Mathematical Modeling and Related Topics

This course helps preservice teachers develop the competence to teach both mathematical modelling and mathematics through modelling. It focuses on how to design and implement mathematical modelling tasks in the classroom and how to assess students’ modelling competence. The course also places emphasis on providing students with practical experience in using digital tools for mathematics teaching, including conducting ICT-based instruction where modelling plays a central role. In addition, different theoretical perspectives on mathematical modelling, including a cognitive perspective, will be discussed. Students will also become familiar with recent research literature in the field of mathematical modelling.

Several constructs from the Anthropological Theory of the Didactic (ATD) are discussed in the course to provide preservice teachers with perspectives on knowledge construction and dissemination. These include the theory of didactic transposition, the notion of praxeology, the paradigm of visiting works, the paradigm of questioning the world, and study and research paths. This is accompanied by a brief discussion of the didactic transposition of elementary algebra and the important role algebra plays in modelling real-world phenomena.

Preservice teachers also learn about critical mathematics education, with particular emphasis on addressing issues related to climate change and sustainability in Norwegian society. The mathematical focus areas in this course align with the core 5-10 curriculum areas, including functions, fractions, algebra and equations, geometry, and statistics. In addition, the course extends preservice teachers’ mathematical knowledge by introducing calculus and separable differential equations as tools for modelling real-world phenomena.

Knowledge

The student

• has advanced knowledge of how to design mathematical modelling tasks and how these differ from problem solving tasks;
• has advanced knowledge of how to design modelling tasks that address core 5-10 mathematics curriculum areas, including statistics;
• has knowledge of different mathematical modelling cycles and how these can be applied in both practical and theoretical situations;
• has knowledge of the general principles of critical mathematics education and of how to design modelling tasks related to climate change and sustainability in Norwegian society;
• has knowledge of how calculus and separable differential equations can be used to solve modelling tasks; and
• has advanced knowledge of how ICT can be integrated into the teaching of mathematical modelling.

Skills

The student

• can design mathematical modeling tasks related to core 5-10 mathematical curriculum;
• can design mathematical modeling tasks related to climate change and sustainability in Norwegian society;
• can solve modelling tasks related to core 5-10 mathematical curriculum;
• can plan and carry out classroom-based activities related to modelling of phenomena;
• can solve modelling tasks related to calculus and separable differential equations;
• can organize students' opportunities for learning mathematics through modelling;
• can analyse observations of modelling activities in mathematics classroom; and
• can plan and analyse the use of ICT tools in mathematics teaching related to modelling.

General competence

The student

• has didactic competence that enables mathematics teaching via a modelling perspective,
• has didactic competence that makes it possible to distinguish between modelling as a goal for teaching and as a method for teaching,
• has didactic competence that enables the design and implementation of teaching where ICT-based modelling is central.

The teaching and learning methods will alternate between lectures, literature studies, work on assignments (individually and groups), discussions, as well as oral students’ presentations. Academic discussions and interactions are important ways of working and learning, and it is expected that the candidates actively contribute to such activities.

Teaching Language

Norwegian or English