GeoGebra in school This is a document that shows in which way all partners of ICT World use GeoGebra in their schools. Germany
France
Czech Republic
Latvia
Spain
Finland
1. Do you teach GeoGebra or similar dynamic geometry software (DGS) (which one?) in your school? Germany: Yes, we use GeoGebra. France: We use Geogebra. Czech Republic: We use GeoGebra only occasionally. Spain: Yes, we use it. Latvia: Yes, we also use GeoGebra. Finland: Yes, we use Geogebra
2. Is it compulsory or voluntary for each student? If you use GeoGebra at school: in which age groups and topics do you teach with it? If not, do you plan to test it in the classroom? Germany: It is compulsory to use it for some geometry topics like congruency, special points and line in triangles (grade 7). A lot of teachers in my school use it for classifying quadrilaterals, sum of angles inside a polygon, theorems of Thales and Pythagore and different proofs, similarity, reflections, rotations, ‌ (grades 8 and 9) and discovering properties of functions. In grade 5 with introduce GeoGebra in the subject called media education. Students there create artwork similar to famous artists. France: It is compulsory to use a DGS for grades 6 to 9. We use it to illustrate parts of the lesson and to discover geometric properties. Students use it to do exercises. There is no particular notion for which we must use ggb in mathematic. Czech Republic: It is voluntary for the teacher to use GeoGebra during his/her lessons but once used, it is compulsory for the students to learn to use it.
Latvia: We use GeoGebra in the framework of many geometry topics for visualization and problem solving (polygons, areas of various figures, figure transformations, rectangular triangles, etc.), and also in algebra topics (functions, graphical methods for solving equations, systems of equations and inequalities). Of course, GeoGebra is used by all project participants to complete the tasks. Spain: In Los Cerros Secondary School, Geogebra is used by students at the 3d level which means that they are 14 years old. Basicly, Geogebra is worked in the subject of Maths. Only recently and because of the development of ICT World, the KA2 Erasmus project and after visiting Germany, we have started to use it in technology lessons as a way to animate objects and texts. See the example: https://twinspace.etwinning.net/16691/pages/page/218331
Finland: We are not using Geogebra regularly. Some teachers and students might use it. We
are planned to use it in the future on some topics. Age group will be 14 and 15 years old.
3. Is the use of DGS implemented in your school curriculum and/or is there an official syllabus from the ministry of education? 4. Germany: Yes, it is implemented in our school’s math curriculum in grade 7. The official curriculum of our ministry of education describes competencies like dealing with tools, visualising geometrical properties, arguing and explaining mathematical relations. In official tests which takes place in grade 8 there always some tasks that require (basic) experience with GeoGebra. France: Yes, there is an official syllabus from the ministry of education that makes it mandatory to use dynamic geometry software in the college. Each student must be introduced to the basic features of DGS (grades 6 to 9) Czech Republic: No, it is not in the school curriculum Latvia: GeoGebra is not an obligatory part of the content of the mathematics course in Latvia. But in our school from 7th to 9th grade we work on our own developed program of the mathematics course. In this program we envisage the use of GeoGebra during the lessons of mathematics.
Spain: Geogebra is not a compulsory ICT resource. Then, it is not often evaluated, in fact very rarely we would say. Finland: No, it is not in the school curriculum 5. How do you use GeoGebra? At home for preparations, for demonstrations in the classroom, for students’ work, for discoveries, proofs, for constructions, ….. Germany: Many teachers in my school use GeoGebra at home for preparation, e.g. for worksheets with graphs, geometric constructions, … and for demonstrations of geometric properties or visuals proofs using dynamic constructions. Students discover e.g. linear and quadratic functions by using prepared applets to analyse the meaning of parameters. All students of grade 7 work with GeoGebra in some learning units (see question 2). France: Mathematic teachers use Geogebra at home for preparation and in the classroom (illustration or demonstrations of geometric properties, corrections of exercises…) Students use it at home or at school in ICT room. Czech Republic: Only for understanding the basic problems and constructions. Latvia: We use GeoGebra for visualizing and solving problems in the classroom and at home, as well as to carry out research work during Research days and Intellectual Marathon. Spain: We are actually preparing an academic calendar using this one as inspiration: https://www.geogebra.org/m/wpE7aNNp Finland: Teachers are using Geogebra for demonstrations and proof some theorems. Students are not using it. 6. Does GeoGebra in your opinion help to understand basic ideas of coding and improve students’ computational thinking? Germany: Yes, but especially if tools are created or in more advanced constructions with lists commands and animation France: It can help, but we use it mainly in the teaching of geometry. Learning coding with Geoebra remains secondary. Czech Republic: It can change the students´ point of view on coding and computer studies but at our school it is basically used only for studying geometry.
Latvia: Yes, of course. Working in GeGeobra develops the skills of creating algorithms, and this is one of the main components of computer thinking. Spain: Depending on the kind of task developed with Geogebra. There tasks as the mentioned in the point before which need to define an accurate sequence very linked to computational thinking. Finland: It is mainly to study geometry not coding. There is also some elements from computational thinking. 7. Is there in-service teacher training to support teacher in using DGS like GeoGebra to really improve their teaching and student’s understanding of geometric concepts? Germany: The ministry of education has started 15 years ago with regular in-service teacher trainings so that almost all teachers have once participated. In some universities they teach GeoGebra for students who like to become a teacher in a secondary school. France: There is no systematic training of teachers to practice ggb but volunteer teachers can apply for one-off training offered by the Ministry of Education. Czech Republic: No, we don´t get any training since GeoGebra is not a part of our curriculum if teachers want to learn more they need to self study. Latvia: The Institute of GeoGebra in Latvia consists of 3 employees. Last year they organized the course for the first time. Inara attended this course, but, unfortunately, learned little new. Spain: No. Only from time to time. The teachers training centers organize a geogebra course specifically for teachers of Maths. Finland: No systematic. But we can find different kind of courses about DGS. 8. Experiences and results in our project – nice creations and art work of our students – show that students are motivated to work with GeoGebra. Do you think that students benefit e.g. for math when using GeoGebra? In which way? Germany: I know it from a lot of experiences that I have made in many classes and grades 7-9. Students have normally success when creating things with GeoGebra. Dynamic constructions and the drag mode help to understand basic concepts behind geometric constructions. Constructions on paper with ruler and compass are static.
Besides this offers GeoGebra a lot of tools to make properties more visible: adding lines and segments, measuring angles, ‌ (see article about the power of GeoGebra). France: DGS brings a lot to students to represent dynamic situations of geometry. Some students need this dynamic visualization to understand some general geometric properties. It is a complementary approach to static figures and constructions made by the student. Czech Republic: The students involved in the project tend to be more enthusiastic about GeoGebra and like to use it and because of that they feel more confident when introduced to new ICT tools during lessons. Latvia: The use of GeoGebra in geometry develops the spatial imagination of students. Performing works related to art students can show creativity, develops a sense of color and artistic taste. Spain: Our students have produced some animations simulating real life actions (https://ggbm.at/GDQg7zhX) and also words presentations which can be adapted to different formats as academic presentations, birthday cards and so on (https://ggbm.at/d8ZygRpC). Finland: Students will benefits, because it is visual. It helps many students. When they are making it, their mathematical and geometrical thinking develops. 9. Do you think that GeoGebra can foster cross-curricular activities? Germany: YES!! As GeoGebra can be used to model and simulate many different areas of real life it has many relations to different subjects. There is a big relation between math and art, math and technology/computer science and maths and physics. France: Yes, it can be used to connect maths and technology or maths and physical sciences (trajectory descriptions for example). Czech Republic: Yes, it is possible. Latvia: Oh sure! I agree with everything written above. Spain: In a way, Geogebra can be a very creative tool which involves students in the development of many curricular activities of different subjects working together. Finland: Yes, it is possible.
10. Is there a tendency from the educational authority in your country to foster students’ progress in computational thinking at schools? Germany: There seem to be no tendency from the ministry in my state to change anything. The word computational thing does not exist in any official curriculum. In my school we have a special course in grades 8,9 that students can choose. About 25% normally chose this course in which we teach (advanced) GeoGebra, Scratch, Arduino, SketchUp, ‌ In a lot of schools there is a limitation of using ICT because of lack of ICT equipment and the impossibility of BYOD. France: There is a recent desire to develop computer thinking in France. For example, since last year, codage learning (with Scratch mostly) is mandatory in math and Technology programs. Geogebra and the use of spreadsheets are also part of the school curriculum. Schools are becoming better equipped with computer equipment. Czech Republic: We are sorry to say that these are just political proclamations. No real actions are undertaken, there is no support for those who want to get themselves involved. At least as far as primary and lower secondary education goes. Latvia: Yes, the second year is implementing a project to modernize the course of computer science and the inclusion of programming in it. This year started a new project on the competency approach to education. Spain: Very lightly and lately our educational regional and state government are fostering the use of tools which develop the computational thinking as Scratch, but not Geogebra. Finland: Yes. Our new school curriculum is coding and computational thinking is compulsory from preschool to higher levels.