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Methods of teaching mathematics 1

Code: 45758
ECTS: 8.0
Lecturers in charge: prof. dr. sc. Aleksandra Čižmešija - Lectures
Lecturers: prof. dr. sc. Aleksandra Čižmešija - Seminar

prof. dr. sc. Aleksandra Čižmešija - 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. Particular attention will be paid to various forms and methods of mathematical thinking and reasoning and to formulation, proving and implementation theorems, as prerequisites for understanding processes of teaching and learning mathematics.

COURSE DESCRIPTION AND SYLLABUS: The course contains lectures, tutorials and seminars. Lectures provide theoretical foundation of teaching and learning mathematics. In tutorials, acquired theoretical knowledge will be applied to selected examples - concrete topics from the 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. Introduction. Mathematics as a science and a subject taught in primary and secondary education - their definitions and relations. Position of mathematics in the Croatian national curriculum and a comparison to selected European countries.
2. Aims and learning objectives of mathematics education. General and specific aims. Three crucial components of mathematics education: mathematical concepts, strategies (problem solving, theorem proving, model building etc.) and algorithms. Learning objectives snd strands (contents) for each education level (according to ISCED 1997). Educational standards (in Croatia and elsewhere).
3. Didactics of mathematics. The notion of the field (mathematical) didactics - interdisciplinary scientific discipline and a theoretical and practical guidance (the know-how) for successfull mathematics teaching and learning.
4. Forms of mathematical thinking and reasoning. The language of mathematics (development, use, symbols). Basics of logic (mathematical ideas, assumptions and concept development). Mathematical notions. Example and counterexample construction. Interpretation and implementation of the definitions of mathematical concepts. Formulation, proving and implementation of theorems in mathematics education. Inductive reasoning - complete and incomplete induction. Deductive reasoning.
5. Methods of mathematical reasoning. Analysis and synthesis. Variation. Analogy. Generalization and specialization. Abstraction and concretization. Distinguishing cases. Superposition of particular cases. Descartes' method. Experiment. The method of undetermined coefficients. Substitution. The method of recurrence relations.
Literature:
  1. M. Pavleković: Metodika nastave matematike s informatikom 1
  2. M. Pavleković: Metodika nastave matematike s informatikom 2
  3. A. Watkins, R. L. Scheaffer, G. W. Cobb: Statistics in Action: Understanding the World of Data
  4. B. Pavković, D. Veljan: Elementarna matematika 1
  5. B. Pavković, D. Veljan: Elementarna matematika 2
  6. D. Palman: Planimetrija
  7. D. Palman: Stereometrija
  8. A. S. Posamentier, J. Stepelman: Teaching Secondary School Mathematics: Techniques and Enrichment Units
  9. B. Dougherty (Ed.): Research in Mathematics Education
  10. M. A. Sobel, E. M. Maletsky: Teaching Mathematics: A Sourcebook of Aids, Activities, and Strategies
  11. J. A. Van De Walle: Elementary and Middle School Mathematics: Teaching Developmentally,5th edition
  12. C. J. Brahier: Teaching Secondary and Middle School Mathematics
  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
1. semester
Mandatory course - Mandatory studij - Mathematics and Computer Science Education
Consultations schedule:

Content

Link to the course former web page: https://web.math.pmf.unizg.hr/nastava/metodika/

Link to the course page on Merlin: https://moodle.srce.hr/2020-2021/course/view.php?id=83781

 

Please follow e-course Methods of Teaching Mathematics 1 on Merlin:

https://moodle.srce.hr/2020-2021/course/view.php?id=83781

especially notices that will be posted there.

Link to the notices web page: http://www.pmf.unizg.hr/math/predmet/mnm1_a