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Methods of teaching mathematics 2

Code: 45762
ECTS: 8.0
Lecturers in charge: prof. dr. sc. Sanja Varošanec - Lectures
Lecturers: doc. dr. sc. Mea Bombardelli - Seminar
doc. dr. sc. Ana Prlić - Seminar

Denis Husadžić, mag. math. - Exercises
doc. dr. sc. Marko Radulović - Exercises
Mateo Tomašević, mag. math. - Exercises
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
Seminar 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: The course aims to introduce students - prospective mathematics teachers to the basic concepts of mathematics teaching and learning (that is, to the mathematical didactics) at primary and secondary school level. It provides insight into various forms, methods and strategies of mathematics teaching (instruction) and learning and provides students with necessary skills to develop proper didactical approaches in their own mathematics classroom. Particular attention will be paid to the didactics of arithmetics and algebra.

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 arithmetics and algebra 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. Didactical principles of mathematics teaching. Principle of adequacy (suitability for child's age). Principle of a systematic and gradual approach (from the whole to the detail, from the known to the unknown, from the simple to the complicated). Teaching based on scientific foundations. Principle of students' motivation, interest, consciousness and activity (linking mathematics teaching to the reality, action learning). Principle of clearness (visuality) and abstraction (from the concrete to the abstract, inquiery of exemplary problems). Principle of problem posing and solving (the so-called problem approach). Principle of creativity. Principle of knowledge, skills, and habits permanency (repeating and reviewing through applications). Principle of effective teaching. Principle of individual pedagogical approach to each student considering personal features and cognitive abilities of the students (learning through individual learning paths). Principle of contemporaneity and historycism. Principle of integration of different knowledge and skills. Principle of holism (interdisciplinary approach).
2. Teaching forms and methods. Social forms of mathematics teaching and learning: frontal and individual work forms. Methods and instructional models for teaching mathematics: project work, problem solving, heuristics, experiments, demonstration, discovery learning, programmed learning, working with written materials (reading techniques), working with other media etc.
3. Teaching mathematical concepts, theorems and proofs. Various methods of introducing proofs and proving in a mathematical classroom. Motivation. Establishing balance between heuristical approach and formal proving in mathematics teaching and learning.
4. Didactics of arithmetics and algebra. Construction of the real and complex numbers - introducing N, Z, Q, R and C. Related didactic approaches. Selected topics from K-12 mathematics curriculum and basic algebra. Various teaching methods, curriculum materials and psychological factors for developing natural, integer, rational, and real number structures, as well as other algebraic concepts.
Literature:
  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
  7. A. S. Posamentier, J. Stepelman: Teaching Secondary School Mathematics: Techniques and Enrichment Units
  8. B. Dougherty (Ed.): Research in Mathematics Education
  9. M. A. Sobel, E. M. Maletsky: Teaching Mathematics: A Sourcebook of Aids, Activities, and Strategies
  10. J. A. Van De Walle: Elementary and Middle School Mathematics: Teaching Developmentally,5th edition
  11. C. J. Brahier: Teaching Secondary and Middle School Mathematics
  12. M. Serra: Discovering Geometry: An Inductive Approach
  13. J. Murdock, Ellen Kamischke, Eric Kamischke: Discovering Advanced Algebra: An Investigative Approach
  14. K. Johnson, T. Herr: Problem Sopving Strategies - Crossing the River with Dogs and Other Mathematical Adventures
  15. R. L. Scheaffer, M. Gnanadesikan, A. Watkins, J. A. Witmer: Activity - Based Statistics
  16. A. Watkins, R. L. Scheaffer, G. W. Cobb: Statistics in Action: Understanding the World of Data
Prerequisit for:
Enrollment :
Passed : Methods of teaching mathematics 1
2. semester
Mandatory course - Mandatory studij - Mathematics and Computer Science Education
Consultations schedule:

Content

E-course Methods of Teaching Mathematics 2 on Merlin
(you can log in using password you will be provided during lecture).


Link to the course former web page: https://web.math.pmf.unizg.hr/nastava/metodika/ or  https://web.math.pmf.unizg.hr/nastava/mnm/ (pages are no longer updated but contain useful materials).

Link to the notices web page: http://www.pmf.unizg.hr/math/predmet/mnm2_a