Student Obstacles and Historical Obstacles to Foundational Concepts of Calculus

Document Type

Presentation Abstract

Presentation Date

2-2-2007

Abstract

240 university calculus students were given a questionnaire about foundational calculus concepts: function, limit, continuity, and the real number line. Based on their responses, and follow-up interviews with a few students, they were categorized according to the epistemological obstacles they displayed. I found that several of the clusters of obstacles commonly co-occurring in students were also prominent in the history of calculus. This indicates that one key to understanding the parallels between student thinking and historical thinking lies in shared epistemological predispositions, such as the disposition toward smooth motion or toward algebraic simplicity. These predispositions support, but do not strictly constrain, the multiple connected conceptions observed in the study.

Additional Details

Friday, 2 February 2007
3:10 p.m. in Math 109

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