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

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

• Working meeting to project EuroMath
• Innsbruck, 2004

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Project E-learning in preparation of mathematics
teachers

• The determining of mathematics teachers
  competence for use of ICT and working-out of
  system of information education 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

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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.

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Superstructure part 6 basic sections

1. 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.
2. 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.
3. 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.

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Superstructure part 6 basic sections

1. 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.
2. 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.
3. 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.

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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

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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

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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)

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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 students work and
  sheets with example solution which is
  supplemented with additional information

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Educational program - ETECIS

• We created at our department several educational
  applications for support of mathematics teaching
  at secondary at 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

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

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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/D
  anka.Timkova
• Other educational applications and study
  materials
• ŠMIS (School Mathematics Information Service)
  kekule.science.upjs.sk

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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.

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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)

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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 schools by means of mathematical
  programmes (Cabri geometry, Derive, MS Excel)

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Thank you for your attention
Stanislav Lukác, Danka Timková, Faculty of
Science of University P.J. Safarik Kosice Jesenná
5, 041 54 Košice, Slovakia slukac_at_kosice.upjs.sk,
timkova_at_science.upjs.sk