In this paper, we extend our previous work on challenges teachers face when engaging with proportional reasoning contexts to investigate two contexts that included four problems for middle grades teachers to solve as well as eight student solutions. Analysis included coding for correct solving of the problem as well as making sense of and…

Teacher knowledge, especially of proportional reasoning, is important, particularly in middle school grades in the United States. In this instrumental case study, one teacher's understanding of constant as it relates to proportions and how that understanding shifted over the course of a six hour professional development experience is discussed.…

In this study, we investigated teachers' abilities correctly to identify situations that are appropriate for proportional reasoning and factors that might influence their ability using data on 148 teachers from the U.S. Learning Mathematics for Teaching assessment and other, similar items (with a smaller sample). Through a quantitative exploratory…

In this study we extend our prior exploration focused on the extent to which middle school teachers appropriately identified proportional situations and whether there were relationships between attributes of the teachers and their ability to identify proportional situations. For this study, we analyzed both a larger dataset (n = 32) and two…

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The…

In this study, we considered how middle school teachers understood the relationship between fractions and ratios. We used two instruments to collect data from 11 teachers and relied on Knowledge in Pieces as a lens for considering understandings teachers have and how coherent those understandings are. From our analysis, we developed three main…

In this study we explored to what extent middle school teachers were able to appropriately identify proportional situations when presented with various mathematical structures and if there were relationships between attributes of the teachers and their ability to identify proportional situations. Interestingly, there were no strong relationships…

In this study, we considered how four teachers reasoned about proportional situations involving geometry. We used pilot interviews conducted with in-service middle grades teachers around a set of proportional tasks. Analysis relied on a knowledge in pieces lens to uncover the resources that each teacher used in solving the tasks and which…

This study presents a qualitative analysis of the knowledge teachers in one professional development course used to reason about proportional relationships with double number lines. We work from the knowledge-in-pieces perspective to consider the existing knowledge the participants did or did not invoke when learning to reason with this…

Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsak, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study…

In this study, we expand the Cohen and Ball triangle of interactions to explore the relationship of professional development to classroom practice. We consider a case study of one teacher's implementation of a task from professional development in her 7th grade classroom. We were specifically interested in how the content and pedagogy of the…

The purpose of this research was to understand how one teacher reflected on different classroom situations and to understand whether the teacher's approach to these reflections changed over time. For the purposes of this study, we considered reflection as the teacher's act of interpreting her own practices and students' thinking to make sense of…

This study examined issues in supporting middle school teachers to become more learner centered when implementing computer-based, workplace simulations in their classrooms. Focuses on a participant observation study of two teachers to develop and evolve a framework for professional development that included reflective skills and proximal goals.…