6: Celina Abar. The Results in Continuous Formation of Mathematics Teachers in a Virtual Learning Environment

Abstract. This work presents the results achieved in continuous training of mathematics’ teachers in the Post-Graduate Program Studies in Mathematic Education, with the use of a virtual learning environment (VLE) Moodle. The use of this environment allowed us to break barriers of time and distance; it was an interactive and collaborative work with very positive results. The participants get involved in the learning’s context; they propose problems and its resolutions, formulate hypotheses, observe and review their previous designs, make decisions, in a dialogue with the reality of their practice teaching. It is expected to lead student-teacher to: recognize the possibilities of information and communication technologies (ICT)  to their professional practice in mathematics and the interface with Mathematics Education and identify procedures, concepts, descriptions and representations which may be useful in their educational practice. To this end, specific modules are scheduled in which the student must act individually and collectively, with the support of a virtual learning environment and underlying theories, to search for information, to develop and evaluate projects that can contribute to his professional practice. The mathematical content developed suppose an practical training, with proposals for activities in which the relevant topic calls the awakening of a knowledge built some time ago, perhaps in a graduation. Activities with content on functions, geometry and algebra were proposed with the use of GeoGebra to support the teaching and learning of such contents. In the studies of Dynamic Geometry the programs Cabri Géomètre and GeoGebra were chosen because they’re used in most schools and also because GeoGebra permit free access and a practical use. All the subjects proposed had as support texts and theoretical research on the use of ICT in teaching and learning of mathematical content to subsidize the development of the training.

Submission #6

 

14: Olivia Gill. Geogebra for Pre Service Mathematics Teachers

Abstract. As a lecturer of mathematics education/mathematics pedagogics in the University of Limerick, it is part of my duties to prepare student mathematics teachers for teaching practice in second level schools.

The Irish second level mathematics curriculum is currently changing. A new initiative entitled 'Project Maths' is currently being phased in 24 pilot schools throughout the country with the intention of all schools participating by September 2010. Project Maths aims to improve the mathematics education of second level students by promoting real-life applications in the mathematics classroom with an enhanced emphasis on IT.

The students I teach in the University of Limerick will be fully qualified to teach mathematics in September 2010. For this reason, I have begun to include lab sessions & lectures on GeoGebra within my mathematics education modules. In addition students had to create applets as part of their course assessment. The students found the work challenging yet very beneficial and will aim to use GeoGebra in their final year Teaching Practice this year.

In this session I will discuss the material covered with my students and the feedback I received. I hope to get ideas from other teacher educators on incorporating GeoGebra and IT into the classroom. 

 

20: Aitzol Lasa, Alvaro Saenz de Cabezon and Miguel R. Wilhelmi. RESTRICTIONS IN THE LECTURE OF GEOMETRY WITH GEOGEBRA IN PRIMARY SCHOOL TEACHER EDUCATION

Abstract. Working Group Topic: E) GeoGebra at Universities and in Teacher Education.

Ages: 21-22, approximately.

Degree course: Science Education for School Teacher

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

Developing GeoGebra materials in accordance with standard of university-level courses;

Discussing issues in relation to pre-service teacher training (e.g., the connection of a learning objective, a GeoGebra activity, a lesson plan, key examples, and an assessment procedure);

Examining various methods of professional development;

Exploring issues in developing textbook support for use of GeoGebra;

Submission #20

 

21: Mohamed Al Sayes. Sharing our work

Abstract. As a lecturer in a college which prepared math and science teachers to the Primary schools, I would like to chair my work and my ideas with my group.

In the workshop I would like to show some files which I achieved concerning with the beauty of Math when using GeoGebra

 

27: Mustafa Dogan and Erol Karakirik. Using GeoGebra in Teacher Training

Abstract. We started a special “dynamic geometry” course in Selcuk University, Faculty of Education, at Primary Mathematics Department in 2006.  Since then final year trainee teachers have been taking this course every academic year specifically to learn about dynamic geometry. GeoGebra software was translated by us then to Turkish to be used in this course. This course also offered them opportunities to explore the advanced features of GeoGebra with the help of the lecturer. Each student’s work usually consisted of at least 10 different GeoGebra worksheets including both geometric and algebraic operations. Thus, more than 3000 GeoGebra worksheets samples have been constructed by around 300 trainee teachers for the last three years. Therefore, we would like to present some selected samples from the students’ original works and share and explore the ideas associated with the use of GeoGebra at the primary mathematics department. We will be specifically talking about the students’ explorations and ideas about the use of GeoGebra at university and in teacher training. We will also discuss the potential applications of GeoGebra and the development of instructional resources in primary classes. We will provide original worksheets of trainee teachers.

Submission #27

 

28: Francisco Perez-Arribas. Teaching Computer Aided Design with the use of GeoGebra

Abstract. I include my proposal in the attached .pdf

Submission #28

 

32: Ada Sargenti, Patrizia Laiolo and Claudia Testa. A virtual class of GeoGebra on Moodle platform at the University of Turin: a blended course of The House of the Teachers.

Abstract. The Faculty of Sciences of the University of Turin used Moodle’s features in order to create an engaging collaborative online learning community of teachers of Physics and Mathematics (DI.FI.MA.), with the purpose of formation, research, comparison, sharing of materials and information on national and international initiatives.

The initiative follows the experiences of using Moodle in the initial teachers’ formation on behalf of the Piedmont SIS (school of specialization for secondary future teachers).

At the moment, among the resources available on the platform DI.FI.MA., there is also a virtual class of GeoGebra, established in collaboration with the association “La Casa degli Insegnanti” (The House of the Teachers).

This is a blended course for teachers who want to learn how to use this DGS, for analyzing new teaching strategies for classroom activities.

This course attempts to combine the elements of the traditional face-to-face meeting with the best aspects of distance education for supporting teachers in the use of GeoGebra and Moodle platform.

Submission #32 

 

35: Tolga Kabaca and Mehmet Bulut. A Suggestion of Using GeoGebra at College Level: The Case of Finding Arc-Length of a Curve

Abstract. It is certain that, GeoGebra is a powerful tool to teach mathematics. Its dynamic feature, which allows constituting a bridge between algebra and geometry, may be used to design a discovery learning environment. In this kind of environment, we can see the student as a GeoGebra user, while we are a GeoGebra programmer. I want to call your attention to another possible use of computers in teaching math. Students should be also seen as a programmer.

Computer programming makes the computers can think and act about something perfect and fluent. Desired mathematical thinking can be thought as a computer program. If the algorithm of the program is perfect and the syntax is completely correct, the program works fluently and operates the correct answer for us, completely like our mathematical thinking structure. If our thinking structure on a certain concept is a well-constructed one, we can make any generalization by the help of that concept.

At this point, we should ask ourselves the question “what do we need to understand by computer programming in the sense of teaching math?” we need to focus on only making a perfect algorithm of programming issue. After the making algorithm, any programming language may be used. But our software is not need to be even a programming language. It is enough that using a software that allows to run our algorithm. Moreover, the software, which we used, should be simple to learn and to use. By running the algorithm, we can provide an opportunity to check thinking structure for the math learners.

Let’s consider on the concept “finding arc-length of a curve” the make more clear what I mean. We can assign two tasks for the students. First, they should construct an algorithm that can evaluate the arc-length of every kind of curve, which is represented by a function. Then, they need to run this algorithm by using GeoGebra.

The algorithm may be something like follow, after an enough discussion environment;

1- plot the graph of the function f(x),

2- determine some points on the curve of f(x) for x = a from x = b if you want to evaluate the arc-length in the interval [a, b]

3- Constitute the line segments, attaching every successive point on the curve.

4- Find the sum of the length of all line segments, which obtained at the previous step.

5- When we increase the number of points on the curve, we will approach to the real value of arc-length of the curve.

Now, we should help our students while running this algorithm on GeoGebra. This kind of approach may be considered as an alternative way instead of presenting ready GeoGebra applications. By this way, students may realize their own thinking structure by simulating GeoGebra’s way of running algorithm.

Let’s see how GeoGebra can execute the algorithm above;

• First, we need to assign necessary free objects (inputs);
  • Function f(x). I defined as “f(x)” here.
  • Initial point and end point. I defined as “a” and “b” here.
  • Difference of the every successive point on the x-axis. I defined as “delta” here.
  • ?Actually, “delta” object is not free. It is dependent to the variable “n” which represents the number of difference between “a” and “b”. Therefore; delta=(b-a)/n

• Then, it is needed to obtain a sequence of points on the curve by following GeoGebra command;

  pointlist=Sequence[(a + i delta, f(a + i delta)), i, 0, n]

• Let’s construct the line segments, attaching every successive points in the sequence above;    segmentlist=Sequence[Segment[Element[pointlist, i], Element[pointlist, i + 1]], i, 1, n]
• Last, we should to evaluate the sum of the every line segment in the list above;

  arclength=Sum[segmentlist,n]

When a student constructs the GeoGebra application above, he or she can change the function, initial and end points and number of difference. So, he or she can either make some experiments or check his or her thinking structure.

Submission #35

 

39: Enrique de la Torre Fernandez and Adelina Silva Muslera. Conceptualization of derivative using GeoGebra

Abstract. The use of technologies in the mathematics classroom worried us very much, and for that reason it seemed to us a good subject to investigate. We questioned ourselves mainly as the students use technology to conceptualize the differential and integral calculus.

We are concerned about to look for software that will adjust to that concern and also we investigated what theoretical frame could fit in our plans of research. We needed much aid to develop the methodology that we would use in this investigation. This it is a first result of that concern.

Submission #39

 

40: Damjan Kobal. The teacher's role in the use of GeoGebra to motivate and to deepen the comprehension of Mathematics

Abstract. GeoGebra is a great tool for teaching and learning. But the role of a teacher remains crucial, if we want to reach the majority of students. Thus, one of the main issues in promoting the creative use of GeoGebra is to make sure that the use of GeoGebra does not remain alien to the working teachers. In teacher’s education GeoGebra can and must be presented as a friendly and mind provoking tool, which presents, motivates and intrigues mathematical thinking. Many mathematical concepts can be presented in a very intuitive way by the use of GeoGebra, but this might not be the best part of GeoGebra. One of the most important values of a program like GeoGebra might be in the educational added value of teacher’s deep comprehension of concepts which is developed in the path of creating high quality applets. True mathematicians and devoted teachers will be impressed by the beauty and simplicity of mathematical thinking, which together with the tool of GeoGebra can convey abstract (dynamic) mathematical concepts in the form of clear visual schemes.

We would like to argue that for the success of GeoGebra use not only technical perfection of the program is required, but also great sensitivity for educational questions. The later should be addressed not by theoretical educational framework, but by examples and promotion of good practice.

 

48: Freyjah Hreinsdottir. GeoGebra in Iceland, activities and plans

Abstract. My GeoGebra activities so far:

1. I started to use GeoGebra in a Calculus course in the education of mathematics teacher  (elementary and lower secondary school) in spring 2008.
2. I translated GeoGebra, version 3.2,  to Icelandic 2008.
3. All prospective mathematics teacher for elementary and lower secondary school  now use GeoGebra in two courses, geometry and calculus.
4. Project course for secondary school teachers of mathematics (current/prospective) in spring 2009. Projects involved writing GeoGebra worksheets in Icelandic.
5. Other activities include: talk/article to introduce GeoGebra to mathematics teachers, advising final projects for Master and Bachelor students etc.

My future plans are to continue work on translation (e. g. help documents, study material, teaching material), create a web page for the material, do research and hopefully establish an Icelandic GeoGebra Institute.

Using University courses to develop teaching material: To involve more people in the writing of worksheets I plan is to develop further the project course activity mentioned above. This spring we gave a semi-distance course (6 ECTS) with 6 teachers for 10 - 12 students at the University of Iceland (University courses are often small in Iceland as the population is only 300.000).  This was an experiment and had not been done before. The students could choose from 6 different topics/teachers (e.g. history of mathematics, motivation in mathematics, GeoGebra) however of the 10 students completing the course, 5 of them did a GeoGebra project where they translated/made several GeoGebra worksheets and wrote papers explaining: the mathematics taught, the GeoGebra/mathematics knowledge needed to use the worksheets and how this fit into the Icelandic curriculum for secondary school in Iceland. They also gave two presentations each and tested this on their own students in some cases.

The students were extremely motivated and there was much discussion following every presentation. The plan is to put their worksheets on a webpage for other teachers to use.

I found that it was very easy to teach GeoGebra to these students and to motivate them to do independent work. The reason for this was that their knowledge of mathematics was good, they all had some teaching experience and last but not least they felt that they were doing something very important by making these worksheets in Icelandic.

My plan is to convince the University to let me create such a course with GeoGebra projects only. This would fit both into teacher education as well as professional development for teachers and this would quickly create a large pool of worksheets that can be shared among teachers.

 

52: Inder K. Rana. GeoGebra in teaching calculus and professional development

Abstract. I am a faculty member at Department of Mathematics, Indian Institute of Technology  Bombay, India

My interest in GeoGebra arises of the fact that it is an easy to use, yet powerful Dynamic Geometry software. The fact that it is open source is a big plus factor for developing countries like India.

I see the following applications of GeoGebra in the India setup:

• Teaching of Algebra and Geometry at school level.
• Teaching of Calculus at school/precollege /University level.

Personally, I am interested is developing a GeoGebra supported text on Calculus. Would like to give a presentation.

I also conduct teacher training workshops for math teachers at secondary level and would like GeoGebra training a part of it and  would like to promote the use of GeoGebra through these workshops. The next workshop is scheduled in June 2009  http://www.math.iitb.ac.in/pdto/

I also organize national conferences in India called TIME (Technology and Innovation in Math Education). Time 2009 is scheduled in December 4-7, 2009 at IIT Bombay, India.

I would like to have some workshop on GeoGebra in this event.

Here are some of the items for my wish list:

• Possibility of increase in font size for labeling in axis
• Choice of function display
• Possibility of incremental display

Submission #52

 

56: Maurice OReilly. Rediscovering geometry in university using GeoGebra

Abstract. The author has just completed teaching a one-semester module on geometry to a small group of students taking a two-subject B.A. programme at an Irish university. Students had little experience of Euclidean geometry since the middle of second level schooling. This experience involved, typically, memorising fourteen theorems isolated from the rest of their mathematical studies which would have included coordinate geometry, vectors and complex numbers, for example. In the module just taught, the emphasis was on reviewing Euclidean geometry in a more connected manner and alongside transformation, projective and non-Euclidean geometry. In this paper the author will consider ideas around teaching geometry to adults with some mathematical maturity, drawing on insights gained from experience with this module. In particular, he will consider a constructivist approach to illuminating geometrical ideas using GeoGebra, of course.

 

59: Linda Fahlberg-Stojanovska. GeoGebra at University: My Experiences and Ideas

Abstract. Because I cannot attend the conference and as requested by Markus Hohenwarter I prepared a short screencast presentation on my experiences and ideas for using GeoGebra at University.

   http://mathcasts.org/gg/resources/present/geogebra_experiences/geogebra_experiences.html

 

74: Anders Sanne. Working group selection

Abstract. I do not want to present a paper, as I will chair group B.

My interests:

• In-service teacher training
• Distant learning
• Moodle integration with GeoGebra

 

75: André Heck. Development and evaluation of GeoGebra-supported lessons as an eye-opener for innovative teaching

Abstract. Teachers of first-year courses in mathematics could benefit from using GeoGebra in their teaching of basic courses in calculus, geometry and algebra. This is already true when they would only use GeoGebra to exemplify mathematics problems and solutions. However, a difficult issue is to convince them and get them started. A teacher professionalization programme might just be a good option. A question is what the contents of such a programme could be.

Maybe it is worthwile to look at positive experiences that we have within the Master of Mathematics and Science Education at the University of Amsterdam with projects in which students develop one or two lessons about a mathematics subject using ICT, teach the lessons at a secondary school, and evaluate them. Such work might be a good option for both a professionalization programme of university teachers and for a teacher training programme. Two examples of GeoGebra-supported lessons developed by students are presented.

 

80: Alexandra Emilia Fortis. GeoGebra as Differential Geometry Visual Support

Abstract. As Assistant Professor at the Computers and Applied Computer Science Faculty, “Tibiscus” University in Timisoara, Romania, I am teaching Mathematics courses (computational geometry, dynamical systems and numerical methods) for Computer Science students.

Currently, for the support of the Geometry classes I am using MathCAD and Maxima. The first one is a commercial product that proved to be limited with respect to some particular problems, while the second one, an open-source product, is not user friendly, and with major limitations regarding the graphical representation of most aspects in the curricula. Considering these aspects, it became imperative to find some free software that could graphically support the curricula for the Geometry course, as follows:

1. Support for 2D graphical representations
2. Support for 3D graphical representations
3. Support for vector calculus in graphical form
4. Support for coordinate transformations in 2D and 3D (such as coordinate systems – Cartesian, polar, cylindrical, spherical - and conversion between them)
5. Support for geometric transformations (such as rotation, translation, scaling, reflexion, symmetries, projections)
6. Support for representation of straight line in plane and in space, the plane, relative positions of lines and planes
7. Support for the differential geometry of planar curves (circle, parabola, hyperbola, ellipsis) and spatial curves
8. Support for the differential geometry of surfaces

Even if I am not, for the moment, a GeoGebra user, the GeoGebra system proved to be one important candidate for supporting the aforementioned issues, despite the fact that 3D is not yet available. The educational aspects in teaching elementary geometry in secondary schools emphasized by some research papers and reports I have recently read offer enough reasons for this choice.

Achieving goals such as the inclusion of GeoGebra in homework evaluation and testing students’ knowledge as well as the adaptation of the course material for presentation in class will be of great importance for a modern approach of understanding theoretical aspects in differential geometry.

 

85: Andreas Philippou and Costas Christou. Acivities with Geogebra in a preservice program

Abstract. The University of Cyprus is responsible for the preservice education of teachers of secondary education. In this framework, we developed a program for preparing math teachers to use integrate computers into their teaching in the mathematics classrooms.

A large portion of this program focused on teaching secondary mathematics using geogebra. In the conference we will present a sample of activities used by preservice teachers to introduce mathematical ideas to students. Most of these activities refer to the concept of limits, derivative, integrals etc.

Submission #85

 

Arne Amdal. Geogebra for Pre Service Mathematics Teachers

Abstract. As a lecturer of mathematics education/mathematics pedagogics in the Norwegian University of Science and Technology (NTNU), it is part of my duties to prepare student mathematics teachers for teaching practice in second level schools.