In this paper, we present the results of an experimental sequence of classroom activities on geometric transformations, proposed to high-school students. The activity is based on the use of a dynamic geometry system. Planned by a group of four people, two university professors and two research teachers, the activity has been elaborated together…

The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…

From the point of view of functional programming, a computational process to solve a problem is described as a mathematical function taking some arguments (corresponding to the data of the problem) and returning as a result its solution. Turtle Graphics can be used to describe the movements of a virtual turtle, which leaves a trail along his path…

Studying geometry is an integral component of learning mathematics because it allows students to analyse and interpret the world they live in as well as equip them with tools they can apply in other areas of mathematics. Therefore, students need to develop an understanding of geometric concepts as well as gaining adequate geometry related skills.…

The GeoGebra Workshop for the degree "Teacher in Primary Education" has been designed to work the main geometric competencies that primary pre-service teachers need to develop. In this paper, some case studies are included in which we analyse the development of geometric skills and the use of GeoGebra dynamic tools in three types of activities:…

Most teachers speak of ICT and the new possibilities that have opened up in education, in particular it is especially worth mentioning the role ICT can play in a classroom as a tool to enhance understanding of mathematical concepts, to make conjectures, economise teaching time in search of resources and to serve as a new way of communication to…

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

This article presents a web-based tool designed to compute certified equations and graphs of geometric loci specified using standard Dynamic Geometry Systems (DGS). Complementing the graphing abilities of the considered DGS, the equations of the loci produced by the application are remotely computed using symbolic algebraic techniques from the…

This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…

The aim of this study was to examine the views of pre-service mathematics teachers on the use of webquests in teaching and learning geometry with reference to a theoretical framework developed by Dodge in 1995. For this study the researcher identified four groups containing nineteen pre-service mathematics teachers, which were then assigned to…

The new representations enabled by the educational computer game the "Juggler" can place vectors in a central role both for controlling and measuring the behaviours of objects in a virtual environment simulating motion in three-dimensional spaces. The mathematical meanings constructed by 13 year-old students in relation to vectors as objects, as a…

Cabri3D is a potentially very useful software for learning and teaching 3D geometry. The dynamic nature of the digital diagrams produced with it provides a useful aid for helping students to better develop concept images of geometric concepts. However, since any Cabri3D diagram represents three-dimensional objects on the two dimensional screen of…

This paper describes a possible dragging experiment in a dynamic geometry environment (DGE) that explores a necessary and sufficient condition for cyclic quadrilateral. The dragging modalities identified by Arzarello, Olivero, Paola, and Robutti (2002) and the functions of variation realized in DGE discussed by Leung (2003) will be used as tools…

Designing successful learning environments entails drawing on theoretical perspectives on learning while, at the same time, being cognisant of the affordances and constraints of the technology. This paper reports on the development of a software environment called "3DMath", a dynamic three-dimensional geometry microworld aimed at enabling learners…

Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…