An exploration of students’ errors in derivatives in a university of technology

• Conceptual errors occur due to failure to grasp the concepts or to appreciate the relationships involved in the problem.
• Interpretation errors arise when students fail to interpret the problem due to poor conceptualisation.
• Procedural errors arise when students fail to carry out manipulations although they understand concepts in the problem.
• Linear extrapolation errors happen as an over-generalisation of the property f(a + b) = f(a) + f(b), which applies only when f is a linear function.
• Arbitrary errors arise when students fail to take account of the constraints laid down in what is given.

This paper reports on an exploration of errors that were displayed by students who studied mathematics in chemical engineering in derivatives of various functions such as algebraic, exponential, logarithmic and trigonometric functions. The participants of this study were a group of twenty students who were at risk in an extended curriculum programme in a university of technology in Western Cape, South Africa. The researcher used a qualitative case study approach and collected data from students’ written work. This research uses action, process, object, and schema (APOS) theory to classify errors into categories and to analyse and interpret the data collected. The students displayed five different kinds of errors, namely, conceptual, interpretation, linear extrapolation, procedural and arbitrary. The use of APOS theory as a framework revealed that several students’ errors might be caused by over-generalisation of mathematical rules and properties such as the power rule of differentiation and distributive property in manipulation of algebraic expressions. This study suggests that teaching of the standard rules of differentiation should put emphasis on its restrictions to eliminate common errors that normally crop up due to over-generalisation of certain differentiation rules.