Students’ perceptions of institutional practices: the case of limits of functions in college level Calculus courses



This paper presents a study of instructors’ and students’ perceptions of the knowledge to be learned about limits of functions in a college level Calculus course, taught in a North American college institution. I modeled these perceptions using a theoretical framework that combines elements of the Anthropological Theory of the Didactic, developed in mathematics education, with a framework for the study of institutions developed in political science. While a model of the instructors’ perceptions could be formulated mostly in mathematical terms, a model of the students’ perceptions included an eclectic mixture of mathematical, social, cognitive, and didactic norms. I describe the models and illustrate them with examples from the empirical data on which they have been built.


Institution Calculus Limits Anthropological Theory of the Didactic Praxeology Institutional Theory 


  1. Artigue, M., Batanero, C., & Kent, P. (2007). Mathematics teaching and learning at post-secondary level. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1011–1050). Reston, VA: NCTM.Google Scholar
  2. Balacheff, N. (1999). Contract and custom: two registers of didactical interactions. The Mathematics Educator, 9(2), 23–29.Google Scholar
  3. Barbé, J., Bosch, M., Espinoza, L., & Gascón, 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.CrossRefGoogle Scholar
  4. Bosch, M., Chevallard, Y., & Gascón, J. (2005). ‘Science or Magic?’ The use of models and theories in didactics of mathematics. 4th Congress of the European Society for Research in Mathematics Education. Sant Feliu de Guixols, Spain, February 17–21, 2005. (
  5. Chevallard, Y. (1985). La transposition didactique. Du savoir savant au savoir enseigné. Grenoble: La Pensée Sauvage.Google Scholar
  6. Chevallard, Y. (1992). Fundamental concepts in didactics: Perspectives provided by an anthropological approach. In R. Douady & A. Mercier (Eds.), Research in didactique of mathematics. Selected papers (pp. 131–167). Grenoble: La Pensée Sauvage.Google Scholar
  7. Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221–266.Google Scholar
  8. Chevallard, Y. (2002). Organiser l’étude. 1. Structures et fonctions. In J.-L. Dorier, M. Artaud, M. Artigue, R. Berthelot & R. Floris (Eds.), Actes de la 11e Ecole d’Eté de Didactique des Mathématiques (pp. 3–22). Grenoble: La Pensée Sauvage.Google Scholar
  9. Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the limit concept: beginning with a coordinated process scheme. Jourmal of Mathematical Behavior, 15(2), 167–192.CrossRefGoogle Scholar
  10. Goldin, G. A. (1997). Observing mathematical problem solving through task-based interviews. Journal for Research in Mathematics Education. Monograph 9, 289–320.Google Scholar
  11. Kidron, I. (2008). Abstraction and consolidation of the limit procept by means of instructional schemes: The complementary role of three different frameworks. Educational Studies in Mathematics, 69(3), 197–216.CrossRefGoogle Scholar
  12. Lithner, J. (2004). Mathematical reasoning in calculus textbook exercises. Journal of Mathematical Behavior, 23, 405–427.CrossRefGoogle Scholar
  13. Ostrom, E. (2005). Understanding institutional diversity. Princeton, NJ: Princeton University Press.Google Scholar
  14. Raman, M. (2004). Epistemological messages conveyed by three college mathematics textbooks. Journal of Mathematical Behavior, 23, 389–404.CrossRefGoogle Scholar
  15. Sierpinska, A., Bobos, G., & Knipping, Ch. (2008). Source of students’ frustration in pre-university level, prerequisite mathematics courses. Instructional Science, 36, 289–320.CrossRefGoogle Scholar
  16. Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics, with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.CrossRefGoogle Scholar
  17. Voigt, J. (1995). Thematic patterns of interaction and sociomathematical norms. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning. Interaction in classroom cultures (pp. 163–202). Hillsdale, NJ: Erlbaum.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada

Personalised recommendations