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\input zb-matheduc
\iteman{ZMATH 2012b.00224}
\itemau{Smart, Angela}
\itemti{A student's symbolic and hesitant understanding of introductory calculus.}
\itemso{Joubert, M. (ed.) et al., Proceedings of the British Society for Research into Learning Mathematics (BSRLM). Vol. 30, No. 1. Proceedings of the British congress of mathematics education, BCME-7, University of Manchester, UK, April 6--9. 2010. London: British Society for Research into Learning Mathematics (BSRLM). 215-222 (2010).}
\itemab
Summary: In this paper I discuss a study that looked at one student's understanding of calculus, and used the framework of Tail's theory of Three Worlds of Mathematics to determine the embodied and symbolic nature of that understanding. Initially, the student's understanding of calculus was explored through a task interview using calculus questions designed to elicit embodied and/or symbolic understanding. Results showed that this student predominantly demonstrated a symbolic understanding, with a very limited embodied understanding on the particular tasks. It was also during this interview that the student exhibited the phenomenon of searching for reassurance as to whether he was answering the task and interview questions correctly. This paper discusses this search for reassurance, speculates on potential causes, and argues that there may be a relationship between this search for reassurance and the student's symbolic understanding of calculus.
\itemrv{~}
\itemcc{C25 C35}
\itemut{reassurance; calculus; symbolic understanding; didactic contract; institutional norms; three worlds of mathematics; case studies}
\itemli{}
\end