Mathematics 2

In the course the students shall develop their competence in mathematics and in didactics of mathematics. This means that the students shall develop their ability to observe, understand and act in learning and teaching situations. The main topics are number theory and geometry, but number strategies in connection with approaches to algebra will also be included.

Didactical topics will be related to identifying, characterising and understanding phenomena and processes that are part of the teaching and learning of mathematics.

Within geometry children's conceptions of shape and space are essential, and how these conceptions may be influenced by the way in which geometry is included in children's play activities. An important aspect in geometry is to study its presence in our surroundings - in daily life, in art and in architecture - in order to make the students appreciate how they can use the local environment as an arena for learning. An important issue is to study and describe figures, shapes, patterns and solids in two- and three-dimensional space. Various types of resources and material for practical activities will be used. Contexts of interest for this work may be geometry in art and culture, such as painting, knitting patterns, origami (paper folding) and tiling. Transformations and symmetries are important topics.

Geometry of the earth, some aspects of cosmology and some basic topics from graph theory may be included. The work with number strategies concentrates on how children develop algorithms and how algebra generalises arithmetical operations and relations. Different approaches to algebra will be discussed.

Experimenting and exploring properties of numbers and number patterns will be an important part of this topic.

Computer software, such as spreadsheets and dynamic geometry programmes, will be used and it will be discussed to what extent such programmes are helpful in and the learning and teaching of mathematics.

In the development of the students' didactical competence questions about how children learn mathematics, how they develop concepts and their ways of thinking will be important aspects. In particular the course will address how different discourses may comply with the demand for a dialogic way of teaching mathematics. This will be linked to discussing the connection between views on the subject, ways of teaching and learning theories.