The number-theoretic experience of 12- to 15-year-olds in a calculator environment: The intertwining coemergence of technique and theory

Number Theory in Mathematics Education: Perspectives and Prospects

Volumn , Issue , 2012, Pages 173-200

  Kieran, Carolyn ^a   Guzmán, José ^b  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

^b DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80053319404     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203053904     Document Type: Chapter

References (28)

1. Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245-274.
2. Artigue, M., Defouad, B., Duperier, M., Juge, G., & Lagrange, J.-B. (1998). Intégration de calculatrices complexes dans l'enseignement des mathématiques au lycée [Integration of complex calculators in the teaching of mathematics at the lycée]. Paris: Université Denis Didirot Paris 7, Équipe DIDIREM.
3. Campbell, S. (1996). On preservice teachers' understandings of division with remainder. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 177-184). Valencia, Spain: PME Program Committee.
4. Campbell, S. R. (2002). Coming to terms with division: Preservice teachers' understanding. In S. R. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp. 15-40). Westport, CT: Ablex.
5. Chevallard, Y. (1999). L'analyse des pratiques enseignantes en théorie anthropologique du didactique [The analysis of teaching practices in didactical anthropological theory]. Recherches en Didactique des Mathématiques, 19, 221-266.
6. Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-123). Boston: Kluwer.
7. Dubinsky, E., & Harel, G. (1992). The nature of the process conception of function. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (MAANotes, Vol. 25, pp. 85-106). Washington, DC: Mathematical Association of America.
8. Grossi, E. (1985). Psychogenèse et apprentissage du concept de multiple [Psychogenesis and the learning of the concept of multiples] (thesis of the 3rd cycle of French graduate studies). Paris: École des Hautes Études en Sciences Sociales.
9. Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3, 195-227.
10. Hiebert, J. (Ed.). (1986). Procedural and conceptual knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
11. Hoyles, C. (2002). From describing to designing mathematical activity. In C. Kieran, E. A. Forman, & A. Sfard (Eds.), Learning discourse: Discursive approaches to research in mathematics education (pp. 273-286). Dordrecht, The Netherlands: Kluwer
12. Lagrange, J.-B. (1996). Analysing actual use of a computer algebra system in the teaching and learning of mathematics. International DERIVE Journal, 3, 91-108.
13. Lagrange, J.-B. (1999). Complex calculators in the classroom: Theoretical and practical reflections on teaching pre-calculus. International Journal of Computers for Mathematical Learning, 4, 51-81.
14. Lagrange, J.-B. (2000). L'intégration d'instruments informatiques dans l'enseignement: Une approche par les techniques [The integration of instruments of information technology within teaching: A technique-based approach]. Educational Studies in Mathematics, 43, 1-30.
15. Lagrange, J.-B. (2002). Étudier les mathématiques avec les calculatrices symboliques. Quelle place pour les techniques? [Studying mathematics with symbol manipulating calculators. What is the role of techniques?]. In D. Guin & L. Trouche (Eds.), Calculatrices symboliques. Transformer un outil en un instrument du travail mathématique: Un problème didactique (pp. 151-185). Grenoble, France: La Pensée Sauvage.
16. Lagrange, J.-B. (2003). Learning techniques and concepts using CAS: A practical and theoretical reflection. In J. T. Fey (Ed.), Computer Algebra Systems in secondary school mathematics education (pp. 269-283). Reston, VA: National Council of Teachers of Mathematics.
17. Ministrère de l'Éducation du Québec. (1993). Mathématique 116, Programme d'études. Québec: Gouvernement du Québec, Ministère de l'Éducation.
18. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht, The Netherlands: Kluwer.
19. Rabardel, P., & Samurçay, R. (2001). From artifact to instrument mediated learning. New Challenges to Research on Learning, 22. Helsinki: University of Helsinki.
20. Ruthven, K. (1992). Calculator strategies. Micromath, 8(1), 31-32.
21. Secretaría de Educación Pública. (2000). Programas de estudio, Educación secondaria, Libro para el maestro. Mexico: Secretaría de Educación Pública.
22. Sfard, A. (1989). Transition from operational to structural conception: The notion offunction revisited. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th International Conference for the Psychology of Mathematics Education (Vol. 3, pp. 151-158). Paris: PME Program Committee.
23. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.
24. Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification-the case of function. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (MAA Notes, Vol. 25, pp. 59-84). Washington, DC: Mathematical Association of America.
25. Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Research agenda for mathematics education: Vol. 2. Number concepts and operations in the middle grades (pp. 141-161). Reston, VA: National Council of Teachers of Mathematics.
26. Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10, 77-101.
27. Williams, D., & Stephens, M. (1992). Activity 1: Five steps to zero. In J. T. Fey (Ed.), Calculators in mathematics education (Yearbook of the National Council of Teachers of Mathematics, pp. 233-234). Reston, VA: NCTM.
28. Zazkis, R., & Campbell, S. (1996). Divisibility and multiplicative structure of natural numbers: Preservice teachers' understanding. Journal for Research in Mathematics Education, 27, 540-563.