MA-427 The nature of mathematics (Autumn 2020)

Norwegian or English.

On successful completion of the course, the student should be able to

• understand the complex interaction between society, mathematics teaching and learning;
• understand the connections between practices, research, theories and methods in the context of the classroom;
• have an insight into mathematics education as an area of research;
• become a research based professional.

 

Mathematics is presented and discussed as the oldest of all sciences, about 4000 years old, comparable to astronomy but much older than physics. The most distinctive feature of mathematics is that it creates its notions and concepts by itself which do not in a simple sense exist in reality (for example real numbers, infinite set, instantaneous velocity and differential quotient). Nevertheless is this creation of mathematical concepts strongly suggested and influenced by practical needs. The course problematizes the notion "applied mathematics" in its historical development, for example modern versions such as modelling and statistics. The course will discuss differences in the notion of mathematicaL proof compared to proof in physics and other sciences, connecting to philosophical discussion (Popper and Lakatos). Also the variability of the notion of rigor in matematics will be discussed. It will be ahown that there exists a long tradition to compare mathematics with art, which is again peculiar to matematics. Finally, the specific relation between mathematics and society is investigated with many aspects of production og ideology, political misuse of mathematics, so - called << aloofness>> of mathematics and its practitioners. All mathematical arguments shall be rather simple and elementary, or simple deducible.

Seminars, lectures and obligatory written papers. The course has an expected workload of around 200 hours.

Parts of the course require attendance, detailed information will be given in Canvas at the start of the course. If needed the teaching can be performed in English.

Approved compulsory attendance in the course. Required assignments must be approved, see Canvas for more information

4 - hour written examination. Graded assessment.

The study programme manager, in consultation with the student representative, decides the method of evaluation and whether the courses will have a midterm- or end of term evaluation, see also the Quality System, section 4.1. Information about evaluation method for the course will be posted on Canvas.