Student strategies for deciding the limit of a multivariable function

Overview & Synopsis

This is a grounded research study focusing on strategies students use to establish the limit of a multivariable function at a point, and student misconceptions. Open coding was used to analyze 688 exam answers in a multivariable calculus course. We provide a fine-grained analysis of 9 categories of student strategies, with a discussion of student understanding or misconceptions in each one. Most students approached the point along different curves or split the function as a sum of terms. Those that chose curves were twice as likely to succeed. Prevailing misconceptions were that checking only several paths approaching the point guarantees a limit, and an automated misuse of the sandwich theorem. We also detected misconceptions regarding the relations between the existence of a limit, continuity, partial derivatives and differentiability in multivariable functions.