Learning and teaching of mathematics (1-7)

This course provides a deeper understanding of theories of learning and teaching in mathematics, and discusses the implication of such understanding for the teaching of 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 7, and analysing such observations. 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 explain how a group, being an algebraic structure, is relevant to topics in school mathematics.
- can plan, implement, and analyse a teaching session in grades 1 through 7 within a mathematical topic that is central in the course, 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 within grades 1 through 7.

The teaching is organised in seminar weeks, and the distribution of seminar weeks is published at the beginning of the semester. 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