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.
Synthetic Proof with the Support of Dynamic Geometry
By Jirí Blažek and Pavel Pech
The paper deals with searching for synthetic solution supported by the means of dynamic geometry. It consists of two parts. The first one describes how software influences searching for synthetic solutions of geometric problems. The second one describes a small pilot experiment in which students of Faculty of Education solved two more difficult tasks of secondary school level. Obtained results demonstrate that the software (GeoGebra) helped considerably, nevertheless many students had troubles with choosing and applying relevant mathematical theorems during the proving process. A few students did not reach the solution even though they found all relevant facts.
Non-Euclidean Geometry with Art by Means of GeoGebra
By Daniela Ferrarello, Maria Flavia Mammana, Eugenia Taranto
In this paper, a teaching path on non-Euclidean geometry focused on the Poincaré-disk model, and its connection with art is shown. We consider as artistic contents the Escher’s hyperbolic art and some paradoxes on Magritte’s work. The mathematical aspects are illustrated thanks to a Dynamic Geometry System (GeoGebra) implemented with a laboratory methodology in a Vygotskijan perspective. The use of the artefact (the DGS) is crucial to build mathematical concepts starting by artistic objects. The path was experimented with inmates in a high security prison and with University students. Some comments on the first experimentation are given.
Towards a Theoretical Foundation for Quality Tablet App-Enriched Learning Environments in Primary School Mathematics Education
By Ana Donevska-Todorova
There has been much research about tasks and learning environments but not yet sufficient regarding those involving mobile technologies for mathematics education. This paper discusses the quality of the expanding amount of tablet applications for primary school mathematics and their eloquent integration in student-centred learning environments (LE). It argues that students’ engagement in LE with tablet apps does not necessarily start with a particular a priori task designed within the LE and through a task-format, as by now reported in literature. An engaging design of touchpad apps may rather encourage explorative activities leading towards a single task formulation and its solution as a result of that process. The paper further aims at framing essential characteristics and potentials of environments enriched with tablet-apps in three main categories: mathematical and curricular meaning, didactical aspects and technical matters. Setting the focus on the didactical potentials of tablet-apps, the overarching categories are further specified finalizing with six categories: (1) mathematical contents and relation to curriculum, (2) communication, collaboration and cooperation, (3) differentiation, (4) feedback and assessment, (5) connections and networking and (6) logistics, obtained through the grounded methodological approach in a theoretical model. The suggested model should also adequately represent the development of task, task-format and LE in it. Additionally, a descriptive case study for illustrating the theoretical model for design and analysis of potentials of tablet apps for elementary geometry is also offered. The proposed model may be meaningful for teachers’ decision making when selecting and implementing touchpad-apps in their instructional practices but also for developmental surveying of existing apps, their re-designs and further novel designs involving identified potentials.
Development of Mathematics Items with Dynamic Objects for Computer-Based Testing Using Tablet PC
By Fumiko Yasuno, Keiichi Nishimura, Seiya Negami and Yukihiko Namikawa
Our study is on developing mathematics items for Computer-Based Testing (CBT) using Tablet PC. These items are subject-based items using interactive dynamic objects. The purpose of this study is to obtain some suggestions for further tasks drawing on field test results for developed items. First, we clarified the role of the interactive dynamic objects on each item, according to the problem-solving process. Then, we conducted the field tests with Japanese high school students. As a result, we identified possible improvements in item design. For example, we had some questions that cannot be asked in Paper-Based Testing (PBT), there is a possibility to evaluate the mathematical competencies more in detail according to the process, and so on. Here we shall show a few examples. Finally, we hope to make a contribution that might inform assessments and examinations to support progression between secondary school and tertiary education.
Exploring Essential Aspects when Technology-Enhanced Flipped Classroom Approaches are at the Heart of Professional Mathematics Teacher Development Courses
By Robert Weinhandl and Zsolt Lavicza
Recently, the idea of the Fourth Industrial Revolution (FIR) is increasingly shaping discussions about the world of work and society. In order to prepare the next generations for such new developments, it is necessary to adjust the way they learn. One possibility for a change in education is Flipped Classroom Approaches (FCA), which are particularly helpful in mathematics education. The aim of our research is to identify essential pillars for teachers, when they are being familiarised with FCA. Therefore, we have chosen a research method that integrates various approaches and diverse data sources. The data from a first sequence of expert interviews indicate, that regulatory changes, the recognition of one’s own learning and its added value, as well as being a member of a learner group are crucial in those cases, where the topic of teacher training utilise both student-centred and technology-enhanced forms of learning. Thus, it would be necessary to modify in-service teacher training in Austria and beyond to utilise FCA.
The Using of Monte Carlo Simulation in the Teaching Process
By Blanka Šedivá
The Monte Carlo method is one of the basic simulation statistical methods which can be used both to demonstrate basic probability and statistical concepts as well as to analyse the behaviour stochastic models. The introduction part of the article provides a brief description of the Monte Carlo method. The main part of the article is concentrated on three practical exercises that demonstrate advantages of the Monte Carlo approach in several parts of mathematics. The exercises are proposed for university courses but can be used also as an advanced application on secondary math school. The first example is focused on the classical use of the Monte Carlo method for calculating the area of polygons, the second and third examples are directed to the application of the Monte Carlo method for demonstrating the basic properties of different types of statistical estimations.
Interdisciplinary Relations Supporting Propaedeutics of Mathematics in Primary Education
By Dagmar Jordánová, Helena Koldová, Vladimíra Petrášková and Přemysl Rosa
This paper presents a way of utilizing interdisciplinary relations between two educational branches, Mathematics and its applications and Information technologies (ICT) in integrated learning by the use of the Scratch programming language. The authors also present how they understand the concept of integrated learning and why they have chosen to integrate mathematics and programming in Scratch. The situation regarding state testing in the Czech Republic and its outputs, which had been the main impulse for why to create presented activities, will be outlined. The main part of this paper is dedicated to created activities. They focus on topics of geometry and tessellations from the educational branch of mathematics and its application and topics of programming and vector graphics from educational ICT branch. At the end of the article, the authors describe the conducted pilot survey and its outcomes.