This research investigates what students' use of statistical language can tell us about their conceptions of distribution and sampling in relation to informal inference. Prior research documents students' challenges in understanding ideas of distribution and sampling as tools for making informal statistical inferences. We know that these…

The expanding use of data in modern society for prediction and decision-making makes it a priority for mathematics instruction to help students build sound foundations of inferential reasoning at a young age. This study contributes to the emerging research literature on the early development of informal inferential reasoning through the conduct of…

Certain mathematical concepts were not introduced to solve a specific open problem but rather to solve different problems with the same tools in an economic formal way or to unify several approaches: such concepts, as some of those of linear algebra, are presumably difficult to introduce to students as they are potentially interwoven with many…

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…

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 describes a task-based dynamic geometry platform that is able to record student responses in a collective fashion to pre-designed dragging tasks. The platform provides a new type of data and opens up a quantitative dimension to interpret students' geometrical perception in dynamic geometry environments. The platform is capable of…

The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that…

This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger…

In this paper, we examine sixth grade students' degree of conceptualization of fractions. A specially developed test aimed to measure students' understanding of fractions along the three stages proposed by Sfard ("1991") was administered to 321 sixth grade students. The Rasch model was applied to specify the reliability of the test across the…

Rate (of change) is an important but complicated mathematical concept describing a ratio comparing two different numeric, measurable quantities. Research referring to students' difficulties with this concept spans more than 20 years. It suggests that problems experienced by some calculus students are likely a result of pre-existing limited or…

Developing deep conceptual understanding of what Ma (1999) calls fundamental mathematics is a well-accepted goal of teacher education. This paper presents a microanalysis of an intriguing episode within a course designed to encourage such understanding. An adaptation of Krummheuer's (1995) elaboration of Toulmin's (1958/2003) diagrams is used to…

The question of how to enhance the learning of low-achieving students in mathematics presents an important challenge to researchers and teachers alike. We investigated whether and how the use of a contextual story presented in a video clip facilitated low-achieving students' understanding of the meaning of fraction expansion. To this end, we (a)…

This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from…

With our conceptualization of Harre and van Langenhove's (1999) positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current mathematics education literature and…

I begin by appreciating the contributions in the volume that indirectly and directly address the questions: Why do gestures and embodiment matter to mathematics education, what has understanding of these achieved and what might they achieve? I argue, however, that understanding gestures can in general only play an important role in "grasping" the…