Examining preservice secondary mathematics teachers' ability to reason proportionally prior to and upon completion of a practice-based mathematics methods course focused on proportional reasoning

The purpose of this study was to examine preservice secondary mathematics teachers' understandings about proportional reasoning prior to and upon completion of a practice-based methods course focused on proportional reasoning, their opportunities to learn the intended content, and their ability to apply what was learned in a new setting. Ten teachers completed a pre/posttest and pre/post interview that was designed to explore their ability to reason proportionally. All classes were videotaped so as to examine teachers' opportunities to learn to reason proportionally and to utilize their understandings in a new setting. In addition, six teachers who were not enrolled in the course served as a contrast group and completed the pre/post instruments.The analysis of the data suggests that teachers learned important aspects of proportional reasoning from the course. Prior to the course, there were no differences between the understandings of the teachers enrolled in the course and those who were not. However, by the end of the course, teachers enrolled in the course utilized a broader range of solution strategies, significantly improved their capacity to distinguish between proportional and nonproportional relationships, and significantly enhanced their understanding of the nature of proportional relationships, while those in the contrast group did not.In addition, the analysis of the class sessions made salient that all of the mathematics that teachers learned during the course was made public during multiple classes and by multiple teachers. The analysis also revealed that even teachers who remained mostly silent during class discussions still learned the same mathematics that more the vocal teachers learned.The results of the analysis of class sessions from a subsequent course on algebra revealed that the teachers who participated in the proportional reasoning course drew upon their enhanced understandings of proportional relationships when appropriate. This result suggests that teachers had not merely memorized discrete facts about proportional relationships, but had developed flexible understandings that allowed them to access their knowledge as they explored different mathematical ideas. Finally, the results of the study suggest that practice-based teacher education courses can be fruitful sites for helping teachers develop mathematical knowledge needed for teaching