M.G. Bartolini Bussi, D.Taimina & M. Isoda (2010). Concrete models and dynamic instruments as early technology tools in classrooms at the dawn of ICMI: from Felix Klein to present applications in mathematics classrooms in different parts of the world, ZDM, Volume 42, Number 1, 19-31

Abstract
Most national curricula for both primary and secondary grades encourage the active involvement of learners through the manipulation of materials (either concrete models or dynamic instruments). This trend is rooted in the emphasis given, at the dawn of ICMI, to what might be called an experimental approach: the links between mathematics, natural sciences and technology were in the foreground in the early documents of ICMI and also in the papers of its first president, Felix Klein. However, the presence of this perspective in teaching practice is uneven. In this paper, we shall reconstruct first an outline of what happened in three different parts of the world (Europe, USA and Japan) under the direct influence of Klein. Then, we shall report classroom activities realized in the same regions in three different research centres: the Laboratory of Mathematical Machines at the University of Modena and Reggio Emilia, Italy (http://www.mmlab.unimore.it); the pedagogical space of Kinematical Model for Design Digital Library at Cornell, USA (http://kmoddl.library.cornell.edu/); and the Centre for Research on International Cooperation in Educational Development at Tsukuba University, Japan (http://math-info.criced.tsukuba.ac.jp/). They have maintained the reference to concrete materials (either models or instruments), with original interpretations that take advantage of the different cultural conditions. Although in all cases the reference to history is deep and systematic, the synergy with mathematical modelling and with information and communication technologies has been exploited, not to substitute but to complement the advantages of the direct manipulations.

Articolo completo

Bibliografia

  • Bartolini Bussi, M. G. (1998). Drawing instruments: Theories and practices from history to didactics. Documenta mathematica, extra volume ICM98, pp. 735–746.
  • Bartolini Bussi, M. G. (2001). The geometry of drawing instruments: Arguments for a didactical use of real and virtual copies. Cubo, 3(2), 27–54.
  • Bartolini Bussi, M. G., & Pergola, M. (1996). History in the mathematics classroom: Linkages and kinematic geometry. In H. N. Jahanke, N. Knoche, & M. Otte (Eds.), Geschichte der Mathematik in der Lehre (pp. 36–67). Goettingen: Vandenhoek & Ruprecht. Campedelli, L. (1958). I Modelli Geometrici. In Commissione internazionale per lo studio e il miglioramento dell’insegnamento della matematica (Ed.), Il Materiale per L’insegnamento della Matematica (pp. 143–172). Firenze: La Nuova Italia.
  • Castelnuovo, G. (1928). La Geometria Algebrica e la Scuola Italiana. Atti del Congresso Internazionale dei Matematici (Vol. I, p. 194). Bologna: Zanichelli.
  • Castelnuovo, E. (2008). L’Officina Matematica. Bari: Edizioni La Meridiana.
  • Cavalieri, B. (1632). Lo specchio ustorio (2001). Firenze: Giunti.
  • Clairaut, A. C. (1741). E´lements de Geometrie (2006). E´ ditions Jacques Gabay.
  • Comenius, I. A. (1657). Didactica Magna (1986). Akal Ediciones.
  • Fischer, G. (Ed.). (1986). Mathematical models: From the collections of Universities and Museums. Braunschweig/Wiesbaden: Friedr. Vieweg & Sohn.
  • France National Constitution. (1791). http://sourcebook.fsc.edu/history/constitutionof1791.html. Accessed 25 August 2009.
  • Giacardi, L. (2008). Bibiligograpy of Castelnuovo, G. http://www.icmihistory.unito.it/portrait/castelnuovo.php. Accessed 21 November 2008.
  • Henderson, D., & Taimina, D. (2005a). Mathematical aspects of the Peaucellier-Lipkin linkage. http://kmoddl.library.cornell.edu/tutorials/11/. Accessed 21 November 2008.
  • Henderson, D., & Taimina, D. (2005b). Experiencing geometry: Euclidean and non-euclidean with history. Upper Saddle River: Pearson Prentice Hall.
  • Isoda, M. (2004). The development of mathematics education. In Japan International Cooperation Agency (Ed.), The history of Japan’s educational development (pp. 159–172). Tokyo: Institute for International Cooperation.
  • Isoda, M. (2008). Sample videos developed by Isoda, M. and Baldin, Y. Y. in 2008 at UFRJ on HTEM4. http://math-info.criced.tsukuba.ac.jp/software/dbook/dbook_eng/dbook_eng05.html. Accessed 21 November 2008.
  • Isoda, M., Hara, K., Iijima, Y., Uehara, E., & Watanabe, H. (2006). e-Textbooks: Advancing mathematics teaching and learning into the future mathematics. In Chu, S. C. et al. (Eds.), Proceedings of the eleventh Asian technology conference in mathematics (pp. 54–63). VA: ATCM, Inc.
  • Isoda, M., & Matsuzaki, A. (2003). The roles of mediational means for mathematization: The case of mechanics and graphing tools. Journal of Japan Society of Science Education, 27(4), 245–257. Isoda, M., Suzuki, A., Ohneda, Y., Sakamoto, M., Mizutahi, N., & Kawazaki, N. (2001). LEGO project. Tsukuba Journal of Educational Study in Mathematics, 20, 77–92.
  • Kempe, A. B. (1877). How to draw a straight line. London: Macmillan.
  • Klein, F. (1924–1925). Elementary mathematics from an advanced standpoints. (Hedrick, E. R., & Noble, C. A., translated, 1939). NY: Macmillan.
  • Klein, F., & Riecke, E. (1904). Neue Beiträge zur Frage des Mathematischen und Physikalischen Unterrichts an den Höheren Schulen. Leipzig: Teubner.
  • Koenigs, G. (1897). Lecons De Cinematique Paris A. Hermann. http://www.archive.org/stream/leonsdecinma00koenuoft#page/242/mode/2up. Accessed 25 August 2009.
  • Kuroda, M. (1920). Geometry for secondary school. Tokyo: Baifukan.
  • Kuroda, M. (1927). New issues of mathematics teaching (selected publication of his posthumous manuscripts). Tokyo: Baifu-kan.
  • Le Blanc, M. (n.d.). Friedrich Froebel: His life and influence on education. http://www.communityplaythings.co.uk/resources/articles/friedrich-froebel.html.
  • Maclaurin, C. (1720). Geometria Organica, Sive Descriptio Linearum Curvarum Universalis. Londini.
  • Maschietto, M. (2005). The laboratory of mathematical machines of Modena. Newsletter of the European Mathematical Society, 57, 34–37.
  • Monbusyo Approved. (1943). Mathematics textbooks for secondary school (II). Tokyo: TyutoGakkoKyokasyo Pub.
  • Moon, F. C. (2002). Franz Reuleaux: Contributions to 19th C. kinematics and theory of machines. http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.htmm/2002-2?abstract=. Accessed 21 November 2008.
  • Mueller, W. (2001). Mathematical Wunderkammern. MAA Monthly, 108, 785–796.
  • Palladino, N. (n.d.). http://www.dma.unina.it/*nicla.palladino/catalogo/. Accessed 25 August 2009.
  • Pan, B., Gay, G. K., Saylor, J., Hembrooke, H. A., & Henderson, D. (2004). Usability, learning, and subjective experience: User evaluation of K-MODDL in an undergraduate class. In H. Chen, M. Christel, & E. Lim (Eds.), Proceedings of the fourth ACM/ IEEE joint conference on digital libraries (JCDL’ 04) (pp. 188– 189). New York: ACM.
  • Parshall, K. H., & Rowe, D. (1991). The emergence of the American mathematical research community 1876–1900: J. J. Sylvester, Felix Klein, and E. H. Moore. Providence: American Mathematical Society, London Mathematical Society (Co-publication).
  • Perry, J. (1913). Elementary practical mathematics. London: Macmillan.
  • Reuleaux, F. (1876). The kinematics of machinery: Outlines of a theory of machines. London: Macmillan (reprinted New York: Dover, 1963).
  • Ruthven, K. (2008). Mathematical technologies as a vehicle for intuition and experiment: a foundational theme of the ICMI, and a continuing preoccupation. Paper prepared for the ICMI centennial symposium, Rome 2008. http://www.unige.ch/math/EnsMath/Rome2008/WG4/Papers/RUTHVEN.pdf. Accessed 21 November 2008.
  • Sanden, H. V. (1914). Praktishe analysis. Leipzig und Berlin: Teubner.
  • Schilling, M. (1911). Catalog matematischer Modelle fu¨r den Ho¨heren Mathematischen Unterricht. Leipzig: Martin Schilling.
  • Schooten, F. V. (1646). De organica Conicarum Sectionum Constructione. Leyden.
  • Schubring, G. (1989). Pure and applied mathematics in divergent institutional settings. In D. E. Rowe & J. McCleary (Eds.), Ideas and reception (pp. 171–207). Boston: Academic Press.
  • Shell-Gellasch, A., & Acheson, B. (2007). Geometric string models of descriptive geometry, hands on history. In A. Shell-Gelasch (Ed.), MAA notes #72 (pp. 49–62). Washington, DC: MAA.
  • Smith, D. E. (1913). Intuition and experiment in mathematical teaching in the secondary schools. L’Einseignement Mathe´matique, 14, 507–534.
  • Taimina, D. (2005a). Linkages. http://kmoddl.library.cornell.edu/linkages/. Accessed 21 November 2008.
  • Taimina, D. (2005b). How to draw a straight line. http://kmoddl.library.cornell.edu/tutorials/04/. Accessed 21 November 2008.
  • Taimina, D., & Henderson, D. (2005). Reuleaux Triangle, learning module. http://kmoddl.library.cornell.edu/tutorials/02/. Accessed 21 November 2008.