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…

There is ample evidence that reasoning about stochastic phenomena is often subject to systematic bias even after instruction. Few studies have examined the detailed learning processes involved in learning probability. This paper examines a case study drawn from a large corpus of data collected as part of a research project that dealt with the…

This paper uses a multilevel analysis of mathematical reasoning rooted in Cultural Historical Activity Theory to examine how mathematical discourse and student reasoning about linear functions developed across 3 weeks in a ninth grade bilingual algebra class. Despite the teacher's expertise teaching with a conceptual focus, and her stated…

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 symbolic manipulation capabilities of computer algebra systems, which we refer to as CAS-S, are now becoming instantiated within secondary mathematics textbooks in the United States for the first time. While a number of research studies have examined how teachers use this technology in their classrooms, one of the most important factors in how…

Finnish students' success on all three content domains of each of the four cycles of the OECD's Programme for International Student Assessment (PISA) has created much international interest. It has also prompted Finnish academics to offer systemic explanations typically linked to the structural qualities of Finnish schooling and teacher…

The data reported in this article come from a large project whose goal was to explore how Latin American students in Catalonia, Spain use their two languages--Spanish and Catalan--to support their learning of mathematics in small groups with other students who are Spanish- or Catalan-dominant. For 5 years, lessons from bilingual mathematics…

Emma Castelnuovo (1913-2014) was an Italian mathematics teacher of grades 6 to 8 in secondary school. During the crucial period of the 1950s and 1960s, when important reforms were proposed, she was involved in significant events such as the first CIEAEM meetings and the Royaumont Seminar. She was an active contributor to the development of…

This paper reports the activity of three secondary school mathematics departments in England in self-initiated states of change that led to overall improvements in students' achievements when compared to previous cohorts. This took place without intervention and without their participation in external projects. They provide examples of…

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…

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…

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…

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…