This contribution focuses on reasoning about quadrilaterals provided by lower secondary school students when working with pre-prepared dynamic constructions. On this topic, we present an exploratory empirical qualitative study carried out within a GeoGebra Classroom environment, and our diagnostic instrument consists of a set of dynamic…

While there are many documented approaches to using technological tools to support collaboration in remote environments, studies related to proof-based courses are overwhelmingly situated in the context of geometry. This study uses instrumental genesis theory to study how students in an introduction to proofs course operationalize the…

Mathematical proof, often regarded as the heart of mathematics, is essential for interconnected mathematical knowledge. However, proof-writing skills do not develop inherently. Effective learning environments are vital for university students to enhance these skills. This study investigates the impact of the ISMAT model on pre-service teachers'…

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…

In this article, we provide an empirical example of how digital technology; in this case, GeoGebra may assist students in uncovering--or whiteboxing--the content of a mathematical proof, in this case that of Proposition 41 from Euclid's "Elements." In the discussion of the example, we look into the impact of GeoGebra's…

The geometric design of roofs is a key element in the design and construction of buildings. Roofs play an important role in protecting buildings from the weather and providing esthetic appearance and functionality. Theoretically, to design a roof over a given plan means to construct the projections of the intersections of the roof planes. All this…

The emergence of interactive mathematics software in the early 1990s has invited mathematics education researchers to consider ways that dynamic geometry environments (DGEs) might influence K-16 learners' growth of geometric understanding. This article examines the applicability of the Pirie-Kieren theory to trace this growth. Data for this…

The purpose of this note is to introduce two challenging problems in geometry that were inspired by some well-known problems in high school geometry. These problems can be explored in the dynamic geometry environments of computer construction programmes.

Meaning Equivalence Reusable Learning Objects (MERLO) items are a new kind of didactical tool that can be designed by teachers and used in classes, in tasks aimed at engaging students in deep reasoning, exploring and arguing about mathematical concepts. The interactions across communities of mathematics teachers and educators in on-line…

This paper reports the multimodal resources that attached to students' reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we…

This is an article about abstraction, generalization, and the beauty of mathematics. We claim that abstraction and generalization in of itself may very well be a beauty of the human mind. The fact that we humans continue to explore and expand mathematics is truly beautiful and remarkable. Many years ago, our ancestors understood that seven stones,…

Digital design and fabrication tools obtain constraints affecting creativity in conceptual design phase. There is a necessity to have a better understanding of issues related to the rationalization process of form, material and fabrication. The objective of this paper is to integrate analogue craft into architectural design studio that can be…

This study takes a closer look at Form Four students' initial mathematical modelling process when solving mathematical problems using GeoGebra. The modelling process was observed from cognitive perspective to learn the difficulties students faced during the process and the result would give ideas for intervention. Qualitative approach by using…

We present an investigative activity that was set as part of a course of pre-service teachers of mathematics. The emphasis in the course was set on the importance of using the computerized technological tool for teaching the subject. The activity focused on investigating interesting geometrical conservation properties which are not known to the…

This paper focuses on students' mathematical discourse emerging from interactions in the digital environment GeoGebra, in which one can construct virtual objects that realize mathematical signifiers and then interact with them. These virtual object realizations can become "dynamic interactive mediators" (DIMs) that influence the…