Area should be experienced, not simply calculated. This task invites students to physically experience areas and the spatial relationships between them, as well as their own community.

Tangrams are a traditional Chinese puzzle comprising seven pieces that fit together to make a square. The seven pieces include two large right angled isosceles triangles, one medium size right angled isosceles triangle, two small right angled isosceles triangles, a small parallelogram, and a small square. The literature shows tangrams have been…

This article discusses a set of tasks that introduce dilations using nonstandard figures, incorporating snippets of classroom conversations as students try to make sense of the specified tasks, to show how they progress in their understanding. The authors provide a theoretical foundation for the tasks and discuss the pedagogical implications for…

In this article, we present an educational proposal designed to work on spatial geometry and three-dimensional thinking with students in the last years of Primary Education. The proposal is comprised of several activities that combine the use of a classroom videogame and working with manipulative materials to create a representation of the…

Design and computer graphics curricula for tertiary education include 3-D modeling skills. Students must learn to represent (complex) 3-D objects by means of parametric surfaces or polygonal meshes. Three-dimensional modeling may be a complex task, and students must be able to accrue a certain deal of experience in the field before passing the…

Spatial reasoning is seen as increasingly important in STEM fields. Within mathematics, geometry is a potential site to study and support young children's spatial reasoning. In this paper we revisit Piaget and his colleagues' theoretical perspective on children's development of geometry concepts and take note of projective geometry in that theory.…

This article discusses the advanced characteristics of a mathematical and geometrical system explained and published in the course of several preceding journal articles (Teia, 2015, 2016, 2018a and 2018b). The reading of the preceding articles is encouraged for a clearer understanding of the discussion that follows.

A recirculating water vacuum pump was constructed from inexpensive materials. The recirculating water vacuum pump has a smaller footprint compared to many commercial models and features a novel, 3D-printed water aspirator pump that also functions with a standard laboratory faucet connection. The performances of both the recirculating water vacuum…

While chemistry exists in three dimensions, it is presented in two. This down-conversion results in a significant loss in information and often necessitates multiple images/figures to convey the complexity, intricacy, and beauty of a given structure. Currently, three-dimensional models are built to allow students to interact with molecules.…

The purpose of this article is to report how Year 6 teachers used geometric reasoning tasks to foster students' mathematical attitudes and dispositions by encouraging communication as students constructed mathematical meaning for themselves. The Year 6 teachers implemented two tasks to provide a rich mathematical assessment opportunity…

In high school, students extend understanding of linear and exponential functions and explore trigonometric functions. This includes using the unit circle to connect trigonometric functions to their geometric foundation, modeling periodic phenomena, and applying (and proving) trigonometric identities. These ideas are fundamental for trigonometric…

Quantum technology is an emerging field of physics and engineering and important applications are expected in quantum computing, quantum sensing, quantum cryptography, quantum simulation, and quantum metrology. Thus the need for education in this field is increasing, while still remaining challenging. While the need for basic education in quantum…

Spatial ability was defined by Lohman (1996) as the ability to create, maintain, retrieve, and change visual pictures. Linn and Peterson (1985) distinguished among spatial perception, mental rotation, and spatial visualization. Spatial perception is the determination of spatial connections with respect to the orientation of the learners' body;…

Spatial visualisation is an essential component of geometric thinking and measurement sense. It is a particular type of spatial skill that involves manipulation of spatial images and may not be naturally occurring for students. However, research shows that it is malleable and can be developed through instruction. This article presents an…

In this article Kay Owens explains how a real-world context can be used to encourage student noticing and deeper analysis of geometric structures when students are asked to draw what they saw. Kay presents examples of students' drawings made during a school trip to the zoo which followed a series of inquiry learning experiences in geometry.