7: J. Benito Bua. Researcher students

Abstract. Notebooks of Mathematics aims the students carry out small researches where they use their knowledge about Mathematics and, if it is necessary, they obtain new knowledge.

The works were always done by volunteers and most of the students carried out the work in their free time.

Submission #7

 

11: Jostein Vage. Summary

Abstract. Summary of ideas

General: GeoGebra is already a formidable tool with a wide area of application. As a teacher educator I realized its potential nearly at first sight. Since then great developments have taken place, and it is still making progress at an amazing rate. The previous software packages, graph-plotter and dynamic geometry system, were replaced by GeoGebra in the courses I gave at the teacher training institution and courses offered to teachers in upper and lower secondary schools,. The combination of algebra and geometry in one system soon proved to be valuable. I now look forward to see the addition of a computer algebra system in the same package.

Areas of application

Problem solving has a high priority in mathematics teaching in Norwegian schools. This activity is facilitated and enhanced by using GeoGebra. Students can experiment and explore, search for common elements, make conjectures which they afterwards may try to verify. One example where GeoGebra can be a great help, is in looking for and investigating loci. A locus for points having equal distances from a point and from a straight line is well known, but what if the locus of points were having equal distances from a straight line and a circle. In fact it could be a of interest to study all the combinations of point, line and circle: Point/point, point/line, point/circle, line/line, line/circle, circle/circle. Some of these are well known like point/point giving the well known perpendicular bisector and some are trivial like line/line resulting in angle bisector for intersecting lines and a new parallel line if the original lines are parallel. Anyway, students in secondary school find investigations of this sort interesting, they get acquainted with ordinary mathematical working methods, and hopefully they will acquire new mathematical knowledge.

Extensions of GeoGebra

I look forward to the inclusion of the two new mathematical fields which have been mentioned: Computer algebra system and 3D-geometry. GeoGebra will then cover nearly all our needs of IT-assistance in the teaching and learning of mathematics in secondary schools.

Wanted: Finally a wish: I would have liked being able to enter functions without using functional parentheses so that sin(x) and ln(x) could be written as sinx and lnx as implemented in for example the CAS Derive 6.

I would have liked being able to write both abs(x), |x| for the absolute value of x.

Submission #11

 

16: Alvaro Saenz de Cabezon, Aitzol Lasa and Miguel Wilhelmi. TIME MANAGEMENT IN GEOMETRY TEACHING

Abstract. In this paper, we discussed the following topics related to working group axis:

Collecting information about already existing projects and ideas in the use of GeoGebra in secondary schools;

Developing ideas for future projects;

Encouraging the creation and sharing of instructional resources (e.g., lesson plans, activities, dynamic worksheets, GeoGebra files) to create a usable pool of GeoGebra-related materials for secondary grades;

Submission #16

 

23: Maria Francisca Cabo. Functions with GeoGebra

Abstract. I worked 20 years at Coimbra University, Mathematical Department, and since two years ago I teach at a Secondary school. I had a lot of work to find motivation for children (between 16 and 20) to learn Maths. I started with GeoGebra and I use it usually in my homework, to create dynamical worksheets to put on an e-learning platform (Moodle), basically in what concerns the study of functions. I studied very carefully Linda Fahlberg Stojanovska lessons and they were indeed a very important way to improve my knowledge and to get new ideas for future work.

I start to encourage my colleagues to work with GeoGebra and next September/ December, I will steer a basic course "Mathematics with GeoGebra".

But I know that I'm only a beginner and that there is a lot to learn.

 

25: Djurdjica Takaci. On the use of GeoGebra for examining functions

Abstract. We presents the results of investigations done with the talented high students  in Novi Sad, Serbia.

The students obtain the following questions:

1) Use of the programme package  GeoGebra to show the properties of logarithmic functions.

2) Use of the programme package  GeoGebra to show the properties of exponential functions.

3) Use of the programme package  GeoGebra to show the properties of trigonometric functions

The answers, done with GeoGebra will be presented and analysed.

Submission #25

Resubmission of Paper #25

 

26: Brian Carroll. Using GeoGebra to facilitate the new senior cycle mathematics curriculum in Ireland

Abstract. The Irish second level mathematics curriculum is currently undergoing a major shift in emphasis away from the traditional teaching and assessment procedures. A new initiative entitled 'Project Maths' is being piloted in 24 schools throughout the country, with the intention of all schools participating by September 2010. Project Maths places greater emphasis on student understanding of mathematics concepts, with increased use of contexts and applications that will enable students to relate mathematics to everyday experience. Furthermore there is an increased emphasis on ICT within this approach.

As part of the pilot phase of my research project entitled: “Using Applications to facilitate the transition from Second-level to University mathematics”, I have designed and implemented a teaching intervention which utilises GeoGebra where possible. I intend to discuss some of the material used throughout the intervention, while I will look closely at a real-life problem in the discipline of pool/billiards which can be solved exclusively through GeoGebra.

 

29: Muharrem AKTUMEN, Yilmaz AKSOY and Seref MIRASYEDIOGLU. DEVELOPPING TEACHING MATERIALS FOR 6TH-8TH GRADES BY A DYNAMIC MATHEMATICS SOFTWARE GEOGEBRA

Abstract. A new curriculum of primary education has been put into practice in Turkey since 2005. The new mathematics curriculum supports the use of dynamic geometric softwares and emphasizes the use of concrete models while teaching mathematics. While examining the new 6th-8th grades curriculum we saw two important points:

(I) It is determined that by the use of dynamic geometry softwares students can develop geometric constructions or they can explore interactively the geometric shapes developed by their teacher.

(II) Also it is indicated in the new curriculum that the necessity of the initiation of the teaching and learning process with concrete models. The students learn more meaningfully in the learning environments that the knowledge is represented with concrete models. In the teaching and learning process we have to use cases in which the knowledge is represented in different ways.

GeoGebra is an important teaching tool that maintains the two situations indicated above with its characteristics. We can compile its other characteristics like: it establishes a relation between algebra and geometry, is free of charge, improves continuously, has an open source code, provides mother langue support. The integration of this software can be ensured easily by these characteristics.

In this study a GeoGebra application about the standard “Student can determine the trigonometric ratios of the acute angles in a right triangle” related to “Triangles” sub-section of “Geometry” section of the 8th grades comprising two cases indicated above was presented. By using a model with this GeoGebra application we aimed to bring students in attaining some trigonometric functions. This application can be reached from the following web address: http://w3.gazi.edu.tr/web/aktumen/geogebra/alt%20site/applications.htm

 

31: Valerian N. Antohe. LIMITS OF EDUCATIONAL SOFT “GeoGebra” IN A CRITICAL CONSTRUCTIVE REVIEW

Abstract. Mathematical educational soft explore, investigating in a dynamical way, some algebraically, geometrically problems, the expected results being used to involve a lot of mathematical results. One of such a soft is GeoGebra. The software is free and poly-platform dynamic mathematics software for learning and teaching, awards in Europe and the USA. This paper describes some critical but constructive investigation using the platform for graph functions and dynamic geometry.

Submission #31

 

34: Michael O'Loughlin. Geogebra for secondary school mathematics

Abstract. In this submission I outline how I use GeoGebra as a teaching aid in several topics in secondary school mathematics.

Geogebra is also useful for constructing diagrams when making out notes, tests or worksheets.

Finally I mention a couple of features that I would like GeoGebra to have.

Submission #34

 

73: Wolfgang Pröpper. Working Group Selection

Abstract. I am retired math teacher, engaged in CAS (Derive, TI-Nspire) and have a little experience with GeoGebra but I would like to learn more about that wonderful software.

I would rather be a listener and learner than coming with papers and suggestions.

 

77: Alison Parish. Using GeoGebra in the Primary and Lower Secondary English Curriculum

Abstract. The curriculum in England Wales and Northern Ireland is governed through the National Curriculum and the National Strategies. Using IT within subjects is an expectation, but there according to inspection reports there is an issue in many schools . Schools in the UK have whiteboards in their classrooms however the manner in which they are used ranges from being a modern day blackboard to being used for teacher-instigated interactive activity through the use of commercial, freeware or teacher-produced materials. 

In many schools, non-specialists teach mathematics, particularly in the primary phase. For these teachers to feel comfortable in using any specialist software it need to be straight forward to use, and linked to the curriculum (they are often teaching ten different subjects).  At the present time there is a push to increase the use of IT in the primary phase.

I have looked at the mathematics curriculum from when the pupils first enter school at the age of four and considered how GeoGebra might be used to deliver this as they progress through into the secondary phase, moving from teacher led activity to increasing participation by pupils as they become familiar with the program and mathematical concepts. In my own experience I have found that when pupils are engaged in active learning, such as using GeoGebra, they will develop ideas away from the classroom.

As part of my own research I am looking at how teachers are introduced to, and given experience of, software and whether more effective methods can be developed to encourage them to use more IT in their mathematics lessons, becoming sufficiently confident to let pupils develop ideas and skills outside of the set task or curriculum.

Submission #77

 

81: Mary Rita Manley. GeoGebra Conference 2009

Abstract. I will be new to the use of GeoGebra this coming school year.  It was introduced to us this past year at our school.  I have been using Geometer’s Sketchpad for nine years, mainly in my work with Geometry, and a bit with Algebra.  Because of my familiarity with Sketchpad, I did not make the switch to GeoGebra.  I will be teaching Algebra once again, along with Geometry this coming year.  What I saw with the work I observed is that it is a powerful presentation tool.  We have Interwrite boards at our school, and the ability to share the dynamic work that is afforded with GeoGebra in a class can change how students learn math.   

Because most of our students will have the ability to use GeoGebra at home, I will be interested in exploring the area of dynamic worksheets.  When students are actively able to manipulate figures or graphs and find measurements and equations and see how their manipulations affect those measurements and equations, they are able to internalize the mathematics behind it all.

I have used GeoGebra very little, and therefore I will be looking for any and all advise on its usage in the classroom.   It would seem very beneficial to form an online community of GeoGebra users to share ideas and work throughout the year.  I look forward to all interaction in this community of GeoGebra users at this first conference.

 

84: Birgit Bardorf. Schüer erstellen Hefteinträge und Aufgaben selber

Abstract. Bei meinen Internetrecherchen in den letzten Wochen bin ich leider nur auf sehr wenige Seiten gestoßen, die GeoGebra in der folgenden Art und Weise einsetzen, deswegen kurz die Erläuterungen meiner Arbeitsweise:

Ausgehend von meinem Unterricht, der im Moment hauptsächlich in der Unterstufe (Jahrgangsstufe 5 bis 7) im Bereich der Förderung besonders begabter Kinder liegt, verwende ich GeoGebra vor allem zur Individualisierung (Personalisierung) und Differenzierung des Unterrichts.

Hierbei erstellen die Schülerinnen und Schüler eigene Aufgaben und eigene Hefteinträge innerhalb eines mehr oder weniger stark vorgegebenen Rahmens. Für die Hefteinträge werden z. B. nur die fachlichen Inhalte gemeinsam besprochen - die Strukturierung, Reihenfolge und Form der Einträge bleibt jedem danach selber überlassen.

Beim Entwerfen einer eigenen Aufgabe wird Geogebra von den Schülern sehr gerne eingesetzt. Hierbei dürfen sie in die Rolle der Lehrkraft schlüpfen und stellen sich dadurch ganz anderen Aufgaben, die zu einer Vertiefung und Vernetzung ihres Wissens beitragen. Die Schülerinnen und Schüler haben damit die Möglichkeit, selbst aktiv Teile des Unterrichts zu gestalten.

Submission #84

englisch Submission #84

 

86: Diane DeHon. Goals for the GeoGebra 2009 Conference

Abstract. Submission of my ideas, experiences and interest.

Submission #86

 

87: Annemarie Schauer. Concentration on short lessons

Abstract. Acting, working with pupils is very different in case of the diversity of the equipment and the actual knowledge of the teacher and the children.

I am an user with a lot of different subjects and forms. I often use geogebra just to have a look on the problem.

I would like to have a catalogue on the subject/the topic/the core skills an the time I have to invest using a lesson. And I really think about modular lessons not objects.My time is always less.

I would like to work on this structure of objects and develope a list of wishes for the groups A and B from the status of a D_teacher.

 

88: Gertrud Aumayr. Geogebra vs. TINspire - Advantages and Disadvantages

Abstract. Computer Algebra Systems like TINspire (c) are presently used in the natural science curriculum at BRG/BORG St. Poelten. It would be interesting to find out, whether freely available software like Geogebra might be used as a replacement.

 

90: Stephanie Roth and Georg Schulte. Mathematical experiments and possibilities of visualisation

Abstract: Having started using GeoGebra for mathematical experiments and visualisation I want to exchange experiences in further use of GeoGebra in Secondary Schools ( German "Gymnasium")

 

92: Maha Ahmed Issa. GeoGebra in Egypt

Abstract. all the teachers that have participated in the training in GeoGebra have said that the program is very important in helping them to integrate technology into their teaching of mathematics in the classrooms and in allowing them to successfully develop technology-assisted practice in the teaching of mathematics.

Submission #92

 

XX: Irmeli Paavolainen. No title.

Note:  Submission via email

Abstract: I have used at our Olari High School in Espoo, Finland GeoGebra in my demonstration for different plots of functions, and in geometry teaching, in derivating and integrales, etc. I have not much made my students to do their home work with GeoGebra. It would be nice to learn what other teachers have asked students to do home work with GeoGebra. I would like also to learn how I could benefit more with GeoGebra in my teaching. Also I would like to have training in new features, and to learn where to find GeoGebra material, etc. e.g. from the network.