This paper focuses on the design of tasks that situate teachers in the work of mathematics teaching. We examine a simple, yet fundamental feature of pedagogical content knowledge tasks: the extent to which pedagogical warrants are necessitated by the pedagogical context. We argue that this feature has implications for the design of tasks, as well…

This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

In this paper, we analyze two episodes from an inquiry-based didactical research; the complete analysis of our research data is still ongoing. By taking into consideration various developments from the history of the geometry of space-time, our general aim is to explore high school students' conceptions about measurement of length and time in…

Purpose: This commentary aims to echo Wilkinson, Bailey, and Maher's (this volume) arguments about the affordances of videos and video databases in studying learning and teaching. Design/Approach/Methods: This article illustrates a multivocal approach to the videos from the "Video Mosaic Collaborative" (VMC). In particular, three…

This article argues for a shift in how researchers discuss and examine students' uses and understandings of multiple representations within a calculus context. An extension of Zazkis, Dubinsky, and Dautermann's (1996) visualization/analysis framework to include contextual reasoning is proposed. Several examples that detail transitions between…

School discursive practices produce and reproduce acceptable notions of the good mathematics teacher, thereby shaping identity and agency in becoming a teacher. In this paper, I draw on key aspects of Bourdieu's social field theory--his conceptual "thinking tools" and his reflexive sociology--to explore the relations and discourses of…

This study examines the classroom practice and craft knowledge underpinning one teacher's integration of the use of GeoGebra software into mathematics teaching. The chosen teacher worked in an English secondary school and was professionally well regarded as an accomplished user of digital technology in mathematics teaching. Designed in accordance…

Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

To succeed in today's economy, students need both proficiency in the "three Rs" (reading, writing and arithmetic) and strong applied skills. Communication skills, team work, and critical thinking have long been at the top of employers' lists of applied skills they seek in employees. States are responding to employers' needs by putting in…

In an innovative, progressive school, students were asked to solve a fairly routine mathematical problem using real money in a "real-world" scenario. Even though the school values students' ideas, the reaction of the teacher to one student's alternative modelling of the problem suggests that he was expecting a particular answer to be…

"Let's Count" is a preschool mathematics intervention implemented by The Smith Family from 2012 to the present in "disdvantaged" communities across Australia. It is based on current mathematics and early childhood education research and aligns with the Early Years Learning Framework. Let's Count has been shown to be effective…

Much of the work on teacher knowledge suggests that content knowledge shapes pedagogical content knowledge, and in fact is primary in the relationship between the two forms of knowledge. In this paper we challenge this view, arguing from a situated perspective on knowledge and learning, that pedagogical content knowledge strongly shapes content…

One-third of the current A-level mathematics curriculum is determined by choice, constructed out of "applied mathematics" modules in mechanics, statistics and decision mathematics. Although this choice arguably involves the most sizeable instance of choice in the current English school mathematics curriculum, and it has a significant…

The project "Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice" aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three…

In this paper, I offer a framework for exploring the academic and disciplinary identities young African American children construct in urban science classrooms. Using interviews, fieldnotes, and videotapes of classroom lessons, I juxtapose the ways in which two children tell about their experiences in school and science with their performances of…