Historical and Philosophical Aspects of Mathematics (5-10)

In this topic, we will examine mathematics’ historical development, and study the nature of mathematics as a subject. A central theme will be the historical development of algebra and geometry. Students will illuminate the subject's philosophy by, among other things, examining how one argues and proves points in mathematics, and how mathematical truths are developed. We will also examine the subject's axiomatic structure, and look at how this has been developed across various eras and cultures.

Knowledge
The candidate has
- thorough knowledge of mathematics as a subject with a long historical development -- both as a scientific subject and as an academic subject
- thorough knowledge of the historical development of central mathematical topics, with special emphasis on algebra and geometry
- thorough knowledge of the mathematical subject's ontological and epistemological foundations
- thorough knowledge of the axiomatic structure of mathematics, and of the development of this from the Euclidean era to the present time
- thorough knowledge of subject didactic aspects of the history of mathematics and the relevance of such knowledge for teaching 5th to 10th grade students

Skills
The candidate can
- place central school mathematical topics into a historical context for students grade 5 to 10
- discuss the historical aspects of mathematics when teaching students grades 5 to 10
- analyze mathematics textbooks for school grades 5 to 10 from a historical point of view
- use and understand selected algorithms that are no longer in common use
- familiarize him- or herself with research on the history of mathematics and mathematics teaching

General competence
The candidate can
- analyze issues related to the subject, the profession, and the research ethics related to the historical and philosophical development of mathematics
- communicate about historical and philosophical issues, analyses and conclusions, both with specialists and the with general public
- contribute to innovation and in innovative processes in schools that deal with the subject's historical and philosophical development

The teaching is organized in seminar weeks. Information about the distribution of seminar weeks will be given at the beginning of the semester. Between seminar weeks, students will engage in literature studies and interpersonal contact through the online platform. The work methods will alternate between lectures, individual and collaborative work on assignments, discussions, as well as oral and written student presentations.

Professional discussions and other professional interaction comprise an important aspect of work and learning, both in and out of class. Therefore, it is expected that all students actively contribute to such activities.