NFKA09006U Advanced Didactics of Mathematics (DidMatV)
MSc Programme in Mathematics
The 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
- Semiotic registers in mathematics
- Instrumental and documentational genesis
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.
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 situations, adidactic situations, objective and subjective didactic milieu, didactic contracts and their levels, fundamental situations, external and internal transposition, praxeologies, mathematical and didactic organisations, 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 analysing 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 analyse 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.
Compendium of newer scientific papers (all in English).
Can also be chosen by PhD students
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- 7,5 ECTS
- Type of assessment
- Written assignmentThe 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.
- Exam registration requirements
Two oral and one written task in the first part of the course. These must be completed by the end of the course in order to qualify for the exam. The assignments do not need to be approved in order to qualify the student for the exam - only handed in.
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
Rexaminations follow the same rules as the ordinary exam. If the students have failed to qualify for the exam, any missing tasks must be submitted to the course leader no later than 2 weeks before the final exam. Students need to hand in the written task and arrange for delivery of oral tasks required to qualify for the exam by contacting the course leader prior to any reexamination.
For reexaminations, the final paper is assigned three weeks prior to reexamination.
Criteria for exam assesment
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).
- Practical exercises
- Theory exercises
- Project work