|
Lecturer(s)
|
-
Červený Petr, PhDr. Ph.D.
-
Křížková Jitka, PhDr. Ph.D.
-
Bílková Linda, 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 Educational games (board and card games) are incorporated to develop spatial orientation, number sense and geometric understanding, and to practise basic mathematical operations (geometric quartets, mathematical matching games, lotto, tangrams and bingo). Students learn how these games can be used not only in mathematics lessons but also in extracurricular activities, such as mathematics clubs. They also design additional activities suitable for both classroom teaching and extracurricular settings. This practical work is followed by the development of study materials and collaborative activities undertaken by students enrolled in a primary teacher education programme using the shared interface of the NotebookLM platform. Students use this tool to plan lessons, organise study materials and create visual resources illustrating mathematical concepts appropriate for primary school pupils. The resulting materials support teaching while also enabling the assessment of students' knowledge and skills in mathematics education.
|
|
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 |
| The student is expected to have basic user skills in working with Microsoft 365 and Google Workspace tools. |
| 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 |
| Understanding the possibilities of using artificial intelligence and digital technologies to support learning, create teaching materials, and develop digital competences. |
| Upon completing the course, the student demonstrates the ability to use artificial intelligence tools effectively and critically, take ultimate responsibility for the outcomes of their work, and consider the ethical implications of the solutions they propose. |
| 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.
-
Umělá inteligence, které pomáhá učitelům s přípravami na výuku. .
-
64 tipů ? Jak využít AI (nejen) ve školství. .
-
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. Praha: Karolinum, 2000.
|