A key motivational tactic in undergraduate mathematics teaching is to launch topics with fundamental questions that originate from surprising or remarkable phenomena. Nonetheless, constructing a sequence of tasks that promotes students' own routes to resolving such questions is challenging. This note aims to address this challenge in two ways.…

This work presents the result of the application of a didactic sequence designed to understand the concept of the Cavalieri's Principle, supported by the GeoGebra application in its version for mobile phones -- 3D Calculator. For this study, the Theory of Categories of Intuitive Reasoning, by Efraim Fischbein, was used as a conceptual basis. The…

Although basing instruction on learning trajectories (LTs) is often recommended, there is little direct evidence regarding the premise of a LT approach--that instruction should be presented (only) one LT level beyond a child's present level. We evaluated this hypothesis in the domain of early shape composition. One group of preschoolers, who were…

Although basing instruction on learning trajectories (LTs) is often recommended, there is little direct evidence regarding the premise of an LT approach--that instruction should be presented (only) one LT level beyond a child's present level. We evaluated this hypothesis in the domain of early shape composition. One group of preschoolers, who were…

The following outlines the rationale and structure of a professional learning initiative that seeks to explore teachers' ways of engaging students more actively in building mathematical connections for themselves. An example of one of the suggested experiences is presented.

As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

Dynamic geometry software (DGS) is often used for development of interactive teaching materials in many subjects, not only mathematics. These interactive materials can contain hundreds of elements in order to represent complex objects, and script programs to control their behavior. We propose an approach for creating, importing and using…

Engineering students use spatial thinking when examining diagrams or models to study structure design. It is expected that most engineering students have solidified spatial thinking skills during K-12 schooling. However, according to what we know about geometry learning and teaching, spatial thinking probably needs to be explicitly taught within…