Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…

The moment-to-moment dynamics of student discourse plays a large role in students' enacted mathematics identities. Discourse analysis was used to describe meaningful discursive patterns in the interactions of 2 students in a 7th-grade, technology-based, curricular unit (SimCalc MathWorlds[R]) and to show how mathematics identities are enacted at…

Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsak, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…

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.…

Our primary purpose in this article is to propose an interpretive scheme for analyzing the identities that students develop in mathematics classrooms that can inform instructional design and teaching. We first introduce the key constructs of normative identity and personal identity, and then illustrate how they can be used to conduct empirical…

This article describes one prevalent practice that a group of 6th- and 7th-grade students engaged in when they used fractions in the context of area and perimeter, decimal operations, similarity, and ratios and proportions. The study's results revealed that students did not simply take the concepts and skills learned in formal fractions units and…

This article reports on models of teaching that developed as outgrowths of a study of middle-grades mathematics classes. Three specific cases are highlighted that represent deductive (associated with univocal), inductive (associated with dialogic), and mixed (a hybrid of deductive and inductive) models of teaching. Teaching practices associated…

Given its important role in mathematics as well as its role as a gatekeeper to future educational and employment opportunities, algebra has become a focal point of both reform and research efforts in mathematics education. Understanding and using algebra is dependent on understanding a number of fundamental concepts, one of which is the concept of…

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…