Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 12 N.º 1 (2009): Marzo

ON EMPIRICAL RESEARCH IN THE FIELD OF USING HISTORY IN MATHEMATICS EDUCATION

Publicado
fevereiro 28, 2009

Resumo

Este artigo aborda a questão da investigação empírica no campo do uso da história em Educação Matemática. Mais precisamente, foca-se no papel que a investigação empírica pode ter na discussão sobre como usar a história em Educação Matemática e o modo de o realizar. Isto é exemplificado, principalmente, a partir dos estudos de investigação empírica sobre o uso da história no programa de Matemática do "bachillerato Danés". Também se ilustra a forma como ambos, quer o desenho quer a metodologia de investigação destes estudos, dependiam do propósito inicial de usar a história como um objectivo mais do que como uma ferramenta. Finalmente, estabelecem-se perspectivas sobre os possíveis benefícios de aumentar a o número de investigações empíricas realizadas no campo do uso da história em Educação Matemática.

Referências

  1. Bakker, A. (2004), Design research in statistics education On symbolizing and computer tools. Ph.D. thesis, The Freudenthal Institute, Utrecht.
  2. Brousseau, G. (1997). Theory of Didactical Situations in Mathematics. Dordrecht: Kluwer Academic Publishers. Edited and translated by Nicolas Balacheff, Martin Cooper, Rosamund Sutherland, and Virgina Warfield.
  3. Cooney, T. J., Shealy, B. E. & Arvold, B. (1998), Conceptualizing belief structures of preservice secondary mathematics teachers. Journal for Research in Mathematics Education 29(3), 306- 333.
  4. Cooney, T. J. (1999). Conceptualizing teachers' ways of knowing. Educational Studies in Mathematics 38 (1-3), 163-187.
  5. Diffie, W. & Hellman, M. E. (1976). New directions in cryptography, IEEE Transactions on Information Theory 21, 644-654.
  6. Epple, M. (2000). Genisis, Ideen, Institutionen, mathmatische Werkstätten: Formen der Mathematikgeschichte Ein metahistorischer Essay. Mathematische Semesterberichte 47. 131-163
  7. Ernest, P. (1998), Why teach mathematics? The justification problem in mathematics education. In: J. H. Jensen, M. Niss, and T. Wedege (Eds.), Justification and Enrollment Problems in Education Involving Mathematics or Physics (pp. 33-55). Roskilde, Denmark: Rosklide University Press,
  8. Fauvel, J. & van Maanen, J. (Eds.). (2000). History in Mathematics Education The ICMI Study. Dordrecht: Kluwer Academic Publishers.
  9. Fauvel, J. (1991), Using history in mathematics education. For the Learning of Mathematics 11(2), 3-6. Special Issue on History in Mathematics Education.
  10. Fréchet, M. (1906). Sur quelques points du calcul fonctionnel. Rend. Circolo Mat. Palermo 74: 1- 74.
  11. Freudenthal, H. (1991). Revisiting Mathematics Education China Lectures. Dordrecht: Kluwer Academic Publishers.
  12. Furinghetti, F. (1993). Images of mathematics outside the community of mathematicians: evidence and explanations. For the Learning of Mathematics 13(2), 33-38.
  13. Furinghetti, F. (2007). Teacher education through the history of mathematics. Educational Studies in Mathematics 66(2), 131-143. Special issue on the history of mathematics in mathematics education: Theory and practice.
  14. Golay, M. J. E. (1949). Notes on digital coding. Proceedings of the IRE 37, p. 657.
  15. Goodwin, D. M. (2007). Exploring the relationship between high school teachers mathematics history knowledge and their images of mathematics Ph.D. thesis, University of Massachusetts, Lowell.
  16. Grassmann, H. (1844). Die lineale Ausdehnungslehre, Leipzig: Otto Wigand, 1844. Gravemeijer, K. & Cobb, P. (2006). Outline of a method for design research in mathematics education. In: J. van den Akker, K. Gravemeijer, S. McKenney, and N. Nieveen (Eds.): Educational Design Research (pp. 17-51). Abingdon, Oxon: Routledge
  17. Gulikers, 1. & Blom, K. (2001). "A historical angle', a survey of recent literature on the use and value of the history in geometrical education. Educational Studies in Mathematics 47(2), 223-258.
  18. Hamming, R. W. (1950), Error detecting and error correcting codes. Bell System Technical Journal 29, 147-160.
  19. Harper, E. (1987), Ghost of Diophanthus. Educational Studies in Mathematics 18 (1), 75-90. Jankvist, U. T. (2007). Empirical research in the field of using history in mathematics education: Review of empirical studies in HPM2004 & ESU4', Nomad 12(3), 83-105.
  20. Jankvist, U. T. (2008a). Evaluating a teaching module on the carly history of error correcting codes. In: M. Kourkoulos and C. Tzanakis (Eds.), Proceedings 5th International Colloquium on the Didactics of Mathematics. Rethymnon: The University of Crete. In press
  21. Jankvist, U. T. (2008b). History of modern mathematics and/or modern applications of mathematics in mathematics education. In: Proceedings HPM2008 (CD-ROM). The HPM Group.
  22. Jankvist, U. T. (2008c). Kodningsteoriens tidlige historie et undervisningsforløb til gymnasiet. No. 459 in Tekster fra IMFUFA. Roskilde: IMFUFA. English translation of title: The Early History of Error Correcting Codes a Teaching Module for Upper Secondary School. 73 pages
  23. Jankvist, U. T. (2008d). Proceedings HPM2004&ESU4: empirical research on using history of mathematics in mathematics education. HPM Newsletter (67), 15-18.
  24. Jankvist, U. T. (2008c). RSA og den heri anvendte matematiks historie et undervisningsforløb til gymnasiet, No. 460 in Tekster fra IMFUFA. Roskilde: IMFUFA. English translation of title: RSA and the History of the Applied Mathematics in the Algorithma Teaching Module for Upper Secondary School. 116 pages.
  25. Jankvist, U. T. (2008). A teaching module on the history of public-key cryptography and RSA. BSHM Bulletin 23(3), 157-168.
  26. Jankvist, U. T. (2009a). A categorization of the 'whys' and 'hows' of using history in mathematics education. Educational Studies in Mathematics. In press (available online first).
  27. Jankvist, U. T. (2009b). History of modern applied mathematics in mathematics education. For the Learning of Mathematics 29(1). In press.
  28. Jankvist, U. T. (2009c). Students' beliefs about the evolution and development of mathematics. Proceedings from the CERME6 Working Group 15. Preprint.
  29. Kjeldsen, T. H. (2008). Egg-forms and measure-bodies: different mathematical practices in the early history of the modern theory of convexity. Science in Context 22(1), 85-113.
  30. Lester, Jr., F. K. (2002), Implications of research on students' beliefs for classroom practice. In: G. C. Leder, E. Pehkonen, and G. Törner (Eds.), Beliefs: A Hidden Variable in Mathematics Education?, Chapter 20 (pp. 345-353). Dordrecht: Kluwer Academic Publishers.
  31. Lester, Jr., F. K. (2005). On the theoretical, conceptual, and philosophical foundations for research in mathematics education. ZDM 37(6), 457-467.
  32. Niss, M. & Jensen, T. H. (eds.). (2002). Kompetencer og matematiklæring Ideer og inspiration til udvikling af matematikundervisning i Danmark. Undervisningsministeriet. Uddannelsesstyrelsens temahæfteserie nr. 18. English translation of title: Competencies and Learning of Mathematics Ideas and Inspiration for the Development of Mathematics Education in Denmark.
  33. Niss, M. (1980). Nogle aspekter for matematikundervisningen i de gymnasiale uddannelser frem til 1990. Normat 28(2), 52-60, 87. English translation of title: Some aspects for mathematics education in upper secondary school approaching 1990.
  34. Niss, M. (1994). Mathematics in society. In: R. Biehler, R. W. Scholz, R. Sträßer, and B. Winkelmann (eds.): Didactics of Mathematics as a Scientific Discipline. Dordrecht: Kluwer Academic Publishers, pp. 367-378.
  35. Niss, M. (2001). Indledning. In: M. Niss (Ed.). Matematikken og Verden, Fremads debatbøger - Videnskab til debat. København: Forfatterne og Forlaget A/S. English translation of title: Introduction to the book: Mathematics and the World.
  36. Philippou, G. N. & Christou, C. (1998). The effects of a preparatory mathematics program in changing prospective teachers' attitudes towards mathematics. Educational Studies in Mathematics 35(2), 189-206.
  37. Rheinberger, H.-J. (1997), Toward a History of Epistemic Things: Synthesizing Proteins in the Test Tube. Stanford: Stanford University Press.
  38. Rivest, R. L., Shamir, A. & Adleman, L. (1978). A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 21, 120-126.
  39. Rosen, K. H. (2003). Discrete Mathematics and Its Applications. New York: McGraw Hill, fifth edition.
  40. Sfard, A. (1995). The development of algebra: confronting historical and psychological perspectives. Journal of Mathematical Behaviour 14, 15-39.
  41. Shannon, C. E. (1948). A mathematical theory of communication I, II. In: D. Slepian (Ed.), Key Papers in The Development of Information Theory, Vol. 27. New York: IEEE Press, pp. 5-18, 19-29. (Pages 379-423 and 623-656 in the original publications by Shannon.)
  42. Singh, S. (1999). The Code Book - The Secret History of Codes and Codebraking. London: Fourth Estate.
  43. Siu, M.-K. & Tzanakis, C. (2004). History of mathematics in classroom teaching - appetizer? main course? or dessert?. Mediterranean Journal for Research in Mathematics Education 3(1-2), v-x. Special double issue on the role of the history of mathematics in mathematics education (proceedings from TSG 17 at ICME 10).
  44. Thompson, T. M. (1983). From Error-Correcting Codes through Sphere Packings to Simple Groups, No. 21 in The Carus Mathematical Monographs. The Mathematical Association of America.
  45. Toeplitz, O. (1927). Das Problem der Universitätsvorlesungen über Infinitesimalrechnung und ihrer Abgrenzung gegenüber der Infinitesimalrechnung an den höheren Schulen. Jahresbericht der deutschen Mathematiker-Vereinigung XXXVI, 88-100.
  46. Tzanakis, C. & Arcavi, A. (2000). Integrating history of mathematics in the classroom: an nalytic survey. In: J. Fauvel and J. van Maanen (Eds.), History in Mathematics Education, Chapter 7 (pp. 201-240.). The ICMI Study. Dordrecht: Kluwer Academic Publishers.
  47. Tzanakis, C. & Kourkoulos, M. (2007). May history and physics provide a useful aid for introducing basic statistical concepts?. In: F. Furinghetti, S. Kaijser, and C. Tzanakis (Eds.) Proceedings HPM2004 & ESU4 (pp. 284-295). Uppsala Universitet, revised edition. Undervisningsministeriet (2007). Vejledning: Matematik A, Matematik B, Matematik C. Bilag 35, 36, 37. Guidance for upper secondary mathematics teachers by the Danish ministry of education.
  48. van Amerom, B. A. (2002). Reinvention of early algebra Developmental research on the transition from arithmetic to algebra. Ph.D. thesis, The Freudenthal Inistitute, Utrecht.
  49. Wells, D. (2005). Prime Numbers - The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons, Inc.

Downloads

Os dados de download ainda não estão disponíveis.