In this article I explore high school students' perspectives on working together in a mathematics class in which they spent a significant amount of time solving problems in small groups. The data included viewing session interviews with eight students in the class, where each student watched video clips of their own participation, explaining and…

In the United States, researchers argue that proof is largely concentrated in the domain of high school geometry, thus providing students a distorted image of what proof entails, which is at odds with the central role that proof plays in mathematics. Despite the centrality of proof, there is a lack of studies addressing how to integrate proof into…

Three experiments used multiple methods--open-ended assessments, multiple-choice questionnaires, and interviews--to investigate the hypothesis that the development of students' understanding of the concept of real variable in algebra may be influenced in fundamental ways by their initial concept of number, which seems to be organized around the…

In two experiments we explored the instructional value of a cross-domain mapping between "number" and "line" in secondary school students' understanding of density. The first experiment investigated the hypothesis that density would be more accessible to students in a geometrical context (infinitely many points on a straight line segment) compared…

Context is identified as an important factor when considering the learning of informal statistical inferential reasoning, but research in this area is very limited. This small exploratory study in one grade 10 (14 year olds) classroom seeks to learn more about the role context plays in learners' inferential reasoning, where both teacher and…

A remarkable feature of the set of papers in this issue is the consistent pattern of tending to deal with non-linear situations as if they are linear that is shown by students widely differing in age and educational systems, and studying various topics within mathematics. Methodological issues about the difficulty of interpretation of student…

Linear models are frequently inappropriately applied to various situations. When misapplied, linearity is traditionally referred to as a tendency, a misconception, or an error. Cognitive linguistic, situated cognition, and sociocultural or cultural-historical activity theory, on the other hand, suggest that linear models are adopted by learners…