Using algebraic habits of mind as a framework, and focusing on thinking about functions and how they work, we examined the relationship between 18 pre-service middle school teachers' ability to use the features of the algebraic thinking (AT) habit of mind "Building Rules to Represent Functions" and their ability to recognize and…

Our study concerns the conceptual mathematical knowledge that emerges during the resolution of tasks on the equivalence of polynomial and rational algebraic expressions, by using CAS and paper-and-pencil techniques. The theoretical framework we adopt is the Anthropological Theory of Didactics ("Chevallard" 19:221-266, 1999), in…

In this paper, we focus on an initiative in England devised to prepare non-mathematics graduates to train as secondary mathematics teachers through a 6-month Mathematics Enhancement Course (MEC) to boost their subject knowledge. The course documentation focuses on the need to develop "understanding mathematics in-depth" in students in…

Interpreting and responding to student thinking are central tasks of reform-minded mathematics teaching. This study examined preservice teachers' (PSTs) interpretations of and responses to a student's error(s) involving finding a missing length in similar rectangles through a teaching scenario task. Fifty-seven PSTs' responses were…

This paper builds on previous work (Black et al., "Educational Studies in Mathematics" 73(1):55-72, 2010) which developed the notion of a "leading identity" (derived from Leont'ev's concept of "leading activity") which, we argued, defined students' motive for studying during late adolescence. We…

The mathematical situations of play and exploration introduced here have been developed as an empirical research instrument for the longitudinal study "erStMaL" (early Steps in Mathematics Learning). They are designed as situations that allow children and a guiding adult to construct situation-related knowledge in common dialogue…

In 2008, the research center "Individual Development and Adaptive Education" was constituted by the Goethe University, the German Institute for International Educational Research, and the Sigmund Freud Institute, all located in Frankfurt am Main, Germany (http://www.idea-frankfurt.eu). The research of the center focuses on the…

While the value of "schematic representations" in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of "schematic…

In this article, I present and build on the ideas of John Threlfall ("Educational Studies in Mathematics" 50:29-47, 2002) about strategy development in mental mathematics contexts. Focusing on the emergence of strategies rather than on issues of choice or flexibility of choice, I ground these ideas in the enactivist theory of cognition,…

In this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10-12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the…

The idea that mathematics is needed for our mundane everyday activities has raised the question of how people deal with mathematics outside the school walls. Much has been written in mathematics education research about the possibility of transferring knowledge from and into school. Whereas the majority of this literature commends the possibility…

Photovoice is a participatory action research tool that is grounded in the literature for critical consciousness (Wang & Burris, 1997). Four creative high school girls who reported struggles with mathematics were given cameras and asked to take photographs to answer the following questions: (1) What is mathematics? (2) What is your ideal…

In this study, a temporal analysis and the analytical category of intersubjectivity are used to investigate how teachers and Latino/a bilingual students constructed shared communicative spaces in group mathematical discussions in an after school mathematics program in a culturally, linguistically, and economically diverse primary school.…

This article presents a theoretical conceptualization of mathematics homework as a social practice. Rather than considering homework as a task or an artifact, this approach frames homework in terms of the social contexts in which students participate and how students participate in those contexts. This perspective has long been suggested by…

Gender differences in mathematical achievement have been examined in a wide range of age groups but only a few studies addressed this issue in preschool children. We compared preschool girls (n?=?570) and boys (n?=?524) from Germany with regard to numerical competencies. Differences in overall group means and the frequency of representation at…