From the early nineties, most reformed curricula at upper secondary level choose to give functions a major position and a priority over rational expressions and equations of traditional algebra. The goal of this paper is to introduce key challenges resulting from this choice and to discuss the contribution that software environments associating…

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…

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 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…

The research presented in this paper relies on Activity Theory and particularly on Engestrom's model, to better understand the use of Electronic-Exercise-Bases (EEB) by mathematics teachers. This theory provides a holistic approach to illustrate the complexity of the EEB integration. The results highlight reasons and ways of using EEB and show…

This study examined the instances of a representational toolkit (RT) in one reform-oriented algebra textbook developed in the United States. The majority of RT uses were active (66%) as opposed to passive and connected (63%) in that the technology results were used in some other manner by either the textbook authors or students as they solved…

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 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…

This paper proposes modelling based learning as a tool for learning and teaching mathematics in high school. We report on an example of modelling real world problems in two high schools in Serbia where students were introduced for the first time to the basic concepts of modelling. Student use of computers and educational software, GeoGebra, was…

Formal requests were recently introduced for integration of ICT in secondary school mathematics. As the main issue, students must develop competence to decide when and how it is appropriate to use available ICT tools and to use them. These new requests put demands on those teachers who have not developed corresponding competencies themselves.…

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…

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…

In this paper, we are proposing the use of forensic case studies as a means to provide students with interesting problem solving opportunities that capitalise on the popularity of several TV series and shows. It also satisfies their natural curiosity about how answers are found to seemingly complex real life problems. We begin with a very brief…