN, M. I. et al. (Ed.). Mathematical working space, proceedings fourth etm symposium. Madrid: Publicaciones del Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 2015. p. 147-163. ROYAL SOCIETY. Brain Waves 2: Neuroscience: implications for education and lifelong learning. 2011. Disponível em: http://royalsociety.org/policy/projects/brain-waves/education-lifelong-learning/ Accessed: 26 Feb 2014. TALL, D. O. How humans learn to think mathematically: exploring the three worlds of mathematics. Cambridge: Cambridge University Press, 2013. VAN HIELE, P. M. Structure and Insight: a theory of mathematics Education. Orlando: Academic Press, 1986. WILLINGHAM, D. T.; LLOYD, J. W. How educational theories can use neuroscientific data. Mind, Brain, & Education, Oxford, v. 1, issue 3, p. 140-149, sep. 2007.