Abstract
Teaching fraction operations is notoriously challenging, especially teaching fraction division. Research field indicated unfavorable results on teachers’ teaching competency, such as teachers might struggle making sense of invert-and-multiply algorithm for their students or have difficulties generating word problems for a fraction division situation. Increasing studies also focus on measuring different teacher knowledge components. However, currently much of the research examines pre-service teachers’ knowledge through assessments and interviews, and mostly investigate on their content knowledge (CK). As teacher knowledge, especially pedagogical content knowledge (PCK), plays a pivotal role in actual teaching practice, there is a need to better understand what does teaching action look like in classroom rather than mainly measure teacher knowledge outside the classroom. To build on more about how teacher knowledge is enacted in the classroom, this qualitative study uncovers how three 6th grade teachers’ knowledge is demonstrated in their teaching practices over the topic of fraction division. Knowledge Quartet (KQ) framework (Rowland, 2009; Rowland et al., 2005) not only serves as the theoretical lens this study dynamically uses to look at how three teacher’s knowledge surfaced in practices, but also frames the coding to analyze data collected through in-class observations as well as follow-up prompted recall interviews. Three different teacher’s practice is bounded as three individual cases. Cross-case analysis was conducted to find out similarities and differences across three individual cases. This study finds out that, characterized by the distributions of four KQ knowledge categories, three teachers’ knowledge all present the least Contingency Knowledge and prominent emphasis on procedural in their didactic teaching. Implications are made about the connections between mathematical perspectives and teachers’ employment of different representations in teaching fraction division, about their use of opportunities in their classes to have more meaningful conversation with students to invoke their thinking, and potential future research aims to understand how to promote more meaningful conversations in class and teachers’ flexibility in/about connecting different mathematical perspectives so that to help students learn fraction division more conceptually rather than by rote memories.