This report details a set of three tasks used in an exploratory study of pre-service teachers' (PSTs) experiences of task design for the mathematics classroom. The three tasks, which I call the "Orange Dot Tasks," were constructed in Desmos, a dynamic geometry environment (DGE), and participants engaged each task through manipulating…

This study aimed to examine the application of a realist hands-on learning approach and its contributions to optimizing the solid geometry conceptual understanding and problem-solving skills of students. It employed a non-equivalent pre-/post-test quasi-experimental research design. The results showed that there was a statistically significant…

PowerPoint is a learning aid, developed for presentations. PowerPoint has "dynamic" features for creating presentations with dynamic actions. The knowledge of the infinite backward multiplier is difficult to understand. One of the difficulties in understanding this knowledge is infinity, "dynamic". In this study, we use the…

In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors,…

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…

Geometry and spatial reasoning form the foundations of learning in mathematics. However, geometry is a subject often ignored by curriculum writers and teachers until high school, leading to students lacking in critical skills in geometric reasoning. As the United States moves into a new curriculum epoch, heralding the commencement of the national…

PWW style are presented. The difference of evidence is based on various additional auxiliary constructions, which in itself is a "mathematical art" that the student can master as a result of much practice. The PWW are accompanied by GeoGebra applets containing HINT buttons that allow the student to get step-by-step help in completing the…

Although research highlights the importance of analyzing the geometric work of teachers, there are few validated instruments in this line. This study presents the processes of design and validation of a forced-choice questionnaire that allows the characterization, from a theoretical basis, of how geometry teachers organize their teaching practice.…

Augmented Reality (AR) technologies allow for holograms to be layered over the real-world, "augmenting" human vision by adding technical information or illustrations onto 3D space. Although AR-based applications are showing positive effects in many systematic reviews and meta-analyses, well-designed, rigorous studies with strong control…

The study examined how local artisans and mathematics teachers think the Akan traditional art might help senior high school students learn geometry. The Akan people live in Ashanti Region of Ghana. The study targeted experienced mathematics teachers and Akan traditional art experts. Seven experienced mathematics teachers and three craftsmen were…

This study identifies characteristics of polygon class learning opportunities for 8-9-year-old children during the whole-class instruction. We consider the interplay between the geometrical tasks demanding different ways of reasoning, features of children's geometrical thinking, and the teacher's moves to identify characteristics of learning…

This article investigates the knowledge arising in mathematics teachers' planning of how to manage transitions within and beyond dynamic geometry environments in the topic of circle theorems. The notion of situated abstraction is used to elaborate the central TPACK construct within mathematics education and address previous criticisms of the…

Geometry education is an important aspect of science, technology, engineering, and mathematics (STEM) education, but it is often overlooked in K-12 education in the United States. Chunking strategy reduces the cognitive load demanded in the processing of information, and it has been applied as a testing accommodation for high school students with…

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…

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…