Miguel A. Abanades

Miguel A. Abanades
Rey Juan Carlos University | URJC · Economía Financiera y Contabilidad e Idioma Moderno

Ph. D. Mathematics, University of New Mexico, USA

About

31
Publications
8,937
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216
Citations
Additional affiliations
August 1994 - June 1999
University of New Mexico
Position
  • Research Assistant
September 1999 - September 2014
Complutense University of Madrid
Position
  • Professor (Assistant)

Publications

Publications (31)
Article
This cross-national study examined students’ evaluation of strategies for solving linear equations, as well as the extent to which their evaluation criteria were related to their use of strategies and/or aligned with experts’ views about which strategy is the best. A total of 792 middle school and high school students from Sweden, Finland, and Spai...
Article
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Background In this cross-national study, Spanish, Finnish, and Swedish middle and high school students’ procedural flexibility was examined, with the specific intent of determining whether and how students’ equation-solving accuracy and flexibility varied by country, age, and/or academic track. The 791 student participants were asked to solve twelv...
Article
Full-text available
El objetivo de este artículo es presentar y justificar el diseño de POEMat.ES, una pauta de observación de acciones del profesor de matemáticas en clase. POEMat.ES ha sido desarrollado por un grupo de investigadores con perfiles diversos en cuanto a experiencia docente e investigadora, a fin de sistematizar la observación de la práctica de enseñanz...
Article
Full-text available
Much effort has been put into the implementation of automatic proving in interactive geometric environments (e.g. Java Geometry Expert, GeoGebra). The closely related concept of automatic discovery, remains however almost unexplored. This software presentation will demonstrate our results towards the incorporation of automatic discovery capabilitie...
Conference Paper
Full-text available
Considerable attention and efforts have been given to the implementation of automatic reasoning tools in interactive geometric environments. Nevertheless, the main goal in such works focused on theorem proving, cf. Java Geometry Expert or GeoGebra. A related issue, automatic discovery, remains almost unexplored in the field of dynamic geometry soft...
Conference Paper
Full-text available
A prototype for the automatic discovery and derivation of elementary geometry statements, based on the implementation of computational algebraic geometry methods onto the dynamic geometry program GeoGebra, is presented. The emphasis is placed on the diverse mathematical and educational challenges posed by the—apparently straightforward—application...
Article
Full-text available
A finalidade de este artigo é o de explicitar de forma exacta e completa alguns dos elementos que organizam um espaço de trabalho efectivo para problemas de lugares geométricos em ambientes tecnológicos. Explora-se como 52 futuros professores de matemática progridem na sua concepção de lugares geométricos através da apropriação das funcionalidades...
Article
We present the experience of the authors teaching mathematics to freshmen engineering students with the help of the open source computer algebra system Sage. We describe some teaching resources and present an ad hoc distribution of Sage used by the authors. Comput Appl Eng Educ © 2012 Wiley Periodicals, Inc.
Article
The automatic determination of geometric loci is an important issue in Dynamic Geometry. In Dynamic Geometry systems, it is often the case that locus determination is purely graphical, producing an output that is not robust enough and not reusable by the given software. Parts of the true locus may be missing, and extraneous objects can be appended...
Article
Full-text available
IntroductionThere is no doubt about the prevalence of dynamic geometry (DG) as the preferred technological tool among math teachers. DG systems are tools for geometric visualization that allow users to construct geometric elements and establish relationships among them. The key property of DG is that the system automatically updates the whole geome...
Conference Paper
Full-text available
We describe here a properly recent application of the Gröbner cover algorithm (GC) providing an algebraic support to dynamic geometry computations of geometrical loci. It provides a complete algebraic solution of locus computation as well as a suitable taxonomy allowing to distinguish the nature of the different components. We included a new algori...
Article
A symbolic tool based on open source software that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction is presented. The prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric constructi...
Conference Paper
Full-text available
An enhancement of the dynamic geometry system GeoGebra for the automatic symbolic computation of algebraic loci and envelopes is presented. Given a GeoGebra construction, the prototype, after rewriting the construction as a polynomial system in terms of variables and parameters, uses an implementation of the recent Gr\"obnerCover algorithm to obtai...
Article
Full-text available
We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction. In one worksheet, diagr...
Article
Dynamic Geometry, also known as Interactive Geometry, refers to computer programs where accurate construction of (generally) planar drawings can be made. The key characteristic of this software is that dragging certain elements of the configuration, the geometric properties of the construction are preserved. In this paper, we describe an educationa...
Article
This paper presents a Named Entity Recognition (NER) system based on Hidden Markov Models. The system design is language independent, and the target language and scope of the NER is determined by the training corpus. The NER is formed by two subsystems that detect and label the entities independently. Each subsystem implements a different approach...
Conference Paper
This paper describes some examples of fruitful cooperation between geometric software tools (in particular, GeoGebra) and a free open source computer algebra system, Sage (Software for Algebra and Geometry Experimentation). We collect some of our efforts for enhancing mathematics education via technologically rich environments. We show that a math...
Article
Full-text available
Resumen Sage es un software que nos permite experimentar con las matemáticas. Gratuito y de código abierto, constituye la apuesta más novedosa para utilizar las TIC en nuestro ámbito. La integración de múltiples herramientas, la posibilidad de acceso remoto por Internet y el énfasis por la decencia y la libertad conforman sus más notables caracterí...
Article
A Dynamic Geometry System (DGS) is a computer application that allows the exact drawing and dynamic manipulation of geometric constructions. DGS have been the paradigm of new technologies applied to Math education, but some authors have claimed that some symbolic capabilities should be added to this systems. We present an example of communication b...
Article
Full-text available
While GeoGebra can work wonders illustrating geometric properties, these can seldom be justified and become no more than visual proofs. Adding symbolic capabilities to GeoGebra would allow not only to prove known results, but also to discover new properties in a mathematically sound way. Botana and Valcarce developed their own DGS (named GDI, see (...
Conference Paper
Full-text available
In this paper we describe the ongoing effort to specify a com- mon file format for Interactive or Dynamic Geometry Systems (DGS). Our approach is based on the OpenMath standard, and uses its flexible extension mechanisms like Content Dictionaries. We discuss the various design decisions, the Content Dictionaries that have been defined, as well as o...
Conference Paper
Full-text available
GLI (Geometric Locus Identifier), an open web-based tool to determine equations of geometric loci specified using Cabri Geometry and The Geometer’s Sketchpad, is described. A geometric construction of a locus is uploaded to a Java Servlet server, where two computer algebra systems, CoCoA and Mathematica, following the Groebner basis method, compute...
Conference Paper
A prototype for a web application designed to symbolically process locus, proof and discovery tasks on geometric diagrams created with the commercial dynamic geometry systems Cabri, The Geometer’s Sketchpad and Cinderella is presented. The application, named LAD (acronym for Locus-Assertion-Discovery) and thought of as a remote add-on for the consi...
Article
Let X be a reduced nonsingular quasiprojective scheme over ℝ such that the set of real rational points X(ℝ) is dense in X and compact. Then X(ℝ) is a real algebraic variety. Denote by H k alg (X(ℝ),ℤ/2) the group of homology classes represented by Zariski closed k-dimensional subvarieties of X(ℝ). In this note we show that H 1 alg (X(ℝ),ℤ/2) is a p...
Article
We show that the ring of bounded meromorphic functions on an irreducible compact real analytic set of dimension d is a Prüfer domain of dimension d. Consequently, every finitely generated ideal in this ring can be generated by d+1 elements, and we show that this bound is sharp.
Article
Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.

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