Reflexiones sobre la calidad en didáctica de la matemática

Se presentan unas notas (para su ulterior desarrollo en el Simposio) relativas: a) a las dificultades genéricas para establecer conceptos de calidad en Didáctica de la Matemática, b) a Ias dificultades propias del contexto socio-académico en el que se han de considerar tales conceptos, c) a un catálogo de tareas pendientes para establecer y afianzar algunos parámetros de calidad

Deciding geometric properties symbolically in GeoGebra

It is well known that Dynamic Geometry (DGS) software systems can be useful tools in the teaching/learning of reasoning and proof. GeoGebra 5.0 was recently extended by an Automated Theorem Prover (ATP) subsystem that is able to compute proofs of Euclidean geometry statements. Free availability and portability of GeoGebra has made it possible to harness these novel techniques on tablets, smartphones and computers. Then, we think it is urgently necessary to address the new challenges posed by the availability of geometric ATP?s to millions of students worldwide

Criterios de calidad en Didáctica de la Matemática

Some remarks are presented, concerning: 1. the generic difficulties arising in order to establish quality concepts and criteria in the realm of Mathematics Education, 2. the intrinsic difficulties to achieve this task within the Spanish socio academic context, 3. a catalog of tasks required to establish and to strengthen some quality parameters that might be of use, in particular, by the officers in charge of scientific evaluation. These issues are analyzed taking into consideration, as a reference, the case of Mathematical Sciences. The reasons for this choice are detailed and discussed in the document

On the Unavoidable Uncertainty of Truth in Dynamic Geometry Proving

The aim of this note is to discuss some issues posed by the emergency of universal interfaces able to decide on the truth of geometric statements. More specifically, we consider a recent GeoGebra module allowing general users to verify standard geometric theorems. Working with this module in the context of Varignon’s theorem, we were driven – by the characteristics of the GeoGebra interface– to perform a quite detailed study of the very diverse fate of attempting to automatically prove this statement, when using two different construction procedures.We highlight the relevance –for the theorem proving output– of expression power of the dynamic geometry interface, and we show that the algorithm deciding about the truth of some –even quite simple– statements can fall into a not true and not false situation, providing a source of confusion for a standard user and an interesting benchmark for geometers interested in discovering new geometric facts

Computing envelopes in dynamic geometry environments

We review the behavior of standard dynamic geometry software when computing envelopes, relating these approaches with the various definitions of envelope. Special attention is given to the recently released version of GeoGebra 5.0, that implements a recent parametric polynomial solving algorithm, allowing sound computations of envelopes of families of plane curves. Specific details on this novel approach are provided in this paper

Using Maple's RegularChains library to automatically classify plane geometric loci

We report a preliminary discussion on the usability of the RegularChains library of Maple for the automatic computation of plane geometric loci and envelopes in graphical interactive environments. We describe a simple implementation of a recently proposed taxonomy of algebraic loci, and its extension to envelopes of families of curves is also discussed. Furthermore, we sketch how currently unsolvable problems in interactive environments can be approached by using the RegularChains library

Using Automated Reasoning Tools in GeoGebra in the Teaching and Learning of Proving in Geometry

ABSTRACT: 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 examples of the use in the classroom of such commands are provided, including one describing how intuitive handling of GeoGebra automated reasoning tools may result in unexpected outputs. In all cases the emphasis is made in the potential utility of these tools as a guiding stick to foster student activities (exploration, reasoning) in the learning of elementary geometry. Moreover, a collection of appendices describing other, more sophisticated, low-level GeoGebra tools (Prove, ProveDetails), as well as instructions on how to obtain the translation of GeoGebra commands into other languages, and details about debugging, are included.Work partially supported by the grant MTM2017-88796-P from the Spanish MINECO and the ERDF (European Regional Development Fund)

Paradigmas en la Educación Matemática para el siglo XXI: Compartiendo experiencias educativas con Asia

Con este nombre se ha celebrado en Valencia, durante los días 22 a 24 de octubre de 2009, un Simposio, organizado por Casa Asia y el CSIC (vía el Instituto de Ciencias Matemáticas, ICMAT) y patrocinado por el Ayuntamiento de Valencia, i-MATH y la Fundación Asia-Europa, cuyo objetivo ha sido conocer, compartir y comparar experiencias sobre la educación matemática en España y Asia