In this paper, I introduce Sfard's discursive framework to examine secondary-school calculus students' communication during exploratory activities mediated by the use of touchscreen dynamic geometry environments (DGEs). Six pairs of secondary-school students participated in an open-ended task to explore calculus relationships using…

The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of subspaces of vector spaces in a series of in-depth qualitative interviews in a technology-assisted learning environment. Fourteen mathematics majors came up with a diversity of innovative and creative ways in which…

Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students' competence in justifying an ellipse. We analyse the complex interactions between…

The study reported here addresses pre-service and in-service teachers' attitudes toward mathematical-geometrical definitions. The goal of the study is to investigate whether understanding the role of definitions as classification and identification criteria will guarantee that participants: (1) accept that there may be more than one equivalent…

This paper reports a study that explored 11 to 12-year-olds' conceptions of the terms 'volume', 'capacity' and 'interior volume'. Semi-structured interviews, supported by the use of measurement resources, were used to gain insight into their thinking. Video-recordings of the interviews allowed analysis of dialogue, actions with the materials and…

This study explored the impact of homogeneity of answer choices on item difficulty and discrimination. Twenty-two matched pairs of elementary and secondary mathematics items were administered to randomly equivalent samples of students. Each item pair comparison was treated as a separate study with the set of effect sizes analyzed using…

The solution of problems and the provision of proofs have always played a crucial part in mathematics. In fact, they are the heart and soul of this discipline. Moreover, the use of different techniques and methods of proof in the same mathematical field, or by combining fields, for the same specific problem, can show the interrelations between the…

One way to ease the solution of physics problems is to visualize the situation. However, by visualization we do not mean the pictorial representation of the problem. Instead, we mean a sketch for the solution of the problem. In this paper a new approach to solving physics problems, based on decomposing the problem into with and without gravity, is…

For 500 years, dream catchers have been cultural symbols of intrigue worldwide. The most common folkloric design is a 12-point dream catcher. According to Native American legend, the first dream catcher was woven by a "spider woman" to catch the bad dreams of a chief's sick child. Once the bad dreams were caught, the chief's child was…

Gestures are associated with powerful forms of mathematical understanding. However, determining the causative role of gestures has been more elusive. In the present study, we inhibit students' gestures by restraining their hands, and examine how this impacts their problem-solving when presented with geometric conjectures to prove. We find no…

As part of a much larger study where spatial reasoning is the focus, this paper draws on the language aspects of this strand of the curriculum. The quarantined part of the project discussed in this presentation is based in remote Indigenous schools. We draw on the challenges of the concept of symmetry and where the language of instruction (and…

Spatial reasoning is critical across the STEM disciplines. Examining deaf and hard of hearing (DHH) children's spatial reasoning in mathematics, particularly geometry, as an embodied phenomenon opens new possibilities for deaf education. The authors inquire into the embodied processes and forms of DHH learners' spatial reasoning, considering how…

The aim of this study is to determine the effect of activity-enriched geometry teaching methods on elementary school students' perceptions, attitudes and self-efficacy towards geometry. In this context, the mixed method was determined to be the research design. Within the scope of the study, a training process was carried out with 22 students who…

Visuospatial thinking is considered crucial for understanding of three-dimensional spatial concepts in STEM disciplines. Despite their importance, little is known about the underlying cognitive processing required to spatially reason and the varied strategies students may employ to solve visuospatial problems. This study seeks to identify and…