Jeffrey Choppin

Middle school students' production of mathematical justifications

Proof in advanced mathematics classes: semantic and syntactic reasoning in the representation system of proof

Curriculum-Context Knowledge: Teacher Learning From Successive Enactments of a Standards-Based Mathematics Curriculum

Abstract This study characterizes the teacher learning that stems from successive enactments of innovative curriculum materials. This study conceptualizes and documents the formation of curriculum-context knowledge (CCK) in three experienced users of a Standards-based mathematics curriculum. I define CCK as the knowledge of how a particular set of curriculum materials functions to engage students in a particular context. The notion of CCK provides insight into the development of curricular knowledge and how it relates to other forms of knowledge that are relevant to the practice of teaching, such as content knowledge and pedagogical content knowledge. I used a combination of video-stimulated and semistructured interviews to examine the ways the teachers adapted the task representations in the units over time and what these adaptations signaled in terms of teacher learning. Each teacher made noticeable adaptations over the course of three or four enactments that demonstrated learning. Each of the teachers developed a greater understanding of the resources in the respective units as a result of repeated enactments, although there was some important variation between the teachers. The learning evidenced by the teachers in relation to the units demonstrated their intricate knowledge of the curriculum and the way it engaged their students. Furthermore, this learning informed their instructional practices and was intertwined with their discussion of content and how best to teach it. The results point to the larger need to account for the knowledge necessary to use Standards-based curricula and to relate the development and existence of well-elaborated knowledge components to evaluations of curricula.

Middle School Mathematics Teachers’ Perceptions of the Common Core State Standards for Mathematics and Related Assessment and Teacher Evaluation Systems

In this study, U.S. middle school teachers’ perceptions of Common Core State Standards for Mathematics (CCSSM), CCSSM-related assessments, teacher evaluation processes, and resources for implementing CCSSM were investigated. Using a mixed methods design, a national sample of 366 teachers was surveyed, and 24 teachers were interviewed. Findings indicated that teachers viewed CCSSM as including new content for their grade level. Teachers also reported using multiple curriculum resources to align with CCSSM and indicated that new assessments would serve as a proxy for CCSSM. Implications for rapidly changing policy, curriculum, assessment, instruction, and professional development related to CCSSM are discussed.

Threats to Validity in the edTPA Video Component.

ABSTRACT The edTPA, a performance assessment designed to generate reliable and valid measures of teaching practice, increasingly is used as a gatekeeping mechanism for beginning teacher licensure in various states, including New York, Washington State, Wisconsin, and Georgia. One of the edTPA’s key components is the demonstration of instructional practice by video recording. This article explores threats to validity associated with using video segments as part of the edTPA. Based on interviews with 24 teaching candidates from New York and Washington State, results show that candidates had difficulty fully addressing the competencies assessed by the edTPA, thoroughly representing their teaching practices, and learning from the process of analyzing their videos, affecting content validity, ecological validity, and consequential validity, respectively. One implication is that the utility of the video records may be limited to corroborating and triangulating claims made in the written commentaries, rather than serving as authoritative approximations of teaching practice.

Inherent Connections Between Discourse and Equity in Mathematics Classrooms

We introduce the book Equity in Discourse for Mathematics Education: Theories, Practices and Policies, making the case that language is the medium of mathematical development and consequently the medium through which equity and inequities are structured and sustained. We review mathematics education research relating to equity and to discourse to explain the structure of the book, which brings together these focuses of attention. To show the inherent connections between discourse and equity in mathematics classrooms, we gather research in which attention to equity draws attention to discourse, and also research in which attention to discourse raises equity issues.

Educational Policy and Classroom Discourse Practices: Tensions and Possibilities

We explore tensions between research on policy that tends to focus at broad scale and at a distance from practice and research on discourse that focuses at small scale and in close proximity to practice. This tension is reflected in how each area conceptualizes equity, with policy researchers generally focused on access and achievement and discourse researchers focused on power and identity. The chapter is posed as a dialogue, using interviews from policy experts and chapters from discourse researchers in this volume, with the goal of identifying both tensions and possibilities for action. These communities described the difficulty of being sensitive to local contexts while at the same time providing opportunities for students to understand and master dominant mathematical forms of language and reasoning. There was some convergence in the two communities, particularly around the notion of building capacity to enact challenging forms of curriculum and instruction across an array of contexts.

Representing Teaching Within High-Stakes Teacher Performance Assessments

Teacher education in the United States is contextualized by efforts among various actors—for instance, state policy makers, teacher educators, and researchers—to wrest control over the terms, conditions, and consequences of accountability in the field. A key mechanism in this campaign is teacher performance assessments (TPAs), which have evolved with the accountability movement to serve the roles of gatekeeping teachers’ entry into the profession and evaluating the outcomes of teacher education. Tensions over TPAs as policy levers first emerged in California in the early 2000s, when—in response to a law mandating that teaching candidates pass a state-approved performance assessment for licensure—universities within the Performance Assessment of California Teachers (PACT) consortium developed an alternative to the existing test that aimed to emphasize subject-specific student learning, position the TPA as a formative assessment tool, and preserve flexibility in teacher education programming.