Explores first-year students' understanding of fundamental calculus concepts using written tests and interviews. Analysis of the written and verbal responses to the test items revealed significant misconceptions on which students' mathematical activities were based. Describes some of those misconceptions and errors relating to students'…

Presents a variety of examples of wrong proofs, misinterpreted definitions, and the mistaken use of theory. Examples are based on experience teaching mathematics to engineering students. Includes elementary examples and more advanced ones taken from different subjects. (Author)

Describes a test using 155 third-year undergraduates in 15 different institutions to examine the extent to which certain core first-year material is retained and understood. Includes an analysis of the answers given by students to each question as well as some of their comments. Students' misconceptions indicate that foundations laid in the first…

Proposes a taxonomy of three levels in increasing order of mathematical demand in order to understand a set of mathematical skills of some importance to beginning undergraduates in engineering and mathematics. Suggests that the constructed instrument is robust and the taxonomy used is effective. (Contains 22 references.) (Author/ASK)

Examines first-year university students' (n=630) understanding of fundamental calculus concepts at three South African universities. Identifies several misconceptions underlying students' understanding of calculus concepts. Addresses some of the common errors and misconceptions related to students' understanding of 'limit of a function' and…

Suggests that the cross product of two vectors can be more easily and accurately explained by starting from the perspective of dyadics because then the concept of vector multiplication has a simple geometrical picture that encompasses both the dot and cross products in any number of dimensions in terms of orthogonal unit vector components. (AIM)