Student teachers' knowledge and understanding of algebraic concepts: The case of colleges of education in the Eastern Cape and southern Kwazulu Natal, South Africa

Abstract

This study is aimed at investigating the knowledge and understanding of algebra amongst final year College of Education students in and around Transkei region of Eastern cape, South Africa. Triangulation methods were used to gather data for the study, which included an algebra test instrument, adapted from the CDMTA and Kaur and Sharon (1994) test instruments, interviews and classroom observations. Six Colleges of Education with a total number of 212 students constituted the sample from the Eastern Cape province and South KwaZulu Natal. Data were collected from August 1997 to July 1998.

The motivation for the study was that such an exploratory investigation could contribute significantly to the understanding of some of the principal reasons underlying the poor results in the final schooling examination (the “matric”) of the teaching and learning of mathematics in rural areas of South Africa. Algebra forms a big proportion of the final matric examination in mathematics. The overall results of the study indicate that the conceptual algebraic knowledge and understanding of these College students is weak and fragile.

In analysing the algebraic knowledge and understanding of students as evidenced by the data, factors such as language, the nature of mathematics, the philosophy underpinning teaching and learning and textbooks were seen to have played important roles in the conceptions and misconceptions which many of the subjects of the study portrayed.

My research clearly shows that College of Education students have misconceptions, poor learning and teaching of algebraic concepts. This suggests that these prospective teachers do not have well developed concepts in algebra. The participants’ knowledge and understanding of algebraic concepts are therefore not good enough to assist learners as far as learning for conceptual understanding is concerned at schools.

The results show that much of the knowledge and understanding of algebra came from previous knowledge and understanding gained during high school. Little change had happened during the years spent at the Colleges. The conceptions and misconceptions arose out of the traditional framework of knowledge acquisition rather than through approaches advocated by the newly implemented South African curriculum (Curriculum 2005), which has been revised to a National Curriculum Statement similar to what NCTM (1991) Standards might have envisaged.

The lack of pedagogical content knowledge in algebra, shown by these student teachers during their teaching practice lessons reflects a deeper problem pertaining to 2 their future teaching after completion of the courses at Colleges. This is bound to have a cascading effect on teaching and learning in schools, perpetuating the cycle of misconceptions in algebra shown by this study, unless something radical is done about the teaching and learning of algebra at Colleges.

The study concludes with recommendations arising out of the results and a number of suggestions for education departments, curriculum implementers, lecturers and future researchers. Strategies are suggested for improving the existing poor state of affairs in the learning and teaching of algebra at Colleges of Education and at secondary schools. These include improvement in algebraic competencies like multiple representations; understanding of basic principles such as: one cannot add unlike terms, checking solutions of equations and inequations. Real life examples should be used to give meaning to the algebraic concept they want to teach where possible.

College of Education lecturers should place emphasis on conceptual understanding and correct usage of algebraic notations and symbols. Curriculum developers should include history and relevance of certain algebraic topics in order to create interest and

meaning for some of the concepts. Instructional materials in school algebra should be designed specifically for local contexts. Researchers should investigate the cause of misconceptions and misunderstandings of algebraic concepts at high schools and try to address them before they are carried through to the College of Education level.