This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with…

We present a case study of proving by three 12-13-year-old students with different levels of mathematical giftedness. After analysing students' proofs, we conclude that: there was a relation on the consistency and the students' levels of mathematically giftedness, being the least consistent the student not mathematically gifted and the most…

In this work, we show the results of a research with pre-service mathematics secondary teachers about their Van Hiele level regarding the proof in Geometry. We observe three different profiles whose characteristics are described. These descriptions allow us to foresee certain differences when carrying out proof teaching in secondary school. The…

Proof and argumentation are essential components of learning mathematics, and technology can mediate students' abilities to learn. This systematic literature review synthesizes empirical literature which examines technology as a support for proof and argumentation across all content domains. The themes of this review are revealed through analyzing…

In this paper we present the process of constructing a test for assessing student performance in geometry corresponding to the first year of Secondary Education. The main goal was to detect student errors in the understanding of geometry in order to develop a proposal according to the Van Hiele teaching model, explained in this paper. Our research…

The present study tries to identify the "picture in mind" that students' have about defining, proving and modelling. We access to it through external representations of their mental representations; in particular, from the way in which these representations are expressed in written form (sentences and situations). In the study we have…

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…

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…