How might a 4-year-old pupil come to conceive a line, created by himself with a continuous gesture, as constituted by a series of points? In this paper, we theoretically introduce and discuss a design study of the educational path in which this possibility emerged. The path aimed at leading pupils to "experience," in the sense of the…

The research question studied in this paper is how teachers' task designing can be enhanced in professional development. We show that this can be done by scaffolding. Scaffolding is used in problem solving and we apply it by considering designing a task as a problem. In the paper, we describe a professional development of four teachers led by a…

Recent research in mathematics education shows that by exploring the properties of figures and making conjectures, especially through dynamic geometry software, students can better develop their understanding of concepts. Furthermore, comparing different geometric worlds and, within them, different representations enhances Euclidean knowledge. In…

We present a theoretical study that allows us to attempt framing in an embodied perspective the effectiveness of the drawing robot GGBot in the learning of geometry. The aim of the article is to set the intertwining of activity, semiotics, perception, and knowledge at the crossover of Radford's theory of objectification (TO) and Borba and…

This paper aims at defining and exploring design principles in a distance technological setting for an educational activity for mathematics undergraduate students, devoted to the construction of basic concepts in general topology, the promotion of problem-solving processes, the development of metacognitive aspects, and, in general, the development…

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

We present a case study that has been developed to inform about the teaching activity of a secondary mathematics teacher in a whole group discussion and the mathematical learning opportunities generated for the students in this classroom context. For data of one lesson we determine the episodes that shape the whole group discussion. For each…

With COVID-19 continuing to make meeting face-to-face impossible, the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) executive decided that, for the first time, the CMESG/GCEDM meeting would be held virtually. By necessity, the program had to be much compressed with no topic…

Much of the evidence provided in support of the argument that mathematical knowing is embodied/enacted is based on the analysis of gestures and bodily configurations, and, to a lesser extent, on certain vocal features (e.g., prosody). However, there are dimensions involved in the emergence of mathematical knowing and the production of mathematical…

Unlike studies on cooperative learning that have focused on the verbal communication aspect of learning, this study focuses on the non-verbal aspect--mindful movement, which is the use of body movement to aid academic learning. Our research examined the link between five learning activities occurring within a cooperative group of children using…

Worksheets and instructions are given for this activity whose objective is to develop the relationship between the lengths of the sides of a triangle and its classification by angle. (MP)

Construction of colorful braided polyhedra can provide upper elementary students with enjoyable geometric experiences. (SD)

Children's perception and understanding of three-dimensional figures and of operations on them is discussed. Piaget's findings are reviewed and more current research is described. Classroom implications are explored. (SD)

Paper-folding activities demonstrate properties of the conic sections and equilateral triangles. (SD)

The lesson described combines mathematics, science, and literature, and is easily adaptable for use with classes in basic mathematics, geometry, analytic geometry, or calculus. (MP)