An Introduction to Theories of Knowledge and Learning of Mathematics

Lessons are not given in the academic year 2025-2026.

Mathematical competencies. Assessment in mathematics. The role of semiotic representations and transitions between representations in the learning of mathematics. Concept definition and concept image, prototypes, the process and object character of concepts. The role of proofs in school mathematics. Aspects of algebra. Topics from didactics of mathematics are illustrated using examples from analysis and algebra.

After having completed the course, the candidate is expected to have acquired learning outcome, defined as knowledge, skills and general competence as specified below:

Knowledge

The candidate has

• good knowledge of core topics from didactics of mathematics, with emphasis on the teaching and learning of algebra and functions,
• good knowledge of the role of argumentation, reasoning and proofs in mathematics in general and in school mathematics in particular,
• good knowledge of assessment in mathematics.

Skills

The candidate can

• use theory from didactics of mathematics to analyse students' learning processes,
• report on results from such analyses both oral, and in writing,
• conduct assessment in mathematics based on relevant theory.

General competence

The candidate is able to

• plan and carry out teaching of mathematics for grades 8-13 based on good knowledge of mathematics and didactics of mathematics.

The teaching is concentrated in seminars, accompanied by Internet based tutoring. Compulsory tasks connected to the candidate's own school practice are given during the semester.