Elogi de la visualització: l'aprenentatge del pensament visual en matemàtiques

Claudi Alsina-Català

Resum


En l’educació matemàtica de tots els nivells es distingeixen quatre tipologies de visualització: il•lustracions, materials, grafs / diagrames i imatges geomètriques. S’analitzarà, a la llum dels mitjans visualitzadors actuals i dels resultats en aquest camp de la recerca educativa, el rol central que les imatges geomètriques poden jugar en el desenvolupament del pensament visual avançat. S’analitzarà, també, com afavorir el pensament visual a través d’aprendre les pròpies tècniques d’elaborar aquests tipus d’imatges.

Paraules clau


Visualització; Tipologies visuals; Pensament visual

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Referències


Alsina, C.; Nelsen, R.B. (2006). Math Made Visual: Creating Images for Understanding Mathematics. Washington: Mathematical Association of America.

Alsina, C.; Nelsen, R.B. (2009). When Less is More. Visualizing Basic Inequalities. Washington: Mathematical Association of America.

Armstrong, T. (1994). Multiple Intelligences in the Classroom. Association for Supervision and Curriculum Development (ASCD).

Arnheim, R. (1969). Visual Thinking. Nova York: Faber & Faber.

Craiven, T.V.; Rubenstein, R. (Eds.) (2009). Understanding Geometry for a Changing World, Reston: NCTM.

Davis, P.J. (1993). Visual theorems. Educational Studies in Mathematics, 24, 333-344.

Gardner, H. (1983). Frames of Mind: The Theory of Multiple Intelligences. Nova York: Basic Books.

Goodman, N. (1976). Languages of Art: An Approach to a Theory of Symbols. Oxford: Oxford University Press.

Hanna, G., Jahnke, H.N. (1996). Proof and proving. A A.J. Bishop et al. (Eds) International Handbook of Mathematics Education, Dordrecht: Kluwer, pp. 877-908.

Hendricks, V.F. et al. (Eds.) (2003). Visualization, Explanation and Reasoning Styles in Mathematics. Dordrecht: Kluwer.

Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24, 389-399.

Lakatos, I. (1976). Proofs and Refutations. Cambridge: Cambridge Univ. Press.

Laspina, J.A. (1998). The Visual Turn and the Transformation of the Textbook. Nova York: Lawrence Erlbaum Associates.

Loomis, E.S. (1969). The Pythagorean Proposition. Washington: National Council of Teachers of Mathematics, Inc.

Malkevitch, J. (Ed.) (1991). Geometry’s Future. Lexington: COMAP.

Mason, J. H. (2004). Mathematics Teaching Practice. A Guide for University and College Lectures, Chichester: Horwood Pub.

Murphy, S.J. (2006). Pictures + Words + Math = Story. Book Links. Volume 16, núm. 2. (November), 34–35.

NCTM (2000). Principles and Standards for School Mathematics. Washington: National Council of Teachers of Mathematics Inc.

Nelsen, R.B. (1993). Proofs without Words: Exercises in Visual Thinking, Washington: Mathematical Association of America (Proyecto Sur, Granada, 2001).

Nelsen, R. B. (2000). Proofs without Words II: More Exercises in Visual Thinking. Washington: Mathematical Association of America.

Pólya, G. (1954). Mathematics and Plausible Reasoning: Induction and Analogy in Mathematics. Vol. I, Princeton: Princeton University Press.

Pólya, G. (1981). Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving (2 vols., combined ed.) New York: John Wiley & Sons.

Rav, Y. (1999). Why do we prove theorems? Philosophia Mathematica, 7 volume 3, 5-41.

Rotman, J. (1998). Journey into Mathematics: An Introduction to Proofs. New York: Prentice Hall.

Senechal, M. (1991). Visualization and visual thinking, in: Geometry's Future, J. Malkevitch, ed., pp. 15-22.

Tufte, E. R. (1990). Envisioning Information. Cheschire: Graphics Press.

Tufte, E. R. (1997). Visual Explanations: Images and Quantities, Evidence and Narrative. Cheschire: Graphics Press.

ZDM (1994). Analyses: Visualization in Mathematics and Didactics of Mathematics, Vol. 1, Karlsruhe: ZDM.

Zimmermann, W.; Cunningham, E. (Eds.) (1991). Visualization in Teaching and Learning Mathematics, Notes 19, Washington: Mathematical Association of America.




DOI: https://doi.org/10.1344/reire2009.2.3232



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