Advanced Didactics of Mathematics (DidMatV)
PhD School at the Faculty of SCIENCE at University of Copenhagen
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
•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.
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).
Teaching and learning methods
Lectures, theorectial and practical exercises, supervision for final paper.
The course is one of the "partially selective" 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/?
Continuous feedback during the course of the semester
Peer feedback (Students give each other feedback)
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