Developing and using mathematical knowledge for teaching fractions: A case study of preservice teachers

Leigh A van den Kieboom, Marquette University


This study investigated how preservice teachers developed and used mathematical knowledge for teaching fractions while enrolled in an integrated mathematics content and field experience course. Qualitative data sources included video recordings of mathematics content classes, audio recordings of preservice teachers working with students in field experiences, semi-structured interviews, and reflective journal responses. Quantitative data in the form of the Content Knowledge for Teaching Mathematics ([CKT-M]) were collected from preservice teachers completing the mathematics course to measure growth over one semester. The CKT-M instrument also served in the selection of four case study participants representing the range of preservice teachers' enrolled in the course. Four preservice teachers served as case study participants in the qualitative study that explored work with elementary and middle school students in two field experiences. Analysis of the CKT-M data revealed that the twenty-four preservice teachers enrolled in the mathematics content course increased their content knowledge for teaching mathematics. The twenty-four preservice teachers strengthened their understanding of mathematics by participating in small group work and whole group presentation that employed the use of problem solving, reasoning, and communication as conceptual tools to build understanding. The mathematics course instructor served as an expert in modeling the actions of mathematical knowledge for teaching for the preservice teachers. A performance rubric was used to explore how four case study participants used mathematical knowledge for teaching to inform their work with students in the field experiences to pose problems, use representations, provide accurate and helpful mathematical explanations, pose questions to probe student understanding, and respond to students. The four case study participants' success in using mathematical knowledge for teaching to perform these teaching actions related to their subject matter understanding and mathematical knowledge for teaching. The case study participants who demonstrated stronger subject matter understanding and growth in mathematical knowledge for teaching during the mathematics content course were more successful in performing these teaching actions. The study expanded and revised Ball and Bass' (2003) descriptors for mathematical knowledge for teaching for preservice teachers to provide a framework that explicitly supports preservice teachers in learning about how to teach elementary mathematics.

Recommended Citation

van den Kieboom, Leigh A, "Developing and using mathematical knowledge for teaching fractions: A case study of preservice teachers" (2008). Dissertations (1962 - 2010) Access via Proquest Digital Dissertations. AAI3326751.