Episode 16: Diverge then Converge: A Strategy for Deepening Understanding through Analyzing and Reconciling Contrasting Patterns of Reasoning
June 18th, 2020 | Season 4 | 31 mins
classroom discourse; enacting mathematical practices; pre-service content courses
One of the challenges of teaching content courses for prospective elementary teachers (PTs) is engaging PTs in deepening their conceptual understanding of mathematics they feel they already know (Thanheiser, Philipp, Fasteen, Strand, & Mills, 2013). We introduce the Diverge then Converge strategy for orchestrating mathematical discussions that we claim (1) engenders sustained engagement with a central conceptual issue and (2) supports a deeper understanding of the issue by engaging PTs in considering both correct and incorrect reasoning. We describe a recent implementation of the strategy and present an analysis of students’ written responses that are coordinated with the phases of the discussion. We close by considering conditions under which the strategy appears particularly relevant, factors that appear to influence its effectiveness, and questions for future research.
May 28th, 2020 | Season 4 | 23 mins 46 secs
Understanding mathematics teacher noticing has been the focus of a growing body of research, in which student work and classroom videos are often used as artifacts for surfacing teachers’ cognitive processes. However, what teachers notice through reflecting on artifacts of teaching may not be parallel to what they notice in the complex and demanding environment of the classroom. This article used a new technique, side-by-side coaching, to uncover teacher noticing in the moment of instruction. There were 21 instances of noticing aloud during side by side coaching which were analyzed and classified, yielding 6 types of teacher noticing aloud, including instances in which teachers expressed confidence, struggle, and wonder. Implications for coaching and future research on teacher noticing are discussed.
May 18th, 2020 | Season 4 | 32 mins 11 secs
professional development; research on professional development; formative assessment
Formative assessment helps teachers make effective instructional decisions to support students to learn mathematics. Yet, many teachers struggle to effectively use formative assessment to support student learning. Therefore, teacher educators must find ways to support teachers to use formative assessment to inform instruction. This case study documents shifts in teachers’ views and reported use of formative assessment that took place as they engaged in professional development (PD). The PD design considered the formative assessment cycle (Otero, 2006; Popham, 2008) and embedded it within a pedagogical framework (Lamberg, 2013, in press) that took into account the process of mathematics planning and teaching while supporting teachers to learn math content. Teachers restructured their definition of student understanding, which influenced how they interpreted student work and made instructional decisions. Teachers’ pre-PD instructional decisions focused on looking for right and wrong answers to determine mastery and focused on pacing decisions. Their post-PD decisions focused on student thinking and adapting teaching to support student thinking and learning. Implications for PD to support teachers to use formative assessment and research are discussed.
Episode 13: Visions of the Possible: Using Drawings to Elicit and Support Visions of Teaching Mathematics
April 21st, 2020 | Season 4 | 26 mins 34 secs
Mathematics Teacher Educators (MTEs) help preservice teachers in transitioning from students to teachers of mathematics. They support PSTs in shifting what they notice and envision to align with the collective vision encoded in the AMTE and NCTM standards. This study analyzes drawings and descriptions completed at the beginning and end of a one-year teacher education program—snapshots depicting optimized visions of teaching and learning mathematics. This study analyzed drawings-and-descriptions by cohort and by participants. The findings suggest that the task can be used as formative assessment to inform supports for specific PSTs such as choosing a cooperating teacher or coursework that challenges problematic beliefs. It can also be used as summative assessment to inform revision of coursework for the next cohort.