| E - course- description and feedback
The organization and the structure of the e - learning course followed our experience from the pre - course and the feedback obtained. 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 course with future and in service teachers. The flexible structure of the 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 instead of following formal algorithmic approach. Common basis was the choice of arguments and topics developed from different partners in the project.
For example the partners from Aarhus (DK) have used Dynamat material in several courses at the teacher education in Aarhus. Typically the teachers tested the materials with GPS, dividing the whole group of 20 25 students in few groups. Two course descriptions in Danishwere prepared. In one of the cases, due to lack of participating teachers (one due to a national lock out in April 2013) the course was not held. In the reports at management meetings one can find evaluation remarks together with description of e-learning course for self-study on the chi-squared distribution. Two others are made in Danish (see directory videos).
Feedback summary: the material on GPS was tested at in - service teacher training course in Skive , teachers liked open ended approach to the work, some of their remarks:
• Endomondo, Garmin, “What-ever-you-have”.
• “Very short time for such a course”
• Recommendation to use Endomondo because of trouble with data transfer from etrexH to computer.
• Some teachers had difficulties in seeing the mathematical points in the material.
• Some teachers could see possibilities and became inspired to try it out with their own pupils.
• “Hard to find the time”.
• Lot of technical problems: how do the Garmin GPS work?
• “ Third year teacher students were insecure in those matters and how much support they needed”,
• Some would like to study the subject further – even for project in connection with the examination to come.
• “ Some would like technical up-qualification”
• Well written as inspiration for teachers and teacher students.
• Perhaps consider a reduced version with gaps (smaller or larger) to encourage students thinking and innovative engagement.
The partners from Nitra (SK) have developed three activities. First activity: Course of professional development for in-service mathematics teachers. Duration: 110 lessons (55 lessons x 60 minutes of presence, 55 lessons of e-learning moodle course). Dynamical softver in geometry topics was taught on 20 presence lessons. Number of participants: 22 in-service teachers of mathematics. Teachers worked with DynaMAT materials: Eulidean eggs, Car wheels, Best spot; in Slovak language. Period: October 2012 – July 2013. Second activity: Course of proffesional development for in-service teachers of science and geography. Duration: 110 lessons (55 lessons x 60 minutes of presence, 55 lessons of e-learning moodle course). Number of participants: 6 in-service teachers of science and geography. Teachers worked with GeoCaching, Mathematics in the nature and modified versions of Geometry in the field using GPS, Finding tall tree using GPS. Period: March 2013 – July 2013. Third activity: Pre-service teacher seminar with support of e-learning moodle course. Duration: 10x90 minutes. Participants: 11 pre-service teachers of mathematics. Students worked with DynaMAT materials: Euclidean eggs, Didactical games, Dynamical simulation, Simulation of Chi-Square distribution in Slovak language. Period: September – December 2013.
Partners from Pisa (IT) developed the course in the period: February - May 2013. The course had total number of 42 lectures, students coming to lectures have been 20 and there where 9 other students following the course through the moodle platform. E - platform: moodle can be found in https://www.dm.unipi.it/elearning/Main topics that were chosen: Napoleon problem, geometric properties of the triangles and quadrilaterals, history of math and teaching in math (games and real life problems), recurrence sequences of numbers (real and complex) and problems from biomedicine, fractals and how to introduce them in class, connection between models in biomedicine, fractals and some problems from dynamical systems, dynamical billiards in ellipse, some chosen topics from probability and combinatory, games and probability. Tools and software: geogebra especially for geometrical constructions and study, excell in different models in biomedicine, linear programming. Final exam: components: preparation of individual evaluation form, based on standard Dynamat form, evaluation of e-book and e-course, preparation and presentation of project based on the course. List of 36 projects is attached. The variety of arguments proposed by future and in service teachers seems to be a real suggestion that this approach supports the development of creative competences. However, in some of the cases the new projects were chosen in autonomous way by the participants in the course, without clear direct connection with the concrete arguments proposed during the lectures. A necessity to help students in their initial steps in the projects was manifested.
Feedback summary: Two groups evaluated the ebook: future teachers ( 9 evaluations) and teachers in service (11 evaluations). Evaluation of materials in the e – book can be summarized as follows. Some of materials have been evaluated very well: probability simulations from Denmark, the project for eggs from Iceland, in some cases the geogebra units from Iceland seem very useful for teachers in service, beautiful art project from Bulgaria should be used for earlier ages of math curricula, fractal units from Austria and Bulgaria, optimization arguments projects developed by Austria and Bulgaria, use of games in primary schools (Slovakia), toxic games (Slovakia), use of complex numbers in geometry (Italy). Some other materials seem to be difficult for concrete applications: GPS seems not very easy to be used in this moment, some of didactic materials have dominant design and software part and the math content and reasoning should be complemented by new creative problems and solutions, in some other cases teachers can find beautiful geogebra designs but less creative math tasks. Other difficulties: in order to develop arguments connected with probability and theory of games some basic introductory lectures are needed, the ebook can not show how to feel this gap, the same is true for some other interesting math models as dynamical system, periodic triangles in ellipse etc, some difficulties have been encountered in giving a reasonable hints to motivated students how to enter interdisciplinary fields ( as math models in biomedicine, chemistry etc).
Partners from Sofia (BG) had also specific structure of the courses: Lectures for the students at the Research Science Institute, MIT – July-August 2012. Give the talent a chance – a conference of “St. Cyril and St. Methodius Foundation” – October, 2012. Teacher training for 21 century academy in Plovdiv – November, 2012. National seminar Inquiry-based math education - 19 December, IMI-BAS – 2012. Training courses with in-service secondary school teachers in mathematics and IT - Gabrovo – 2013, February – 15-17. Mini-course of Oleg Mushkarov on Napoleon Polygons, Usana 2013 . Mini-course of Neli Dimitrova on Models in Biology, Borovetz 2013. Feedback summary: For lectures on Napoleon theorem: various ideas for possible generalizations, the students and teachers need more examples and didactic materials of this type, m ore materials had to be translated. For the materials Art and Mathematics: very well accepted by primary school teachers, “nice introduction in geometry”.
The partners from Vienna (AT) had two activities. First activity was developed in the period March 5 – June 18, 2013, had duration of 12x1.5 hours. Participants: 20 pre-service mathematics teachers. Framework: Regular compulsory seminar in mathematics education. E-Learning platform: Moodle 2.5 Link:
https://moodle.univie.ac.at/course/view.php?id=21937 (the Moodle system of the University of Vienna is only accessible with a valid student or teacher ID of the University of Vienna!) Description: Participants had a selection of 10 DynaMAT materials from all partners to choose from, and 3 non-DynaMAT materials as alternative. Materials chosen were Art and Photography (BG), Best spot (SK), Dynamical Simulations (DK), Euclidean Eggs (IS), Fractals (AT), Geometry in the Landscape (DK), Tall Tree (DK), and GeoCaching (AT) in their final versions. One part of the materials was available in English, the other part in German. These materials (including the corresponding software where appropriate) were available on the Moodle platform. Participants were asked to form groups of 2 and 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. The presentation was video-taped and the videos were also available on the Moodle platform. At the end of the course, participants were asked to fill out the DynaMAT feedback form and hand it back to the DynaMAT team. Until the end of the course, participants were asked to summarize their findings and upload these summaries onto the Moodle platform. Feedback summary was the following. Total number of participants was 20 - 13 female and 7 male. The question “How did you like the course” had mean result 3.9 (of maximum 4), the question “How did you like E-Learning part” had score 3.8, the question “Was the material adequate” had score 3.3, while “Encouragement to engage” had 3.9 as evaluation result. Other evaluation data: Best spot – investigations with circles - 3.9 , Euclidean Eggs: - 3.8, The tall tree (+ GeoCaching) - 3.9, Art and photography - 3.7, Fractals - 3.0, Dynamical simulation using Excel - 2.8, GPS – Geometry in the landscape - 3.7. Below materials, used in the course are together with corresponding suggestions, evaluation remarks. Best spot – investigations with circles (“Very good material”, “Easy to localize”, “Shows practical application of circles”, “Is the biggest angle the best viewpoint? What if angle = 170°?”, “Good”). Euclidean Eggs (“Very original, I never thought about how to create an egg!”, “Finally: GeoGebra is not only triangles …”, “Please give us the GeoGebra files” ). The tall tree (+GeoCaching) (“Realistic problem, also in Vienna”, “Good to show the “hand made” solution, too”, “Different co-ordinate systems can be difficult for children”, “Google Earth in mathematics – great!”), Art and photography (“Finally art and mathematics!”, “Sometimes too detailed (GeoGebra instructions)”, “What can you do with it curriculum-wise? Give some hints, please”). Fractals (“Good to show complex numbers are not only useful in electrical engineering”, “More interesting for bright kids, average students may have difficulty understanding this”, “Please explain more about what use Fractals are, aside from being pretty”, “Too complicated”). Dynamical simulations using Excel (“Good and detailed instructions”, “A new use for Excel – not only drawing graphs”, “Maybe use colors to distinguish elements”). GPS – geometry in the landscape (“Tried it out in Vienna, works very well”, “A good combination between GeoGebra and Google Earth”, “Very good step-by-step instructions”, “Almost impossible without proper GSP receiver”).
The second activity was a pre-service teacher seminar and had duration: 12x1.5 hours. It was held in the period March 5 – June 18, 2013. Participants were 33 pre-service mathematics teachers. Framework can be characterized as regular compulsory seminar in mathematics education. Description of the course follows. This was the control group for final course 1 without E-Learning usage. Participants had a selection of 10 DynaMAT materials (same as final course 1) from all partners to choose from, and 10 non-DynaMAT materials as alternative. Materials chosen were Geometry in the Landscape (DK), Geometry in the playground (SK) and Geometry on Car Wheels (SK) in their final versions. Most students chose alternative materials. One part of the materials was available in English, the other part in German. These materials (including the corresponding software on USB stick where appropriate) were given to the students as hardcopies. Participants were asked to form groups of 3 and 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 the course, participants were asked to fill out the DynaMAT feedback form and hand it back to the DynaMAT team. Until the end of the course, participants were asked to summarize their findings and hand them in. Qualitative feedback results: there were 33 students ( 25 female and 8 male). The question “How did you like the course” had mean evaluation 3.8 (of maximum 4), the question”Was the material adequate” was evaluated 3.7, the question “Encouragement to engage” was evaluated with score 3.9. Different materials have the following evaluation results: GPS – geometry in the landscape: 3,6, Geometry on the playground: 3.5, Geometry on carwheels: 2.5. Some of evaluation suggestions can be seen below. For “GPS – geometry in the landscape” - “Very practical, tried it ourselves at home”, “ Difficult with SmartPhone, “In school: Going outdoor is difficult, alternative?”. For “Geometry on the playground” – “Very good, can try this on school grounds”, “Most kids have phones with cameras”, “Different levels of geometry (2D/3D)”, “ makes it hard to place it in the curriculum”, “Divide it into two different units”. For “Geometry on carwheels” – “Clear instructions, easy to follow”, “Maybe not interesting for many female kids”, “Bus problem” not very realistic”, “Add other symmetrical objects, so that it is not reduced to car wheels”, “Also add “inscribed circle” for polygons”. | | | |
