Philosophiae Doctor - PhD / The purpose of the study was to investigate prospective 'A' level mathematics teachers' knowledge of the concept of a function. The study was a case study of six prospective Zimbabwean teachers who were majoring in mathematics with the intention of completing a programme leading to certification as secondary mathematics teachers. At the time of the study the six prospective teachers were in their final year of study. Prospective teachers' knowledge of the concept of a function was assessed through task-based interviews and reflective interviews. These interviews, which were done over a period of three months, were structured to capture the prospective teachers' subject matter knowledge and pedagogical content knowledge for teaching the concept of a function. The interviews were also meant to capture the prospective teachers' underlining pedagogical reasons for their choices of the examples, representations and teaching approaches when planning to teach the concept. As part of the study a theoretical framework for understanding prospective teachers' knowledge of the concept of a function was developed. The framework, which was developed, was used as an analytical tool in analyzing prospective teachers knowledge of the concept of a function. The results of the study indicated that the prospective teachers had a process conception of a function although some of them had given a set-theoretic definition of a function in which a function is perceived as a mathematical object. They also confined the notion of a function to sets of real numbers. Functions defined on other mathematical objects (for example, the differential operator and the determinant function) were not considered as functions by five of the six prospective teachers.

The purpose of the study is to find answers to the following questions. 1. Is there a significant difference in any of the three simple pair-wise comparisons of the attitudes of the three groups of mathematics instructors of college preparatory courses toward teaching those courses? 2. Is there a significant difference in any of the three simple pair-wise comparisons of the attitudes of the three groups of mathematics instructors of college preparatory courses toward the MAA-NCTM recommendations? 3. Is there a significant correlation between the attitudes toward the MAA-NCTM recommendations and the attitudes toward teaching the college preparatory mathematics courses held by the mathematics instructors in each of the three groups? The data led to the conclusion that all three groups held the same favorable attitude toward teaching college preparatory mathematics courses. Also, there were no significant differences among the three groups' attitudes toward the MAA-NCTM recommendations. However, while no significant correlation was found for the high school instructors, there did exist a significant positive correlation between the two attitudes for each of the other two groups studied.

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