Abstract:

A nuanced understanding of what aspects of ambitious mathematics instruction teachers take up and use from professional learning (PL) is important, and what teachers continue to use years after their participation in PL is critical for the design and implementation of PL and contributes to research on inservice teacher learning. Investigations of what teachers learn overtime from professional learning experiences is understudied and this study sought to better understand the long term outcomes of PL by exploring which ambitious mathematics practices advocated in PL were sustained over time and in particular, if and how visual representations play a role in teachers’ learning and instructional practice.

A qualitative case study approach was used to dig deep into the experiences of two teachers who participated in two different PL projects. Both PL projects focused on the use of mathematical visual representations (VRs) to support mathematical learning. Both projects also encouraged and modeled ambitious teaching practices to support mathematics learning. The two teachers we focus on in this study were selected as they indicated high levels of uptake from the PLs. Four to five years after their experiences in this project, the two teachers recorded six classroom lessons and selected clips they felt reflected their use of ideas from the PL. They also participated in four interviews. The first part of these interviews asked teachers to reflect on their experiences with the PL, what they remembered related to the goals and intentions of the PL and what strategies, content, and resources they used from the PL in the past and continue to use currently in their classrooms. The second part of these interviews followed a think aloud protocol, where teachers and researchers watched video clips that the teachers selected. The teachers then described their own interpretation of uptake and implementation of content, pedagogy, and resources from the PL. The use of video allowed teachers to reflect on their practice and describe how they perceived uptake in specific contexts and how they attributed specific learning to the PL.

A multiple-case study design was used to analyze the ways in which ambitious mathematical teaching practices were taken up and used in each of the teacher’s individual contexts and how the teachers attributed this use to the PLs they attended. Findings suggest that (1) the teachers’ use of VRs appears to be strongly connected to teachers' own active learning of VRs in PL, (2) VRs appears to be a key factor that supported the teachers’ use of other ambitious teaching practices in their classroom and (3) the two teachers remembered and continued to use ambitious practices and VRs in their classrooms in ways that not only aligned to the goals and intention of the PL, but also adapted and extended representations to different mathematical domains and settings. This study contributes to the literature by providing examples of how learning about a specific pedagogical tool, in this case VRs, along with specified content, can have an impact on teacher learning and pedagogy over time. Implications for PL providers suggest that a focus on VRs may be one tool to anchor learning to deepen teachers’ abilities to engage in ambitious teaching practices.

Keywords:

Professional learning, mathematics education, representations.