Some South African mathematics Teachers' concept images of the equation concept

Abstract

In this paper, we examine the concept definitions a group of South African upper secondary school mathematics teachers (N = 47) express and how their understanding of the truth value, the role of variable and the syntax of expression appear in the participants' explanations for their assessment of examples and non-examples of equations. We use content analysis and standard quantitative methods. The data consists of the participants' answers to a questionnaire reflecting both Teachers' concept definitions of equation and their skills in classifying examples and non-examples of equation. Altogether 27 participants were able to give a correct definition of the equation concept. Ten participants' definition was slightly ambiguous yet meaningful and ten participants failed in this task. In general, the participants had very high confidence in the sufficiency of their skills in classifying examples and non-examples of equations. Nevertheless, on average, they only succeeded in correctly identifying an equation in 13 of 24 items, with most of the equations being quite simple and none beyond the upper secondary school level. The findings of this study also reveal a common and dominant conception that equations should always possess the truth value ‘true’ although truth value is discussed only in one participant's concept definition. Secondly, the participants are quite careless about the syntax and the involved binary relation in particular despite the fact that the correct form of equations and the equality relation were regularly mentioned in their concept definitions of equation. Finally, some participants seem to think that there is only one equation related to each algebraic problem.