The 1989 good old days' quote from the "Field of Dreams" by Kevin Costner that "If you build it, he or they will come" is no longer going to be attractive, especially in the field of mathematics education. One such challenging subject in the field of mathematics education is the teaching and learning of geometry. It is the aim…

The ability to solve geometric construction problems is justly regarded as an essential component of mathematical culture. The dynamic, general nature of objects provided by dynamic geometry systems allows the development of intuitive methods for solving construction problems. The core mathematical concept underlying this approach is the loci…

Exploring non-Euclidean geometries is a common way for College Geometry instructors to highlight subtleties in Euclidean geometry. The concept of congruence, going undefined or informally defined in multiple axiomatic systems, is particularly susceptible to conflation with the idea of "same measure." Taxicab geometry provides a context…

This paper seeks to answer the question: How does the handling of the contradictions that emerge in activities of initial mathematics teacher education contribute to the learning of geometric knowledge when pre-service teachers and the teacher educator solve geometric construction problems with GeoGebra? A dialectical-materialist approach is used…

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

As a distinct mode of mathematical representation and communication, geometry diagrams are both signs that represent abstract geometric concepts and visual images that offer graphical-spatial properties. Dynamic geometly environment offers a wide range of tools for its users to create and interact with geometry diagrams. In this paper, I propose a…

Undergraduate mathematics instructors are called by many current standards to promote prospective teachers' learning of geometry from a transformation perspective, marking a change from previous standards. The novelty of this situation means it is unclear what is involved in undergraduate learning and teaching of geometry from a transformation…

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…

This paper discusses strategies that two high school geometry teachers employed to solve a challenging geometry problem with the aid of dynamic geometry software (The Geometer's Sketchpad (GSP). The teachers were part of a group of teachers who participated in a summer professional institute funded by the National Science Foundation. The paper…

We present an investigative activity that was set as part of a course of pre-service teachers of mathematics. The emphasis in the course was set on the importance of using the computerized technological tool for teaching the subject. The activity focused on investigating interesting geometrical conservation properties which are not known to the…

Educational institutions around the world have been integrating AI into their educational practices. Many studies and reports highlight both the advantages and disadvantages of this integration. This paper focuses on the positive aspects of AI in education, specifically through the lens of a high school geometry project at a technology-focused…

The shift of evidence-based, active and inquiry-based pedagogy to online modalities has typically been done with a synchronous model, using video conferencing technology to facilitate interaction and collaboration amongst students. Such an approach can be infeasible for some students and create inequitable situations within a class. This paper…

In this paper, I share an activity that reinforces students' understanding of translations, reflections, and rotations via body movement. As a result of this activity, students gain a different perspective compared to previous explorations on paper, communicate mathematics, and visualize transformations as rigid motions on the plane. Furthermore,…

When examining students' participation in these mathematics discussions, the focus is on their verbal contributions. However, students' nonverbal contributions--such as pointing, drawings, and models-- can be crucial resources for advancing the mathematical thinking and the collective activity of a classroom community (Johnson et al., 2023; Webb…

A key topic throughout school geometry is measurement--namely, distance, area, and volume. This article focuses on one key idea for finding and justifying the area of two-dimensional (2D) shapes: area-preserving transformations. Although especially pertinent to geometry teachers, this article highlights a vertical connection of ideas progressing…