COURSE AIMS AND OBJECTIVES: This course provides student - mathematics teachers with necessary knowledge and skills for effective planning, management, implementing and reflecting mathematical lessons at primary and secondary school level and with various assessment techniques. Particular attention will be paid to the didactics of geometry, trigonometry and mathematical modelling, and to mathematical applications in other fields.
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 geometry, trigonometry and mathematical modelling, as well as to some frequent mathematical applications from 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. Assessment of students' achievments. Continuous (classroom) assessment and grading methods. Self-assessment. Assessment of group work. Development of written proofs and tests.
2. Didactics of geometry and trigonometry. Goals of teaching and learning geometry and trigonometry. Axiomatic approach to the plane and space geometry in the primary and secondary mathematics education. Development of the spacial orientation and reasoning. Syntetic and analytic (coordinate) geometry. Gender differences in the spacial reasoning. Teaching methods, curriculum materials, psychological factors for developing geometric and measurement concepts.
3. Didactics of mathematical modelling. Mathematics of finance and business. Role of applications in mathematics curriculum. Applications in the natural and social sciences (especially in business and finances). Notion of mathematical model - relation between "real world" and mathematical problems. The process of mathematical modelling. Design and development of mathematical models. Teaching methods and curriculum materials.