The aim of this study is to explore how structural and process aspects of secondary school students' mathematical reasoning support each other in a collaborative learning environment through the integration of "GeoGebra" software and the ACODESA method. The study involved four eighth-grade secondary school students, who participated in…

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these…

Logical statements are prevalent in mathematics, science and everyday life. The most common logical statements are conditionals, 'If H … , then C … ', where 'H' is a hypothesis and 'C' is a conclusion. Reasoning about conditionals depends on four main conditional contexts (intuitive, abstract, symbolic or counterintuitive). This study tested a…

In this article, the authors present the use of digital tape diagrams--implemented using GeoGebra (2001) dynamic mathematics software--as a support to static diagrams to pose and solve proportional reasoning tasks. They show how dynamic sketches can allow students to explore standard tasks in proportional reasoning in ways that emphasise…

Proving in school geometry is not just about validating the truth of a claim. In the school setting, the main function of the proof is to convince someone that a claim is true by providing an explanation. Students consider proving to be difficult; in fact, they find the very concept of proof demanding. Proving a claim in planar geometry involves…

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a…