Interdisciplinary Approach in Mathematics Education - Innovative Method or Returning to the Roots? University. design and education

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1 Interdisciplinary Approach in Mathematics Education - Innovative Method or Returning to the Roots? Teaching Mathematics and Arts at Kaposvár University Mathematics in architecture and civil engineering design and education MAY 26-28, 2011 Pécs A projekt a Baross Gábor keitti09 projekt keretében valósul meg.

2 Contents 1. Mathematics and Arts subject at the Kaposvár University 2. Experience Workshop at the Kaposvár University 3. Zometool in the education of three-dimensional geometry

3 Sciences and arts at the Faculty of Pedagogy Mathematics and arts at the Faculty of Arts Optional subject at the Faculty of Pedagogy Special Needs Teacher and Primary School Teacher Optional subject for all students of the University 26 correspondence students 19 full time students Majors: Agricultural Engineer, Agricultural Rural Development, Nature Protection Engineer, Animal Production Engineer, Communication and Media Science, Primary School Teacher-Music, Special Needs Teacher, Computer Librarian, Finance and Accounting

4 The aim of the subject s education: A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. Godfrey Harold Hardy Mathematics brings in spiritual powers that are not very much different from those required by poetry and arts." Dan Barbilian To picture the unity of the sciences and arts using mathematical train of thought illustrated with artworks. To develop the problem solving skill by mathematical games and by the analysis of the mathematical content hidden in the artworks. We approach the topics through minimal formalism emphasizing the intellectuality of mathematics.

5 Topics of the subject: Connection of mathematics (sciences) and arts in general The golden ratio and the Fibonacci-series Symmetries, patterns, tiling M. C. Escher s art Dimensions 1 dimensional shapes, lines, knots 2 dimensional shapes, orientable, non-orientable surfaces, playing on the different surfaces Minimal surfaces 3 dimensional shapes, Platonis solids, archimedien solids, Euler theorem 4 dimensional shapes, projection to 2 and 3 dimension Impossible shapes, optical illusions

6 Lecture Practice with hand -- ZomeTool building with Computer -- drawings, graphics Inscape, Cali, Euler3D, etc. Requirements: self made creation, work connected to either of the topics, by hand, or by computer, or essay

7 The works of special needs teacher student in 2010 by Inkscape program

8 Pattern 1 dolphins d o l p

9 Pattern 2 flowers

10 Pattern 3

11 Pattern 4

12 Pattern 5

13 Pattern 6 birds

14 Pattern 7 similar to folk motifs

15 Fractals The smaller, the darker

16 rosettes

17 The students helped me to organize a ZomeTool exhibition at the Training and Practise Conference.

18 Special needs teacher student in Photos in connection with the topics Primary school teacher, correspondence student in 2011 On the basis of 5st year pupils

19 Nature Protection Engineers in 2011

20 Communication and Media Science student in 2011

21 1st year Agricultural Rural Development student 6 different prisms can be made of 8 small triangular prism and meanwhile 10 coherent pictures can be constracted Now she is working on Euler3D animation

22 Caleidocycle consists of 48 tetrahedra Half rhombic dodecahedron The work of a post-graduate correspondence finance student Rhombic dodecahedron, hollow inside

23 Rhombic dodecahedron Cube, octahedron are inscribed in the rhombic dodecahedron

24 Experience workshop, creative schooldays at the Kaposvár University for high school student s in 2009 and 2010

25 Program: Lectures, presentations workshops by artists, scientists and teachers exhibitions

26 Participants: 300 high school students and their teachers, in 2009 and in 2010 too.

27 How can the ZomeTool be used in the education of the How can the ZomeTool be used in the education of the 3-dimensional geometry?

28 Why the three-dimensional geometry? The most problematical topic of mathematics education The suggested number of lesson is less than 30 during the 4 years of high school in Hungary It is difficult to make good figure for teacher and for students too The students have the worst results in three-dimensional geometry in the matura examination The importance of demonstration

29 1835. We cut the vertex of the 6 cm edges cube with flat to cross midpoint of the edges. What is the volume of the remainder solid? Czapáry Endre Czapáry Endréné Csete Lajos Hegyi Györgyné Iványiné Harró Ágota Morvai Éva Reiman István Matematika Gyakorló és érettségire felkészítő feladatgyűjtemény III. Geometriai feladatok gyűjtemény, Nemzeti Tankönyvkiadó,

30 1912. Prove that -- from 4 congruent regular tetrahedra and one regular octahedron regular terahedron with twice as long edges can be built. Czapáry Endre Czapáry Endréné Csete Lajos Hegyi Györgyné Iványiné Harró Ágota Morvai Éva Reiman István Matematika Gyakorló és érettségire felkészítő feladatgyűjtemény III. Geometriai feladatok gyűjtemény, Nemzeti Tankönyvkiadó,

31 Volume calculation: triangular pyramid, triangular prism, parallelepiped

32 A symmetrical square-based pyramid has base length 26 cm and the angle of the adjacent sides are 120º. What is the height of a pyramid? (OTV I. 3.) Molnár Emil Molnár Matematikai Emil Matematikai versenyfeladatok versenyfeladatok gyűjteménye gyűjteménye , Tankönyvkiadó, 1974

33 Shadows, projections of this three dimensional figure

34 Shadows, projections of a cube

35 Thank you for your attention!

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