Conceptual mis(understandings) of beginning undergraduates

Abstract

In order to understand a set of mathematical skills of some importance to beginning undergraduates in engineering and mathematics, a taxonomy of three levels in increasing order of mathematical demand is proposed. The construction of a test instrument is discussed relating its purpose to the concerns of the preparation of students voiced by such as Anderson et al., to underlying theories of learning, Slavit, and to other taxonomies, Smith et al. The results of applying the questionnaire to 423 students in the period 1994–1996 is analysed and evaluated, focusing on the distributions of the distractors chosen by the students. Results suggest that the instrument is robust, that the taxonomy used is effective and raises questions that affect the teaching and learning paradigms used for mathematics pre-university and on entry to university.