Abstract
In this paper the role of algebra in students’ mathematical reasoning about limits of
functions in undergraduate mathematics is analysed, considering the students’ educational
setting. Data from a video study where six students worked in pairs to solve
problems on limits of functions, and an analysis of their calculus lectures, indicate
that algebra is at the same time a key and a lock to reach the limit in these problems.
This double effect is related to the mathematical organisation taught, as well as the
students’ sense of authority as internal or external.
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