Concept development in mathematics : teaching and learning of quadratic equations, inequalities and their graphs.

Abstract

This was an evaluative study undertaken to unpack some of the factors which could explain Transkei matriculation students' apparent poor conceptual understanding of Mathematics and to throw some light on possible solutions to their problems. In addition the study attempted to examine how Mathematics as well as the learning and teaching of Mathematics, were viewed by Transkei teachers and students at the high school level. The theory of quadratic equations, inequalities and their graphs constituted the mathematical content research area of this study. This topic was chosen because of the key role that it plays in the matriculation Mathematics syllabus. There were 8 research questions which led to 8 hypotheses. The research sample comprised 311 matriculation students taking higher grade Mathematics and their 10 Mathematics teachers from 10 schools in the Umtata education circuit. Four researcher-designed instruments, namely: a diagnostic test (students'), a student interview schedule, a teachers' questionnaire, and a teacher interview schedule were used. The diagnostic test consisted of 38 items aimed at addressing the first 7 research questions. Students' mean scores for each group of items of the test addressing a particular research question were computed and compared against a criterion score of 60%, using the "Z” statistic. In addition, an analysis of students' scripts was carried out and clinical interviews on a sample of the subjects (students) were conducted to find out their conceptual difficulties/misconceptions. The teachers' questionnaire and interview schedule were used to ascertain the teachers' disposition towards Mathematics teaching. Accordingly, teachers were divided into two groups A and B on the basis of their scores in relation to the median for the whole group. This enabled the testing of hypothesis 8. In this regard, means for the students taught by the two respective groups of teachers were comared by using "Z" statistic to establish if they were statistically different from each other. Teachers' reasons for their responses to some of the items in the questionnaire were analyzed and discussed with a view to finding out their favourite teaching styles and some of the difficulties they faced in order to be as effective as they wished to be. Analysis of data for research questions 1-7 showed that students did not have sufficient pre-requisite knowledge, and did not display a satisfactory level of mastery in solving quadratic equations and inequalities, and interpretation of graphs for quadratic equations and inequalities. Students' difficulties identified from the findings of this study were classified into 7 categories, namely: mathematical terms, mathematical symbolic language, mathematical skills, form in mathematics, over generalisations, translation and conceptual difficulties. The "Z" test for hypothesis 8 showed that students taught by teachers whose teaching strategies were more student-centred performed better than those who were taught by teachers whose teaching was inclined towards teacher-centredness. Finally, recommendations for teachers, curriculum planners, education authorities and other researchers are also made.