Course: Mathematics and Its Teaching Methodology (Arithmetic)

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Course title Mathematics and Its Teaching Methodology (Arithmetic)
Course code KMT/MSD3
Organizational form of instruction Lecture + Seminar
Level of course Master
Year of study 2
Semester Winter and summer
Number of ECTS credits 2
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)
  • Honzík Lukáš, PhDr. Ph.D.
  • Brožová Miroslava, Mgr.
  • Huclová Miroslava, PhDr. Ph.D.
Course content
1. Indeterminate equations 2. Word problems solved by indeterminate equations 3. Field of rational numbers, numerical operations with real numbers 4. Ordered field of rational numbers 5. Fractions in primary school 6. Real numbers 7. Decimal expansions of real numbers, approximate expression of a real number with a decimal fraction 8. Decimal numbers in primary school 9. Word problems and their position in primary school subject matter 10. Solution of simple word problems (addition, subtraction) 11. Solution of simple word problems (multiplication, division) 12. Compound word problems 13. Unconventional word problems

Learning activities and teaching methods
Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, Collaborative instruction, Cooperative instruction, Seminar classes
  • Contact hours - 26 hours per semester
  • Preparation for formative assessments (2-20) - 15 hours per semester
  • Presentation preparation (report) (1-10) - 10 hours per semester
prerequisite
Knowledge
to master the basics of propositional logic
to master the basic concepts of set theory
to master the basic concepts of relation theory
to define individual mathematical operations
to know the concepts and properties related to the semicircle of natural numbers and the range of integers (KMT/MSD2 exit level)
to explain the principles of counting in the decimal system
to explain the principles of numerical operations in non-decimal number systems
to summarize the possibilities of using number systems in other science subjects
to explain the basic principles of the construction of the integer integrity field
to summarize and describe the criteria for the divisibility of natural numbers by 2, 3, 4, 5, 8, 9, 10, 11
to distinguish the different ways of determining the greatest common divisor
to distinguish the different ways of determining the least common multiple
Skills
demonstrate different strategies for solving equations and inequalities with regard to the knowledge of children at primary school
apply theoretical knowledge of non-integer number systems to the mathematics curriculum at primary school
search for and create problems with integers leading to the integration of mathematics and science
decide whether a given number is a prime number
solve practical problems using indefinite equations and evaluate other methods suitable for primary school
Competences
N/A
N/A
learning outcomes
Knowledge
construct the solid of rational numbers
clarify properties of real numbers
classify decimal development of real numbers
summarize phenomena affecting the student's word problem solving process
distinguish between analytic and synthetic methods of solving compound word problems and their application to specific problems
Skills
solve practical problems using indefinite equations and evaluate other methods suitable for pupils of primary school
propose various activities leading to the creation of the rational number concept at primary school
demonstrate ways of converting fractions into rational numbers and vice versa
propose arithmetic and algebraic strategies for solving simple word problems at primary school
propose ways of visualising the structure of simple and compound word problems
demonstrate work with error in mathematics lessons
Competences
N/A
teaching methods
Knowledge
Interactive lecture
Practicum
Collaborative instruction
Multimedia supported teaching
Task-based study method
Skills
Interactive lecture
Practicum
Multimedia supported teaching
Discussion
Competences
Collaborative instruction
Discussion
Task-based study method
assessment methods
Knowledge
Test
Continuous assessment
Skills
Test
Skills demonstration during practicum
Continuous assessment
Competences
Skills demonstration during practicum
Continuous assessment
Recommended literature
  • Učebnice, pracovní sešity a metodické příručky matematiky pro 1. st. ZŠ.
  • Coufalová, Jana. Matematika s didaktikou : pro 2. ročník učitelství 1. stupně ZŠ. 5. vydání. 2016. ISBN 978-80-261-0650-0.
  • Frobisher, Anne, Frobisher, Len. Didaktika matematiky: Porozumieť, riešiť, počítať. Bratislava, 2015. ISBN 978-80-8140-180-0.
  • Novotná, J. Analýza řešení slovních úloh. Karolinum, Praha, 2000.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (16) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (17) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (16) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (15) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (12) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (13) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (17) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (15) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (19) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (18) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (18) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (14) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer