Course: Didactics of mathematics I

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Course title Didactics of mathematics I
Course code UMB/020
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study 1
Frequency of the course In each academic year, in the winter semester.
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Pazourek Karel, Mgr. Ph.D.
  • Kalová Jana, doc. RNDr. Ing. Ph.D.
Course content
Content of this course is pedagogical interpretation of mathematical theories and practices focusing on the content of secondary school curriculum. Thematic units follow secondary schools curriculum, part of these is supported by mathematical software. 1. Definition of mathematical concept, determining of subject, personality of the teacher of mathematics, strategy of his work, motivation of students, organization of education 2. Cognitive process, formalist approach, transmission model and constructivist concept 3. Mathematical thinking, its content, scope, ontogeny and phylogeny, methodology 4. Communications with students in mathematics, equipment, importance and impact of ICT on students 5. Assessment, classification, students with different mathematical talent Methodology: 6. Classification of numbers, natural numbers, integers, divisibility, rational numbers, discrete set and its visualization 7. Irrational and real numbers, limits, infinity, continuity 8. Complex numbers, applications, mathematical software 9. Mathematical logic, mathematical proof 10. Variable, basic arithmetic and algebra, expression, polynomial, equation, function 11. Set, cartesian product, relation, map, function and its properties, derivative 12. Elementary functions, calculus, mathematical software 14. Systems of linear and nonlinear equations, inequalities, matrices, context with geometry, mathematical software 15. Problems and solutions of mathematical olympiad (continuously)

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Projection, Work with multi-media resources (texts, internet, IT technologies)
  • Class attendance - 52 hours per semester
  • Preparation for classes - 80 hours per semester
  • Preparation for credit - 10 hours per semester
  • Preparation for exam - 20 hours per semester
Learning outcomes
The goal of this course is to link knowledge of mathematics, didactics and pedagogical disciplines and to train students to manage their teaching at secondary school.
Students will acquire skills necessary for managing their practical stay at secondary schools.
Prerequisites
Perfect level of high school math knowledge.

Assessment methods and criteria
Oral examination, Student performance assessment, Test, Interim evaluation

- active attendance of practicals - at least 70% points from one written test - exam: successfully answered questions from one topic
Recommended literature
  • Hejný, Milan a kol. 25 kapitol z didaktiky matematiky. 2004. ISBN 80-7290-189-3.
  • Polák, Josef. Didaktika matematiky. 2014. ISBN 978-80-7238-449-5.
  • Polák, Josef. SŠ matematika v úlohách II. Prometheus, 2011. ISBN 80-7196-116-3.
  • Polák, Josef. SŠ matematika v úlohách I. Prometheus, 1996. ISBN 80-7196-337-2.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (2012) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter