Creatures are approximately symmetrical and reflections in water are a common example of mirror symmetry. Human beings are naturally appreciative of symmetry, possibly because it is prevalent in the natural world. The mathematics of symmetry is found in decorative design, like kowhaiwhai in wharenui, and wallpaper patterns, and motifs such as logos. Since the logo maps onto itself three times in a full turn of 360⁰, the figure has rotational symmetry of order three. Each turn of 120⁰ (one third of one full rotation) maps the logo onto itself. This logo also has rotational symmetry about a point. T here are three lines where a mirror could be placed and the whole figure could be seen, with the image in the mirror forming the hidden half. A shape has symmetry if it has spatial pattern, meaning it maps onto itself either by reflection about a line, or rotation about a point.Ĭonsider the Mitsubishi logo. Vergnaud, G.: 1982, ‘Cognitive and development psychology research on mathematics education: Some theoretical and methodological issues’, For the Learning of Mathematics 3(2), 31–41.This unit centres on symmetry, particularly reflective and rotational symmetry, although there is some reference to translation symmetry. Kearsley (ed.), Artificial Intelligence and Instruction: Application and Methods, Reading MA: Addison-Welsey. Thompson, P.: 1987, ‘Mathematical microworlds and intelligent computer-assisted instruction’, in G. and Roschelle, J.: 1993, ‘Misconceptions reconceived: A constructivist analysis of knowledge in transition’, Journal of the Learning Sciences3(2), 115–163. Glaser (ed.), Advances in Instructional PsychologyVol. and Arcavi, A.: 1993, ‘Learning: The microgenetic analysis of one student’s evolving understanding of a complex subject matter domain’, in R. and Globerson T.: 1991, ‘Partners in cognition: Extending human intelligence with intelligent technologies’, Educational ResearcherApril, 2–9. Children, Computers, and Powerful Ideas, Brighton: Harvester. and Hoyles, C.: 1996, Windows on Mathematical Meanings: Learning Cultures and Computers, Mathematics Education Library, Dordrecht: Kluwer. Noss (eds.), Learning Mathematics and Logo, Cambridge, Massachusetts: MIT Press, pp. and Hoyles, C.: 1992, ‘Looking back and looking forward’, in C. (ed.), Geometry’s Future, Arlington, Massachusetts: COMAP Inc, pp. Malkevitch, J.: 1995, ‘Geometry: Yesterday, today and tomorrow’, in Malkevitch, J. and Zazkis, R.: 1992, ‘Of geometry, turtles and groups’, in C. Hart (ed.), Children’s Understanding of Mathematics11–16, London: John Murray, pp. E.: 1981, ‘Reflections and rotations’, in K. (eds.): 1992, Learning Mathematics and Logo, Cambridge, Massachusetts: MIT Press. and Sutherland, R.: 1990, ‘Pupil collaboration and teacher intervention in the logo environment’, Journal für Mathematik–Didaktik90(4), 323–343. Shire (eds.), Language in Mathematical Education: Research and Practice, Milton Keynes: Open University Press, pp. and Healy, L.: 1991, ‘Children talking in computer environments: New insights on the role of discussion in mathematics learning’, in K. and Healy, L.: 1997, ‘Un micro-monde pour la symetrie axiale: une base de co-construction deconcepts mathématiques?’, Sciences et Techniques Educatives4(1), 67–97. Kilpatrick (eds.), Mathematics and Cognition, A Research Synthesis by the International Group for the Psychology of Mathematics Education, ICMI Study Series (31–52), Cambridge University Press. Herschkowitz, R.: 1990, ‘Psychological aspects of learning geometry’, in P. (eds.): 1991, Constructivism, Norwood, New Jersey: Ablex Publishing Corporation. Vinner (eds.), Geometry working group report from the 10th conference and some subsequent reactions, Report presented by the 11th International Conference for the Psychology of Mathematics Education, Montréal, Canada, pp. Grenier, D.: 1987, ‘The pupils’ conceptions on axial symmetry: An individual activity’, in R. and Zazkis, R.: 1993, ‘Transformation geometry: Naive ideas and formal embodiments’, Journal for Computers in Mathematics and Science Teaching12(2), 121–145. D.: 1992, ‘A comparison of children’s learning in two interactive computer environments’, Journal of Mathematical Behaviour11, 73–81.Įdwards, L. D.: 1991, ‘Children’s learning in computer microworld for transformation geometry’, Journal of Computers in Mathematics Education22(2), 122–137.Įdwards, L. DiSessa, A.: 1985, ‘A principled design for an integrated computational environment’, Human Computer Interaction1, 1–47.Įdwards, L.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |