Dan Battey

Teacher Questioning to Elicit Students’ Mathematical Thinking in Elementary School Classrooms:

Cognitively Guided Instruction (CGI) researchers have found that while teachers readily ask initial questions to elicit students’ mathematical thinking, they struggle with how to follow up on student ideas. This study examines the classrooms of three teachers who had engaged in algebraic reasoning CGI professional development. We detail teachers’ questions and how they relate to students’ making explicit their complete and correct explanations. We found that after the initial “How did you get that?” question, a great deal of variability existed among teachers’ questions and students’ responses.

Exposing Color Blindness/Grounding Color Consciousness Challenges for Teacher Education

As teacher educators we have been struck by the consistency, urgency, and frequency in which students employ color-blind perspectives. This orientation has negative consequences in K-12 settings. In this manuscript, we lay out the multiple meanings of color blindness, drawing from legal, educational, and social science traditions, and offer arguments for color consciousness in education. In addition, we use this theoretical perspective to investigate interventions for countering color blindness in teacher education. Using a framework steeped in the tenets of color consciousness, we draw from scholars as well as our own work to provide interventions designed to challenge color-blind orientations in teachers.

Access to Mathematics: “A Possessive Investment in Whiteness”†

Abstract While mathematics education gives access to elite universities, higher‐paying jobs, and the accumulation of wealth, it continues to be framed as a neutral curricular domain. However, data continually show differential access provided to students of color and their White peers through tracking, the availability of Advance Placement courses, and counselor referrals. This article frames mathematics education within a broader racial context to show how it functions along the same dominant racial ideologies within society. I analyze national data sets in the United States to calculate the wage‐earning differential attributable to differences in mathematics coursework by ethnic/racial groups across three time points: 1982, 1992, and 2004. This analysis projects advantages for Whites due to differential access to mathematics that total in the hundreds of billions of dollars. The article explores one way to see how color‐blind ideology and whiteness produce material stratification through the institution of mathematics education. Drawing on the constructs of interest convergence and divergence, the article ends with envisioning ways to enact a more race conscious mathematics curriculum.

Integrating Professional Development on Mathematics and Equity: Countering Deficit Views of Students of Color.

Research commonly finds that urban teachers bring deficit views about students of color with them into classrooms, and professional development efforts focused on this critical problem have been met with limited success. Therefore, scholars have called for work that integrates content and equity as a way to challenge teachers’ deficit views at the same time as they transform content instruction. However, few examples exist that describe how to do this. This article helps to fill this gap. Rather than a research paper, it conceptually details one perspective on integrating mathematics and equity within professional development for urban elementary teachers. The focus is to support teachers in gathering counter evidence to challenge dominant deficit narratives about students of color. This builds a teacher community that tells different stories as they develop their mathematics teaching. The authors use three vignettes from this work to illustrate the professional development perspective in action.

Building Community and Relationships that Support Critical Conversations on Race: The Case of Cognitively Guided Instruction

The focus of mathematics professional development for elementary teachers has shifted over time. In the case of Cognitively Guided Instruction (CGI), it started with building a cognitive framework of the development of children’s thinking and carried this cognitive perspective into work with teachers (Carpenter, Fennema, & Franke, 1996). Over the years, some scholars have shifted toward a more situated perspective in working with teachers (Franke, & Kazemi, 2001). The focus of this work has moved from seeing individual teacher change to change in communities, relational identities, and generative growth (Franke, Carpenter, Levi, & Fennema, 2001; Franke, Kazemi, Shih, Biagetti, & Battey, 2005; Battey & Franke, 2008). More recently we have been searching for a way to build upon our work with school communities to foreground issues of race and equity. We continue our focus on children’s mathematical thinking, but more explicitly address the deficit ideology that can remain despite the amount that has been achieved in this professional development work (Franke 2009; Battey & Franke, 2009). This chapter describes our progression from a focus on students’ mathematical thinking to engaging teachers in grappling with the complexities of race in their classrooms. We leverage critical concepts in our earlier work such as community, relationships, and evidence to explore such conversations with teachers.

Educational Software Reviews under Investigation

The purpose of this study was to examine reviews of mathematical software for elementary classrooms, looking particularly at the implicit rubrics used for these reviews. Examination of the software reviews allowed an understanding of the type of information educators receive about the software available and how that information fits with current views of learning as well as the National Council of Teachers in Mathematics (NCTM) standards. Using professional publications for mathematics teachers, a content analysis of 95 reviews of rational number software published over the last 20 years was conducted. Findings indicate that the reviews written for teachers provide little information about what and how students will learn mathematically as they engage with particular educational game software. The reviews focused on how easy the software was to use, how motivating or relevant it may be and the degree to which students could use it on their own. It was found that while the language to describe the educational game software shifted over the 20 years, the games themselves did not, thus indicating that the NCTM standards have only had superficial impact on computer game software in the rational number domain. The analyses suggest that review criteria based on principles of mathematical inquiry could help reviewers evaluate with more assurance the actual potential and benefits even in the absence of such features in the investigated software, and provide teachers with better information on how to select and integrate educational software in their classroom.

Strategies for caring mathematical interactions

How we handle classroom relationships between teachers and students plays an important role in how all students experience mathematics.

Making the Implicit Explicit: Building a Case for Implicit Racial Attitudes to Inform Mathematics Education Research

Scholars continue to document that African American kindergartners bring the same competencies as their white peers (Ginsburg et al, Int J Psychol 16(1):13–34, 1981; O’Connor et al, Rev Res Educ 33(1):1–34, 2009). Research has found, however, that they experience low-quality mathematics instruction (Davis and Martin, J Urban Math Educ 1(1):10–34, 2008; Lubienski, J Negro Educ 71(4):269–287, 2002), which does not leverage the mathematical abilities of African American students. The mechanisms for how these disparities are produced are less clear (Battey, Educ Stud Math 82(1):125–144, 2013a; Lubienski, J Negro Educ 71(4):269–287, 2002). For instance, we do not understand the mechanism through which mathematics instructional quality or the cognitive demand of tasks is reduced for African American children. In this chapter, we argue that a potentially missing piece in understanding mechanisms that produce disparities in mathematics education is implicit racial attitudes. To make this theoretical case, we draw on work both inside and outside of mathematics education across four literatures: (1) the quality of mathematics instruction that African American students receive, (2) relationships developed with teachers, (3) racialized teacher perceptions of behavior and academic aptitude, and (4) racial microagressions in mathematics. The chapter ends with two examples of how implicit racial attitudes can be embedded in existing research in order to illustrate how the field could study ways to disrupt the perpetuation of deficit perspectives shaped by racial ideologies and systemic forms of oppression.