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Mathematical Beliefs and Conceptual Understanding of the Limit of a Function

Jennifer Earles Szydlik
Journal for Research in Mathematics Education
Vol. 31, No. 3 (May, 2000), pp. 258-276
DOI: 10.2307/749807
Stable URL: http://www.jstor.org/stable/749807
Page Count: 19
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Mathematical Beliefs and Conceptual Understanding of the Limit of a Function
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Abstract

In this study, I investigated 27 university calculus students' mathematical beliefs and connections between those beliefs and their understandings of limit. Participants were selected on the basis of questionnaire and interview responses to real-number, infinity, function, and sources-of-conviction items. Data obtained in a subsequent limit interview suggest a relationship between sources of conviction and understanding of limit; students with external sources of conviction gave more incoherent or inappropriate definitions of limit, held more misconceptions of limit as bound or unreachable, and were less able to justify limit calculations than those with internal sources of conviction. The influence of content beliefs on understanding of limit is less evident.

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