Course content

In this course, we will examine mathematics historical development, and study the nature of mathematics as a subject. The historical development of the number concept and geometry will be central in the course. As a part of this we will work on proving mathematical claims and with mathematical argumentation. The epistemological and ontological foundation of mathematics will also be discussed. The students will get experience with different kinds of semiotic representation and the axiomatic structure of mathematics. Different topics in number theory and geometry will be discussed, like divisibility, prime number factorization, congruence and Euclidean geometry.

Learning outcome

Knowledge

The candidate

• has thorough knowledge of the mathematical subject's ontological and epistemological foundations for selected concepts in number theory and geometry
• has thorough knowledge of how various basic topics within number theory and geometry are relevant for the school mathematics
• has thorough knowledge about the significance of different semiotic representations in mathematics, especially in work with number and geometry
• has thorough knowledge of the axiomatic structure of mathematics
• has thorough knowledge of subject didactic aspects of the history of mathematics and the relevance of such knowledge for teaching and learning

Skills

The candidate

• can use knowledge of and the historical development and the epistemological and ontological basis of selected concepts within number theory and geometry to plan and analyse mathematics teaching
• can update his/her knowledge on research on the number concept and geometrical concepts, for example connected to use of different representations, and use this to analyse episodes from practice
• can use and understand selected algorithms and prosedures that have been used throughout time
• can analyze issues related to the subject, the profession, and the research ethics related to the historical and philosophical development of mathematics
• can communicate about historic and philosophic problems, analyses and conclusions, with both specialists and the general public

General competence

The candidate

• has knowledge of mathematics as a subject in continuous development
• can use current research in mathematics education to plan, implement, and analyse teaching plans
• can contribute with perspectives on the historical and philosophical development of mathematics in innovative processes in schools

Learning methods and activities

The teaching is organised in seminar weeks. Between the seminars, the course is based on literature studies, assignments, practice in schools, and contact through an online classroom platform. The teaching and learning methods will alternate between lectures, work on assignments (individually and in groups), discussions, as well as oral and written student 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 can be in English.

Compulsory work

There will be no more than five mandatory written assignments. Some of these will require that the students gather empirical data from the classroom. These assignments will be assessed as approved or not approved. Participation on some of the seminars will be mandatory. Information about which seminars can be found in the semester plan at the beginning of the semester.

All mandatory assignments must be passed and all mandatory participation must be completed before the students can take the exam.

Compulsory assignments

• Written tasks and obligatory presence

Recommended previous knowledge

Passed teacher education or equivalent with an emphasis on mathematics.

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. It can also be found on Innsida.

Credit reductions