Learning and teaching of mathematics

This course provides a deeper understanding of theories of learning and teaching in mathematics. The candidates will develop through theory and practice their ability to make justified choices for facilitating pupils learning opportunities in mathematics. Further, by using video and other documentation methods, the candidates will develop their competence in observing the learning and teaching of mathematics from grades 1 to 10, and analysing such observations using theory. Special emphasis is placed on the work of reading research in mathematics education and writing academic texts. The mathematical topics in the course are mainly taken from algebra. The candidates will, among other things, work with two different approaches to algebra in school mathematics: algebra as generalised arithmetic, and algebra as generalisation of patterns. Abstract algebra (group theory) will be an important topic for elucidating the structural aspects of algebra.

Knowledge

The candidate

• has advanced knowledge of theories for learning in mathematics, both from an acquisition perspective and a participation perspective. Key concepts are representations in mathematics and semiotics.
• has knowledge of various elements that comprise algebra, and how these elements are related to other topics in school mathematics.
• has thorough knowledge of key aspects of the learning and teaching of algebra. - has thorough knowledge of algebra as an example of an axiomatic structure.

Skills

The candidate

• can read and familiarise him/herself with the research in relevant areas of mathematics education.
• can present as academic text his or her own empirical studies related to key topics in the course.
• can analyse pupils algebraic thinking, informed by results published in the research literature.
• can analyse a teaching and learning in mathematics in different mathematical topics, based on relevant literature.

General competence

The candidate

• can make theoretically anchored choices in order to facilitate pupils opportunities for learning the mathematical topics that are central in the course.
• has knowledge of relevant and recent research in mathematics education on the topics covered by the course.
• can present the results of theoretically anchored and empirically based investigations

The teaching is organised in seminar weeks. Between the seminars, the course is based on literature studies, assignments, practice in schools, and contact through an online classroom platform. The teaching and learning methods will alternate between lectures, work on assignments (individually and in groups), discussions, as well as oral and written student presentations. Academic discussions and interactions are important ways of working and learning, and it is expected that the candidates actively contribute to such activities. The teaching can be in English

Compulsory work

• Two compulsory and individually written academic texts, based on empirical investigations, of which both texts must be approved.
• One group oral presentation.
• Three assignments given between the seminar weeks of which a all assignments must be approved.

The compulsory work is assessed as approved/not approved. The compulsory work must be approved before the student can complete the exam.