## | ## Prelininary course - description and feedback
The organization and the structure of the pre - course was not uniform for all partners, but depended on the concrete curricula and specific conditions in the partner institutions. The flexible structure of the pre - course is closely connected with similar property associated with the E - book and whole work on the project, this choice was done with the intention to give maximal possibilities for developing new ideas and stimulate the creative content of the dynamical approach in teaching mathematics inste ad of following formal algorithmic approach. Common basis was the choice of arguments and topics developed from different partners in the project. We decided to develop different topics in the e-book and this variety of topics enabled us to choose quite different arguments for preliminary courses in partners institutions. However, we followed two conditions: each of the partner has to implement at least one "external" topic and the partners had the freedom to choose how long shall be the local course/courses so that the minimal requirements in the application form had to be satisfied. This specific flexible organization was already planned in the initial application.
Aarhus DK topics and organization: Pre – course and network:16 students, diversity of qualifications/experienced newcomers. Upper secondary teachers (21). The key argument was the application the GPS. Materials of the e-book concerning this argument have been involved. The key feedback remarks from teachers were – ”very interesting”, ”enjoying”, ”I can probably use it” , ”should have known to weeks earlier”, ”can you realley do this with Excel?” Detailed presentation is here.The evaluation form also can be dowloaded as word file or as pdf file.
Nitra SK topics for pre – course: The target group involves 15 pre-service teachers. There were 2 seminars introduction/refreshment, 2 seminars the topic: Euclidean Eggs, 4 seminars on Geogebra, the seminars were for 90 minutes weekly. The course started in February 2012 and finished in May 2012. DynaMAT materials were piloted also on special event: Summer school for PhD students and pre-service teachers on 23 – 30 June 2012. Number of participants: 14 PhD students and 10 pre-service teachers. DynaMAT materials dealing with GPS and were presented and practiced. Detailed presentation with feedback information is hereThe evaluation form also can be dowloaded aswordfile or aspdffile.
Pisa IT topics for the pre-course: The course started in March 2012 and the main part of the Course finished end of May 2012. Totally we had 4 hours per week = 40 hours totally with a group of 12 future teachers participating the course and 9 more following the moodle platform. They prepared different projects. The projects have been discussed and evaluated during the course and a program to visit High schools in the domain around Pisa was prepared. We visited several High Schools and in each of the Schools the future teachers presented their projects. The program chosen covered the following topics from the e-book:Didactic games Nitra (SK), Modelling of the fly Vienna (AT), Number theory and games (IT), Napoleon problem (IT), Billiards (IT). Some feedback summary: Didactic game (“ highly evaluated by students and teachers and even was very useful in the preparation of the final written exam, where probability problems have been included”, “the students and teachers participating the presentation of the project have been able to pose questions, even to make a conjecture connected with the use of conditional probability”, “However the Excell part needs some further development in the practical realization”), Flight models ( “quite interesting approach, the use of google earth works very well”), Number theory and games (“ Diophantine equation seems to be difficult for hight school students, very attractive problem”, “to improve – the quality of pictures”), Napoleon problem (“ Feedback remarks: Discussion was very active, students and teachers posed interesting questions: What will happen with Napoleon construction if we have poligons”), Billiards (“some of calculations have to be improved”, “perimeter of periodic triangles is very difficult topic”, “some of the tools has to be explained in better way”). Detailed presentation with feedback information is here.The evaluation form also can be dowloaded as word file or as pdf file.
Reykjavik IS topics for pre-course: Group of teacher and students/ learn the basics of GeoGebra. Special focus was on their area of interest e.g. material they are teaching or want to teach – hand in a plan. Tasks: create/find at least 5 different worksheets/problems and hand in a paper (+ 20 pages), evaluate 2 of their fellow students work, give a talk on their work and demonstrate worksheets, evaluate (write 3 – 4 pages + q.form) on a DynaMat chapter of their choice. Some feedback remarks: "Dynamat material was perhaps too advanced for students, since they are just starting to use ICT material", "I don't know how to operate a GPS but it would be interesting to learn this. Possibly something a group of teachers could do together.". Detailed presentation with feedback information is here. The evaluation form also can be dowloaded as word file or as pdf file.
Sofia BG topics for pre-course: Dynamat pre - course and seminars with primary school teachers, with secondary school teachers, mixed groups, national seminar on math education, seminars in IMI (experimenting new technology). Two-day course on inquiry-based learning of mathematics in the primary school based on GG – June 2012, argument Napoleon problem: pupils had for construction 10 min. and they spent 10 more min. to make an appropriate design. In Blagoevgrad the group of teachers involved teachers in : Primary -8, Mathematics 3 , Art -2, History and geography – 1, IT – 1, 4-34 years as teachers. National seminar: The inquiry-based approach in math education – December 2011. Detailed presentation with feedback information is here. The evaluation form also can be dowloaded as word file or as pdf file.
Partners in Vienna (AT) participated in the pre-course with two main activities. First activity was annual in-service mathematics teacher training day, organized by Austrian Mathematical Society's Math Education Commission on April 13, 2012, 13:00 – 15:00. Participants were 27 in-service mathematics teachers. Participants received a 30-minute oral presentation of the DynaMAT materials Lens (AT) and Extreme Value (AT) in their first versions, a hardcopy printout of these materials, and a USB stick containing the electronic version of the materials, including the corresponding software. They were then asked to form groups of 3-5 and continue study the materials in group work, then fill out the DynaMAT feedback form and report to the whole audience about their findings.
Feedback summary and suggestions: for “ Lens” (“ Very good for physics teachers”, “Useful context (math teachers)”, “To improve: Explanation why hyperbolic lens is ideal lens (construction of hyperbola, eventually also construction of parabola, with GeoGebra)”), for “Extreme Values” (“Classic content in unusual way”, “Nice tasks”, “To improve: Calculus with CAS”).
The second activity was the Regular compulsory seminar in mathematics education held in the period March 13 – June 12, 2012, 7x1.5 hours. Participants had (amongst other materials) a selection of DynaMAT materials from all partners to choose from. Materials chosen were Fractals (AT), GeoCaching (AT), Aviation (AT), Tall Tree (DK), and Geometry on the Playground (SK) in their first versions. They were asked to form groups of 2 and received electronic copies of the materials (including the corresponding software) to analyze these materials as to their practicability and usefulness for teaching (this part was done outside the seminar hours). Each group presented the material and the analysis in a 1-hour presentation, which was followed by a 30-minute discussion session. At the end of each discussion session, participants were asked to fill out the DynaMAT feedback form and hand it back to the DynaMAT team.
Feedback summary and suggestions: for Fractals (“Beautiful and interesting, even for less talented”, “How to fit into curriculum?”, “To improve: Better explain logo code”, “To improve: Better explain step from real to complex case (Julia and Mandelbrot sets)”), for GeoCaching (“Very interesting for most students”, “Most have smartphones and can do this”, “Good explanation how GPS works”, “To improve: Hints for tasks (interpreting data)”), for Aviation (“Fear that it is mostly interesting for male students did not turn out to be true”, “Very much real-life”, “Tasks are explained well”, “Problem: Can not use smartphone-GPS while flying”, “To improve: Tasks for the non-flying section (walking, biking, hiking)”, for “Tall Tree (DK)” (“Many students reported similar observations (mainly tall houses or towers), or reverse problem (you are at the tall tower, how do you find e.g. your house?)”, “Shows how to use math for something useful”, “To “improve”: localizing the context (i.e. for AT course, use tree in Vienna ...)”). Detailed presentation with feedback information is here. The evaluation form also can be dowloaded as word file or as pdf file.
FAQ: In addition some other documents raise the impression that not one course was developed for all partners but partners developed independently national courses.
Reply: The organization and the structure of the pre - course was not uniform for all partners, but depended on the concrete curricula and specific conditions in the partner institutions. Common basis was the choice of arguments and topics developed from different partners in the project. We decided to develop different topics in the e-book and this variety of topics enabled us to choose quite different arguments for preliminary courses in partners institutions. However, we followed two conditions: each of the partner has to implement at least one "external" topic and the partners had the freedom to choose how long shall be the local course/courses so that the minimal requirements in the application form had to be satisfied. This specific flexible organization was already planned in the initial application. Therefore the choice of didactic materials, period of development as well target groups ware not the same for all partners, depending on the concrete possibilities to implement arguments and materials from the e – book in pre - course with future and in service teachers. | | ## | |