Employing genetic 'moments' in the history of mathematics in classroom activities

Educational Studies in Mathematics

Volumn 66, Issue 1, 2007, Pages 83-106

  Farmaki, Vassiliki ^a   Paschos, Theodorus ^a,b  

^a UNIVERSITY OF ATHENS   (Greece)

^b NONE   (Greece)

Author keywords

Euclidean geometry; Functional approach; Graphical representations; Integration of history; Motion problems; Transformations

Indexed keywords

EID: 34547667157     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-006-9056-y     Document Type: Article

References (34)

1. Boero, P., Pedemonte, B., & Robotti, E. (1997). Approaching theoretical knowledge trough voices and echoes: A Vygotskian perspective. In Proceedings 21st PME, vol. 2 (pp. 81-88). Lahti, Finland.
2. Boyer, C. (1959). The history of the Calculus and its conceptual development. New York: Dover.
3. Brousseau, G. (1983). Les obstacles épistémologiques et les problémes en mathématiques. Recherche en Didactique des Mathématiques, 4(2), 165-198.
4. Brousseau, G. (1997). Theory of didactic situations in mathematics. In N. Balacheff et al. (Eds.), Mathematics education library. Dordrecht, The Netherlands: Kluwer (translated by N. Balacheff et al.).
5. Clagett, M. (1959). Science of mechanics in the middle age. Madison: University of Wisconsin Press.
6. Clagett, M. (1968). Nicole Oresme and the medieval geometry of qualities and motion. Madison: University of Wisconsin Press.
7. Duval, R. (2002). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt (Ed.), Representations and mathematics visualization (pp. 311-336). Mexico: PMENA, Cinvestav-IPN.
8. Even, R. (1998). Factors involved in linking representations of functions. Journal of Mathematical Behavior, 17(1), 105-121.
9. Farmaki, V., Klaoudatos, N., & Paschos, T. (2004). Integrating the history of mathematics in educational praxis: An Euclidean geometry approach to the solution of motion problems. In Proceedings 28th PME, vol. 3 (pp. 505-512). Bergen, Norway.
10. Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3-6.
11. Fauvel, J., & van Maanen, J. (2000). Introduction. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI study (pp. xi-xviii). Dordrecht, The Netherlands: Kluwer.
12. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Reidel.
13. Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht, The Netherlands: Kluwer.
14. Furinghetti, F., & Somaglia, A. (1998). History of mathematics in school across disciplines. Mathematics in School, 27(4), 48-51.
15. Goldin, G., & Janvier, C. (1998). Representations and the psychology of mathematics education. Journal of Mathematical Behavior, 17(1), 137-165.
16. Goldin, G., & Kaput, J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. Steffe et al. (Eds.), Theories of learning mathematics (pp. 159-196). Hillsdale, New Jersey: Erlbaum.
17. Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A Calculus course as an example. Educational Studies in Mathematics, 39, 111-129.
18. Grugnetti, L., & Rogers, L. (2000). Philosophical, multicultural and interdisciplinary issues. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI study (pp. 39-62). Dordrecht, The Netherlands: Kluwer.
19. Hitt, F. (2002). Representations and mathematics visualization. Mexico: North American Chapter of the International Group for the PME, Cinvestav-IPN.
20. Kaput, J. J. (1987). Representation systems in mathematics. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 19-26). Hillsdale, New Jersey: Erlbaum.
21. Kaput, J. J. (1994). Democratizing access to Calculus: New routes to old roots. In A. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 77-156). Hillsdale, New Jersey: Erlbaum.
22. Krysinska, M., & Hauchart, C. (2000). Teaching projects inspired by history: Examples from algebra and analysis. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI study (pp. 243-245). Dordrecht, The Netherlands: Kluwer.
23. Lacasta Zabalza, E. (1995). L'usage des graphes dans l'enseignement. Université Bordeaux 1, Label Européen.
24. Piaget, J., & Garcia, R. (1989). Psychogenesis and the history of science. New York: Columbia University Press (H. Feider, trans.).
25. Radford, L. (1997). On psychology, historical epistemology and the teaching of mathematics: Towards a socio-cultural history of mathematics. For the Learning of Mathematics, 17(1), 26-33.
26. Radford, L. (2000). Historical formation and student understanding of mathematics. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI study (pp. 143-170). Dordrecht, The Netherlands: Kluwer.
27. Schneider, M. (1988). Des objets mentaux «aire» et «volume» au calcul des primitives, Thèse de Doctorat, Université de Louvain-la-Neuve.
28. Schneider, M. (2000). A heuristic introduction to analysis implicitly inspired by its historical development. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI study (pp. 245-248). Dordrecht, The Netherlands: Kluwer.
29. Slavit, D. (1997). An alternate route to the reification of function. Educational Studies in Mathematics, 33, 259-281.
30. Tzanakis, C., & Arcavi, A. (2000). Integrating history of mathematics in the classroom: An analytic survey. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: An ICMI study (pp. 201-240). Dordrecht, The Netherlands: Kluwer.
31. Vergnaud, G., & Errecalde, P. (1980). Some steps in the understanding and use of scales and axes by 10-13 year old students. In Proceedings 4th PME (pp. 285-291). Berkeley, California.
32. von Glasersfeld, E. (1987). Preliminaries to any theory of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 215-225). Hillsdale New Jersey: Erlbaum.
33. Vygotsky, L. S. (1997). The history of the development of higher mental functions. In R. W. Rieter (Ed.), Collected works of L. S. Vygotsky, vol. 4. New York: Plenum.
34. Yerushalmy, M., & Gilead, S. (1999). Structures of constant rate word problems: A functional approach analysis. Educational Studies in Mathematics, 39, 185-203.