In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the…

To deepen our understanding of those aspects of problems that cause the most difficulty for solvers, this study integrated eye-tracking with handwriting devices to investigate problem solvers' online processes while solving geometry problems. We are interested in whether the difference between successful and unsuccessful solvers can be identified…

The purpose of this paper is to provide examples of "non-traditional" proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to…

This article argues that mathematical knowledge, and its related pedagogy, is inextricably linked to the tools in which the knowledge is expressed. The focus is on digital tools and the different roles they play in shaping mathematical meanings and in transforming the mathematical practices of learners and teachers. Six categories of digital…

According to the constructivist approach in mathematics education, knowledge is actively created or invented by the students, not passively received from the teacher or the environment. In this regard, learning environments should be designed so that students have to use effectively their "own" knowledge and thus students achieve desired…

Developing students' geometric reasoning skills is dependent on the quality of task designs and the role of the teacher. The purpose of this study was to apply Sfard's (2008) interpretive framework to analyse changes in students' mathematical discourse. This paper reports on the results of an investigation into the ways one class of Year 7…

GeoGebra is a free tool that has the potential to change both how and what is taught in mathematics. GeoGebra allows teachers and students to explore various mathematical ideas either through the full applet (https://www.geogebra.org/graphing) or by sharing applets via GeoGebra's Materials site (https://www.geogebra. org/materials/). It has many…

Educational modules can play an important part in revitalizing the teaching and learning of complex analysis. At the Westmont College workshop on the subject in June 2014, time was spent generating ideas and creating structures for module proposals. Sharing some of those ideas and giving a few example modules is the main purpose of this paper. The…

The objective of this present research is to analyze the implementation of learning geometry through a scientific learning consisting of three aspects: 1) teacher's activities, 2) students' activities and, 3) the achievement results. The adopted approach is a descriptive-quantitative one and the subject is the Class VII students of Islamic Junior…

This study investigates three teachers' uses of a dynamic geometry program (The Geometer's Sketchpad) in their high school geometry classes over a 2-year period. The researchers examine teachers' actions and questions during pivotal teaching moments to characterize mathematics instruction that utilizes technology. Findings support an association…

The authors who are mathematics teacher educators, have found that classifying, composing, and transforming shapes (in particular, rotations and reflections) are areas of difficulty for adults as well as for children. However, these are also some of the most important geometric ideas. They are fundamental topics in the K-8 Geometry and Measurement…

The application of ethnomathematics and mathematical modelling allow us to see a different reality and give us insight into mathematics accomplished holistically. In this context, a pedagogical action that connects ethnomathematics and the cultural aspects of mathematical modelling with its academic features is referred to as ethnomodelling. This…

Body-based activities have the potential to support mathematics learning, but we know little about the impact they have in the classroom. This study compares high school geometry students learning through either body-based or analogous non-body-based activities over the course of a two-week unit on similarity. Pre- and post-tests revealed that…

A student, Stuart, related perimeter to pixels and the professor, Beth, moved back and forth between "reserved believing" and "reserved doubting" and "doubting" teacher actions (Elbow, 1986; Harkness & Noblitt, 2017) while assessing the merit of his conjecture in the moment. Video allowed the researchers to…

This monograph provides in-depth mathematical logic as the foundational rationale for the novel and innovative online instructional methodology called the 4A Metric Algorithm. The 4A Metric has been designed to address and meet the meta-competency-based education challenges faced by 21st century students who must now adapt to and learn in a…