In the research reported in this paper, we develop a theoretical perspective to describe and account for the growth of collective mathematical understanding. We discuss collective processes in mathematics, drawing in particular on theoretical work in the domains of improvisational jazz and theatre. Using examples of data from a study of elementary…

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…

Making inferences about population differences based on samples of data, that is, performing intuitive analysis of variance (IANOVA), is common in everyday life. However, the intuitive reasoning of individuals when making such inferences (even following statistics instruction), often differs from the normative logic of formal statistics. The…

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…

Teachers notice through the lens of their professional knowledge and views. This study hence focuses not solely on teachers' noticing, but also on their knowledge and views, which allows insight into how noticing is informed and shaped by professional knowledge. As a discipline-specific perspective for noticing we chose dealing with multiple…

The research is a study of the Husserlian approach to intuition, informed by Merleau-Ponty's theory of perception, in the case of a prospective teacher of mathematics. It explores the two major stages-categories of intuition, the essential relations between them, and their vital role in the emergence of empirical and abstract mathematical…

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…

A teaching experiment-using Mathematica to investigate the convergence of sequence of functions visually as a sequence of objects (graphs) converging onto a fixed object (the graph of the limit function)-is here used to analyze how the approach can support the dynamic blending of visual and symbolic representations that has the potential to lead…

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,…

We introduce "virtual duoethnography" as a novel research approach in mathematics education, in which researchers produce a text of a dialogic format in the voices of fictional characters, who present and contrast different perspectives on the nature of a particular mathematical phenomenon. We use fiction as a form of research linked to…

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…

Mathematics educators have shown increasing interest in theorizing knowing and learning as something alive or as something that comes alive through the involvement of the body. Almost all current efforts attempt doing so by focusing on the body in which the otherwise invisible living being exhibits itself, thereby failing to consider everything…

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. We contribute to these efforts by expanding the constructs in Cobb and Yackel's (Educational Psychologist 31:175-190, 1996) interpretive framework that allow for coordinating social and individual…

Statistical reasoning focuses on properties that belong not to individual data values but to the entire aggregate. We analyze students' statements from three different sources to explore possible building blocks of the idea of data as aggregate and speculate on how young students go about putting these ideas together. We identify four general…

Currently, instruction pays little attention to the development of students' sampling variability reasoning in relation to statistical inference. In this paper, we briefly discuss the especially designed sampling variability learning experiences students aged about 15 engaged in as part of a research project. We examine assessment and…