Pre-service elementary teachers learning to facilitate students' engagement of the common core state standards' mathematical practices: Balancing attention to English language learners, to all learners, and to one's own mathematical learning.

摘要

In this dissertation I examine the experiences of eight pre-service elementary teachers (PSTs) in a mathematics methods course as they learned how to teach Mathematical Practice 1 (make sense of problems and persevere to solve them) and Mathematical Practice 3 (construct viable arguments and critique the arguments of others) from the Common Core State Standards to elementary students in general, and to English language learners in particular. While the principal question that motivated this study concerned PSTs' preparation to teach mathematical practices to English language learners, it became apparent that that question could not be answered without considering how PSTs prepare to teach the mathematics practices to all learners, and how they learned mathematics themselves.;This descriptive case study, which uses qualitative methods, involves collection of the following data: open response surveys (pre-and post); homework reflections; lesson plans; university supervisors' and host teachers' reports; and semi-structured interviews of PSTs, university supervisors, and host teachers. I drew initial categories for coding these data from relevant literature, and transcribed, coded, categorized, and generated additional themes from the data (Glaser & Strauss, 1967). The study benefited from, and was limited by, the fact that I was both the researcher and the instructor of the course in which the PSTs were enrolled.;Applying sociocultural theory, I consider both PSTs' personal experiences and their interpretation of their students' personal experiences in their field placements (Forman, 2003). They understood these experiences in terms of six themes: making personal connections with mathematical content, providing access for individual students, holding high expectations for each student, facilitating productive struggle, facilitating social interactions, and developing students' mathematical language and discourse. All of these themes are important in preparing PSTs to teach mathematics to all elementary students, but each of them has special significance for their preparation to teach English language learners. The PSTs appeared to learn the Mathematical Practices deeply, in part, by reflecting on the significance of these themes for their own mathematical learning.;The PSTs had similarities and differences in their beliefs and practices. As other researchers have suggested, it appeared that PSTs needed positive dispositions toward mathematics and the ability to help students make personal connections with mathematics to engage students in Mathematical Practice 1 (Kilpatrick, Swafford, & Findell, 2001), they needed high expectations and strategies for facilitating access in order to engage students in productive struggle (Moschkovich, 2013), and they needed strategies for facilitating social interactions and developing students' mathematical language and discourse to develop their facility with Mathematical Practice 3.;There seemed to be both a general and specific order for learning these themes. In general, PSTs grasped easily and most thoroughly those themes that were similar to ones infused throughout the teacher education program, and they were more likely to struggle with those that were new to them. PSTs who had no direct experience working with ELLs in their field placements had fewer opportunities to develop an understanding of how to engage these students, but some of these PSTs nevertheless developed understandings and skills that would be valuable for teaching ELLs, while one who did work with ELLs still maintained low expectations for their performance. Writing lesson plans helped PSTs think through how to facilitate students' engagement with mathematical practices; a student whose host teachers insisted they follow scripted lesson plans did not have that opportunity. My summary chapter presents two trajectories for depicting PSTs' overall learning: one a general trajectory that seems to apply to their learning of any particular theme, and one a trajectory for depicting the order in which different themes are likely to be mastered.