Historical and Philosophical Aspects of Mathematics (5-10)

In this subject, 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 student 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 student 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 student 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 working methods alternate between lectures, work on assignments, individually and in groups, discussions, as well as oral and written student presentations. Academic discussions and other academic interactions are an important form of work and learning, and it is expected that all students actively contribute to such activities.