This paper explores the performance of ChatGPT and GeoGebra Discovery when dealing with automatic geometric reasoning and discovery. The emergence of Large Language Models has attracted considerable attention in mathematics, among other fields where...
GeoGebra is an interactive geometry, algebra, statistics, and calculus application designed for teaching and learning math, science, and engineering. Its dynamic interface allows its users to accurately and interactively visualize their work, models,...
Technologies came to revolutionize the teaching of technical design; they brought resources that enabled 3D and 2D graphic simulation. The objective of this research is to understand how the implementation of the dynamic software GeoGebra on the topi...
Recently developed GeoGebra tools for the automated deduction and discovery of geometric statements combine in a unique way computational (real and complex) algebraic geometry algorithms and graphic features for the introduction and visualization of...
In the study and design of planar mechanisms, graphical techniques for solving kinematic analysis/synthesis and kinetostatics problems have regained interest due to the availability of advanced drawing tools (e.g., CAD software). These techniques off...
This paper presents an initial output of the project “Augmented Intelligence in Mathematics Education through Modeling, Automatic Reasoning and Artificial Intelligence (IAxEM-CM/PHS-2024/PH-HUM-383)”. The starting hypothesis of this proje...
Confidence in mathematics is a key factor for academic success, being influenced by emotional, behavioral, and technological aspects. The integration of digital tools, such as GeoGebra, has shown potential to promote engagement and develop mathematic...
We compare the performance of two systems, ChatGPT 3.5 and GeoGebra 5, in a restricted, but quite relevant, benchmark from the realm of classical geometry: the determination of geometric loci, focusing, in particular, on the computation of envelopes...
Our goal is to discuss the different issues that arise when attempting to visualize a joints-and-bars cube through GeoGebra, a widespread program that combines dynamic geometry (DGS) and computer algebra systems (CAS). As is standard in the DGS frame...
The presented study analyzes the usage of the didactic efficiency of multiple representations in a computer environment in learning absolute value functions and equations. It is known that the axis of symmetry of the graph of the absolute value funct...
This paper reports the research work carried out with the goal of geometrically and algebraically describing, as well as topologically classifying, the curves resulting from the intersection of a torus with families of parabolic and elliptical cylind...
We report, through different examples, the current development in GeoGebra, a widespread Dynamic Geometry software, of geometric automated reasoning tools by means of computational algebraic geometry algorithms. Then we introduce and analyze the case...
This paper explores the application of automated reasoning tools, specifically those implemented in GeoGebra Discovery, to the perimeter-area inequality in triangles. Focusing on the computational complex and real algebraic geometry methods behind th...
Spatial intelligence is an essential skill for understanding and solving real-world problems. These visuospatial skills are fundamental in the learning of different Science, Technology, Engineering and Mathematics (STEM) subjects, such as Technical D...
There is an ongoing need to evaluate whether commonly used educational software effectively supports inquiry-based learning and computational thinking skills development, which are key objectives in secondary STEM curricula. This research establishes...
There are many computational applications and engines used in mathematics, with some of the best-known arguably being Maple, Mathematica, MATLAB, and Mathcad. However, although they are very complete and powerful, they demand the use of commercial li...
Proof, a key topic in advanced mathematics, also forms an essential part of the formal learning experience at all levels of education. The reason is that the argumentation involved calls for pondering ideas in depth, organizing knowledge, and compari...
It has always been a challenge for teachers to engage and motivate students to learn mathematics, due to the abstractness of some topics and the need for visual representation and technological resources. This study explores the effectiveness of usin...
This study investigates strategies to empower Cape Verdean mathematics teachers in adopting Science, Technology, Engineering, Arts, and Mathematics (STEAM) methodologies, focusing on mathematics education. Using an interactive, reflective continuous...
In the literature, it is usually assumed that Leibniz described proof for the Fundamental Theorem of Calculus (FTC) in 1693. However, did he really prove it? If the answer is no from today’s perspective, are there works in which Leibniz introdu...
Study of dimensions (biometry) and shapes (geometric morphometry) of bone structures in ungulates is of extreme importance in wildlife population management. Unlike classical biometry, which involves the use of a caliper for measurements, geometric m...
This study models customer patterns using fractal analysis and examines how touchpoints and customer journey mapping shape value to enhance sustainable organizational and customer performance. The analysis is made at cell-level using mathematical mod...
This article presents the solution to an optimization problem concerning the longest wooden log that can be floated through two perpendicularly intersecting water canals. This application problem is further generalized and solved using a graphical me...
This study presents research aimed at analyzing whether, in contrast with traditional methodologies, the usage of information and communication technologies (ICTs) in the process of learning mathematics affects gender distinctions by affecting the lo...
The main goal of this work is to present the method designed and put into practice by the Department of Mathematics at I.E.S Norba Caesarina for creating digital books (e-books) in EPUB 3 format, including videos and MathML. The natural way of genera...
This study aims to document the extent to which the use of digital technology enhances and extends high school teachers’ problem-solving strategies when framing their teaching scenarios. The participants systematically relied on online developments s...
In this paper we propose STEAM practices that would foster mathematics learning through modelling architecture while connecting to culture and history. The architectural modelling process is applied by the teachers as participants of these practices...
Computer-extended Descriptive Geometry (CeDG) is a new approach to solving and building computer models of three-dimensional (3D) geometrical systems through descriptive geometry procedures (thus inheriting invariant-symmetry properties from projecti...
This study investigates the use of GeoGebra, a Dynamic Geometry Software (DGS) for math learning in Virtual Reality (VR) using head-mounted displays. We conducted a study with n = 20 middle school students receiving a mathematics tutoring interventio...
This paper presents a method of simulating a capacitive sensor using COMSOL Multiphysics. A petal-form sensitive electrode structure applied to a capacitive angle sensor was simulated using COMSOL software; the angle was calculated using sines and co...
In this paper, we will explain the development of a mathematical activity involving narrative and short stories in particular, with the aim of investigating whether it is possible to use the narrative approach to promote the construction of recursive...
In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software en...
Two Geogebra-based interactive applications to teach the Special Relativity Energy-Mass-Momentum relation are presented. They are useful tools to visualise the mathematical relation from a geometrical perspective, thus helping students facing calculu...
Task design constitutes a growing core of research in mathematics education. In particular, task design in Dynamic and Interactive Mathematics Learning Environments (DIMLEs) has become very popular, although it remains under-researched. This study ai...
Smocking is a handicraft technique of sewing and making pleats to produce shapes over the surface of cloth, and has been widely used in clothing and fashion. However, it is not easy to combine several pieces of smocking without wrinkles on cloth, sin...
Universities play a pivotal role in knowledge production and in transforming teaching methodologies across various subjects. This research is a case study detailing the pedagogical implementation of a game-based methodological approach in a dual-degr...
The emergence of computer-aided design (CAD) has propelled the evolution of the sheet metal engineering field. Sheet metal design software tools include parameters associated to the part’s forming process during the pattern drawing calculation. Curre...
This paper presents SPARK_AI, a prompt-orchestrated system architecture for governing how large language models (LLMs) conduct structured and adaptive reasoning in human–AI interaction. The framework mitigates ad hoc LLM use by replacing direct...
Dynamic mathematics software, such as GeoGebra, is one of the most important teaching and learning media. This kind of software can help teachers teach mathematics, especially geometry, at the elementary school level. However, the use of dynamic math...
This article proposes a possible path devoted to upper secondary school and early university students, as well as training teachers, with the aim to build a conscious approach to the learning/teaching of the conics, which uses, for an educational pur...
This feature paper explores the comparative pedagogical roles of concrete and virtual manipulatives in preservice mathematics teacher education. Based on a design-based research (DBR) methodology, this study investigates the effects of tangible tools...
This systematic review examines mathematics teachers’ knowledge for teaching using digital technologies (DTs), understood as the intersection of disciplinary, pedagogical, and technological domains that teachers mobilize when designing, impleme...
In this paper, we describe subskills of visual communication based on the skill structure outlined in the Common European Framework of Visual Literacy. We have developed this Framework further through assessing the development of subskills related to...
Spatial ability (SA) is the mental ability to create, maintain, and manipulate abstract visual representations. Studies have shown that SA is a strong predictor of success in the fields of science, technology, engineering, and mathematics (STEM). Mor...
Introduction: Pediatric prosthetic knee joints must be appropriately scaled from adult designs to ensure proper gait biomechanics. However, direct dimensional scaling without considering the biomechanical implications may lead to functional discrepan...