CADGME 2018 SPECIAL ISSUE
Guest Editors: Csaba Sárvári and Zsolt Lavicza
From editorial: “This issue of IJTME contains papers presented at the Seventh CADGME Conference on Digital Tools in Mathematics Education that organised in Coimbra, Portugal in June, 2018. The original name of the conference was Computer Algebra and Dynamic Geometry Systems in Mathematics Education, this is the source of the acronym CADGME, but the range of tools emerged in mathematics teaching and learning encouraged us to widen the scope of the conference and alter its original title. Similarly as at previous CADGME conferences, our seventh meeting mainly created a forum for Central and Eastern European colleagues and connected them with all interested academics from around the globe, making it possible to exchange ideas and nurture collaboration.
The participants were then invited to submit their papers to the International Journal for Technology in Mathematics Education (IJTME), and this issue presents seven papers. IJTME was chosen because of its aim and scope of the journal “IJTME exists to provide a medium by which a wide range of experiences in the use of computer software and hand-held technology in mathematics education can be presented, discussed and criticised so the best practice can be assimilated into the new curricula of schools, colleges and universities”.”
Peer Review Methodology in a Blended Course for Mathematics Teacher Education
By Umberto Dello Iacono1, Anna Pierri, Eugenia Taranto
In the last years, the interest of mathematics educators in digital tools has progressively increased, having as consequence a great impact on how teachers plan their teaching activities. In this paper we investigate, by using the Meta-Didactical Transposition, if the peer review methodology, carried out in a blended course, can facilitate the teachers as instructional designers. The aim of the metadidactical praxeologies put in action by the trainers was focused on the sharing and reflection with the teachers on a specific topic relative to the argumentative competence. A qualitative analysis of the educational activities produced by the teachers has shown that the peer review methodology enables the teachers to improve their role of the instructional designer.
An Engineering Technology Problem-Solving Approach for Modifying Student Mathematics-Related Beliefs: Building a Robot to Solve a Rubik’s Cube
By Jose M. Diego-Mantecón, Óscar Arcera, Teresa F. Blanco, and Zsolt Lavicza
This paper shows an alternative to the traditional teaching approach, focusing on the application of a STE(A)M-based learning methodology. In particular, we present an engineering technology problem-solving approach to encourage and motivate the mathematics learning of high
school students by promoting positive beliefs about this subject. We report on qualitative data from a group of seven students and two teachers, who developed high-tech engineering projects during a two-year period, applying mathematical concepts and procedures. This data is part of a quasi-experimental study carried out with more than one hundred Spanish students. The findings revealed that solving
problems in an engineering technology context helps to develop a practical sense of the applicability of mathematics, generating students’ positive beliefs about this discipline.
Investigation and Visual Explanation in Dynamic Geometry Environment
By Mária Kmetová, Renáta Vágová and Tibor Kmet
Dynamic geometry environment allows us to investigate geometric relationships and problems more efficiently than the pencil-and-paper method. Continuous variation of geometric configurations shows the relationship from different points of view. This paper aims to provide some indications of how a dynamic geometry environment, especially GeoGebra software, can be used to offer insight and support understanding of geometry problem solving and proofs through investigation and experimentation. Our case studies show in particular how prospective teachers of mathematics deal with difficult geometry problems, designated initially to mathematically gifted students for competition, using investigation in GeoGebra. We attempt to reveal the prospective teachers’ consideration systematically when they are solving a geometric problem. The prepared visual explanation and visual proof steps serve as clues or scaffolding to facilitate geometric problem solving, and they can be useful also for mathematics teachers in preparing their students for mathematics competitions.
Enhancing Kuwaiti Teachers’ Technology-Assisted Mathematics Teaching Practices
By Mamdouh Soliman, Zsolt Lavicza, Theodosia Prodromou, Maryam Al-Kandari and Tony Houghton
This paper outlines results of the first cycle of a mathematics education project in Kuwait aimed to integrate technology into teaching and learning in Kuwaiti schools. The project design and methods are based on two previous studies carried out in Cambridge, UK and the Geomatech project in Hungary. Studies showed that adequate preparation of teachers is necessary to have impact on students learning with
technology. In the first cycle of this project we carried out an extensive teacher training to introduce practices and resources with the GeoGebra application and materials developed in the Geomatech project. The research design was based on Design Experimental and Community of Practice approaches involving the close collaboration of teachers and researchers to jointly develop resources and pedagogies. In this paper, we will offer an outline of the study design and the frameworks based on previous projects as well as highlight some initial findings from interviews conducted in the first cycle of the project.
Designing Tasks Supported by GeoGebra Automated Reasoning Tools for the Development of Mathematical Skills
By Tomás Recio, Philippe R. Richard and M. Pilar Vélez
This paper reflects on the design of tasks that could take profit from the new features for Automated Reasoning, recently available in the dynamic geometry program GeoGebra. We report on some ongoing experiment, involving initial mathematics teacher students, aiming to develop and evaluate the characteristics of tasks that, with the concurrence of these new tools, could guide the student to enhance investigating, conjecturing and discovering geometric properties on a given construction.
Geometrography in Dynamic Geometry
By Vanda Santos, Nuno Baeta, and Pedro Quaresma
Geometrography, “alias the art of geometric constructions” was proposed by Émile 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 simplicity and exactitude; teach the simplest way to execute an assigned construction; allow the discussion of a known solution to a problem and eventually replacing it with a better solution; compare different solutions for a problem, by deciding which is the most exact and the simplest solution from the point of view of geometrography. Since then some authors proposed different approaches and perspectives to the study of geometrography. In this article the extrapolation of geometrography to the new tools of dynamic geometry systems is presented and its application to education is foreseen.
Subject-Specific Components in Dynamic Geometry Software
By Djordje Herceg, Davorka Radakovic, Dejana Herceg and Vera Herceg Mandic
Computer-aided visualization provides meaningful insight into geography teaching, which helps improve comprehension. With dynamic geometry software (DGS), a teacher can easily create interactive mathematical learning materials. To fully benefit from DGS applied to subjects other than mathematics, their functionality must be extended with features which are inherent to those subjects. We demonstrate
how a DGS, extended with components, can be applied to geography teaching. For this purpose we have developed SLGeometry, an experimental platform for dynamic geometry, which supports extensibility via components. Through experiments, we confirmed the benefits of our approach in practice.