This paper reports on two students' work on geometry tasks in a dynamic geometry system. It augments prior work on students' instrumental geneses via a consideration of emergent goals that arise in students' work. It offers a way to interpret students' (working with new software) awareness of what software can and cannot do and…

In this paper we aim to contribute to the process of networking between theoretical frames in mathematics education by means of forging connections between Constructionism and Instrumental Theory to discuss a design for instrumentalisation. We specifically focus on instrumentalisation, i.e. the ways in which students make changes to digital…

The goal of this paper is to evaluate the contribution of the anthropological approach (AA) concurrently to Activity Theory (AT) in view of overarching questions about classroom use of technology for teaching and learning mathematics. I will do it first from a philosophical point of view, presenting the main notions of AA that have been used to…

This paper offers a framework, an extension of Valsiner's "zone theory", for the analysis of joint student-teacher development over a series of technology-based mathematics lessons. The framework is suitable for developing research studies over a moderately long period of time and considers interrelated student-teacher development…

This paper presents a case of collaboration with three teachers and a didactician on task development within a developmental research project based on ideas of inquiry and learning community. The teachers' goal was to utilise a spreadsheet to orchestrate the pupils' investigations and build a library of tasks for the classroom. The focus…

This paper looks at research based models that have been put forward to describe how teacher use of technology develops. There have been a variety of studies that have proposed levels that describe teacher use of technology and identify the different aspects of use that distinguish these levels. Very few of these studies have shown how teachers…

The main purpose of this paper is to present an ongoing research study on the evolution of pre-numerical and pre-inductive levels of ordinal thought in students from three to seven years old. Our methodology is based on multimedia technology, an automatic and objective record of the data and minimal interaction between students and researcher. A…

Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve"…

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…

This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…

This article will expand upon the techniques of Criminologist, D. Kim Rossmo, and Social Psychologist, David Canter for determining a serial criminal's base of operations. The basic framework for our investigation is that of Rossmo, but uses a different criterion for analysing the relationship of points within the hunting area defined by the crime…

Many researchers claim that children from a very young age form intuitive conceptions of probability, which may be adapted through properly designed learning activities. In addition, the random number generators as well as the dynamic interactive representations offered by digital technologies, open up new possibilities in learning probability…

This article explains the didactical design of M@th Desktop (MD), a teaching and learning software application for high schools and universities. The use of two types of MD resources is illustrated: notebooks and palettes, focusing on the topic of exponential functions. The handling of MD in a blended learning approach and the impact on the…

In the Dutch secondary education system, students must carry out at the end of their school career a research or design project to demonstrate their ability to apply acquired knowledge and skills while pursuing a rather large research question or design goal in some depth. They are encouraged to choose the topic themselves and they are to some…

This article reports on research at the crossroads of on the one hand the procedural-conceptual cut in algebra in the transition from secondary education to higher education, and on the other hand the potential of ICT. Three key topics come together: algebra didactics (symbol sense), theories on tool use (instrumental genesis) and assessment…