Coordinating informal and formal aspects of mathematics: Student behavior and textbook messages

Journal of Mathematical Behavior

Volumn 21, Issue 2, 2002, Pages 135-150

  Raman, Manya ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Calculus textbooks; Formal mathematics; Informal mathematics; Precalculus textbooks

Indexed keywords

EID: 0036389721     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0732-3123(02)00119-0     Document Type: Article

References (17)

1. Alibert, R., & Thomas, M. (1991). Research on mathematical proof. In: D. Tall (Ed.), Advanced mathematical thinking (pp. 215-230). Dordrecht: Kluwer Academic Publishers.
2. Asiala, M., Brown, A., Devries, D., Dubinsky, E., Matthews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. CBMS Issues in Mathematics Education, 6, 1-30.
3. Brodie, S. (1999). On "Rethinking Rigor in Calculus⋯" or Why We Don't Do Calculus on the Rational Number. The College Mathematics Journal, 30(2), 135-138.
4. Demana, F., Waits, B., & Clemens, S. (1993). Precalculus: functions and graphs. Reading, MA: Addison-Wesley.
5. Dall' Alba, G., Walsh, E., Bowden, J., Martin, E., Masters, G., Ramsden, P., & Stephanou, A. (1993). Textbook treatments and students' understanding of acceleration. Journal of Research in Science Teaching, 30(7), 621-635.
6. Fischbein, E. (1994). The interaction between the formal, the algorithmic, and the intuitive components in a mathematical activity. In: R. Biehler, R. W. Scholz, R. Stässer, & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 231-245). Dordrecht: Kluwer Academic Publishers.
7. Howson, G. (1995). Mathematics textbooks: a comparative study of grade 8 texts (Vol. 3). Vancouver, Pacific Educational Press.
8. Kaput, J. (1997). Rethinking calculus: learning and teaching. American Mathematical Monthly, 104(8), 731-737.
9. Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: tasks, learning, and teaching. Review of Educational Research, 60(1), 1-64.
10. Niss, M. (2000). Key issues and trends in research on mathematics education. Plenary Address, ICME-9, Makuhari, Japan.
11. Poincaré, H. (1952). Science and method. New York: Dover.
12. Polya, G. (1968). Mathematics and plausible reasoning. Princeton, NJ: Princeton University Press.
13. Schoenfeld, A. (1991). On mathematics as sense-making: an informal attack on the unfortunate divorce of formal and informal mathematics. In: J. F. Voss, D. N. Perkins, & J. W. Segal (Eds.), Informal reasoning and education (pp. 311-343). Hillsdale, NJ: Lawrence Erlbaum.
14. Stewart, J. (1995). Calculus: early transcendentals (3rd ed.). Pacific Grove, CA: Brooks/Cole.
15. 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.
16. Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In: D. Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Dordrecht: Kluwer Academic Publishers.
17. Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. In: E. Dubinsky, A. H. Schoenfeld, & J. Kaput (Eds.), Research in collegiate mathematics education IV (pp. 103-127). Providence, RI: American Mathematical Society.