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 socalled 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 K12 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.
