Students' and teachers' understandings of mathematical functions - Burnett-Bradshaw, Camille S. (Tufts Archival Research Center, 2005)
A qualifying paper submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Math, Science, Technology, and Engineering Education. Abstract: The goal of the study presented in this paper is to describe students' and teachers' understandings of: (1) the definition of function and (2) the transformations of functions in different representations. This will be achieved through a case study analysis of two ninth grade students, two twelfth grade students, and two mathematics teachers. The six participants were recruited from the same high school in Boston, Massachusetts, which serves a diverse racial, ethnic, and cultural community. The participants were interviewed individually about questions pertaining to the definition of function and the transformations of functions. Analysis of the results revealed that the ninth grade students have a less sophisticated understanding of the concept of function than do twelfth grade students. It was expected that both teachers would have a similar understanding of functions, but it was found that the twelfth grade teacher had a more theoretical and rigid understanding of the concept of function than did the ninth grade teacher, who had a more practical and flexible understanding of the concept of function. In this case, flexible means translating to other representations of functions and/or using different approaches to functions, while rigid means the opposite.