This study concerns expository writing in mathematics as well as the contribution of assessment strategies to the development of mathematics communication. We studied four 8th grade students (aged 12-13) working in a group, in order to perform three expository writing tasks, which were assisted by feedback and the use of supporting assessment…

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…

The article reports aspects of the evolution of a teaching approach over repeated trials for beginning symbolic algebra. The teaching approach emphasized the structural similarity between arithmetic and algebraic expressions and aimed at supporting students in making a transition from arithmetic to beginning algebra. The study was conducted with…

The mixed method sequential nested study examines whether and how the cognitive type of teachers' content knowledge is associated with student achievement, and correlated with teaching practice. In the context of this study, the "cognitive type" refers to the kind of teacher content knowledge and thinking processes required to accomplish a task…

In this research article, I present evidence of the existence of visual templates in pattern generalization activity. Such templates initially emerged from a 3-week design-driven classroom teaching experiment on pattern generalization involving linear figural patterns and were assessed for existence in a clinical interview that was conducted four…

There is an international trend in mathematics education of antiauthoritarianism, emphasising cooperative learning and students' autonomous search for knowledge. In Sweden, this is framed by "students' independent work", characterised by only limited amounts of teacher-student and student-student interaction and communication and a low level of…

This study examines eighth grade students' use of a representational metaphor (cups and tiles) for writing and solving equations in one unknown. Within this study, we focused on the obstacles and difficulties that students experienced when using this metaphor, with particular emphasis on the operations that can be meaningfully represented through…

Understanding that mathematics is founded on reasoning and is not just a collection of rules to apply is an important message to convey to students. Here we examined the reasoning presented in seven topics in nine Australian eighth-grade textbooks. Focusing on explanatory text that introduced new mathematical rules or relationships, we classified…

The main goal of the study reported in our paper is to characterize teachers' choice of examples in and for the mathematics classroom. Our data is based on 54 lesson observations of five different teachers. Altogether 15 groups of students were observed, three seventh grade, six eighth grade, and six ninth grade classes. The classes varied…

Using Freudenthal's method of historical phenomenology, the history of statistics was investigated as a source of inspiration for instructional design. Based on systematically selected historical examples, hypotheses were formulated about how students could be supported in learning to reason with particular statistical concepts and graphs. Such a…

Compared to studies in general education, authority has received little attention in mathematics education, despite an increasing interest in sociological perspectives in mathematics classroom research. The subject of authority is particularly important in mathematics education, on the one hand, because of the immense authority mathematics itself…

In this paper, we use the theory of didactic situations to characterize a mathematics teaching practice, currently used in secondary schools in France, which we have called "interactive synthesis discussion." We have studied this practice in ordinary classes, i.e. classes where the researcher intervenes neither in the preparation nor in the…