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Students’ understanding of the interplay between geometry and algebra in multidimensional analysis: representations of curves and surfaces

The aim of the study is to investigate mathematics students’ understanding of geometrical objects such as curves and surfaces in space, when these objects are presented algebraically, that is, by their equations. Flexible use of different representations, in this case geometric and algebraic, as well as the ability to convert between implicit and parametric types of equations, is often assumed as a prerequisite in multivariable calculus. We have performed an in-depth analysis of students’ answers to exam questions to identify types of students’ difficulties in these conversions. However, our results also point to the impact of the didactic contract on students’ productions which possibly prevented students to fully present their understanding.

Transition across university mathematics, multivariable calculus, curve, representation, didactic contract

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