As part of a module on mathematical problem solving in an Initial Teacher Education programme, the student teachers are encouraged to produce alternative solutions to the problems they tackle and, in particular, to consider whether ICT can help. In this paper we discuss a number of unusual solutions produced for some of the problems, specifically…

This paper discusses some of the results of a study carried out with two classes of grade 7 students (11-12 years old); the aim of the project was to design, develop, and test interactive geometry tasks for use in future research into how (or whether) interactive applets help students learn mathematics. The study tasks were developed around the…

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…

Numbers can be represented in a variety of ways--through pictures, diagrams, symbols. Each representation highlights different features of the number and the number system. This study aims to explore pupil understanding of number both within and across representations. A computer environment (suite of programmes) was created within which…

This paper reports on a design experiment in the domain of number sequences conducted in the course of the "WebLabs" project. We iteratively designed and tested a set of activities and tools in which 10-14 year old students used the "ToonTalk" programming environment to construct models of sequences and series, and then shared their models and…

The Aplusix system has been designed for helping students to learn algebra. Its capacity to tell the students whether their calculations are correct or not, to provide families of exercises of a chosen level, and to give scores after tests allows this system to be used in the regular functioning of the class. Its capacity to record the students'…

T-algebra is a project for creating an interactive learning environment for expression manipulation tasks of elementary algebra. Our main didactical principle has been that all the necessary decisions and calculations at each solution step should be made by the student, and the program should be able to understand the mistakes. This paper…

Practical investigation tasks are part of the Dutch examination programme of senior secondary education. In mathematics and science, pupils are expected to develop a broad range of research skills, which includes connecting real world phenomena with the scientific world, understanding the problems at hand and asking the right questions, making a…

This report is part of a long-term research on the construction of mathematical meanings through the interaction with various technologies. The research involved a set of teaching experiments based on body motion with sensors and calculators at different school levels, from kindergarten to secondary school. Here I refer to the one developed in a…

This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, and…

This paper extends and develops theories of mathematical learning to provide a framework for the analysis of classroom video data of students working at a computer in a task aimed at increasing understanding of multiple representations of quadratic functions. Student interactions are coded using novel software tools in the process of analysis, and…

Within this paper I report on aspects of a study aimed at not only discovering how and when students use a graphical calculator within an Advanced-Level (pre-University) Mathematics course, and what operations and calculations they perform with such calculators, but also the depth and type of learning that takes place when students use graphical…

This paper argues that better understanding of the educational integration of new technologies calls for broader account to be taken of the complex ongoing practices of school mathematics education. To frame its concerns, the paper opens by drawing on key studies of the general place of technology in classroom practice and teacher thinking. The…

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…

In this paper, difficulties of students in the case of computer-mediated teaching of geometry in a traditional classroom are considered within the framework of "transactional distance", a concept well known in distance education. The main interest of this paper is to record and describe in detail the different forms of "distance" during students'…