1. komponenta

Lecture type	Total
Lectures	30
Exercises	30
Seminar	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: The course aims to provide student - mathematics teachers with necessary knowledge and skills for effective planning, management, implementing and reflecting mathematical lessons at primary and secondary school level. Particular attention will be paid to the didactics of combinatorics, statistics, probability and mathematical analysis.

COURSE DESCRIPTION AND SYLLABUS: The course contains lectures, tutorials and seminars. Theoretical part (lectures) focuses on the basics of mathematics teaching and learning. Students - prospective teachers will be introduced to the didactics of combinatorics, stochastics and mathematical analysis in primary and secondary school curricula. In tutorials, acquired theoretical knowledge will be applied to selected examples - topics from school mathematics, through various forms of instruction and working methods (individual study, hands - on activities, pair work, group work, team - collaborative work, project work). Seminars consist of students' group or individual oral presentations of assigned topics from school mathematics, followed up by group discussions.
The headlines of the course are:
1. Types of mathematical subjects (courses) approaches to children with special needs. Compulsory, elective, optional, additional and remedial courses. Modified curriculum for students with special needs (with mild mental retardation or fine motor problems). Mathematically gifted children. Mathematical competitions in Croatia and abroad.
2. Lesson planning and classroom management. Insight into mathematics curricula and syllabuses in the primary and secondary education. Pedagogical documentation. Lesson planning and preparing. Lesson structure. Development of materials for mathematics instruction. Didactical means.
3. Mathematical problems. Theories and methods of mathematical problem solving. Open - ended and close - ended problems. Posing, solving and extending mathematical problems. Problem solving strategies. Communicating mathematical problems and solutions.
4. Didactics of combinatorics, probability and statistics. Basics combinatorial concepts. Dirichlet (pigeonhole) principle. Basic principles of counting. Inclusion - exclusion principle and its connection to the operations with sets. Data handling and statistics. Different conceptions of randomness and probability. Fundamental stochastic ideas. Exploratory data analysis. Association and causality. Inference and induction. Various teaching methods, curriculum materials and psychological factors for developing combinatorial and stochastical concepts. Errors, difficulties and misconceptions in probability, graphing, averages, association, distributions and inference.
5. Didactics of mathematical analysis. Developing the fundamental concepts of real analysis at different educational stages: functions, limits, differential and integral calculus. Presentation of various didactical approaches to selected topics, followed up by group disscusions.

1. M. Pavleković: Metodika nastave matematike s informatikom 1
2. M. Pavleković: Metodika nastave matematike s informatikom 2
3. B. Pavković, D. Veljan: Elementarna matematika 1
4. B. Pavković, D. Veljan: Elementarna matematika 2
5. D. Palman: Planimetrija
6. D. Palman: Stereometrija
9. A. S. Posamentier, J. Stepelman: Teaching Secondary School Mathematics: Techniques and Enrichment Units
10. B. Dougherty (Ed.): Research in Mathematics Education
11. M. A. Sobel, E. M. Maletsky: Teaching Mathematics: A Sourcebook of Aids, Activities, and Strategies
12. J. A. Van De Walle: Elementary and Middle School Mathematics: Teaching Developmentally,5th edition
13. C. J. Brahier: Teaching Secondary and Middle School Mathematics
14. M. Serra: Discovering Geometry: An Inductive Approach
15. J. Murdock, Ellen Kamischke, Eric Kamischke: Discovering Advanced Algebra: An Investigative Approach
16. K. Johnson, T. Herr: Problem Sopving Strategies - Crossing the River with Dogs and Other Mathematical Adventures
17. R. L. Scheaffer, M. Gnanadesikan, A. Watkins, J. A. Witmer: Activity - Based Statistics
18. A. Watkins, R. L. Scheaffer, G. W. Cobb: Statistics in Action: Understanding the World of Data

Enrollment :
Passed : Methods of teaching mathematics 2

Mandatory course - Regular study - Mathematics and Physics Education