In this commentary, we explore tensions between engaging students in authentic disciplinary mathematical activity and insights from critical theorists who analyze equity in mathematics education. The tensions arise as engaging students in authentic mathematical activity usually involve having students adopt the language and norms of another…

Mathematics education researchers frequently use task-based interviews to gain insight into mathematicians' practice. However, there are a number of factors that should prevent mathematics educators from extrapolating how individual mathematicians respond to researcher-generated tasks in laboratory conditions, to how mathematicians practice their…

In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reach these goals. Using the data from this study as well as data from a separate study (Weber, "Journal for Research in Mathematics Education" 39:431-459,…

In "Elementary School Mathematics Priorities," Wilson (2009 [this issue]) presents a list of five core concepts that students should master in elementary school so that they can succeed in algebra. As researchers in mathematics education, the authors enthusiastically endorse Wilson's recommendations. Learning algebra is key to further study of…

Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked undergraduate students to study a novel concept by either tackling example generation tasks or…

In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications,…