Calculus in European classrooms: curriculum and teaching in different educational and cultural contexts

ZDM - International Journal on Mathematics Education

Volumn 46, Issue 4, 2014, Pages 549-560

  Törner, Günter ^a   Potari, Despina ^b   Zachariades, Theodossios ^b  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84926365913     PISSN: 18639690     EISSN: 18639704     Source Type: Journal    
DOI: 10.1007/s11858-014-0612-0     Document Type: Article

References (45)

1. Artigue, M. (2000). Teaching and learning calculus: What can be learned from education research and curricular changes in France? In E. Dubinsky, A. H. Schoenfeld, & J. Kaput (Eds.), Research in collegiate mathematics education (Vol. IV, pp. 1–15). Boston: American Mathematical Society.
2. Artigue, M. (2003). Learning and teaching analysis: What can be learned from the past in order to think about the future? In D. Coray, F. Furinghetti, H. Gispert, B. R. Hodgson & G. Schubring (Eds.), Proceedings of the EM-ICMI Symposium (Monograph No. 39; pp. 213–223). Geneva: L’ Enseignement Mathématique.
3. Artigue, M. (2005). The integration of symbolic calculators into secondary education: Some lessons from didactical engineering. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators (pp. 231–294). New York: Springer.
4. Barbe, J., Bosch, M., Espinoza, L., & Gascon, J. (2005). Didactic restrictions on the teacher’s practice: The case of limits of functions in Spanish high schools. Educational Studies in Mathematics,59, 235–268.
5. Berry, J. S., & Nyman, M. A. (2003). Promoting students’ graphical understanding of the calculus. Journal of Mathematical Behavior,22, 481–497.
6. Biza, I. (2011). Students’ evolving meaning about tangent line with the mediation of a dynamic geometry environment and instructional example space. Technology, Knowledge and Learning,16, 125–151.
7. Biza, I., Christou, C., & Zachariades, T. (2008). Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean geometry to analysis. Research in Mathematics Education,10, 53–70.
8. Bloch, I. (2003). Teaching functions in a graphic milieu: What forms of knowledge enable students to conjecture and prove? Educational Studies in Mathematics,52, 3–28.
9. Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo-Ferri, & G. Sillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). Dordrecht: Springer.
10. Blum, W., & Törner, G. (1983). Didaktik der Analysis. Göttingen: Vandenhoeck & Ruprecht.
11. Choppin, J. (2011). Learned adaptations: Teachers’ understanding and use of curriculum resources. Journal of Mathematics Teacher Education,14(5), 331–353.
12. Clandinin, D. J., & Connelly, F. M. (1992). Teacher as curriculum maker. In P. W. Jackson (Ed.), Handbook of research on curriculum (pp. 363–401). New York: Macmillan.
13. Clarke, D. J. (2013). Contingent conceptions of accomplished practice: The cultural specificity of discourse in and about the mathematics classroom. ZDM - The International Journal on Mathematics Education,45, 21–33.
14. Clayton, M. J. (1997). Delphi: A technique to harness expert opinion for critical decision-making tasks in education. Educational Psychology: An International Journal of Experimental Educational Psychology,17(4), 373–386.
15. Dennis, D., & Confrey, J. (1995). Functions of a curve: Leibniz’s original notion of functions and its meaning for the parabola. The College Mathematics Journal,26, 124–131.
16. Elia, I., Gagatsis, A., Panaoura, A., Zachariades, T., & Zoulinaki, F. (2009). Geometric and algebraic approaches in the concept of ‘limit’ and the impact of the ‘didactic contact’. International Journal of Science and Mathematics Education,7, 765–790.
17. Ferrini-Mundy, J., & Gaudard, M. (1992). Preparation or pittfall in the study of college calculus. Journal for Research in Mathematics Education, 23, 56–71.
18. Freudenthal, H. (1978). Change in mathematics education since the late 1950s—ideas and realisation: The Netherlands. Educational Studies in Mathematics,9(3), 261–270.
19. Giacardi, L. (2009). The school as a ‘laboratory’. Giovanni Vailati and the project for the reform of the teaching of mathematics in Italy. International Journal for the History of Mathematics Education,4(1), 5–28.
20. Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics,39, 111–129.
21. Hahkioniemi, M. (2006). Associative and reflective connections between the limit of the difference quotient and limiting process. Journal of Mathematical Behavior,25, 170–184.
22. Hauchart, C., & Schneider, M. (1996). Une approche heuristique de l’analyse. Reperes IREM,25, 35–62.
23. Hoffkamp, A. (2011). The use of interactive visualizations to foster the understanding of concepts of calculus: Design principles and empirical results. ZDM - The International Journal on Mathematics Education,43, 359–372.
24. Hopmann, S. T. (2003). On the evaluation of curriculum reform. Journal of Curriculum Studies,35(4), 459–478.
25. Howson, A. G. (1978). Change in mathematics education since the late 1950s—ideas and realization: Great Britain. Educational Studies in Mathematics,9, 183–223.
26. Judson, T., & Nishimori, T. (2005). Concepts and skills in high school calculus: An examination of a special case in Japan and the United States. Journal for Research in Mathematics Education,36, 24–43.
27. Kilpatrick, J. (1992). A history of research in mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 3–37). New York: Macmillan.
28. Kilpatrick, J. (2012). The new math as an international phenomenon. ZDM - The International Journal on Mathematics Education,44, 563–571.
29. Kraft, A. (1953). Entwurf eines Lehrplanes für den mathematischen Unterricht an den deutschen höheren Schulen – Kasseler Lehrplan von 1953. Math. Naturwissens. Unterricht,6, 285–287.
30. Mamona-Downs, J. (2001). Letting the intuitive bear on the formal; a didactical approach for the understanding of the limit of a sequence. Educational Studies in Mathematics,48, 259–288.
31. Mayring, P. (2000). Qualitative content analysis. Forum: Qualitative Social Research, 1(2), Art. 20. http://www.qualitative-research.net/index.php/fqs/article/view/1089/2385. Accessed 16 June 2014.
32. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings. Dordrecht: Kluwer.
33. Potari, D., Zachariades, T., Christou, C., Kyriazis, G., & Pitta-Pantazi, D. (2007). Teachers’ mathematical knowledge and pedagogical practices in the teaching of derivative. In Proceedings of the 5th Conference of European Research in Mathematics Education (CERME), 1955–1964. Larnaca, Cyprus. http://ermeweb.free.fr/CERME5b/WG9.pdf. Accessed 16 June 2014.
34. Przenioslo, M. (2005). Introducing the concept of convergence of a sequence in secondary school. Educational Studies in Mathematics,60, 71–93.
35. Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research,75(2), 211–246.
36. Robert, A., & Speer, N. (2001). Research on the teaching and learning of calculus/elementary analysis. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 283–299). Dordrecht: Kluwer.
37. Servais, W. (1975). Continental traditions and reforms. International Journal of Mathematics Education in Science and Technology,6, 37–58.
38. Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics,18, 371–397.
39. Siu, M. K. (2003). Learning and teaching of analysis in the mid twentieth century: A semi-personal observation. In D. Coray, F. Furinghetti, H. Gispert, B. R. Hodgson & G. Schubring (Eds.), One Hundred Years of L’ Enseignement Mathematique, Proceedings of the EM-ICMI Symposium (Monograph no. 39; pp. 179–190). Geneva: L’ Enseignement Mathématique.
40. Tall, D. (2009). Dynamic mathematics and the blending of knowledge structures in the calculus. ZDM - The International Journal on Mathematics Education,41(4), 481–492.
41. Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics,12, 151–169.
42. Thomas, M., & Yoon, C. (2014). The impact of conflicting goals on mathematical teaching decisions. Journal of Mathematics Teacher Education, 17, 227–243.
43. Tsamir, P. (2002). When ‘the same’ is not perceived as such: The case of infinite sets. Educational Studies in Mathematics,48, 289–307.
44. Verhoef, N., Tall, D., Coenders, F., & Smaalen, D. V. (2014). The complexities of a lesson study in a Dutch situation: Mathematics teacher learning. International Journal of Science and Mathematics Education, 12, 859–881.
45. Zachariades, T., Potari, D., Pitta-Pantazi, D., & Christou, C. (2008). Aspects of teacher knowledge for calculus teaching. In O. Figueras & A. Sepúlveda (Eds.), Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education (PME) (Vol. 4, pp. 449–455). Michoacán: Morelia.