E-learning in preparation of mathematics teachers and in mathematics teaching

1. E-learning in preparation of mathematics teachers and in mathematics teaching Working meeting to project EuroMath Innsbruck, 2004

2. Project E-learning in preparation of mathematics teachers • The determining of mathematics teachers’ competence for use of ICT and working-out of system of informationeducation of mathematics teachers • The projection and realization of courses with using of ICT and educational materials for preparation of future mathematics teachers and also as a part of further education of mathematics teachers • The exploitation of ICT for modernization of traditional methods and forms of mathematics teaching and learning

3. The information education of mathematics teachers • After determination of educational aims of information education we develop a educational content divided into two degrees. • General knowledge and skills comprise basic level, which is described in ECDL standards. • We divided superstructure part typical for information education of mathematics teachers into six basic sections.

4. Superstructure part – 6 basic sections • Production of mathematical documents and presentations – technology of production of documents and presentations containing various kinds of objects enabling accurate processing of educational content and active elements to provide individual educational ways and feedback. • Exploitation of Internet in mathematical education – mathematical portals, searching and gaining information, teaching materials and educational programmes, electronic collection of tasks, dynamic WWW sites. Evaluation of possibilities of use of gained sources in educational process. • Basics of algorithmization – proposing and notation of algorithms, evaluating effectiveness of algorithms for solutions of problems in various fields of Mathematics. Writing and implementation of algorithms in languages Pascal and Logo.

5. Superstructure part – 6 basic sections • Mathematical calculations and modelling with spreadsheets – use of numerical and graphical tools for quantitative processing and analysis of data in tables, realization of iterative calculations, implementation of mathematical algorithms into the tables. • Dynamic geometrical systems – construction and examination of dynamic geometrical constructions, measurements of figures and their use in calculations, graphical display of dependence between quantities, analytical expression of figures and its exploitation in tasks solutions. • Mathematical software of CAS type (Computer Algebra System) – carrying out numerical and symbolic calculations, graphical representation of data, production of interactive mathematical documents, searching for accurate ways of use of programmes of this kind in solving mathematical tasks.

6. The courses for information education • Described contents of information education have been implemented mainly in three one-term courses starting in the 2nd year: • Introduction to ICT – general part • ICT – general part and the first 2 sections of superstructure part • ICT applications in teaching Mathematics – the last 3 sections of superstructure part • Voluntary subject – Basics of algorithmization

7. The development of information education • Considering quick development of ICT, it is very important to lead students towards self-study and active development of their knowledge in this field • It has been created an electronic educational course for teaching of the subject ICT applications in teaching Mathematics which covers numerical and graphical tools of program MS Excel for solution of mathematical tasks

8. The description of educational course • The course is built on basic principles of modern conception of education (e-learning) • Implementation of electronic teaching materials is based on linking www technologies with technologies united in MS Office package • To provide an interactive and motivating working environment there are www sites enriched with dynamic elements (two and more -phase pictures, active tables, active text fields with buttons for checking of their content)

9. Educational contents of course • The content of the course is divided into seven lectures.Each of the lectures consists of 2 to 4 teaching units • Each teaching unit contains tasks, which are solved directly in environment of program MS Excel • Workbooks contain sheets for student’s work and sheets with example solution which is supplemented with additional information

11. Educational program - ETECIS • We created at our department several educational applications for support of mathematics teachingat secondaryat primary schools • Educational program ETECIS is focused on teaching of elementary theory of numbers. The program produces attractive and stimulating environment for computer assisted learning of Mathematics • Next picture shows motivational problem for topic Remainder from division and divisibility

12. The motivational problem ftp://ftp.upjs.sk/pub/education/matematika

13. Computer assisted learning of Mathematics • These courses are parts of a multimedia CD aimed at integration of ICT into teaching of Mathematics that has been produced at our department for support of mathematics teaching at primary and secondary schools • Educational multimedia CD is provided for schools through project Infovek, which administrates integration of ICT into education in Slovakia.

15. Computer assisted learning of Mathematics • Educational program and hypertext GRULP • Graphical solution of linear programming problems • Slovak version www.science.upjs.sk/diplom/grulp • English version www.mathe-online.at/materialien/Danka.Timkova • Other educational applications and study materials • ŠMIS (School Mathematics Information Service) kekule.science.upjs.sk

16. The electronic collection of mathematic problems • Is a part of School Mathematics Information Service • Allows to improve preparation of teachers to mathematics teaching • Is based on database system MySQL and its interface is implemented in JavaNet • Development and verification of electronic collection is realized at present by teachers of mathematics at two secondary schools.

17. The possibilities of collection • Selecting problems by specifying of classification criteria, printing a copy of selected problems (for every user) • Inserting new problems into the collection, changing the text of a problem, changing the classification of a problem, deleting a problem (for selected users) • Inserting, changing, deleting criteria for the classification of problems (for administrator)

18. Another intentions and plans • To create interactive multimedia courses for teaching of Mathematics in the system ToolBook II Instructor • To specify the parts in didactical preparation of mathematics teachers - suitable for realization through e-learning • To compose selected sections as educational courses, which will be provided in LMS Moodle • To develop a system of further education of mathematics teachers focused on integration of ICT to mathematics teaching at primary and secondary schoolsby means of mathematical programmes (Cabri geometry, Derive, MS Excel)

19. Thank you for yourattention Stanislav Lukáč, Danka Timková, Faculty of Science of University P.J. Safarik Kosice Jesenná 5, 041 54 Košice, Slovakia slukac@kosice.upjs.sk,timkova@science.upjs.sk