This article presents an original puzzle that supports students' development of visual thinking and geometry ideas based on the Van Hiele levels of geometric thought. The "Triangle Puzzle" is one of many tools teachers can use to guide students' learning of geometry. The Van Hiele's theory provides a way to assess and support this…

This article focuses on the experience of viewing polyhedra in modified kaleidoscopes, highlighting the perceptive acts that take place. It presents aspects of geometry, such as concepts and ideas involved in the visualization of polyhedra in kaleidoscopes, through an analyticalmathematical study of the reflection of images in mirrors and…

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.

Large drop towers let you experience a couple of seconds of nearly free fall before stopping gracefully in magnetic brakes or bouncing a number of times on compressed air, as in the Turbo Drop tower considered in this work, where many complementary representations are used. An accelerometer taken along on the ride captured the forces experienced…

Sequences are an important topic--not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns…

Reasoning is handled as a basic process skill in mathematics teaching. When the literature was examined, it was seen that many types of reasoning related to mathematics education were mentioned. In the present study, it was focused on visual reasoning, which is one of the types of reasoning and also used in different research areas. The purpose of…

In this work, recurrent and linear sequences are studied, exploring the teaching of these numbers with the aid of a computational resource, known as Google Colab. Initially, a brief historical exploration inherent to these sequences is carried out, as well as the construction of the characteristic equation of each one. Thus, their respective roots…

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.

Virtual images are often introduced through a "geometric" perspective, with little conceptual or qualitative illustrations, hindering a deeper understanding of this physical concept. In this paper, we present two rather simple observations that force a critical reflection on the optical nature of a virtual image. This approach is…

The authors introduce the readers to a project that highlights digital heritage in early childhood. The highlighted teachers partnered with an anthropologically-trained archaeologist who utilizes advanced digital technologies to enhance public understanding of cultural heritage. This collaboration emphasized social studies and reinforced…

Perceiving a 3-dimensional (3D) diagram on a 2-dimensional (2D) surface or plane can be a challenging endeavor for students at the elementary or primary grade levels. Adding to this challenge are the intricacies present in understanding the processes involved in geometric problems of such a nature. To ease the comprehension of these processes,…

We present an accessible implementation of augmented reality projections for the depiction of complex structures and motifs, including atomic orbitals and elemental allotropes. The utilization of a free, cross-platform-compatible, online database of these structures provides the access route for closer examination, either via augmented reality or…

The standard deviation (SD) of a random sample is defined as the square-root of the sample variance, which is the "mean" squared deviation of the sample observations from the sample mean. Here, we interpret the sample SD as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This…