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Two major challenges in mathematics teacher education are developing teacher understanding of: (1) culturally responsive, social justice--oriented mathematics pedagogies; and (2) mathematical modeling as a content and practice standard of mathematics. Although these challenges may seem disparate, the innovation described in this article is designed to address both challenges in synergistic ways. The innovation focuses on a mathematical modeling task related to the ongoing water crisis in Flint, Michigan. Through qualitative analysis of instructor field notes, teacher-generated mathematical models, and teacher survey responses, we found that teachers who participated in the Flint Water Task (FWT) engaged in mathematical modeling and critical discussions about social and environmental justice. The evidence suggests that integrating these 2 foci--by using mathematical modeling to investigate and analyze important social justice issues--can be a high-leverage practice for mathematics teacher educators committed to equity-based mathematics education. Implications for integrating social justice and mathematical modeling in preservice and in-service mathematics teacher education are discussed.

This study documents and describes efforts to develop robust forms of pre-service teachers' pedagogical content knowledge through a culturally responsive mathematics teaching approach. Embedded in a university K-8 mathematics methods course emphasising the connections among mathematics, children's mathematical thinking, and children's cultural/linguistic funds of knowledge, pre-service teachers (N = 40) were given an assignment to analyse their own mathematics lessons utilizing a rubric tool with categories about children's mathematical thinking, academic language supports, cultural funds of knowledge, and critical math/social justice. Utilizing a mixed methods approach to analyse the pre-service teachers' (PST) work, we found the highest average self-ratings across the categories associated with children's mathematical thinking and high variability in the categories related to language, culture, and social justice. To understand the variation within the latter three categories we qualitatively analysed PST written reflections. We found strong PST receptivity to supporting academic language for second language learners and integrating cultural funds of knowledge into mathematics lessons, and mixed receptivity to integrating social justice into mathematics lessons. However, a more nuanced analysis of teacher resistance revealed challenges with pedagogy rather than ideology. Implications for mathematics teacher education and strengthening pedagogical content knowledge of pre-service teachers are discussed.

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.

Assessing the preparation of preservice candidates for quality teaching, both for mainstream students and for ELs, requires reliable and valid assessments that pay close attention to context, process, and reflection, factors that traditional evaluations of teaching either ignore or undervalue. In this article, the authors focus on one high-stakes preservice teacher performance assessment designed to meet these guidelines. The Performance Assessment for California Teachers (PACT), currently used in 32 teacher preparation programs throughout California, is a comprehensive assessment of knowledge and skills in which candidates analyze and reflect on their own instruction and their students' learning during a "Teaching Event" in their student teaching placements. The authors document how eight elementary teacher candidates from teacher preparation programs throughout California discussed issues related to language and learning for ELs in their extensive written materials about their teaching and their students' learning submitted as part of their PACT Teaching Events. While candidates for elementary credentials can choose to complete a mathematics or a language arts/literacy Teaching Event, the authors focused on those candidates who chose mathematics. The authors focus on mathematics because it is often misunderstood to be a language-free endeavor and because it represents an area in which schools have failed many ELs and other students from non-dominant linguistic backgrounds. The authors argue that the PACT, beyond its function as a high stakes examination used for state licensing decisions, has the potential to provide important information that can serve as formative assessment and feedback for teacher candidates themselves, individual teacher educators, and teacher education programs as a whole. (Contains 1 table and 7 notes.)

Mathematical modeling is a high-leverage topic; it is critical to students' participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary level has been underemphasized, particularly research on supports and challenges for teachers who engage in designing authentic modeling tasks. In this study, we employed qualitative case study methods to investigate how elementary teachers designed and implemented authentic mathematical modeling tasks, with an explicit focus on how their tasks evidenced different dimensions of authenticity. We analyzed three cases of teams of elementary teachers as they developed modeling tasks connected to school and community contexts. The three cases were: 1) a student-driven modeling task related to paper and plastic waste in a school cafeteria, 2) a modeling task based on authentic situations at a community-run resource center, and 3) a modeling task focused on designing and monitoring a school community-building art project. Our cases illustrate that elementary teachers can successfully design and implement modeling activities that utilize different entry points and evidence multiple dimensions of authenticity. Furthermore, we found that the specific dimensions of authenticity may vary depending on the design supports and curriculum challenges within each context. [ABSTRACT FROM AUTHOR]

Throughout the United States, teacher educators are developing new strategies to improve the preparation of mainstream teachers for linguistic diversity. In this article, we explore teacher candidates' responses to the Performance Assessment for California Teachers (PACT), a preservice assessment required for credentialing that requires candidates to consider the English language demands of content-area instruction, to enact supports for English learners and others who may struggle with those demands, and to develop ways to promote the academic language development of these students. We report on a study examining written responses on the PACT from 8 elementary teacher candidates who chose mathematics as the focus for their teaching event. We found that the PACT induced teacher candidates to consider language issues and the needs of language learners in a content area often thought to be language-free, yet one in which language in fact plays a crucial role. Such responses provide important information that can be used not only for credentialing decisions but also by teacher educators, teacher-education programs, and teacher candidates themselves in supporting the academic-language development of ELs in content areas such as mathematics.

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. (Contains 1 table and 1 figure.)

In the United States, there is a need for pedagogical tools that help teachers develop essential pedagogical content knowledge and practices to meet the mathematical education needs of a growing culturally and linguistically diverse student population. In this article, we introduce an innovative lesson analysis tool that focuses on integrating mathematical thinking, language, culture, and social justice. We argue that these are essential components to culturally responsive mathematics teaching. Using data collected from a 3-year professional development initiative focused on culturally responsive mathematics teaching including teacher discussions, lesson artefacts, and interviews, the study yields two main results about the tool and its impact on teacher thinking: (1) the tool enabled teachers to systematically analyse and critique mathematics lessons with multiple dimensions including mathematical thinking, language, culture, and social justice; (2) the tool fostered purposeful pedagogical dialogue to improve a mathematics lesson along specific culturally responsive dimensions. The findings illustrate the potential of this tool to engage teachers in strategic lesson planning and purposeful discussions to make mathematics lessons culturally responsive and improve the quality of mathematics teaching in the classroom.

The article describes an activity program for third grade students which offers lessons on the standard algorithm for subtraction.