We use Action-Process-Object-Schema (APOS) theory to study students' geometric understanding of partial derivatives of functions of two variables. This study contributes to research on the teaching and learning of differential multivariable calculus and its didactics. This is an important area due to its multiple applications in science,…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

Action-Process-Object-Schema (APOS) theory and the triad of schema development are used as the framework in this study to investigate students' understanding of the concept of "circle." In this report, results are presented from the data analysis of responses to questions in semi-structured interviews of 15 students enrolled in a college…

Learning to calculate the area of composite shapes is an important application of area measurement but evidence suggests that many middle school students struggle to calculate the area of even simple composite shapes. In this article, I report the findings of a classroom design study conducted to investigate the collective development of…

Digital technologies for mathematics education are continuously developing. Still, much remains unknown about how students use these tools and how this affects learning. For example, tablets nowadays come with multi-touch options that allow for a more embodied approach to geometry education, compared to mouse interactions. However, little is known…

In this paper, the aim is to make a theoretical contribution by focusing on the origin, characteristics, and potential values of the concepts of instrumental and relational understanding. Five characteristics are identified to make it easier to operationalise the concepts and use them as an analytical framework. There is also a focus on how the…

The investigation at scale of the tensions that teachers need to manage when deciding to follow recommendations for practice has been hampered by the problem of occurrence: The conditions in which those decisions could be made need to occur during an observation in order for observers to document how teachers handle them. Simulations have been…

We used an assessment platform to study the potential of rich student data obtained online to influence classroom instruction and help teachers respond to students' needs. The article focuses on technology-based formative assessment in the course of teaching a unit on quadrilaterals. We studied example-eliciting tasks, requiring students to…

Variance and invariance are two powerful mathematical ideas to support geometrical and spatial thinking, yet there is limited research about teachers' knowledge of variance and invariance. In this paper, we examined how high school teachers deal with the task of looking for invariant properties in a dynamic geometry environment (DGE) setting.…

Students' issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students' outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

This paper focuses on students' mathematical discourse emerging from interactions in the digital environment GeoGebra, in which one can construct virtual objects that realize mathematical signifiers and then interact with them. These virtual object realizations can become "dynamic interactive mediators" (DIMs) that influence the…

In this paper, we identify various forms of geometric work carried out by student teachers who were asked to perform a geometric task for the estimation of a land area. The theory of Mathematical Working Spaces is used to analyze and characterize the work produced. This study provides evidence that students developed forms of geometric work that…

We investigated how US secondary mathematics teachers expect students to present geometric proofs at the board. We analyzed video records of geometry classrooms and found students to be engaged in a practice that we call proof transcription--i.e., mark-for-mark reproductions of previously completed proofs that were not reasoned reconstructions of…

Promoting mathematical creativity is an important aim of mathematics education, which may be promoted by engaging students with open-ended tasks. Most studies of students' creativity have investigated the creativity of students working individually. This study concerns the mathematical creativity of students working as individuals as compared with…