Course content

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 mathematical definitions and different semiotic representations. In this course we will be working with aspects of the number concept in the early years. 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.

Learning outcome

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 early years
• has thorough knowledge about the significance of semiotic representations for conceptual development in mathematics

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 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

Learning methods and activities

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 and attend. Parts of the teaching will be in English.

Compulsory assignments

• Compulsory assignments according to course description
• Compulsory assignments according to course description
• Compulsory assignments according to course description

Specific conditions

Recommended previous knowledge

Passed Mathematics 2 (30 ECTS) or equivalent.

Required previous knowledge

Passed Mathematics 1 (30 ECTS) or equivalent. Candidate must have successfully passed Mathematics 1 (30 ECTS) or equivalent and completed Mathematics 2 (30 ECTS) or equivalent to begin Cycle 2 courses. Passing is understood as the student completing the course and passing the examination. Completed is understood as having all obligatory coursework approved and qualifying the student for the course examination.

Course materials

The final curriculum will be published on Blackboard before the start of the semester.

Credit reductions