SZc0058 Didactics of mathematics 2

Faculty of Education
Spring 2025
Extent and Intensity
0/0/1.7. 3 credit(s). Type of Completion: z (credit).
Taught in person.
Teacher(s)
doc. RNDr. Jaroslav Beránek, CSc. (lecturer)
Mgr. Irena Budínová, Ph.D. (lecturer)
RNDr. Břetislav Fajmon, Ph.D. (lecturer)
Mgr. Jana Veseláková (lecturer)
Bc. Tereza Mikulášková (seminar tutor)
Guaranteed by
Mgr. Irena Budínová, Ph.D.
Department of Education – Faculty of Education
Contact Person: Mgr. Irena Budínová, Ph.D.
Supplier department: Department of Education – Faculty of Education
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After completing the discipline, the student:
• Understands the taught content – teaching arithmetic topics in elementary school, teaching algebraic topics in elementary school, teaching geometric topics in elementary school, methods of solving mathematical problems.
• Can set lesson objectives and understands how to follow them in the lesson fulfillment.
• Reflects knowledge from practice and connects it with mathematical and didactic knowledge.
Learning outcomes
After completing the course, the student is able to:
• Choose math problems that are adequate to the student's needs.
• To solve these problems with methods corresponding to the pupil's year and his mathematical skills abilities.
• Reflect knowledge from practice and relate it to theoretical mathematics didactic knowledge.
• Transform didactic knowledge into mathematics teaching.
• Establish the objectives of the mathematics lesson.
Syllabus
  • Numerical fields. Algebraic expressions. Natural numbers, integers, rational numbers, real numbers. (1 throw.)
  • Powers with natural, whole and rational exponents, square roots. Polynomials, broken expressions, expressions with powers and roots. (2 hours)
  • Geometric constructions of algebraic expressions. (2 hours)
  • Elementary theory of numbers, divisibility in the field of whole numbers. Methods of determining the least common multiple and greatest common divisor, divisibility criteria, prime numbers, composite numbers. (1 hour)
  • Percentage, word problems with percentages. Basic concepts of financial mathematics. (1 hour)
  • Mathematical problem and its solution. Methods of solving mathematical problems: experiment, arithmetic solution, algebraic solution. The importance of geometric representation in the analysis of the task. (1 hour)
  • Equations and inequalities in school mathematics solved from the 1st grade of elementary school. Propedeutics of equations, linear equations and inequalities. Equivalent and consequent adjustments of equations and inequalities. Solutions of some types quadratic equations, use in word problems. (2 hours)
  • Elementary functions in primary and secondary school mathematics. Linear function. Quadratic function. Linear curve function. Methods of introducing elementary functions in elementary school. Ways to enter functions. Properties of functions. (2 hours)
  • Planimetry in the school mathematics course. Approaches to introducing basic planimetric concepts school. Angle, triangle, quadrilateral, circle, circle. Properties of these formations. Basic geometric constructions. The phase of solving the construction task. Solving design problems with utilization basic theorems of shape determination, sets of points with a given property, geometric representations. (2 throw.)
  • Geometric representations in the course of school mathematics. Matching views: axial symmetry, central symmetry, rotation, translation. Similar representations: similarity, sameness. Use methods of manipulative activities to derive individual representations. (2 hours)
  • Stereometry in the school mathematics course. Developing spatial imagination in elementary school. Circumferences and contents of plane geometric shapes. Surface and volume of bodies. Derivation of relationships. (2 throw.)
  • Combinatorics in primary and secondary school. Tasks to develop basic combinatorial thinking school (1 hour)
  • Probability and statistics in school mathematics. Development of probabilistic thinking on elementary School. (1 hour)
Literature
    required literature
  • Rendl, M., Vondrová, N., Hřibková, L., Jirotková, D., Kloboučková, J., Kvasz, L., & Žalská, J. (2013). Kritická místa matematiky na základní škole očima učitelů. Univerzita Karlova v Praze, Pedagogická fakulta.
  • Vondrová, N. (2019). Didaktika matematiky jako nástroj zvládání kritických míst v matematice. Univerzita Karlova, Pedagogická fakulta.
  • Vondrová, N. (2020). Matematická slovní úloha: mezi matematikou, jazykem a psychologií. Charles University in Prague, Karolinum Press.
  • Budínová, I. (2018). Přístupy nadaných žáků 1. a 2. stupně základní školy k řešení některých typů úloh v matematice. Masarykova univerzita.
  • Budínová, I., & Pavlíčková, L. (2020). Konstrukční úlohy. Učební text pro studenty učitelství matematiky 2. stupně základní školy. Masarykova univerzita.
Teaching methods
Lecture, workshop, independent work, consultation, portfolio creation.
Assessment methods
The following will be evaluated:
• Continuous active work.
• Solving assigned tasks.
• Creating a portfolio: creating didactic aids suitable for forming an opinion in individual parts of school mathematics.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: in blocks.
Information on the extent and intensity of the course: 20 hodin.
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