This exploratory qualitative case study design aims to examine the mathematization process employed by pre-service mathematics teachers during instruction grounded in Realistic Mathematics Education (RME) within Plane Geometry. It was studied as this shall have a cascading effect on the teaching-learning of schools. Carried out at a teacher…

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…

In a previous article, "The Shape of Reasoning: Using Geometry to Promote the Reasoning Proficiency Strand" (EJ1286217), the author put forward the argument that no medium is more powerful than geometry as a vehicle for developing the mathematical proficiency strand of Reasoning. Because geometry is so visual and tactile, the…

The complexity of the art of teaching and learning, especially in the field of mathematics, calls for a broader approach than the traditional status quote. Proof without words in geometry coupled with the dynamic and interactive GeoGebra applet have the capacity to be used in all levels of mathematics education from grade schools to higher…

It is well known that there is a unique circle passing through three specified points if and only if they are non-collinear. We show that there is also a unique circle passing through the endpoints of diameters of three specified circles if and only if they have non-collinear centres.

The role of probability in curricula for children has fluctuated greatly over the past several decades. Recently, some countries have removed probability from their preschool and primary curricula, and others have retained it. One reason for such lack of agreement is that theory about early probability learning is still relatively new and under…

A standard problem for physics students is to calculate or measure the acceleration of an object down an inclined plane. Additional information can be obtained by measuring the angular acceleration as well as the linear acceleration. An experiment is described where a billiard ball was filmed as it rolled down an inclined plane at different…

Complementary to existing "normative" models, in this paper we suggest a descriptive phase model of problem solving. Real, not ideal, problem-solving processes contain errors, detours, and cycles, and they do not follow a predetermined sequence, as is presumed in normative models. To represent and emphasize the non-linearity of empirical…

Discovering the implications of a theorem takes time. This process relates to fundamental theorems, such as the Pythagorean theorem, and practically has intemporal ramifications. After all, new proofs are still being discovered today (Scimone, 2009). The theorem in itself is not changing, but rather our perspective of it is. That is, the…

In this article, the author describes an occurrence of the golden ratio in the context of regular hexagons. The method described can be used to construct the golden ratio. This is one of many ways one can construct the golden ratio.

This article reports on the design and implementation of a didactic sequence in the frame of a design-based research study. The research aim is to test the hypothesis that affordances of dynamic geometry may support students' awareness of logical relationships between geometrical properties of constructed figures. We elaborate on the task design…

The purpose of this study was to compare the concept images and hierarchical classification skills of students at different educational levels (middle school, high school, and university) regarding parallelograms. In this study, a cross-sectional research design was utilized. The study group consisted of a total of 357 students from middle school…

Can You Build It? is an engaging Improve It! task that asks children to construct 3D shapes based on 2D depictions. Students' initial 3D creations often need revision, and as they build and re-build, they develop spatial relationships. This task was implemented in a first-grade class, connected to composing 3D geometric shapes to address the…

Purpose: Ethnomathematics are used in motifs by the Dayak Ngaju Tribe in Central Kalimantan. The motifs contain some Ethnomathematical objects and concepts for Geometry and values. Therefore, this study aimed to describe the motifs based on mathematical objects and concepts of Geometry and value viewed from ethnomathematics aspects. Methodology:…

External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to…