The aim of this research is to advance in the teaching-learning process of representing quadratic functions, both with pencil and paper and with a technological tool. For this purpose, a didactic experience is presented. Firstly, it is explained in the traditional way how to graph a quadratic function; secondly, students are introduced to the…

When technologies like GeoGebra are implemented in mathematics lessons, the focus should be on learners and their learning processes rather than on technologies. Student-centeredness is a core characteristic of flipped classroom approaches. Recent further developments of flipped classroom approaches aim to foster learning through inquiry in…

The article presents some examples of plane geometric variance of an area with the use of computer technology. These tools can offer teachers opportunities for adaptation and preparation of pedagogical presentations which will help students along the process of fruitful conjectures formation and eventually construction of formal deductive proofs.…

This paper discusses the conception of an online formative assessment tool in the field of functional thinking and focuses on the first cycle of a design-based research project. This tool is based on a preceding qualitative research project in an Austrian grade 7 class for examining students' conceptions as well as possible influences of designed…

This paper provides a set of five indicators of CAS use, which provide a means to analyse a student's written solution to determine whether they used CAS for solving a given problem. These indicators provide a way for researchers and teachers to determine CAS use without requiring classroom observation or the explicit recording of extra…

Studies of the impact of various types of computer use on the results of learning and student motivation have indicated that the use of computers can increase learning motivation, and that computers can have a positive effect, a negative effect, or no effect at all on learning outcomes. Some results indicate that it is not computer use itself that…

This study investigated how a group of 10 prospective secondary mathematics teachers (PST) read, evaluated, and adapted a textbook lesson involving the symbolic manipulation capabilities of computer algebra systems (CASS). PST read the entire lesson and tended to focus on the organizing question at the beginning of the student lesson and the CAS-S…

Using Mathematical Modelling has become a useful tool in teaching-learning mathematics at all levels. This is so because mathematical objects are seen from their very applications, giving them meaning from the beginning. In this paper we present some details on the development of a teacher's training course called Modelling in the Teaching of…

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 is on one…

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…

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…

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…

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…

This paper reports on a design experiment conducted to explore the construction of meanings by 17 year old students, emerging from their interpretations and uses of algebraic like formalism. The students worked collaboratively in groups of two or three, using MoPiX, a constructionist computational environment with which they could create concrete…

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…