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March 2014, Volume 2, Issue 2

FEATURES

EDITORIAL: Building a Professional Knowledge Base
Margaret S. Smith
This editorial discusses the mission statement for Mathematics Teacher Educator, that the journal “will contribute to building a professional knowledge base for mathematics teacher educators that stems from, develops, and strengthens practitioner knowledge,” what this means and how the members of the mathematics education community can contribute to the development of this knowledge base.

Use of Video Analysis to Support Prospective K-8 Teachers’ Noticing of Equitable Practices
Amy Roth McDuffie, Mary Q. Foote, Corey Drake, Erin Turner, Julia Aguirre, Tonya Gau Bartell, and Catherine Bolson
Mathematics teacher educators (MTEs) designed and studied a video analysis activity intended to support prospective teachers (PSTs) in learning to notice equitable instructional practices. PSTs from 4 sites (N = 73) engaged in the activity 4 to 5 times during the semester, using a set of 4 “lenses” to analyze teaching and learning as shown in videos. In an earlier analysis of this activity, the authors found that PSTs increased their depth and expanded their foci in noticing equitable instructional practices (Roth McDuffie et al., 2013). In this analysis, the authors shift the focus to their work as MTEs: They examine their decisions and moves in facilitating the video analysis activity with a focus on equity and discuss implications for other MTEs.

Breaking Conventions to Support Quantitative Reasoning
Kevin C. Moore, Jason Silverman, Teo Paoletti, and Kevin LaForest
Quantitative reasoning is critical to developing understandings of function that are important for sustained success in mathematics. Unfortunately, pre-service teachers often do not receive sufficient quantitative reasoning experiences during their schooling. In this paper, we illustrate consequences of underdeveloped quantitative reasoning abilities against the backdrop of central function concepts. We also illustrate tasks that can perturb pre-service teachers thinking in ways that produce opportunities for quantitative reasoning. By implementing strategically designed tasks, teacher educators can support pre-service teachers – and students in general – in advancing their quantitative reasoning abilities and their understanding of secondary mathematics content.

Improving Preservice Secondary Mathematics Teachers’ Capability With Generic Example Proofs
Shiv Karunakaran, Ben Freeburn, Nursen Konuk, and Fran Arbaugh
Preservice mathematics teachers are entrusted with developing their future students’ interest in and ability to do mathematics effectively. Various policy documents place 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, pictorial proofs, and so on. 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.

Teacher Goals and Dilemmas in the Use of Mathematical Representations
Edd V. Taylor and Elizabeth Dyer
The purpose of this article is to describe the reported goals of teachers participating in professional development related to their efforts to consider multiple representations in their teaching. Through analysis of monthly written reflections and group discussion, the authors describe 3 teacher dilemmas that emerged related to their efforts to consider multiple representations in their teaching, (a) equitable practices when particular representations result in differential success, (b) a teacher’s need to balance exposure and choice, and (c) a potential dilemma related to conflicts between competing goals. The authors provide suggestions of how mathematics educators might use these findings to support future professional development efforts.