PRE-SERVICE MATHEMATICS TEACHERS’ KNOWLEDGE OF MATHEMATICS FOR TEACHING: QUADRATIC FUNCTIONS

Abstract

Many researchers and education stakeholders in South Africa point to the need to develop teachers' personal knowledge of the mathematics concepts that they teach to their learners. In this research study we explore the understanding of 42 pre-service mathematics teachers of one aspect of school level mathematics, that of quadratic functions. Data were generated from the written responses to an assessment as well as semi-structured interviews. The purpose was to explore the methods used by pre-service mathematics teachers to derive a symbolic equation for a quadratic function expressed in graphical form. Furthermore, we looked at whether the pre-service teachers were able to use different methods to generate the symbolic equation. The results showed that 25 participants were able to determine the equation of a parabola using one method, while 11 of them were able to use two different methods. The most common method used was based on the intercept form of the equation. Some students identified different forms that the equation of a quadratic function could be expressed as but were unable to apply this to derive the equation. These results indicate that these students are not yet ready to teach these school level concepts even though they have studied advanced mathematics topics as part of their pre-service training. The study recommends that pre-service teachers should also be provided with more structured opportunities to help develop pedagogic content knowledge of the school level content as part of their teacher training programme. Keywords: graphical representation, parabola, pre-service mathematics teachers, quadratic functions, symbolic representation.