On errors in elementary differential calculus: a case study at a technikon

Abstract

The thesis sought to investigate the errors made in elementary differential calculus by students studying engineering at technikons. A sample of 45 first year students from a technikon's engineering faculty were interviewed and questioned on their understanding of ideas considered to be important in elementary differentiation. Differentiation tasks were used to determine the kind of errors first year technikon students make in elementary differential calculus. Subsections of the tasks were regrouped to form twelve items, each item relating to one aspect of differentiation. These aspects were grouped into four sections: elementary algebra, EE of change, limits and infinity, and differentiation. The errors in the four sections were analysed according to a classification of errors. This classification of errors was linked to concepts in cognitive theory. Analysis of the data reveals that there were more structural errors than executive or arbitrary errors in the sections on elementary algebra, rate of change and differentiation. There were more executive errors than structural errors in the section on limits and infinity. The structural errors were due to the students not applying the correct group of principles to the tasks while the executive errors were due to the students either omitting or replacing one substage in a correct rule by an inappropriate or incorrect operation. It is recommended that the errors can be alleviated by the use of appropriate computer technology such as spreadsheet and differential calculus software.