Document Type

Conference Paper

Publication Date


Publication Title

Proceedings of ICME-12



Conference Name

12th International Congress on Mathematical Education ( ICME-12), Seoul, South Korea, July 8 - July 15, 2012


Access to advanced study in mathematics, in general, and to Calculus, in particular, depends in part on the conceptual architecture of these knowledge domains, and in this paper we outline an alternative architecture. Our general strategy is to separate advanced concepts from the particular advanced techniques used in their definition and exposition. This alternative architecture, thus, affords access to advanced concepts from an elementary standpoint to a larger group of learners than is presently accomplished. In the case of the Calculus we develop the beginning concepts of the Differential and Integral Calculus using only concepts and skills found in secondary algebra and geometry. The purpose of this reconstruction is not to alter the teaching of limit-based Calculus but rather to affect the content and pedagogy of the secondary mathematics courses which precede it while developing student understanding of key foundational concepts that may enhance the potential for success in post-secondary Calculus for more students.


0000-0001-5396-0732 (Grant)

Original Publication Citation

Crombie, B., & Grant, M. (2012). Polynomial calculus: Rethinking the role of architecture and access to advanced stud. In the Proceedings of the12th international congress on mathematical education: Intellectual and attitudinal challenges.12th International Congress on Mathematical Education (ICME-12), Seoul, South Korea (pp. 2670- 2679).