Examination arrangement

Course content

This course contains topics that show the role of mathematics in selected practical and theoretical situations. One will look at models related to phenomena in nature and society and study the mathematics used in these models. Another topic is students' concept development and mathematization processes in modeling.

The mathematical topics in this course will be taken from various domains. One will, among other things, work with contexts for unlimited and limited growth, and for ratios and change.

Mathematical modeling will be discussed from different viewpoints, including a cognitive perspective. Here, the differences between problem solving and mathematical modeling will be important. Other central themes of the course could be transition from models of realistic contexts to students' models for mathematical reasoning as well as mathematizing real situations.

Emphasis will be placed on giving students practical experience with the use of digital tools in mathematics teaching, including conducting ICT-based teaching where modeling is central. Also, the current literature on mathematical modeling is discussed.

Learning outcome

Knowledge

The student

• has advanced knowledge of how selected mathematical concepts, such as functions with special focus on rate of change and difference equations, can be applied in practical and theoretical situations,
• has advanced knowledge of how statistics can be used in modeling,
• has knowledge of different mathematical modeling cycles and how these are applied in practical and theoretical situations,
• has knowledge of how to design mathematical modeling tasks and how it is different from a problem solving task,
• has knowledge of the transition from models of realistic contexts to models for mathematical reasoning,
• has advanced knowledge of how ICT can be integrated in teaching mathematical modeling.

Skills

The student

• can organize students' opportunities for learning mathematics through modeling,
• can use different contexts where change processes can be explained through the concept of rate of change,
• can facilitate the transition from models of realistic contexts to models for mathematical reasoning,
• can plan and carry out classroom-based activities related to modeling of phenomena,
• can analyze observations of modeling activities in the mathematics classroom,
• can plan and analyze the use of ICT tools in mathematics teaching related to modeling,
• - can use statistics to model different realistic phenomena.

General competence

The student

• has didactic competence that enables mathematics teaching via a modeling perspective,
• has didactic competence that makes it possible to distinguish between modeling 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 modeling is central.

Learning methods and activities

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. The teaching could be in English.

Compulsory assignments

• One oral presentation
• Up to eight written assignments

Further on evaluation

Compulsory work in the course:

• One oral presentation
• Up to eight written assignments. The number will be specified at the beginning of the semester.

The compulsory assignments are evaluated as approved/non approved. The oral presentation and 80% of the written assignments must be approved.

Assessment:

Written school exam (6 hours). The exam is assessed with letter grades A to F.

Aids: PC with specified software and websites. Permitted software and websites will be given at the start of the semester.

Specific conditions

Recommended previous knowledge

Mathematics 1 and 2 (60 credits) or equivalent.

Required previous knowledge

Passed Mathematics 1 (30 credtis) or equivalent.

Course materials

The course material is mainly scientific papers written in English. The final reading list will be published on Blackboard at the beginning of the semester.