Course content

This course contains topics that show the role of mathematics in selected practical and theoretical situations. It involves modelling related to phenomena in nature and society and studying the mathematics used in such models. Another topic is students’ concept development and mathematization processes. This is about the transition from models of contexts to models for mathematical reasoning. Under this topic, semiotic representations will also be discussed. An important part of the course is linked to further development of competence in carrying out joint planning and observation of teaching in a community of colleagues and competence in leading development in mathematics teaching. The mathematical topics in this course are mainly taken from functions. Among other topics, one will work with rate of change as a basis for differential equations in contexts from e.g. biology and medicine, where growth models will be central: exponential growth, limited growth and logistic growth. The transition from models of realistic contexts to students’ models for mathematical reasoning will be central. This will be linked to the theoretical perspective represented by RME (Realistic Mathematics Education). Emphasis will be on offering students practical experiences with the use of digital tools in mathematics teaching, including conducting ICT-based teaching where modelling is central. Furthermore, work will be done on the way digital tools can be used to design tasks where particular pieces of mathematical knowledge are at stake.

Learning outcome

Knowledge

The candidate has:

• advanced knowledge of how selected mathematical concepts are applied in practical and theoretical situations
• knowledge of key aspects of mathematical modelling
• advanced knowledge of the concept of function, with special focus on rate of change and differential equations
• knowledge of different mathematical models and how these are applied in practical and theoretical situations
• knowledge of the transition from models of realistic contexts to models for mathematical reasoning
• advanced knowledge of ICT in mathematics teaching and how various ICT tools can contribute to change and development of mathematics teaching in schools
• knowledge of semiotic representations and their significance in mathematics, especially with respect to ICT-supported mathematics teaching

Skills

The candidate can:

• organize students’ opportunities for learning mathematics through modelling
• use different contexts where change can be explained through the concept of instantaneous rate of change rate
• facilitate the transition from models of realistic contexts to models for mathematical reasoning
• initiate and lead classroom experiments in a community of colleagues where modelling is used as a teaching tool
• analyze observations of modelling activities in the mathematics classroom
• plan and analyze the use of ICT tools in mathematics teaching related to modelling
• use ICT in a way that promotes students’ learning of mathematics

General competence

The candidate has:

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

Learning methods and activities

The course is conducted with six compulsory gatherings (seminars) in Trondheim. Students must take this course at the same time as they take the course Task Design and the roles of the mathematics teacher (11th-13th grade) (7.5 ECTS credits) in the autumn semester and the course Research Methods in Mathematics Education (8th-13th grade) (7.5 ECTS credits) in the spring semester. Blackboard is used as the learning platform of the course.

Compulsory assignments

• Compulsory assignments
• Compulsory attendance

Specific conditions

Required previous knowledge

The course is part of the study programme Continuing Education for Teacher Specialists in Mathematics, Grade 8-13. It cannot be taken as a single subject, but must be included in the comprehensive study programme of 60 ECTS credits. Participants are recruited through the Norwegian Directorate for Education and Training.

Credit reductions