D.Ed. (Didactics) / The main objective of this research is to develop a diagnostic model for the prediction of mathematics achievement for first year university students. In order to design this model of prediction, the following objectives were formulated: * to establish a profile of a typical successful and unsuccessful student in Mathematics; * to calculate the probable final mark achieved by a student in Mathematics; * to establish the probability of success by a student in Mathematics. In this research various factors determinating the academic performance of first year students at a university are discussed. Firstly the transition from school to university and its implications on the student, the teaching of a subject and its influence, and those factors inherent in the student are investigated. The factors inherent to the student are described as cognitive factors (intelligence, aptitude and previous performance) and non-cognititve factors (study methods and attitudes, interest, anxiety, personality and adjustment).

D.Ed. / Each student undergoing tuition, is unique and one of a kind. Each student has his own personality and individuality. Students have different ways of learning; progress differently and reach different degrees of success with their methods of study. The success of the student's learning process is closely related to the student's existing pre-knowledge. The orientation student at the technical college finds himself in a unique situation. As this course is a bridging course, the student must overcome the backlog in his field of study and also be prepared for the studies that will follow. Learning of mathematics is a complex matter. No two answers will correspond if inquiring into the method in which mathematics is mastered. The same is also true if inquiring into the teaching strategies to be followed in order to acquire success in teaching this subject. In this study the theories of Piaget, Bruner, Ausubel among others, were scrutinised. Numerous teaching strategies can be followed to ensure success in the classroom. This study concentrates on co-operative learning, since the point of view is held that it provides the overall framework within which effective tuition can be achieved. Cooperative learning has been researched by applying it in the mathematics classroom. A very positive response was received from the students as well as the teachers concerned. However, certain problems were experienced. These include, inter alia, that some students found the classroom discipline lacking. Others complained that the lecturers did not do enough explaining. The following conclusions can be drawn from this study: Traditionally the classroom is where the lecturer has the sole right to teach. A change is necessary. New teaching strategies will have to be looked at. To achieve this change, co-operative learning is strongly recommended. It provides for active involvement of the student in the learning process; it provides the opportunity for the student to accept responsibility for his own learning success as well as that of his fellow students and it provides the opportunity for mastering social skills which are a necessity for our modern, complex and integrated society.