Identity is an important tool for understanding students' participation in mathematics lessons. Researchers usually examine identity at a macro-scale: across typical classroom activity and in students' self-reports. However, learning occurs on a micro-scale: in moments during a lesson. To capture identity in these moments, I used…

The release of the Common Core State Standards for Mathematics and their adoption across the United States calls for careful attention to the alignment between mathematics standards and assessments. This study investigates 2 models that measure alignment between standards and assessments, the Surveys of Enacted Curriculum (SEC) and the Webb…

This study investigated discursive positioning moves that facilitated Latino/a English learners' (ELs) opportunities to take on agentive problem-solving roles in group mathematical discussion. A focus on mechanisms that support students' agentive participation is consistent with the authors' view that recurrent experiences…

Based on Piaget's theory of logico-mathematical knowledge, 126 students in grades 2-5 were asked 6 questions about elapsed time. The main reason found for difficulty with elapsed time is children's inability to coordinate hierarchical units (hours and minutes). The educational implications drawn are that students must be encouraged to think about…

Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the…

This study investigated how elementary teachers in a mathematics lesson study made sense of student learning, teaching, and content, as related to using representations in teaching multidigit subtraction, and how changes occurred over time in their talk and practice. The lesson-study process paved a group talk path along which teacher talk shifted…

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.…

Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. The authors investigated whether (besides the missing-value formulation of word problems) the numbers appearing in word problems are part of…

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…

Algebra instruction has traditionally been postponed until adolescence because of historical reasons (algebra emerged relatively recently), assumptions about psychological development ("developmental constraints" and "developmental readiness"), and data documenting the difficulties that adolescents have with algebra. Here we provide evidence that…

Fourth-grade students who participated in a yearlong, whole-class teaching experiment not only reconceptualized natural numbers but also generated flexible solution strategies to perform numerical computations mentally and in writing. Students' reconceptualization of number was mediated by their perceived resemblance between the physical action of…