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    Učitelství všeobecně vzdělávacích předmětů pro základní školy a střední školy - matematika (7504T221)

    Fakulta: Pedagogická fakulta
    Studijní program: Učitelství pro střední školy (N7504)
    Forma studia: kombinovaná
    Druh studia: navazující magisterské
    Jazyk výuky: angličtina
    Minimální předpokládaný počet přijímaných: 5
    Standardní doba studia: 2 roky
    Forma přihlášky: Elektronická

    • Na tento program/obor nyní nelze podat elektronickou přihlášku.

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      Termín podání přihlášky: 28.02.2019
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      The goal of the study is to provide graduates with complete master education which will prepare them for the profession of a mathematics teacher at the lower and upper secondary schools of all types. The study is based on the balance of cognitive, didactic and pedagogic-psychological parts of teacher education. An emphasis is put on the use of didactic innovations in the teaching of mathematics with regard to the up-to-date didactic conceptions. The graduates will be prepared for the construction of school educational programmes with the focus on the integration of various areas of mathematics (arithmetic, algebra, geometry, statistics, financial mathematics, etc.) and various educational fields. The graduates will acquire sufficient amount of knowledge and skills to work in a differentiated way with pupils talented for mathematics.

      See study plan on http://studium.pedf.cuni.cz/karolinka/

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      1. Oral exam. Maximum number of points is 30 (2 questions, 15 points each). 
          The oral examination consists of problem solving and a theoretical part.
          The applicant is asked to bring a list of completed mathematical courses with brief syllabuses from the previous university study.

      2. Oral exam – assessing the applicants’ general awareness of pedagogy and psychology, and their motivation to study the chosen subjects – a maximum score of 30 points.

      Total score – 60 points maximum.

      1. Mathematics

      Topics: 
      Basics of mathematics (mathematical logic, sets); positional systems, divisibility tests, Diophantine equations, Euclidean algorithm, congruence; linear algebra (matrices, determinants, systems of linear equations, vector spaces, linear mappings); relational structures (order, equivalence); polynomials (algebraic and functional definitions of the polynomial, divisibility, algebraic and numerical solutions to equations); vectors, shapes in E2, E3, E4 and their incidence relationships studied via vectors; coordinate systems, basis; algebraic structures (group, field, ring, homomorphism, isomorphism); geometric transformations in a synthetic and analytic ways in E2: congruencies in plane (combination, classification, group of congruence); similar transformations in plane (classification, group of similarities); homothety (Monge theorem, Menelaus theorem); affine transformations in A2 (classification, synthetic and analytic descriptions, group of affine transformations); circle inversion, problems of  Appolonius; conics (affine and metric properties); elementary functions; calculus (continuity, limit and derivative – definition, properties, calculation; properties of functions continuous on an interval; mean value theorem; maximum and minimum; properties of a function and the construction of its graph); integrals (primitive function and definite integral – definition, properties, calculation; use in geometry, improper integral); differential equations (simple equations with independent variables, linear differential equations of the first order; linear differential equations of the second order with constant variables – general solution and solution with an initial condition); number sequences and series (number sequences – properties, limit of a sequence and its calculation; number series – properties, convergence criteria for series with non-negative terms, alternating series, absolute and non-absolute convergence).

      2. Pedagogy and Psychology

      Oral exam – assessing the applicants’ general awareness of pedagogy and psychology, and their motivation to study the chosen subjects – a maximum score of 30 points.

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      Podmínkou přijetí ke studiu v magisterském studijním programu je dosažení středního vzdělání s maturitní zkouškou. Podmínkou přijetí ke studiu v magisterském studijním programu, který navazuje na bakalářský studijní program, je rovněž řádné ukončení studia v kterémkoliv typu studijního programu.

      Způsob ověření: přijímací zkouška
      Datum ověření (přijímací zkoušky) od: 06.06.2019 Do: 14.06.2019
      Náhradní termín (přijímací zkoušky): 24.06.2019Do: 25.06.2019
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      University textbooks with the topics given above. For example:

      Coxeter, H.S.M. Introduction to Geometry. John Wiley & Sons, USA 1989

      Gans, D. Transformations and geometries. New York, Appleton-Century-Crofts, Meredith Corporation, 1969.

      Brannan, D.A., Esplen, M.F. Gray, J.J. Geometry. Cambridge, UK, Cambridge University Press, 2000.

      Cameron, P.J.: Introduction to Algebra. Oxford University Press, 2001.

      Ross, K.A.:Elementary Analysis: The Tudory of Calculus. Undergraduate texts in Mathematics, Springer Verlag New York-Heidelberg-Berlin 1980

      Fischer, E.: Intermediate Real Analisis. Undergraduate Texts in Mathematics, Springer Verlag NewYork-Heidelberg-Berlin 1983

      Ross, K. A.:Elementary Analysis: The Tudory of Calculus. Undergraduate texts in Mathematics, Springer Verlag New York-Heidelberg-Berlin 1980

      Kra, I. Abstract algebra with applications. Online textbook: http://www.math.sunysb.edu/~irwin/algbk.pdf

      Brin, M. G. Modern algebra. Online textbook: http://www.math.binghamton.edu/matt/m402/pack402.pdf

       

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      Graduates gain knowledge and skills necessary for the profession of a fully qualified mathematics teacher at the lower and upper secondary levels. They have rich mathematical, didactic and pedagogic-psychological education. They can apply modern didactic methods and forms of work in a creative way in their teaching of mathematics at different levels and types of schools. They are able to identify both talented pupils and pupils with special needs in mathematics and provide them with appropriate help. They can work outside the school system, for instance, in media, offices and institutions aimed at education and work with talented pupils in mathematics. They can continue their education within the PhD study in Mathematics Education.
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      Výše poplatků [CZK] / za období: 60000 CZK / rok