In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof.…

The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the…

We have updated a version of the coordination geometry table of the d-block elements and their ions that Moore and co-workers presented in 1997. This table is constructed by searching and analyzing the data in the Cambridge Structural Database. In this updated version, we have also analyzed impact of ligands on the coordination geometry and…

Previous research and experiences have indicated the potential that games have in educational settings. One of the possible uses of games in education is as game-based assessments (GBA), using game tasks to generate evidence about skills and content knowledge that can be valuable. There are different approaches in the literature to implement the…

The current study is part of a comprehensive research on linking visualization, students' construction of geometrical concepts and their definitions, and students' ability to prove. The aim of the current study is to investigate the effect of learners' understanding of definitions of geometrical concepts on their understanding of the essence of…

Proportional reasoning has been greatly influencing the development of students' mathematical abilities. Along with the area conservation ability, it helps elementary students comprehend area measurement. This exploratory study aimed to produce qualitative-descriptive data on elementary students' proportional reasoning in solving the conservation…

This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

It is well established that spatial reasoning skills (i) support mathematics achievement, (ii) are malleable, and (iii) can be improved through training. More recently, there has been interest in using spatial training to causally support corresponding improvements in mathematics achievement; however, findings so far appear to be mixed. The…

Habermas' construct of rationality is a tool adapted from social sciences into mathematics education to identify the difficulties in the proving process and to plan the teaching of proof for reducing these difficulties. According to Habermas, people engaged in an activity/action are considered to "act rationally" if they choose and use…

This study was intended to examine the progress of the geometric reasoning skills of pre-service mathematics teachers (PSMTs) in the College of Teacher Education, Oromiya, Ethiopia. In the study, there were three different classes: EG1 (n=48), EG2 (n=38), and CG (n=30), where PSMTs in EG1 were treated with technology into guided inquiry-based…

The aim of this study is to examine the effect of the learning environment designed based on different approaches on the change in pre-service teachers' approach preferences and geometry achievement in geometry problems. Twenty pre-service mathematics teachers were involved in geometry lessons for 10 weeks in a learning environment designed based…

The aim of this study is to characterize ways of reasoning and arguing that first year university mathematics students exhibit in problem-solving activities from a course that emphasizes the importance of formulating conjectures and the search for different ways to support or validate them. The use of a Dynamic Geometry System in the…

In this article, we describe a fully computational laboratory exercise that results in an increase of students' understanding of what quantum chemical geometry optimization calculations are doing to find minimum energy structures. This laboratory exercise was conducted several times over multiple years at a small private undergraduate institution,…

Relying on the students' cultural background to teach mathematics may be a strong incitement for the learning process. This background can include artistic creations, items from the news, among others. Because of the strong presence of space related news (in particular the almost simultaneous launching of three spacecrafts towards Mars), we…

In this article, we will give a geometric interpretation of certain finite arithmetic progressions. For this purpose, we will introduce the concept of the "n-regular partition (P[subscript n]) of a quadrilateral.