Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.
In the last decade, mathematics teacher educators have begun to design learning opportunities for preservice mathematics teachers using a pedagogies-of-practice perspective. In particular, learning cycles provide a structure for engaging PSTs in learning to teach through the use of representations, approximations, and decompositions of practice (Grossman et al., 2009). In this article, we provide details of one learning cycle designed to support secondary mathematics preservice teachers' learning to elicit and use evidence of student thinking and pose purposeful questions (National Council of Teachers of Mathematics, 2014). Through qualitative analyses conducted on learning reflections, we provide evidence of the impact on engagement of this cycle through the lens of the Framework for Learning to Teach (Hammerness et al., 2005).
The purpose of this study was to investigate changes in a cohort of secondary preservice teachers’ (PSTs) vision of the role of a teacher within the context of a mathematics methods course designed around pedagogies of practice. We analyzed data collected in the first and last 2 weeks of the course, consisting of recordings of small- and whole-group discussions, PSTs’ written work, and individual interviews. We first coded using Munter’s Role of Teacher rubric and identified significant differences between beginning-of-semester data and end-of-semester data. We then conducted three rounds of constant comparative analysis resulting in four themes that describe the changes in visions of role of teacher. Findings indicate that engaging in pedagogies of practice in preservice education has the potential to influence PSTs’ visions of their role as mathematics teachers. This study extends both the literatures on pedagogies of practice and on teachers’ instructional vision.
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