Tonya Gau Bartell

The Role of Learning Goals in Building a Knowledge Base for Elementary Mathematics Teacher Education

In this article, we describe features of learning goals that enable indexing knowledge for teacher education. Learning goals are the key enabler for building a knowledge base for teacher education; they define what counts as essential knowledge for prospective teachers. We argue that 2 characteristics of learning goals support knowledge‐building efforts. First, learning goals should be targeted; they must be sufficiently well specified to suggest interventions for supporting learners in achieving them and to indicate the types of evidence needed to determine if the goals have been achieved. Second, learning goals should be shared; they must be mutually understood and committed to by all participants in the knowledge‐building process. By drawing on our experience in our local efforts to develop knowledge for preparing prospective elementary mathematics teachers, we illustrate how targeted and shared learning goals support efforts to build a knowledge base for teacher education. We then propose the use of learning progressions for supporting knowledge‐building endeavors across sites.

Making Connections in Practice: How Prospective Elementary Teachers Connect to Children’s Mathematical Thinking and Community Funds of Knowledge in Mathematics Instruction

This study examines the ways prospective elementary teachers (PSTs) made connections to children’s mathematical thinking and children’s community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that asks PSTs to visit community settings and develop problem solving mathematics lessons that connect to mathematical practices in these settings (Community Mathematics Exploration Module). Using analytic induction, we identified three distinct levels of connections to children’s mathematical thinking and their community funds of knowledge evidenced in PSTs’ work (emergent, transitional, and meaningful). Findings describe how these connections reflected different points on a learning trajectory. This study has implications for understanding how PSTs begin to connect to children’s mathematical funds of knowledge in their teaching, a practice shown to be effective for teaching diverse groups of children.

Core Teaching Practices: Addressing Both Social Justice and Academic Subject Matter:

The recognition that knowledge alone is insufficient as a foundation for effective teaching has led in recent years to a call for significant and programmatic investment in the support of teaching practices which will support the learning of students (Ball & Forzani, 2011; Grossman et al., 2009; McDonald, Kazemi, & Kavanagh, 2013). While a focus on “core,” “high leverage,” or “ambitious” teaching practices is instructive (see, for example, the works of Lampert et al., 2013; Windschitl, Thompson, & Braaten, 2011), much less attention has been paid toward how educators might be more inclusive with respect to such practices. Indeed, it could be claimed that the focus on core practices has been at the cost of attention to practices that are powerful in their capacity to support learning by helping students feel connected to the spaces where learning is taking place, to ideas or principles that lie at the heart of a discipline, and to their own developing identities as learners. These practices arise from a commitment to value the cultural backgrounds of learners and to not only leverage but to highlight culturally bound lived experiences. They also collectively reflect what Gloria Ladson-Billings proposed as culturally relevant pedagogy (Ladson-Billings, 1995), a concept which Django Paris has more recently expanded to culturally sustaining pedagogy, a pedagogy that “ . . . seeks to perpetuate and foster—to sustain—linguistic, literate, and cultural pluralism as part of the democratic project of schooling” (Paris, 2012, p. 95). The work highlighted in the articles in this issue of Journal of Teacher Education (JTE) all speak to the importance of these inclusive practices as they are supported and shaped in different contexts, from our university teacher preparation classrooms to classrooms in K-12 schools. The Native American community has worked with states like Washington and Oregon to create curriculum materials relevant to American Indian/Alaskan Native students (AI/ AN). Such materials are primarily aimed at giving students an understanding of history and society that more accurately reflects events as seen from the perspective of Native populations. Less has been done to produce materials that combine core teaching practices in reading, mathematics, and science with pedagogical practices that take account of cultural differences between AI/AN students and those from other cultural groups. Similarly, professional development for teachers working with Native students often focuses on making connections to families and communities, rather than exploring how core teaching practices can link to teaching students from a variety of cultures. The article by Vincent, Tobin, and Van Ryzin in this issue draws on the National Indian Education Study (NIES) to describe the extent to which AI/AN students experienced reading and mathematics instruction that integrates Native Language and Culture (NLC) into instruction. The NIES also permitted the authors to describe how many AI/AN students were taught by teachers who had taken advantage of opportunities to learn ways to integrate NLC into their teaching. Because the NIES is done as part of the National Assessment of Educational Progress (NAEP), it supports inferences that are nationally representative. The authors found that more than half of AI/AN students in the United States are taught by teachers who have taken advantage of NLC-oriented professional development less than 3 times in the past 2 years. The most common experience for AI/AN students is that their teacher integrates material related to AI/AN issues only once during the year, perhaps as part of a holiday lesson, rather than as a regular part of reading or mathematics instruction. Students in schools with high concentration of AI/AN students were more likely to experience the curricular integration, as were those whose teachers were themselves AI/AN or fluent in AI/AN language. Further analysis of such nationally representative data, for AI/AN and other cultural groups, will provide a baseline picture of the current connections—or the extent of disconnect—between core practices and culturally relevant pedagogy in both professional development and teaching practice. The article by Greg Vass, also in this issue, reminds us that what is critical is not only how much and how integrated elements of culturally responsive or sustaining teaching practices are in our teacher preparation programs; the actual implementation of such practices is shaped in significant ways by interactions with the experienced teachers with whom our candidates work, even when those candidates are 732950 JTEXXX10.1177/0022487117732950Journal of Teacher EducationRichmond et al. editorial2017

Using Lesson Study as a Means to Support Teachers in Learning to Teach Mathematics for Social Justice

A growing number of researchers argue that teaching mathematics for social justice can support the ongoing struggle for equity in mathematics education (Frankenstein, 1995; Gutstein, 2006). One way to support mathematics teachers in developing mathematics pedagogies for social justice may be to use lesson study, a powerful form of professional development in Japan that is increasingly used in the United States (Lewis & Tsuchida, 1998), to engage them in goal-oriented, reflective practice. To date, no published studies exist suggesting lesson study has been used in the context of supporting teachers in developing pedagogies for social justice. Moreover, little research exists that examines mathematics teachers learning to teach for social justice. This chapter reports on a study of eight secondary mathematics teachers who participated in a graduate course that engaged them in a version of lesson study to create, implement, observe, revise, and reteach math lessons that incorporated social justice goals. The research reported examines the challenges teachers faced in learning to teach mathematics for social justice and the ways the use of lesson study may have supported or constrained teachers’ negotiations of these challenges.

“How I Want to Teach the Lesson”: Framing Children’s Multiple Mathematical Knowledge Bases in the Analysis and Adaptation of Existing Curriculum Materials

We consider how prospective elementary teachers think about multiple mathematical knowledge bases as they consider adapting existing mathematics curriculum materials to meet the needs of culturally, linguistically, and socioeconomically diverse students. Multiple mathematical knowledge bases include both children’s mathematical thinking and the cultural-, home-, and community-based funds of knowledge that children inevitably bring into the classroom. We explored how prospective elementary teachers attended to multiple mathematical knowledge bases as they used a lesson analysis tool, the Curriculum Spaces Table, to evaluate existing curriculum materials and identify spaces for adapting these curriculum materials to more efficiently meet the needs of all students. Our analysis examined 47 written reflections on the analysis of and adaptations for a Grade 3 lesson. Findings showed that prospective teachers paid considerable attention to children’s mathematical thinking and gave some attention to funds of knowledge, but they considered these knowledge bases largely in isolation of each other. Attention to integrating children’s mathematical thinking with funds of knowledge was rare. Nonetheless, prospective teachers overwhelmingly found the Curriculum Spaces Table useful for analyzing an existing lesson and identifying spaces for adaptations to more effectively build on children’s mathematical knowledge bases. Thus, we argue that a lesson analysis tool that draws attention to multiple mathematical knowledge bases offers a promising start for prospective elementary teachers’ development of pedagogical practices that integrate children’s mathematical thinking with diverse cultural-, home-, and community-based funds of knowledge.

What Data and Measures Should Inform Teacher Preparation? Reclaiming Accountability

For at least two decades, the policy context surrounding teacher education has emphasized the importance of teacher quality and a need for reliable systems to evaluate teacher preparation programs (Cochran-Smith et al., 2018; Feuer, Floden, Chudowsky, & Ahn, 2013). The No Child Left Behind Act (NCLB, 2002) mandated “highly qualified” teachers in every classroom, and the subsequent Race to the Top (RTTT, 2011; GovTrack.us, 2018) legislation of the Obama administration continued this trend with a focus on “highly-effective teachers” (Hess & McShane, 2014). During this time, teachers’ impact on student learning, especially, as represented by value-added scores based on state testing programs, was strongly emphasized in policies about the quality of teachers and teacher preparation programs (Noell & Burns, 2006; U.S. Department of Education, 2011), and causes of school failure were attributed in large part to teacher education programs and schools lacking evidencebased data to inform program reform. More recently, national level accountability systems that could help evaluate teacher preparation programs and teachers’ performance have gained prominence (Floden, Richmond, Drake, & Petchauer, 2017). Evaluations of teacher preparation programs have been done by the Council for the Accreditation of Educator Preparation (CAEP) and the National Council on Teacher Quality (NCTQ). A nationally available teacher performance assessment, the Educative Teacher Performance Assessment (edTPA), has been adopted in 12 states (edtpa.aacte.org/faq). Various measures were proffered, examined, and cautioned, such as value-added models (e.g., Floden, 2012; Goldhaber, Cowan, & Theobald, 2017; Henry, Kershaw, Zulli, & Smith, 2012), student assessment scores (e.g., Lavery, Nutta, & Youngblood, 2018), and frameworks for teaching (e.g., Nava et al., 2018). The types of measures selected and what they measure are not neutral, however, but rather reflect specific priorities and goals for schooling. For example, some view what they call the “dominant accountability paradigm” (Cochran-Smith et al., 2018) as reflecting market ideology and neoliberalism in education, privileging subject matter and often disconnected from the experiences and needs of students and teachers from nondominant communities (Lipman, 2011; Richmond, Bartell, & Dunn, 2016). Others call for building on what they see as a rich body of research that identifies knowledge and skills aimed at promoting democratic and socially just education and commitments in practice (e.g., Cochran-Smith et al., 2009; Crowley & Apple, 2009; Kumashiro, 2015; McDonald, 2005; Zeichner, Payne, & Brayko, 2014). Still others call for a focus on student performance on measures aligned with national content standards such as the Next Generation Science Standards (NGSS, Achieve Inc., 2013) and the Common Core State Standards (CCSS; National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010). This poses a dilemma for teacher education, which we have described in earlier editorials (Richmond et al., 2016): As we necessarily work within a system that warrants accountability, how might we “reclaim” accountability (Cochran-Smith et al., 2018) to support teacher candidates’ preparation for the realities of today’s schools and for their effective participation in “critical democracy” (Carter Andrews, Richmond, & Floden, 2018)? In this editorial, we call for casting a broader net that is both (a) more comprehensive with respect to the knowledge, skills, and practices evaluated and (b) more inclusive of the types of measures we use to obtain data. We also note that much still needs to be learned about how to overcome the challenges involved in using data to improve teacher preparation programs. With regard to the first issue, namely, the knowledge, skills, and practices that should be added to those typically evaluated; we see the work by such researchers as Melanie Acosta and her colleagues which appeared in the previous issue of JTE (Acosta, Foster, & Houchen, 2018) and Maria del Carmen Salazar in this issue (Salazar, 2018) to be particularly on-point. Through their work, both sets of scholars deepen and make more comprehensive the set of knowledge, skills, and practices that are important for quality teaching. Below, we provide some detail about how they make this case. In their paper, Acosta et al. (2018) proposed that community-focused and citizenship-focused pedagogical approaches of successful Black teachers—“African American Pedagogical Excellence” (AAPE)—be considered as standard practice for 797326 JTEXXX10.1177/0022487118797326Journal of Teacher EducationBartell et al. editorial2018

Curriculum spaces for connecting to children’s multiple mathematical knowledge bases

Abstract Elementary mathematics curriculum materials can serve as a lever for instructional change. In this paper, we promote a particular kind of instructional change: supporting teachers in learning to integrate children’s multiple mathematical knowledge bases (MMKB), including children’s mathematical thinking and children’s home and community-based mathematical funds of knowledge, in instruction. A powerful means of supporting pre-service teachers in integrating children’s MMKB in instruction may be to scaffold teachers’ noticing of potential spaces in elementary mathematics curriculum materials for connecting to children’s MMKB and then developing practices for leveraging these spaces during instruction. We focus on existing and potential spaces in written curriculum materials, or curriculum spaces, so as to better support teachers in enacting curriculum that opens spaces for connecting to children’s MMKB.

To Engage Students, Give Them Meaningful Choices in the Classroom.

Providing students with choice can be a powerful means of supporting student engagement. However, not all choice opportunities lead to improved student engagement. Teachers can increase the likelihood that students will value choice by analyzing how students associate feelings of autonomy, competence, and relatedness with the choice provided them. To illustrate, the authors present three cases of teachers providing their students with choices and explain the resultant student engagement in terms of these key student feelings.

Wherever You Go, There You Are: Bringing Experiences of Race, Class, Language, Gender, and Culture to Research in Mathematics Education.

Through this performance ethnography the authors present the stories of emerging scholars who in their research identify an interest in equity issues in the field of mathematics education. The article is based on life-story interviews with 26 participants. Six composite characters were developed to represent the voices of the participants. Particular attention is devoted to issues of race and how other experiences can provide windows into the racialized experiences that exist in learning and teaching mathematics.