Recalibrating Beliefs and Teaching Practices
Amanda L. Cullen
A Critical Lens on Cognitively Guided Instruction: Perspectives from Mathematics Teacher Educators of Color
Luz A. Maldonado Rodríguez, Naomi Jessup, Marrielle Myers, Nicole Louie, and Theodore Chao
Elementary mathematics teacher education often draws on research-based frameworks that center children as mathematical thinkers, grounding teaching in children’s mathematical strategies and ideas and as a means to attend to equity in mathematics teaching and learning. In this conceptual article, a group of critical mathematics teacher educators of color reflect on the boundaries of Cognitively Guided Instruction (CGI) as a research-based mathematical instructional framework advancing equity through a sociopolitical perspective of mathematics instruction connected to race, power, and identity. We specifically discuss CGI along the dominant and critical approaches to equity outlined by Gutiérrez’s (2007, 2009) framework. We present strategies used to extend our work with CGI and call for the field to continue critical conversations of examining mathematical instructional frameworks as we center equity and criticality.
Eight Unproductive Practices in Developing Fact Fluency
Gina Kling and Jennifer M. Bay-Williams
Basic fact fluency has always been of interest to elementary school teachers and is particularly relevant because a wide variety of supplementary materials of varying quality exist for this topic. This article unpacks eight common unproductive practices with basic facts instruction and assessment.
Developing Skills for Exploring Children’s Thinking From Extensive One-on-One Work With Students
Corey Webel and Sheunghyun Yeo
In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a “Math Buddy") on mathematics for 30 minutes per day. We focus on the development of PSTs’ skills for exploring children’s thinking and the structures and tools that we used to support this development. Data sources include screencast recordings of interactions with Math Buddies and written reflections completed by PSTs. Although the responsiveness of interactions varied across individuals and interactions, in general, PSTs showed improvements in exploring children’s thinking. We share implications of these findings for similar field experience models and for practice-based approaches to teacher education generally.
Support and Enrichment Experiences in Mathematics (SEE Math): Using Case Studies to Improve Mathematics Teacher Education
Crystal Kalinec-Craig, Emily P. Bonner, and Traci Kelley
This article describes an innovation in an elementary mathematics education course called SEE Math (Support and Enrichment Experiences in Mathematics), which aims to support teacher candidates (TCs) as they learn to teach mathematics through problem solving while promoting equity during multiple experiences with a child. During this 8-week program, TCs craft and implement tasks that promote problem solving in the context of a case study of a child’s thinking while collecting and analyzing student data to support future instructional decisions. The program culminates in a mock parent–teacher conference. Data samples show how SEE Math offers TCs an opportunity to focus on the nuances of children’s strengths rather than traditional measures of achievement and skill.
Supporting Preservice Teachers’ Growth in Eliciting and Using Evidence of Student Thinking: Show-Me Narrative
Esther M. H. Billings and Barbara A. Swartz
Diverge Then Converge: A Strategy for Deepening Understanding Through Analyzing and Reconciling Contrasting Patterns of Reasoning
Theresa J. Grant and Mariana Levin
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.
