This article suggests that a critical perspective of the notion of social representations can offer useful insights into understanding practices of teaching and learning in mathematics classrooms with immigrant students. Drawing on literature using social representations, previous empirical studies are revisited to examine three specific…

As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

Many studies have reported on the economical, social, and educational difficulties encountered by Ethiopian Jews since their immigration to Israel. Furthermore, the overall academic underachievement and poor representation of students of Ethiopian origin (SEO) in the advanced mathematics and science classes were highlighted and described. Yet,…

The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…

This study aimed at analysing traditionally taught children's acquisition and use of shortcut strategies in the number domain 20-100. One-hundred-ninety-five second, third, and fourth graders of different mathematical achievement levels participated in the study. They were administered two tasks, both consisting of a series of two-digit additions…

The introduction of the concept of the variable represents a critical point in the arithmetic-algebraic transition. This concept is complex because it is used with different meanings in different situations. Its management depends on the particular way of using it in problem-solving. The aim of this paper was to analyse whether the notion of…

We examine teachers' classroom activities with the spreadsheet, focusing especially on episodes marked by improvisation and uncertainty. The framework is based on Saxe's cultural approach to cognitive development. The study considers two teachers, one positively disposed towards classroom use of technology, and the other not, both of them…

Ireland has two official languages--Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoiri) in the transition from Gaeilge-medium mathematics education to English-medium mathematics…

This paper reports the outcomes of an empirical study undertaken to investigate the effect of students' cognitive styles on achievement in measurement tasks in a dynamic geometry learning environment, and to explore the ability of dynamic geometry learning in accommodating different cognitive styles and enhancing students' learning. A total of 49…

This paper investigates the construction of systems of competence in two middle school mathematics classrooms. Drawing on analyses of discourse from videotaped classroom sessions, this paper documents the ways that "agency" and "accountability" were distributed in the classrooms through interactions between the teachers and students as they worked…

Design-based research studies are conducted as iterative implementation-analysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even…

It is widely recognized that purely cognitive behavior is extremely rare in performing mathematical activity: other factors, such as the affective ones, play a crucial role. In light of this observation, we present a reflection on the presence of affective and cognitive factors in the process of proving. Proof is considered as a special case of…

Our work is inspired by the book "Imagining Numbers (particularly the square root of minus fifteen)," by Harvard University mathematics professor Barry Mazur ("Imagining numbers (particularly the square root of minus fifteen)," Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of…

The study reported here is the third in a series of research articles (Harkness, S. S., D'Ambrosio, B., & Morrone, A. S., in "Educational Studies in Mathematics" 65:235-254, 2007; Morrone, A. S., Harkness, S. S., D'Ambrosio, B., & Caulfield, R. in "Educational Studies in Mathematics" 56:19-38, 2004) about the teaching practices of the same…

We investigate experienced high school geometry teachers' perspectives on "authentic mathematics" and the much-criticized two-column proof form. A videotaped episode was shown to 26 teachers gathered in five focus groups. In the episode, a teacher allows a student doing a proof to assume a statement is true without immediately justifying it,…