Understanding part-whole relations is crucial in early mathematics education. However, both analogue and digital learning environments often lack systematic approaches to foster part-whole understanding. With the rising popularity of educational apps, it is essential to evaluate how they implement learning of part-whole relations. Accordingly,…

In mathematics, students' abilities to make transformations between mathematical representations are fundamental. The recent implementation of digital technologies, such as Dynamic Geometry Environments (DGEs), have changed students' access to mathematical representations by providing a variety of different representations, available just by…

In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of…

Developmental mathematics courses play a critical role in ensuring that students have the foundational mathematical skills necessary to succeed in higher educational mathematics coursework. With the introduction of the corequisite format in recent educational reforms, there has been a growing trend towards transferring developmental mathematics…

Spatial ability is frequently encountered in professional disciplines and daily life. In general, it includes abilities such as rotating objects, estimating the appearance of objects based on a person's position, and being able to think of open and closed forms of three-dimensional objects. It is essential in learning and teaching geometry. In…

The use of online learning objects in teaching algebra is examined in this research, emphasizing its benefits, such as accessibility, flexibility, interactive involvement, differentiated instruction, quick feedback, and links to real-world situations. Strategies include conceptual comprehension, interactive practice, individualized learning,…

Previously defined profiles for using a computer algebra system (CAS) describe prototypical uses of such a tool. When students use a dynamic geometry environment (DGE), however, new opportunities arise for transitions within and beyond the DGE. In this article, CAS profiles are used to explore students' uses of a DGE. Four cases of students, all…

I explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

Despite the surge in efficacy studies, the relative effectiveness of any two math interventions is largely unknown and replications are rare. To ensure that students benefit from high-quality learning experiences, the current conceptual replication of Wang and Woodworth, a randomized control trial, evaluated the relative impacts of two computer…

In their daily work teachers are responsible for several complex tasks; might AI be harnessed to support teachers in the challenging work of planning lessons? In this paper we investigate the use of an AI tool, namely ChatGPT, to generate a lesson plan that may be of use to teachers in their planning. A carefully worded prompt, informed by…

Mathematical writing (MW) can support students' mathematical learning and is common in mathematics assessment. However, MW is known to be particularly challenging for students with learning disabilities. While the use of model compositions of both high- and low-quality writing and the act of revision are evidence-based practices in writing…

Aim/Purpose: This study aims to assess the effectiveness of a tessellation-based instructional program supported by digital technologies for enhancing geometric learning in primary school pupils. Background: Digital education offers various benefits, including increased motivation and engagement, and has been shown to be effective in teaching…

Second-order covariation is a form of mathematical reasoning that needs to be characterized both concerning students' cognitive processes and the design of tasks that promote it. This contribution aims to shed light on these two issues by comparing data related to the same learning experiment performed in two different learning environments:…

In this study, we explore automated reasoning tools (ART) in geometry education and we argue that these tools are part of a wider, nascent ecosystem for computer-supported geometric reasoning. To provide some context, we set out to summarize the capabilities of ART in GeoGebra (GGb), and we discuss the first research proposals of its use in the…