An evaluation of the function knowledge of a selected group of prospective secondary mathematics teachers

This study was an exploratory analysis of prospective secondary mathematics teachers' knowledge of function. There were three major purposes of the study. One purpose was to determine the variety of function definitions given by prospective secondary mathematics teachers and to identify those most common. A second purpose was to examine the main concept images of function given by these students in classification, translation and construction tasks. A third purpose was to assess what prospective teachers view as appropriate content objectives for teaching the function concept to ninth grade algebra students.

The subjects in this study were prospective mathematics teachers enrolled in a required secondary mathematics methods course offered by the University of Maryland, College Park.

Each prospective teacher was asked to complete a function definition task, a card sort task, a function applications questionnaire, and a lesson plan task. Two mathematicians with ten years college teaching were asked to complete the same tasks as the prospective teachers with the exception of the lesson plan task. This was done to compare experts' knowledge of mathematics with beginning teachers' understanding of functions.

Data from the function definition task indicated that a majority of the prospective teachers viewed functions as formulas, equations, or rules, but the mathematicians defined functions with a formal Dirichlet-Bourbaki definition.

Results of the card sort task indicated a majority of the prospective teachers could not recognize various functional relationships as the same when presented in different representational form. The mathematicians grouped equivalent relationships regardless of representational form and indicated which relationships were functions.

The results of the function applications questionnaire showed that a majority of prospective teachers could apply appropriate procedures to classify graphs of functions, but they had difficulty constructing functions given specific conditions.

The lesson plan task results indicated that a large majority of the prospective mathematics teachers are not aware of the type of a mathematics that takes place in an algebra class or the recent school reform efforts to incorporate functions as a unifying concept in mathematics.

The findings of this study suggest that there is a need for a component within the teacher education program to address preservice teachers knowledge of function and the role of this concept within the school mathematics program.