In this article, we focus on how spatial knowledge can be articulated with the integration of programmable floor robots in the mathematics classroom. We describe the observation grid we conceived to take into account three distinct dimensions: spatial knowledge, robotics and computer programming. Then, we implement this tool to analyse mathematics…

Geometrography, "alias the art of geometric constructions" was proposed by Emile Lemoine between the late 1800s and the early 1900s. It consisted originally of a system to measure the complexity of ruler-and-compass geometric constructions, capable of: designate every geometric construction by a pair of values that manifests its…

This document introduces, describes and exemplifies the technical features of some recently implemented automated reasoning tools in the dynamic mathematics software GeoGebra. The new tools are based on symbolic computation algorithms, allowing the automatic and rigorous proving and discovery of theorems on constructed geometric figures. Some…

Stepwise program refinement techniques can be used to simplify program verification. Programs are better understood since their main properties are clearly stated, and verification of rather complex algorithms is reduced to proving simple statements connecting successive program specifications. Additionally, it is easy to analyse similar…

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…

The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting of nineteen prospective mathematics teachers. The data were collected from the video records of…

In recent years, a considerable number of teachers in Spain have been using DERIVE to teach math subjects in High Schools and Universities. This software has been used by the authors of this work as a support tool in Mathematics courses for Engineering. Since Texas Instruments does not support DERIVE, we were faced with finding an alternative…

This article begins with a comparison of two groups of teachers, working on the same tasks in Analytic Geometry. One group has only basic experience in CAS-assisted problem solving, and the other group has extensive experience. The comparison is discussed in terms of the interplay between reflection, operative knowledge and execution. The findings…