Strengthening pedagogical content knowledge in division of fractions through a three-part professional development series : a multiple case study.

Abstract

Good teaching matters. The teacher represents the most dominant factor affecting student achievement. Understanding the knowledge teachers bring to the classroom and how to effectively strengthen this knowledge for in-service teachers has been under investigation for the past several decades. Rational numbers represent the most dominant area of K – 8 mathematics content and standards; however, research has revealed significant deficiencies in teachers’ understanding of fractions, especially fraction division. The purpose of this case study was to explore how a series of focused professional development workshop-type sessions can impact teacher participants’ understanding of and instructional practices for the division of fractions. The study also explored how a workshop model of professional development can be used as an intervention to increase the teachers’ pedagogical content knowledge. The participants in this study included seven fifth-grade teachers from the same school district, teaching the Texas Essential Knowledge and Skills, and working in the same small Texas town. Teachers participated in a professional development workshop series that consisted of three similarly formatted workshop sessions which included instruction designed using recommendations from the field of fraction research, discussion, an analysis of student work and incorporated practices that help develop a deeper understanding of fractions by building on students’ informal knowledge, creating meaningful contexts, and constructing an understanding based on whole number operations. Data was collected in the form of pre- and post-assessments, interviews, workshop session observations and field notes, written teacher reflections, both a demographic and workshop feedback questionnaire. Each participant was analyzed as a separate case and a cross case analysis was conducted to show common themes. Results from this case study reveal an increase in teacher participants’ understanding of fractions and a positive impact on their instructional practices. In addition, results revealed significant findings related to developing teachers’ understanding of the division of fractions, including connecting whole number division with the division of fractions, developing lessons and learning experiences centered on real-world situations and familiar context. This report included implications and recommendations for state agencies, curriculum leaders and professional development facilitators, and teachers. Areas of future research are also identified by the researcher.