Magister Educationis - MEd / Algebraic graphs are a difficult topic for most secondary school mathematics learners. My experience as a Mathematics teacher in the Further Education and Training Phase (FET) is that learners solve problems involving graphs with difficulty. Consequently, the purpose of this research was to investigate learners’ ways of working with algebraic graphs in high-stakes examinations including their errors and misconceptions in this respect. The investigation carried out to identify learners’ errors and misconceptions is based on the analysis of 444 scripts from the 2012 grade 12 final Mathematics examination. More specifically, the study aimed to investigate the ways learners used to solve questions related to graphs in this examination. The focus of the study was the algebraic graphs tested in Paper 1 of the National Senior Certificate (NSC) examination with an emphasis on the identification of errors exhibited in the learners’ scripts. The study adopted a qualitative approach using documentary analysis methodology. As data, the study used the scripts of the final grade 12 Mathematics examinations of schools participating in a project for the improvement of Mathematics based at the University of the Western Cape (UWC). The analysis of learners’ scripts reveals that learners make many errors when they work with algebraic graphs. These errors that have been found in this investigation were coordinate, intercept, domain and range, asymptote, identification, drawing and function errors. Additional errors which were identified are transformation and inverse errors.

In South Africa the National Senior Certificate (NSC) examination is the capping external examination taken at the culmination of twelve years of schooling. Levels of success in the examination offer examinees access to a variety of career options. High levels of success in the mathematics examination are a pre-requisite for entry into studies linked to so-called elite careers. However, performance of examinees in the NSC Mathematics examination is not of a requisite standard and only a few examinees achieve results that fall within the high levels of the achievement bands. In order to give mathematics teachers and others insight into performance in the NSC Mathematics examination, various forms of feedback are provided. One purpose in doing so is to provide teachers with an understanding of the examinees' ways of working in order for them to adjust their classroom practice to address mistakes displayed in the work of the examinees. The feedback provided is primarily of a superficial kind with the mere listing of such mistakes. The purpose of this study was to investigate whether or not it is possible to analyse the production of the responses of examinees in the NSC mathematics examinations more meaningfully.

Test anxiety involves a variety of physiological, cognitive, and emotional components. Those suffering from high test anxiety seem to perform poorly on examinations because test anxiety can contribute to information processing challenges both while studying for tests and during evaluative situations. Current research indicates that when a training program is applied that incorporates cognitive behavioral techniques as well as study skills training, highly test anxious individuals can overcome information processing challenges, increase their academic performance, and earn higher scores on tests. In this study, a training program (Counseling Exam Test Anxiety Intervention) combining cognitive behavioral techniques and study skills training was applied to highly test anxious counselors and counselors in training preparing to retake the National Clinical Mental Health Counseling Examination (NCMHCE) after failing it at least once. This study makes the first known attempt to examine test anxiety specifically associated with the NCMHCE. The research questions guiding this study related to exploring the nature of test anxiety, any changes that occurred during administration of the Counseling Exam Test Anxiety Intervention (CETAI), and whether or not the CETAI was effective in terms of decreasing test anxiety and increasing academic performance. The findings revealed that when participants in this study applied the skills they learned from the CETAI, they improved their scores on practice tests, experienced an increase in confidence, and the majority of them successfully passed the NCMHCE when they retook it.