1: Douglas McDougall and Zekeriya Karadag. Mathematical thinking in techno-mathematical environments

Abstract. Techno-mathematical environments are designed for learning and studying mathematics. Mathematical thinking is a cognitive process associated with the use of mathematics as a cognitive tool. This cognitive tool could vary from paper and pencil to the most sophisticated software such as GeoGebra.

We are interested in exploring and understanding the implications and challenges of mathematical thinking by using contemporary cognitive tools. We also interested in contributions of techno-mathematical environments to mathematics education and mathematical thinking. We would like to have opportunities to collaborate with international research to address these research topics.

8 (A): Tomas Recio and Rafael Losada. Bisectors and Cubes

Abstract. An intriguing (and old) problem in elementary geometry deals with deciding when a triangle will have two or three angle bisectors of equal length.  A second problem we will consider is the simulation, with GeoGebra, of the flexibility of a bar-joint cube. We will show how both problems can be solved through a combination of symbolic computation and some "ad hoc" GeoGebra tools.

Moreover, both problems (and solutions) could be considered as mere instances of more elaborated proposals that we would like to present to the consideration of this Working Group, as potentially interesting for future developments of GeoGebra. One is about including theorem discovery features; the other supports the specific interest and peculiarities of the 3D extension.

Work partially supported by ECP 2006 EDU 410016 Intergeo and ALGORITMOS EN GEOMETRIA ALGEBRAICA DE CURVAS Y SUPERFICIES (MTM2008-04699-C03-03)

9: Katarzyna Winkowska-Nowak. GeoGebra stimulates education

Abstract. One of the most important sign of our times is constant change. This is especially true in a field of ICT and in the field of education. Teachers have to become learners for life if they want to follow the changes and challenges of modern society.

GeoGebra is a perfect example of a phenomenon which help create communities of active, ever leafing teachers. First it is a perfect tool for exploration in mathematics and sciences.  It brings enthusiasm at all levels: in university faculty, students, teachers and pupils. The ideas behind the GeoGebra: Forums, Wikis, communities, shearing the resources and training help to organize around the enthusiasm.

I will talk in my short presentation of possibilities which GeoGebra gives both to researcher, teacher and to a person who organized teachers association with aim of bringing ICT to Polish schools.

Submission #9

22: Jan Guncaga and Janka Majherova. Some possible local and international research projects in GeoGebra

Abstract. In this article we describe some project possibilities for research and application of GeoGebra in education. In order to do this, we use open information sources from different projects’ programs from the Internet. Moreover, we present our own experiences with the implementation of projects, which aim at education of teachers.

Submission #22

37: Sanela Mehanovic. Integral calculus in GeoGebra based learning environment

Abstract. Integral calculus

Students’ concept development in a learning environment based on the dynamic software GeoGebra

Submission #37

41: Mats Brunström and Maria Fahlgren. GeoGebra A Tool to Create Favorable Learning Situations with Emphasize on  Logical Reasoning and Communication

Abstract. Logic reasoning and communication are general competencies, important in all areas of mathematics. We think that one of the major advantages of GeoGebra is the possibility to create favorable learning situations for these competencies. We would like to investigate these possibilities. Our main interest is to find out how students use logic reasoning and how they communicate when they work in pairs with GeoGebra. We think that investigating the validity of certain geometrical statements is a kind of task appropriate for this purpose.

Submission #41

46: Carlos Giménez Esteban. Our experience in Catalonia

Abstract. Since early 2008 I've been involved in the inception and creation of the Associació Catalana de GeoGebra, the local IGI Institute in Catalonia (Spain), so I’m here to share our short experience with the members of this discussion group, and also to get your feedback in this field.

According to Markus’s idea, the main goals of our organization are focused in spreading the use of GeoGebra in our community, carrying out workshops, seminars, courses and other activities that may lead to a viral growth of the use of computer aided technologies in our teaching activity.

We are also studying different ways of promoting our association, starting with the creation of a Moodle based environment (http://acGeoGebra.cat) and following up with the publication of a periodical bulletin in the near future.

On the other hand, we must face the main problem related to small associations, which is searching for funding opportunities to enable us to develop our projects.

Finally, I think that this first International GeoGebra conference may offer local institutes the possibility of establishing a certain kind of collaborative (net)work among them, with the aim of generating positive synergies.

Submission #46

54: Sevinc Gulsecen, Zerrin Ayvaz-Reis and Murat Tas. Future Learning Conference 2010 and GeoGebra: Collaboration for the future

Abstract. Istanbul University, one of the leading universities in Turkey, has organized three conferences to explore the features of computer based education and online learning environments. We are going to organize the fourth of this series, Future Learning Conferences, in May 2010.

GeoGebra provides promising opportunities to learn algebra and calculus. Its dynamic and open source characteristics make the software more valuable. In order to discuss possible opportunities to collaborate and to seek possible research topics, we would like to participate in the First GeoGebra Conference in Austria. On behalf of organization committee of Future Learning Conference 2010, we would like to discuss the opportunities to organize a pre- or post-conference workshop with a focus of GeoGebra.

In addition, Istanbul University is going to launch a distance education program, which consists of mathematics courses. We would like to discuss how we can integrate GeoGebra into the curriculum of our online program. Moreover, we would like to be more than happy if we can develop a research agenda in the First GeoGebra Conference.

58: Tolga Kabaca, Yilmaz Aksoy and Ibrahim Bayazit. Ideas of GeoGebra Institute of Turkey

Abstract. I want to mention about brief history of our GeoGebra institute of Turkey: Our institute has been established at the beginning of the 2009. Our all members have a PhD degree in Math Education and all of us have already studied on using technology to teach math. We have used Maple dominantly to teach math and in our research studies. GeoGebra is new software for our country as in world. The first presentation was done in 2006 by the Turkish academicians, who are also translators of GeoGebra into Turkish, Mustafa DOGAN and Erol KARAKIRIK. We thank them to introduce us to GeoGebra.

Although Maple is a very strong symbolic tool, we had lived some difficulties during our studies;

• Our elementary students’ ability of using English is not sufficient to use Maple efficiently as most of our teachers.
• We need to organize a serious training session of using Maple, because Maple does not work dynamically between geometry and algebra. So the user must learn most of the codes to start using.
• Maple is very expensive because of its commercial characteristic. This is a very important obstacle to make it widely usable in teaching.

GeoGebra is very good alternative using technology widely in our math classes. This is the reason why we decided to study on GeoGebra. I want to summarize our several studies on GeoGebra from the beginning of 2009;

• First, we started to study on converting our previous studies into GeoGebra environment. By this way, we aimed to develop our GeoGebra knowledge and ability.
• We used GeoGebra in teacher education in our university departments. Students of GeoGebra courses learned how to use GeoGebra. Then, they developed dynamic worksheets and web pages for teaching mathematics at secondary school levels. They linked real life situations to mathematical concepts in their worksheets. According to their responses they found GeoGebra helpful tool for mathematics education. For answering questions of Turkish GeoGebra users in forum, Markus helped us for opening a section in GeoGebra User Forum. After that, we used this forum for sharing and discussing ideas.
• We used GeoGebra in our math education courses. After teaching pre-service teachers how to use tools of GeoGebra, we taught them how to develop dynamic materials for teaching mathematics in the classes. They used the developed materials at 6th -8th classes to see the effects of them on the students’ learning mathematics. By this way they experienced the use of dynamic materials in the classes.
• First formal organization was in April as a workshop in The First International Congress of Educational Research Association in Canakkale. Almost all math educator and people, related to math education, participated to our workshop. Almost all participants have used GeoGebra in our workshop. Especially, teacher participants ask us to organize a training session in their schools.

One of our near plans for GeoGebra was organizing GeoGebra workshops in some cities of Turkey for the math teachers in various levels. We need financial support to carry out this project.  We may use European grants for this purpose. An international relationship can be constructed in an EU project. We are all ready to establish this kind of project as GeoGebra Institute of Turkey.

61: Peter Kortesi. GeoGebra Institute of Miskolc

Abstract. Structure of GeoGebra Institute

Our Hungarian GeoGebra Didactical Research Group will function in the framework of the Hungarian Mathematics Learning Centre established through the European Virtual Laboratory of Mathematics Leonardo project, and will be hosted by the Department of Analysis of the University of Miskolc

People of GeoGebra Institute

• Péter Körtesi (matkp@uni-miskolc.hu, pkortesi@gmail.com) chair, coordinator of the EVLM project, and founder of the series of European Computer Algebra Driving Licence Summer Universities in the CEEPUS Network HU- 0028 – leader of the Didactical research in using GeoGebra, organizer of workshops.
• Jeno Szigeti (matjeno@uni-miskolc.hu, jenoszigeti@yahoo.com), chair of the Department of Analysis, expert in Algebra, developing materials in Discrete Mathematics.
• Sándor Radeleczki (matradi@uni-miskolc.hu), expert in Ordered structures, developing materials in Analysis and Discrete Mathematics.
• Imre Juhász (JuhaszI@abrg.uni-miskolc.hu), chair of the Department of Descriptive Geometry of the University of Miskolc, expert in Geometric visualisation, developing the theoretical background of Geometry applets
• Laura Veres (lauracicu@freemail.hu), part time teaching assistant, PhD student, developing materials

External collaborators

Pellumb Kllogjeri, University of Elbasan (kallogjeri5162@yahoo.co.uk) PhD student of the University of Debrecen, scientific advisor Péter Körtesi, planning his research and thesis in the applications of GeoGebra. 

László Daróczi, (daroczy4@freemail.hu) undergraduate student, developing and testing materials. Attila Hajdú, (rawfl@freemail.hu) undergraduate student, developing and testing materials.

Péter Madarász, (pmadarasz@chello.hu) secondary school teacher, deputy director of the Herman Grammar School.

Pál Veres, (veres@ffg.sulinet.hu) secondary school teacher, director of the Földes Grammar School.

Activities and Goals of GeoGebra Institute

We plan to develop a student project data- base, available to all partners through the European Virtual Laboratory of Mathematics (EVLM) project, and even to a larger cooperation. The wise use of the available Internet based educational technology, computer based teaching materials and computer algebra software, without reducing the students’ mental contribution is important to promote the good learning skills. Individual and group projects are meant to catalyse the usual didactical methods, and increase their efficiency. In the EVLM project we have created a network including the 9 partners, and we offer a portal each university with teaching materials, and software description. The portal will last longer, and we plan to develop it (http://www.uni-miskolc.hu/evml/). One of the most intensive directions for developing is the dissemination of the use of GeoGebra. This is the site where the files we produce appear (http://www.uni-miskolc.hu/evml/geogebra/).We will continue the international cooperation of educators in exchanging of experience in mathematical education to promote the recent methods in tutorials and lectures, due to CEEPUS (Central European Exchange Programme for University Studies) and Leonardo projects, and partners working in grammar schools, and vocational schools in the area of the University of Miskolc. Increasing the participation of teachers and students in meetings organized by the partners we will attract student communities in the use of GeoGebra and their teachers in research.

The European Computer Algebra Driving Licence (ECADL) is a future project, based on a series of summer universities with the same title. The idea was made up in international cooperation in the Active Methods in Teaching and Learning Mathematics CEEPUS Network (Hu- 028), coordinated by Péter Körtesi, University of Miskolc, and involving 18 partner universities from 13 countries. We do want to teach students the basic, intermediate and professional level of using CAS. We plan to include the presentation of GeoGebra as part of curriculum in the basic level course. The ECADL activities end up with a certificate named European Computer Algebra Driving Licence - which will be accepted as partial study form. We plan to elaborate the intermediate level and advanced level of the ECADL, to be extended to a set of joint courses, involving the courses with appropriate content available at the partners. We plan to continue to organize the Intensive Course/ Summer University in the topic of the ECADL - Right use of computer algebra software in learning Mathematics, and we will include in it the GeoGebra software in more extent. As concerning our plans, we plan to develop materials in teaching and learning mathematics for the university, to do didactical research on the methodology to apply in teaching, and collaborative learning the software. We do plan to offer teacher and student training for the use of the software. We teach computer science students as well, and we plan to contribute in developing the software as well.

66: Douglas McDougall, Dragana Martinovic, Viktor Freiman, Oana Radu, Daniel Jarvis and Zekeriya Karadag. First Canadian GeoGebra Competition

Abstract. This proposal is about the First Canadian GeoGebra Competition, which will be announced at the Canadian Mathematics Society (CMS)2009 Winter Meeting and to be held at the University of Windsor, Ontario.

In the conference, we would like to seek for opportunities to collaborate with the other GeoGebra Institutes to facilitate and obtain funding for an International GeoGebra Competition.

Submission #66

67: Douglas McDougall, Dragana Martinovic, Viktor Freiman, Oana Radu, Daniel Jarvis and Zekeriya Karadag. GeoGebra Institute of Canada (GIC)

Abstract. This paper shares the experiences we had during the establishment process of Canadian GeoGebra Institute.

Submission #67

72: Markus Hähkiöniemi. INVESTIGATIVE MATHEMATICS WITH GEOGEBRA

Abstract. I present a research plan on how a carefully designed teaching-learning sequence, which includes GeoGebra activities, supports teachers’ and students’ investigative mathematical work. The mathematical topic of the teaching-learning sequence is numerical approximation of the definite integral.

Submission #72

91: Mark Dabbs. The Sheffield Hallam University GeoGebra Institute

Abstract: As the UK's first local GeoGebra Institute we submit an overview of our proposed activities and goals and the staff involved in the project.

Submission #91

XX: Akihito Wachi

Submission Wachi

XX: Sigbjorn Hals

Submission Hals 1: Project Description

Submission Hals 2: Conference Notes