The paper explores the division of a polygon into equal-area pieces using line segments originating at a common point. The mathematical background of the proposed method is very simple and belongs to secondary school geometry. Simple examples dividing a square into two, four or eight congruent pieces provide a starting point to discovering how to…

The purpose of this study was to explore how university students construct the relationship between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method. The participants in this study were 33 pre-service mathematics teachers. An open-ended questionnaire, knowledge test, tasks, and participants'…

Almost 50 years ago, Arthur Coxford and I developed a high school geometry course in which geometric transformations were fundamental to the mathematical development. Properties of reflections and size changes (dilations) were taken as postulates and used to deduce properties of symmetric figures, the traditional theorems of triangle congruence…

A Steiner chain is defined as the sequence of n circles that are all tangent to two given non-intersecting circles. A closed chain, in particular, is one in which every circle in the sequence is tangent to the previous and next circles of the chain. In a closed Steiner chain the first and the "n"th circles of the chain are also tangent…

Due to the COVID-19 pandemic, countries have had to adapt their usual teaching environment and processes to distance education. The purpose of this study was to investigate the Grade 9 geometry course contents shared on the Education Information Network (EBA) platform in terms of mathematics values (mathematical values and mathematics educational…

The aims of this study are investigating the attention ability and geometry skills of 60-72-month-old children according to the socio-economic status and determining whether the attention ability significantly predicts the geometry skill when the socio-economic status is controlled. The accessible population of the research in the relational…

The goal of this paper was to investigate the role of formal constraints (e.g. definitions, theorems) in geometric reasoning. Four students participated in a task-based interview including 2D Euclidean geometric locus problems. Data were obtained from observations, interviews, and video recordings and analyzed by Toulmin's argumentation model. The…

This study presents a bibliometric analysis of research on mathematics education from 1980 through 2020. The purpose of the study is to provide scientific data on the distribution pattern of mathematics education journals, the most prolific authors, countries, institutions, current research topics, potential international collaboration, and…

This article presents theoretical knowledge, sample activities, and reflections from the implementation process on how teachers can benefit from the Variation Theory to help students enhance their mathematical comprehension. In this context, "congruence of triangles" was conceptualized as an object of learning. Critical aspects were…

The paper explores one episode from a larger study, where a multilingual student (10-year-old) described her understanding of what makes a shape 2D or 3D. Bakhtin's dialogic theory and Garfinkel's ethnomethodology inform the theoretical framework. Transcribed data of the episode is presented, which is analysed at micro-level and macro-level. The…

The purpose of this case study was to explore the nature of instructors' gestures as they teach Euclidean transformations in a synchronous online setting, and to investigate how, if at all, the synchronous online setting impacted the instructors' intentionality and usage of gestures. The participants in this case study were two collegiate…

U.S. students have consistently demonstrated poor performance in spatial reasoning in standardized testing (e.g., National Assessment of Educational Progress). One possible reason is students' lack of conceptual understanding of measurement concepts (length, area, volume, capacity). This paper describes different ways that mathematics textbooks…

The formal acceptance of a mathematical proof is based on its logical correctness but, from a cognitive point of view, this form of acceptance is not always naturally associated with the feeling that the proof has necessarily proved the statement. This is the case, in particular, for proof by contradiction in geometry, which can be linked to a…

In this work we describe a teaching proposal to calculate the eccentricity of the Moon's trajectory by applying a geometrical technique. The values of the ratios between the Earth-Moon distance and the diameter of the Moon at apogee and at perigee were calculated from a kinematic model associated with a geometrical technique of image analysis. The…

Mathematical creative ability is one of the most important skills students must have to process the information provided in resolving the problem. Before using mathematical creative skills, prior knowledge becomes the most crucial thing that allows students to connect all existing information so that they can construct new knowledge through…