This study investigated the effect of van Hiele Phase-based Instruction (VHPI) on Ghanaian Pre-service Teachers' (PTs') geometric thinking in terms of the van Hiele Levels. A pre-test post-test quasi-experimental design was employed. There were 75 PTs each in the experimental group and the control group. Van Hiele Geometry Test (VHGT) was…

In this article, Clay and Rhee use the mathematics topic of circles and the lines that intersect them to introduce the idea of looking at the single mathematical idea of relationships--in this case, between angles and arcs--across a group of problems. They introduce the mathematics that underlies these relationships, beginning with the questions…

School mathematics tends to have developed from the major cultures of Asia, the Mediterranean and Europe. However, indigenous cultures in particular may have distinctly different systematic ways of referring to space and thinking mathematically about spatial activity. Their approaches are based on the close link between the environment and…

These proceedings are a written record of the research presented at the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Mazatlán, Mexico, virtually beginning May 27, 2021 and in-person June 2-6, 2021. The conference was originally scheduled to take place…

Students in this era need to grasp the concept of geometry instead of memorizing formulae. This is important for them to further their knowledge in geometry. The purpose of the research was to determine whether GeoGebra software influences year one students' performance in geometrical reflection. The research utilized an experimental research…

The case study focuses on the interactional mechanisms through which online collaborative teams co-construct a shared understanding of an analytical geometry problem by using dynamic geometry representations. The collaborative study consisted of an assignment on which the learners worked together in groups to solve a ship navigation problem as…

Research in mathematics education has established that gestures--spontaneous movements of the hand that accompany speech--are important for learning. In the present study, we examine how students use gestures to communicate with each other while proving geometric conjectures, arguing that this communication represents an example of extended…

When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…

The subject of the article is usage of modern computer technologies through the example of interactive geometry environment Geogebra as an innovative technology of representing and studying of geometrical material which involves such didactical opportunities as vizualisation, simulation and dynamics. There is shown a classification of geometric…

In this article, I (a) illustrate how the K-2 CCSSM reflect the major findings from research studies carried out over the last 30 years on early mathematical abilities that indicate these standards are developmentally appropriate for young children, and (b) offer insights into some types of instructional strategies (e.g., student-centered…

With the rise of personal desktop 3D printing, a wide spectrum of educational opportunities has become available for educators to leverage this technology in their classrooms. Until recently, the ability to create physical 3D models was well beyond the scope, skill, and budget of many schools. However, since desktop 3D printers have become readily…

In this paper we present the process of constructing a test for assessing student performance in geometry corresponding to the first year of Secondary Education. The main goal was to detect student errors in the understanding of geometry in order to develop a proposal according to the Van Hiele teaching model, explained in this paper. Our research…

These proceedings are a written record of the research presented at the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Nashville, Tennessee, and virtually. This year's conference theme is "Critical Dissonance and Resonant Harmony." The aim of this…

The increasing availability of new technologies in schools provides new possibilities for the integration of technology in mathematics education. However, research has shown that there is a need for new kinds of task that utilize the affordances provided by new technology. Numerous studies have demonstrated that dynamic geometry environments…

In this article, the author features "Flatland," by Edwin Abbott, a fantastic story about a square who lives in a two-dimensional world and who receives a visitor from the third dimension. Written in 1884 by a teacher-theologian who dabbled in mathematics, the novel is full of rich themes, including social class structure, the treatment of people…