Subject-Matter Knowledge and Elementary Instruction: A Case from Functions and Graphing

Abstract

The purpose of the present investigation was to describe the relationship between teachers’ knowledge of mathematics and their instructional practice. An experienced fifth grade teacher was videotaped as he taught a lesson sequence on functions and graphing. In addition, a subject matter knowledge interview and card sort task were conducted with the teacher and a mathematics educator. The results suggest that the teacher’s knowledge of functions and graphing was missing several key mathematical ideas and that it was not organized in a manner to provide easily accessible, cross representational understanding of the domain. These limitations were found to relate to a narrowing of his instruction in three ways: the lack of provision of groundwork for future learning in this area, overemphasis of limited truths, and missed opportunities for fostering meaningful connections between key concepts and representations.