Module Handbook

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Module MAT-20-00-M-2

Specialised Scientific and Didactic Requirements (M, 6.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-20-00-M-2 Specialised Scientific and Didactic Requirements 6.0 CP (180 h)

Basedata

CP, Effort 6.0 CP = 180 h
Position of the semester 2 Sem. from WiSe/SuSe
Level [2] Bachelor (Fundamentals)
Language [DE] German
Module Manager
Lecturers
Lecturers of the department Mathematics
Area of study [MAT-EDU] Mathematics (B.Ed./M.Ed.)
Reference course of study [MAT-31.105-SG] B.Ed. LaGR Mathematics
Livecycle-State [NORM] Active

Notice

For students who complete their Bachelor's examination according to the examination regulations for the examination in B.Ed. Mathematics of 24 October 2007, the version of the module from the SS 2019 (9 CP (GYM, RSP) or 10 CP (BBS) including the module part "Introduction to Scientific Programming" - see [MAT-14-00L-M-3]) applies.

Module Part #A "Didactic and methodological principles of mathematics teaching" (Obligatory, 3.0 LP)

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-20-01-K-2
Introduction to Didactics of Mathematics
P 28 h 62 h
U-Schein
- no 3.0 WiSe/SuSe
  • About [MAT-20-01-K-2]: Title: "Introduction to Didactics of Mathematics"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MAT-20-01-K-2]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Module Part #B "Elementary mathematics" (Obligatory, 3.0 LP)

In this part of the module, either one of the courses on "Elementary mathematics from a higher perspective" or a subject-specific proseminar of choice from the range of courses offered by the Department of Mathematics is to be chosen.
Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2S MAT-20-02-K-3
Proseminar Elementary Mathematics from a Higher Perspective
WP 28 h 62 h
PS-Schein
- no 3.0 SuSe
2V MAT-20-02A-K-2
Elementary Mathematics from a Higher Perspective
WP 28 h 62 h
U-Schein
- no 3.0 WiSe
2S MAT-16-10R-K-3
Proseminar (Pure Mathematics)
WP 28 h 62 h
PS-Schein
- no 3.0 WiSe/SuSe
2S MAT-16-10P-K-3
Proseminar (Applied Mathematics)
WP 28 h 62 h
PS-Schein
- no 3.0 WiSe/SuSe
  • About [MAT-20-02-K-3]: Title: "Proseminar Elementary Mathematics from a Higher Perspective"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MAT-20-02-K-3]: The study achievement [PS-Schein] proof of successful participation in the proseminar must be obtained.
  • About [MAT-20-02A-K-2]: Title: "Elementary Mathematics from a Higher Perspective"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MAT-20-02A-K-2]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.
  • About [MAT-16-10R-K-3]: Title: "Proseminar (Pure Mathematics)"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MAT-16-10R-K-3]: The study achievement [PS-Schein] proof of successful participation in the proseminar must be obtained.
  • About [MAT-16-10P-K-3]: Title: "Proseminar (Applied Mathematics)"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MAT-16-10P-K-3]: The study achievement [PS-Schein] proof of successful participation in the proseminar must be obtained.

Evaluation of grades

The module is not graded (only study achievements)..


Contents

  • Elementary mathematics from a higher perspective (specialised science): Geometry (symmetries, areas and volumes, geometric introduction of the infinitesimal calculus, analytical geometry); numbers (prime numbers, elementary number theory, complete induction, Pascal's triangle, structure of the number system from N via Z to Q, order relations, the real numbers R, countability and uncountability, complex numbers C); probability theory and statistics (probabilty theory of finite event spaces: throwing dice, drawing balls with and without putting them back, drawing coloured balls, etc.; elementary combinatorics, binomial distribution); graph theory (nodes and edges, paths, circles, Hamiltonian circles, spanning trees, shortest paths, networks and flows); set theory (sets, families of sets, equivalence relations, functions).
  • Didactic and methodological foundations of mathematics teaching (introduction to the didactics of mathematics): Aims of mathematics teaching, contribution of the subject to general education, basic principles of subject didactics and subject methodology, teaching concepts from the perspective of subject didactics, learning mathematics in class and its specific learning theoretical foundations (e.g. concept and rule learning, justification and proof, practising and modelling, possibilities of differentiation), significance of the use of media for mathematics teaching, differentiation in mathematics teaching.

Competencies / intended learning achievements

The students
  • acquire a deeper understanding of elementary mathematics (mostly even school mathematics) beyond their school education, which serves as a solid foundation for building up knowledge in higher mathematics in further studies. In the course of this specialisation, they become familiar with mathematical argumentation and reasoning and special proof techniques; by linking didactic commentaries to the contents covered, they acquire subject-related didactic knowledge on concrete subjects which are, however, largely familiar to them;
  • know the aims and concepts of mathematics teaching, know how to respond to different types of learners on the basis of their knowledge of learning psychology and biology, know the components of lesson planning, the structure of lesson implementation, the significance of social forms, differentiation and the use of media in teaching; they are able to observe mathematics teaching in a targeted manner and describe it according to different criteria.

Literature

Literatur zu „Einführung in die Didaktik der Mathematik“:
  • U.P. Tietze, M. Klika, H. Wolpers: Mathematikunterricht in der Sekundarstufe II, Band 1: Fachdidaktische Grundfragen – Didaktik der Analysis,
  • T. Leuders: Mathematikdidaktik.

Die Literatur zum Modulteil Elementarmathematik wird in den jeweiligen Lehrveranstaltungen bekannt gegeben.

Materials

Further literature for the course "Introduction to the Didactics of Mathematics" will be announced in the lecture;

exercise material will be provided.

Registration

Registration for the exercise classes and the proseminar via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

None

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-20-00-M-2]

Course of Study Section Choice/Obligation
[MAT-31.105-SG] B.Ed. LaGR Mathematics Compulsory Modules [P] Compulsory
[MAT-47.105-SG] B.Ed. LaBBS Mathematics Compulsory Modules [P] Compulsory
[MAT-B2.105-SG] ZEP LaRSP Mathematics Compulsory Modules [P] Compulsory
[MAT-B5.105-SG] ZEP LaBBS Mathematics Compulsory Modules [P] Compulsory