Math Is More Than Numbers: Beginning Bilingual Teachers’ Mathematics Teaching Practices and Their Opportunities to Learn

In this article, the author provides results from a 3-year, longitudinal study that examined two novice bilingual teachers’ mathematics teaching practices and their professional opportunities to learn to teach. Primary data sources included videotaped mathematics lessons, teacher interviews, and field notes of their teacher preparation methods courses. Findings revealed that the teachers were oriented toward differing views of learning that shaped how they organized students’ learning of language and mathematics during classroom instruction. While both teachers used similar teaching strategies to support students’ development of mathematics specific literacies, there were variances in how the learners were positioned within the classroom community and how and which repertoires of language practices were available and used during mathematics instruction. The teachers’ differing orientations toward learning are traced to their own professional opportunities to learn to teach. The significance of recognizing both the acquisition and participation metaphors of learning and the development of linguistically and culturally relevant teacher education are discussed

Moving Beyond Numbers: Examining Language in Mathematics Classrooms

There is growing attention on the mathematics learning experiences of emergent bilingual students, a term used rather than English language learners to emphasize the rich linguistic knowledge of students who know and speak two or more languages instead of how they are often positioned of not knowing English, in the field of mathematics education. The majority of past and current studies have examined the impact of students’ language proficiency on academic performance. While this work has deepened understanding of mathematics learning for emergent bilinguals, language is only one of many semiotic resources (e.g. physical control of space, gestures, and gaze) at play in bilingual/multilingual classrooms. Research is needed that unpack the development of principled instruction that supports students’ engagement in meaningful disciplinary discourse practices. Using Cultural Historical Activity Theory (CHAT) as a framework, I examine classrooms as complex activity systems. Learning is considered a social endeavor that occurs as students engage individually and collectively with each other and with mediational tools that impact student participation. Study findings demonstrate the importance of using a systems approach to examining individual and intersectional impact of teacher’s decision-making (e.g. tasks, mediating artifacts, division of labor, community, and norms) on student learning. Findings offer guidance to mathematics educators on the design classroom learning spaces that better leverage emergent bilingual students’ individual and collective abilities

Mathematics for Whom: Reframing and Humanizing Mathematics

Mathematics for social justice allows students to see mathematics as an analytic tool to understand and influence issues important to them and their communities. Existing work in teaching mathematics for social justice often connects to secondary curriculum. But what about elementary mathematics? This paper describes the theoretical frames and gives an example of social justice-oriented mathematics with elementary-age students. We share the process of analyzing published K-6 mathematics curriculum as an entryway to engage in investigations that raise students’ awareness of social issues and to develop their mathematical power and sense of self as mathematics thinkers and doers

Learning to Teach Mathematics and to Analyze Teaching Effectiveness: Evidence from a Video- and Practice-Based Pre-Service Course

Although emerging consensus exists that practice-based approaches to teacher preparation assist in closing the distance between university coursework and fieldwork experiences and in assuring that future teachers learn to implement innovative research-based instructional strategies, little empirical research has investigated teacher learning from this approach. This study examines the impact of a video- and practice-based course on prospective teachers’ mathematics classroom practices and analysis of their own teaching. Two groups of elementary prospective teachers participated in the study—one attended the course and one did not. Findings reveal that the course assisted participants in making student thinking visible and in pursuing it further during instruction and in conducting evidence-based analyses of their own teaching. Conclusions discuss the importance of teaching these skills systematically during teacher preparation

Pre-Service Teachers Learning to Generate Evidence-Based Hypotheses on the Effects of Teaching on Student Learning

This study examines the development of a specific sub-skill for studying and improving teaching—the generation of hypotheses about the effects of teaching on student learning. Two groups of elementary preservice teachers (PSTs) were compared: one group that attended a typical mathematics-methods course and one that attended a course integrating analysis skills for learning from teaching. Data consist of PSTs’ comments on video clips of mathematics instruction administered before and after course completion. Findings reveal that PSTs at the beginning of the program struggled to generate hypotheses with relevant evidence, often equating teacher behavior or student correct answers as evidence of student understanding. After course participation, PSTs who attended the course with integrated analysis skills significantly improved in their ability to generate hypotheses based on student evidence whereas their counterparts continued to display difficulties. Implications for teacher education and future research are considered

Mathematics for Whom: Reframing and Humanizing Mathematics

In this paper, we share a process in which we, as mathematics teacher educators and education researchers, have worked in collaboration with K–6 teachers and students to analyze the purported neutrality of mathematics textbook word problems and to consider ways to use mathematics to analyze social inequities in the world. In the sections that follow, we describe the framework that grounds our development of justice-oriented mathematics curriculum and share an example of how textbook analysis can serve as an entryway to investigations that raise students’ awareness of social issues while developing their power as mathematics thinkers and doers. Drawing from these experiences of creating and teaching mathematics projects, we end with a discussion of the complexities, challenges, and possibilities of creating justice-oriented mathematics curriculum in elementary-school settings

Preparing Elementary School Teachers to Learn from Teaching: A Comparison of Two Approaches to Mathematics Methods Instruction

Teacher preparation programs face a significant challenge in determining how to design learning experiences that develop the combination of knowledge, practices, and dispositions needed for effective classroom teaching. Time constraints and the theory-practice divide are two well-documented concerns. We introduce the conceptual framework and design elements of a video-enhanced mathematics methods course that targets these concerns. The course centers on systematic reflection and analysis of practice intended to foster career-long learning. We then examine the impact of this course on several facets of learning-from-teaching competencies, including teacher knowledge, beliefs, and practices. Sixty-two pre-service teachers, enrolled in a one-year post-bachelor elementary teacher preparation program, were randomly assigned to attend this course or a more typical mathematics methods course. Findings suggest that teacher preparation experiences centered on systematic reflection and analysis create opportunities to develop certain aspects of learning-from-teaching competencies that remain otherwise underdeveloped. Implications for the design of teacher preparation include the integration in mathematics methods courses of cycles of analysis through video-enhanced discussions; collaborative planning, implementation, and reflection on teaching; and live observation and co-constructed interpretations and considerations of next steps

New Working Group: Teaching Mathematics for Social Justice in the Context of University Mathematics Content and Methods Courses

There are three goals for this new working group: 1) To create a community of mathematics teacher educators (MTEs) who are (or are interested in) collaboratively teaching mathematics for social justice (TMfSJ) in their university content and/or methods classes. 2) To collaboratively select/develop/modify TMfSJ tasks and implement those in mathematics content/methods classes. 3) To research the implementation of TMfSJ tasks in content and methods classes

Mathematics, Language, and Learning: A Longitudinal Study of Elementary Teachers and Their Mathematics Teaching Practices

Elementary school mathematics has gained increased attention in the last few decades. A growing field of research has studied the programmatic design and development of elementary mathematics teaching in teacher education, however, few studies have examined longitudinally the mathematics teaching of novice elementary teachers. Existing longitudinal studies on elementary mathematics teaching have generally focused on the effects of teacher preparation on their beginning practices and have examined novice teachers as a homogenous group. This dissertation consists of two studies that examined longitudinally novice elementary teachers and their mathematics teaching practices during their first two years of professional teaching. The first paper examined how three novice bilingual teachers organized mathematics learning for their emergent bilinguals. Data are drawn from three longitudinal case studies and include videotaped classroom observations and interviews of their mathematics instruction. Specifically, the study examined the type of supports the teachers provided to develop student learning of the language of mathematics, how learners were positioned within the classroom community, and how, and what, student repertoires of practice were utilized. The study findings highlight the complexity of bilingual teaching in the context of supporting students in learning the language of mathematics. The second paper examines the role of reflection as a vehicle for teacher change. Reflection has been identified in teacher education as a vehicle for professional growth and development. However, there are few studies that specifically look at the relation between reflection and teaching. This pair of case studies details the mathematics teaching practices and the teaching reflections of two novice teachers over a two-year period, examining their relationships, and how they may contribute to their development over time. Findings from this study highlight the generative potential in attending to student thinking in teaching and lesson reflection. In light of the two study findings, specific recommendations for teacher preparation are provided. A model of teacher knowledge from a situated perspective is proposed

The Role of Perception, Interpretation, and Decision Making in the Development of Beginning Teachers’ Competence

This study investigates beginning US elementary teachers’ competence for teaching mathematics and its development during teacher preparation and into the first 2 years of full-time teaching. Data are drawn from three longitudinal case studies and include the classroom video analysis survey, classroom observations and interviews about teachers’ instructional decisions, and whole-day shadowing. A multi-case study design was used to examine the processes of perception, interpretation, and decision making in participants’ comments on video clips of teaching episodes and in reflections about their own teaching. Findings support the central role of these processes in teacher competence and the generative power of reflections revolving around student thinking and tools, such as classroom discourse and visuals. Teachers’ communities also played an important role in teachers’ decision making. A model of teacher competence from a situated perspective is proposed and the classroom video assessment is discussed as a measure of teacher competence in context