Perspectives on The Number Concept (1-7)

The central theme of this course is the concept of number and different perspectives on it that are relevant for teaching at the primary level. In the course, we will specifically look at different aspects of the concept of number from a beginner's education perspective. An entry point to this can be through the historical development of the concept of number, especially the development of different sets of numbers and different number systems and arithmetic within them. Topics from the philosophy of mathematics, as the epistemological and ontological basis for mathematics, will also be natural to look at in relation to concept learning. In particular, the role of mathematical definitions and different semiotic representations will be discussed in this context. Mathematical topics beyond sets of numbers will be linked to number theory, such as divisibility, prime numbers, prime factorization, Diophantine equations, and congruence. The course is based on relevant mathematics didactic theories about concept learning, especially cognitive theories.

Knowledge

The student

• 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 childrens development of the number concept in the initial primary education from different theoretical standpoints
• has thorough knowledge about the significance of semiotic representations for conceptual development in mathematics, especially for working with numbers

Skills

The student

• 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 about numbers 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 apply mathematical concepts that are central to the subject in practical and theoretical situations

General competence

The student

• 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 course work varies 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 and attend. Parts of the teaching will be in English.