Perspectives on the number concept (1-7)

The central topic of this course is the number concept and various perspectives that are relevant to teaching at the primary level. The historical development of the number concept will be addressed, especially the development of various types of numbers (such as negative numbers) and number systems. Subjects from the philosophy of mathematics as an epistemological and ontological basis for mathematics will also be addressed. Conceptual development is another central topic, particularly the role of different semiotic representations. Also, the role of the historical development and the ontological foundations of a given concept will be addressed. Furthermore, there will be work on various topics in number theory, such as divisibility, prime numbers, prime number factorization, Diophantine equations, and congruence. The work in number theory is related to mathematics at the primary level, but is also seen as an example of the historical and philosophical development and construction of a mathematical area. One will also look at modelling as a work method and what this may mean for work in mathematics at primary level, especially in terms of working with numbers.

Knowledge
The candidate
- has thorough knowledge of the historical development of various aspects related to the concept of numbers
- has thorough knowledge of epistemological and ontological foundation for the concept of numbers
- has thorough knowledge of various basic topics within number theory that are relevant for the primary level
- has thorough knowledge about the significance of semiotic representations for conceptual development in mathematics
- has thorough knowledge of modelling as a teaching method at the primary level

Skills
The candidate
- can explain the significance of the historical development of the number concept and its epistemological and ontological basis for mathematics teaching at primary level
- can use knowledge in number theory to plan and analyse teaching at the primary level
- can update his/her knowledge in research on conceptual development in mathematics, and use this to analyse episodes from practice
- can use modelling as a work method
- can apply mathematical concepts that are central to the subject in practical and theoretical situations

General competence
The candidate
- has knowledge of mathematics as a subject in continuous development
- has knowledge about the significance of the teaching profession being research based
- can use current research in mathematics education to plan, implement, and analyse teaching plans

The teaching is organized in seminars, and the schedule of seminar weeks will be given at the start of the semester. Between the seminar weeks, there will be literature studies, assignments, practice in schools, and contact in online forums.

The work methods vary between lectures, work on tasks (individually and in groups), discussions, and oral and written student presentations.

Academic discussions and other academic interactions are important ways of working and learning, and it is expected that all students actively contribute to such activities. It is therefore important to participate in the seminars.