While in traditional mathematics teaching methods, it is possible to prove concepts while teaching geometry and to reach generalizations that require more complex definitions by using concept findings, while in today's geometry teaching, learning that activates the student's discovery process gains importance. In this context, the aim of this…

A central goal of lesson-centered professional development programs (PD) for mathematics teachers is to learn by constructing an artifact, for example, by designing and improving a lesson plan together. That leads to the questions, what does it mean, for mathematics teachers, to improve a lesson? And how can improvements be accounted for in the…

Augmented Reality (AR) and Virtual Reality (VR) platforms now support shared, immersive experiences that enable people to directly physically and perceptually engage with mathematical objects, including shared objects. These new forms of AR/VR technology -- which we call "shared holographic AR/VR" (shAR) -- enable multiple learners to…

Students with dyscalculia often face significant challenges in visual memory, which is critical for mathematical learning, particularly in recognizing and differentiating geometric shapes and their properties. This study aims to explore the extent to which an action plan, tailored to the unique learning characteristics of students with…

Limited literature addresses how elementary preservice teachers (PSTs) can advance their thinking about hierarchical geometric relationships. Informed by a commognitive perspective, we investigated this phenomenon as a matter of discursive change, focusing on word use, visual mediators, and narratives. We report on a teaching experiment involving…

The visualization of chemical compounds in three-dimensions is a foundational skill in the study and practice of chemistry and related fields, and one which has the potential to be supported by interaction with virtual models. Here, we present a collaborative learning activity piloted in first-year chemistry which investigates if inquiry-driven…

GeoGebraBook is a pedagogical resource in the form of a digital book created and developed for free on the GeoGebra online page. This paper presents preliminary research using GeoGebraBook to support explaining the area of a flat figure and the volume of a solid. The study was based on qualitative and quantitative research and involved forty-four…

As a multifaceted concept, the learning of angle concepts takes years to achieve and is beset with challenges. This paper explores how the processes of constructing and validating a learning progression in geometric reasoning can be used to generate targeted teaching advice to support the learning of angle concept. Data from 1090 Year 4 to Year 10…

This study surveyed and analysed four secondary school students' writing about a square. Sfard's discursive approach to understanding mathematical discourse was used to analyse the responses collected from 214 Australian secondary school students. The results showed that geometric knowledge was developed experientially and not developmentally.…

This paper reports on a study of learners' use of immersive spatial diagrams to make arguments about three-dimensional geometric figures. Immersive spatial diagrams allow learners to use the movement of their bodies to control their point of view, while immersed in three-dimensional digital renderings. We present analysis of two pairs of…

Generalization has been a major focus of curriculum standards and research efforts in mathematics education. While researchers have documented many productive contexts for generalizing and the generalizations students make, less attention has been given to the processes of generalizing. Moreover, there has been less work done with high school…

In this study, we devised research design that provides pre-service teachers to effectively experience embodied geometric thinking with the goal that it will impact teachers' instruction to students in their classrooms. Using a motion-capture video game and design tool, we offered opportunities for pre-service teachers to experience of performing…

This study aims to explore an educational learning environment that supports students to learn conceptual modelling with the unified modelling language (UML). In this study, we call the describing models "UML programming." In this paper, we show an educational UML programming environment for science, technology, engineering, art, and…

The following outlines the rationale and structure of a professional learning initiative that seeks to explore teachers' ways of engaging students more actively in building mathematical connections for themselves. An example of one of the suggested experiences is presented.

This study describes how a secondary school teacher in Trinidad and Tobago implemented opportunities for reasoning and proof in Geometry. Data were collected via teaching observations, teacher interviews, audio, and video recording. The analysis of the data suggested that the teacher used open-ended questioning, revoicing, group work, and…