An examination of prospective middle grades mathematics teachers’ construction of linear equations and functions

Abstract

This study was designed to examine prospective teachers’ changes in concepts, building from ratios, rates, and proportions to the construction of linear equations and functions. The 3 participants were all prospective middle grades teachers with two concentrations: mathematics and language arts. Audio-recorded interviews, audio-recorded classroom instruction, and discussions, along with field notes and assessment items such as pretests, posttests, and quizzes, were used to find patterns relating to understanding of the concepts as well as changes in conceptual understanding. Instruction and quizzes were used to track and examine changes in concepts. The posttest was used to mark the end result in terms of growth of prospective middle grades teachers’ understanding of proportional reasoning and their ability or inability to construct linear equations and functions.