Course objectives:
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Providing students with an overview of school mathematics and knowledge necessary for following study and exercising a profession of teacher. Acquiring basic knowledge and skills needed for solving mathematical problems. Improvement of communicative competences and competences for solving problems. Acquiring knowledge needed for following study and exercising a profession of teacher.
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Requirements on student
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Two tests. It is necessary to gain at least 14 points out of 20 in each paper. Tests contain types of problems solved during semester. Each of two tests consists of four problems, at most five points apiece. To the points gained in this way points given for individual work can be added - correctly solved problem, its presentation and explanation to others students.
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Content
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Direct methods for solving determinative problems (the experimental method, method for solving equations and inequalities). Higher order algebraic equations and inequalities. Systems of equations and inequalities. Indirect methods for solving determinative problems (the method of dividing the problem to partial problems, substitute and graphical method for solving equations and inequalities). Parametrical systems of functions and utilization of their graphs. Equations, inequalities and their systems with parameters. Problems in school mathematics, typology of problems.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Basic:
Odvárko, O. a kol. Metody řešení matematických úloh.. Praha : SPN, 1990. ISBN 80-04-20434-1.
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Recommended:
Hecht, T., Sklenáriková, Z. Metódy riešenia matematických úloh. SPN Bratislava, 1992.
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Recommended:
Herman, J., Kučera, R., Šimša, J. Metody řešení matematických úloh I.. Brno : Masarykova univerzita, 1996. ISBN 80-210-1202-1.
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Recommended:
Bušek, Ivan. Řešené maturitní úlohy z matematiky. 1. vyd. Praha : SPN, 1985.
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Recommended:
Polák, J. Středoškolská matematika v úlohách I., II. Prometheus Praha (1996, 1999), 1999.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for comprehensive test (10-40)
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26
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Contact hours
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26
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Total
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52
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
master mathematical language and procedures at the level of the bachelor's study field Mathematical Studies |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
master mathematical language and procedures at the level of the bachelor's study field Mathematical Studies |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
classify methods for solving mathematical problems |
describe the principle of basic methods for solving problems |
describe the procedure for solving simpler algebraic equations of higher orders and their systems |
explain the function of the parameter in equations and inequalities |
Skills - skills resulting from the course: |
choose a suitable method for solving a mathematical problem |
solve a mathematical problem with the chosen method |
determine the solution of an equation or inequality depending on the parameter |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Test |
Skills demonstration during practicum |
Self-evaluation |
Individual presentation at a seminar |
Skills - skills achieved by taking this course are verified by the following means: |
Test |
Self-evaluation |
Continuous assessment |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Test |
Skills demonstration during practicum |
Self-evaluation |
Continuous assessment |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture with visual aids |
Lecture supplemented with a discussion |
Seminar |
Collaborative instruction |
Group discussion |
One-to-One tutorial |
Discussion |
Seminar classes |
Lecture |
Task-based study method |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Seminar |
Skills demonstration |
Group discussion |
Task-based study method |
Seminar classes |
Discussion |
One-to-One tutorial |
Collaborative instruction |
Competences - the following training methods are used to achieve the required competences: |
Lecture with visual aids |
Practicum |
Self-study of literature |
Individual study |
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