We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

This study investigates the effectiveness of the Responsive Classroom (RC) approach, a social and emotional learning intervention, on changing the relations between mathematics teacher and classroom inputs (mathematical knowledge for teaching [MKT] and standards-based mathematics teaching practices) and student mathematics achievement. Work was…

This paper examines a pre-service teacher's content knowledge for teaching early algebra from two perspectives, i.e. using "Rowland's Knowledge Quartet" theory and "Ball's framework for Mathematical Knowledge for Testing" (MKfT). The study intends to examine the differences between the influences using each framework and to…

In this article, I present an initial analysis of an empirical study that was undertaken in an attempt to elicit what subject-matter knowledge, pedagogic content knowledge and curriculum knowledge teachers bring to bear on decisions for teaching. The analysis is based on interview data with 46 Grade 3 teachers, who were presented with two…

Despite over thirty years of theoretically based research investigating "how" teacher mathematical knowledge and instructional practice relate to student learning, it is still largely unclear how these constructs are related, and policy makers and practitioners are still situated in a context with insufficient data to make decisions. Thus, there…

This study sought to identify components of an asynchronous online teacher professional development program, "Prime Online," that potentially affected participants' mathematical knowledge for teaching (MKT). Twenty-three third- through fifth-grade general education and special education teachers completed a yearlong online teacher…

Against the background of concerns around teaching and learning outcomes in primary school mathematics in South Africa, this article presents two studies conducted in American Samoa and seeks to draw implications for the teaching and learning of mathematics in South Africa. American Samoa has a very similar educational context to South Africa. The…

Teams of educators conducted lesson study independently, supported by a resource kit that included mathematical tasks, curriculum materials, lesson videos and plans, and research articles, as well as protocols to support lesson study. The mathematical resources focused on linear measurement interpretation of fractions. This report examines the…

This article presents results from a case study analyzing the process of change for early childhood educators as they engage in a semester-long professional development (PD) experience focused on developing a teacher research agenda related to mathematics instruction. During this PD experience, 11 participants (5 second-grade and 6 third-grade…

This study examines the impact of a nationally disseminated professional development program, Developing Mathematical Ideas (DMI), on teachers' specialized knowledge for teaching mathematics and illustrates how such research could be conducted. Participants completing 2 DMI modules were compared with similar colleagues who had not taken DMI.…

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of…

The purpose of this study was to determine the competence of beginning California K-6 teachers in basic algebra topics, and to investigate their level of math anxiety and attitudes toward math. The sample for this study was beginning California elementary teachers in the Bay Area of California. An algebra content assessment and a self-report…

This article begins to unravel the question, "What curricular materials work best under what kinds of conditions?" The authors address this question from the point of view of teachers and their ability to implement mathematics curricula that place varying demands and provide varying levels of support for their learning. Specifically, the…

Despite the long history of the study of pedagogical content knowledge (PCK), two facts remain obvious. First, there are almost as many conceptions regarding the definition of PCK as there are researchers interested in it. Second, it is largely unclear which methods enable teacher educators to best prepare teacher candidates to use PCK. Recently,…

This study explored whether and how teachers' mathematical knowledge for teaching contributes to gains in students' mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders' mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found…