Advanced Didactics of Mathematics (DidMatV)

Course content

The Didactics of Mathematics is an applied science at the borderline between applied mathematics and social science. It produces knowledge of direct relevance to the profession of mathematics teaching, including methods and results which form part of the education of mathematics teachers in all developed countries.

This course enables the student to become familiar with a selection of current theories and methods in the didactics of mathematics, including:

  • The theory of didactical situations in mathematics
  • The anthropological theory of the didactic
  • Instrumented mathematical techniques
  • Mathematical knowledge for teaching

 

Concretely, the students will read a number of recent papers in which these theories and methods are introduced and exemplified, work with exercises related to the papers, and at the end of the course produce a smaller theoretical study of a mathematical topic based on the course material and further relevant literature.

Education

MSc Programme in Mathematics

Learning outcome

Knowledge 

At the end of the course, the student should know the meaning of and relations among a selection of fundamental methods and notions in the didactics of mathematics, including:

  • A priori and a posteriori analysis
  • Didactic and adidactic situations
  • Objective and subjective didactic milieu
  • Didactic contracts and their levels
  • Fundamental situations
  • External and internal didactic transposition
  • Praxeologies
  • Mathematical and didactic organizations
  • Levels of didactic co-determination
  • Study- and research paths
  • Semiotic representations of mathematical objects
  • Semiotic registers, instrumentation and instrumentalisation

 

The student must be familiar with research results based on and contributing to these theoretical constructions.

 

Skills 

At the end of the course, the student should have basic skills in analyzing a mathematical topic in view of design and observation of teaching situations, and in identifying and selecting relevant research literature to be used in the analysis. The student must also be able to produce focused and structured text on topics from the didactics of mathematics using appropriate scientific method.

 

Competences

At the end of the course, the student should be able to:

• Work autonomously with fundamental topics in mathematics, using pertinent theory from the didactics of mathematics

• Explain the domains of use, relations and differences between the theories introduced in the course, discuss others’ use of the theories, and relate critically to specific choices of theoretical perspective

• Identify and analyze a problem related to mathematics as a taught discipline, and give it a precise formulation in a relevant theoretical framework from the didactics of mathematics

• Carry out a theoretically and methodically well founded investigation of such a problem within didactics of mathematics.

Lectures, theorectial exercises and supervision for final paper.

Compendium of newer scientific papers (all in English).

Bachelor in mathematics or similar.

Academic qualifications equivalent to a BSc degree is recommended.

The course is one of the 'restrective elective' courses in the M.Sc. studies in mathematics (there are a total of 10 such courses, and each student must take at least four of these). The course is mandatory for those who aim at getting the Nordic double degree in mathematics (from U. Copenhagen) and didactics of mathematics (from the U. of Agder, Norway); you can read more about this programme here: http:/​/​www.science.ku.dk/​english/​courses-and-programmes/​degree-programmes/​mathematics/​didactics/​

Oral
Individual
Collective
Continuous feedback during the course of the semester
Peer feedback (Students give each other feedback)
ECTS
7,5 ECTS
Type of assessment
Written assignment
The final exam constists of an individual written final paper. Work on the final paper begins in the 6th week of the block and must be delivered in week 9.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
Criteria for exam assessment

The grade is given for the extent to which the student in his final paper has demonstrated to have achieved the course aims (cf. above).

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 12
  • Preparation
  • 90
  • Theory exercises
  • 26
  • Project work
  • 75
  • Guidance
  • 3
  • English
  • 206