Module Catalogue for the Subject. Mathematics. as Unterrichtsfach with the degree "Erste Staatsprüfung für das Lehramt an Grundschulen"

Transcription

1 Module Catalogue for the Subject as Unterrichtsfach with the degree "Erste Staatsprüfung für das Lehramt an Grundschulen" Examination regulations version: 2015 Responsible: Faculty of and Computer Science L H 2015

2 The subject is divided into 5 s used, Conventions, Notes, In accordance with 6 Scientific Discipline 7 Cumpulsory Courses 8 Elementary Number Theory 9 Elementary Stochastics 10 Basic Linear Analysis 11 Basic Analysis 12 Elementary Geometry 13 Analytic Geometry 14 Basic Differential Equations 15 Review Course (German Grundschule/Mittelschule/Realschule) 16 Teaching 17 Compulsory Courses 18 Didactics of - Geometry (German Grundschule) 19 Didactics of - Arithmetics and Application of (German Grundschule) 20 Extra Skills Selected Topics in Didactics of 1 (German Grundschule) 23 Methodology of Teaching in 1 (German Grundschule) 24 Selected Topics in Didactics of 2 (German Grundschule) 25 Methodology of Teaching in 2 (German Grundschule) 26 E-Learning and Blended Learning in Mathematical Teaching (virtual Course) 27 Basics in Arithmetics (virtual course) 28 Basics in School Geometry (virtual course) 29 Stochastics in Sekundarstufe I (virtual course) 30 in grade 10 (virtual course) 31 Basics of für German Grundschule 1: Arithmetics and Orders of Magnitude (virtual course) 32 Basics of für German Grundschule 2: Geometry and Stochastics (virtual course) 33 Basic Notions and Methods of Mathematical Reasoning 34 Didactics of Geometry (virtual course) 35 Didactics of Algebra (virtual course) 36 Exam Tutorial Didactics of (virtual course) 37 1 (virtual course) 38 2 (virtual course) 39 Methods and Media in Teaching 1 (German Grundschule) 40 Methods and Media in Teaching 2 (German Grundschule) 41 School from a Higher Perspective 42 A comparison of Education Systems 43 Employing media and interactive methods at school and in classrooms 44 Learning through the arts - Learning theories and classroom experience 45 Self-assessment and career planning 46 Communicative competence and teaching competence 47 Practical work experience in the classroom 1 48 School social work: various fields of activity 49 School social work: focus on projects 50 Further development of pedagogical competences in schools 51 European Education Systems 52 Special Challenges to Teacher Education - Inclusion 53 Special Challenges to Teacher Education - Inclusion 54 Special Challenges to Teacher Education - Inclusion 55 Special Challenges to Teacher Education 56 (2015) page 2 / 135

3 Special Challenges to Teacher Education 57 Special Challenges to Teacher Education 58 Innovative learning methods - teachers and learners: learning from each other - special subjects 59 Innovative learning methods - teachers and learners: learning from each other - special schoolforms 60 Innovative learning methods - teachers and learners: learning from each other - key-competences 61 Intercultural Education - theoretical and applied 62 Learning and teaching practical Experience in foreign Countries 63 Intercultural competence 64 Practical work experience in the classroom 2 65 Interactive Whiteboards (Basic Course) 66 Radio Play Workshop (Basic Course) 67 Radio Play Workshop (Advanced Course) 68 Radio Play Workshop (Intensive Course) 69 Electronic Graphic Design (Basic Course) 70 Electronic Graphic Design (Advanced Course) 71 Electronic Graphic Design (Intensive Course) 72 Media Psychology (Basic Course) 73 Media Psychology (Advanced Course) 74 Media Psychology (Intensive Course) 75 Film Studies (Basic Course) 76 Film Studies (Advanced Course) 77 Film Studies (Intensive Course) 78 AVC-Media (Basic Course) 79 AVC-Media (Advanced Course) 80 AVC-Media (Intensive Course) 81 Computer Based Presenting (Basic Course) 82 Computer Based Presenting (Advanced Course) 83 Computer Based Presenting (Intensive Course) 84 Broadcasting (Basic Course) 85 Broadcasting (Advanced Course) 86 Broadcasting (Intensive Course) 87 Information Literacy (Basic Level) 88 Student Lab Supervision (Physics) 89 Low Cost - High Impact. Low-budget Experiments for Science Courses (Physics) 90 Teaching Science with Hands-on-Exhibits (Physics) 91 Protestant religious education 92 Inclusive religious education 93 Practical Experience in transfer of knowledge obtained in the Teaching-Learning-Garden 1 94 Practical Experience in transfer of knowledge obtained in the Teaching-Learning-Garden 2 95 Methods and tools for Nature- and Environmental Education I2 96 Methods and tools for Nature- and Environmental Education 2 97 Professional skills in handling school groups 1 98 Professional skills in handling school groups 2 99 Music Education - Basic Module 1: Music Practice and Performance 100 Project Module: Music Practice and Performance in Everyday School Life 101 School and Museum - Extracurricular Education and Learning in Museums 102 Intercultural competences 103 Intercultural spheres of activities 104 Introduction to educational science of emotional and behavioral disorders 105 Theories to explain emotional and behavioral disorders 106 Greek Basic Course 107 Greek Advanced Course 108 Hebrew Basic Course 109 Hebrew Advanced Course 110 Theology by Interdisciplinary Approach 111 Selected Theological Methods 112 Theological source studies and auxiliary sciences 113 (2015) page 3 / 135

4 Prospects of cultural and social studies in Theology Prospects of cultural and social studies in Theology Prospects of cultural and social studies in Theology Seminar on interdisciplinary issues in Theology Seminar on interdisciplinary issues in Theology Studyworkshop: Mathematical understanding and arithmetic operations in heterogeneous learning groups 119 Studyworkshop: Inquiry based education in science and social studies 120 Studyworkshop 121 German as a second language - German as a foreign language: Basics 122 Study Workshop Writing Skills 123 Study Workshop Learning Strategies 124 Study Workshop Presentation 125 Service Learning Study Workshop 126 Study Workshop Readind Skills 127 Study Workshop Public Speaking 128 Helping and saving 129 Intercultural Education 130 Organic Chemistry for students of medicine, biomedicine, dental medicine and natural sciences 131 Introduction to Inorganic Chemistry for Students of Biology, Medicine and Dentistry 132 Developing and improving writing skills 133 Paper 134 Thesis in (German Grundschule) 135 (2015) page 4 / 135

5 The subject is divided into Module Catalogue for the Subject section / sub-section ECTS credits starting page Scientific Discipline 7 Cumpulsory Courses 8 Teaching 17 Compulsory Courses 18 Extra Skills Paper 134 (2015) page 5 / 135

6 s used Course types: E = field trip, K = colloquium, O = conversatorium, P = placement/lab course, R = project, S = seminar, T = tutorial, Ü = exercise, V = lecture Term: SS = summer semester, WS = winter semester Methods of grading: NUM = numerical grade, B/NB = (not) successfully completed Regulations: (L)ASPO = general academic and examination regulations (for teaching-degree programmes), FSB = subject-specific provisions, SFB = list of modules Other: A = thesis, LV = course(s), PL = assessment(s), TN = participants, VL = prerequisite(s) Conventions Unless otherwise stated, courses and assessments will be held in German, assessments will be offered every semester and modules are not creditable for bonus. Notes Should there be the option to choose between several methods of assessment, the lecturer will agree with the module coordinator on the method of assessment to be used in the current semester by two weeks after the start of the course at the latest and will communicate this in the customary manner. Should the module comprise more than one graded assessment, all assessments will be equally weighted, unless otherwise stated below. Should the assessment comprise several individual assessments, successful completion of the module will require successful completion of all individual assessments. In accordance with the general regulations governing the degree subject described in this module catalogue: LASPO2015 associated official publications (FSB (subject-specific provisions)/sfb (list of modules)): 5-Oct-2015 ( ) This module handbook seeks to render, as accurately as possible, the data that is of statutory relevance according to the examination regulations of the degree subject. However, only the FSB (subject-specific provisions) and SFB (list of modules) in their officially published versions shall be legally binding. In the case of doubt, the provisions on, in particular, module assessments specified in the FSB/SFB shall prevail. (2015) page 6 / 135

7 Scientific Discipline ( ECTS credits) (2015) page 7 / 135

8 Cumpulsory Courses ( ECTS credits) (2015) page 8 / 135

9 Elementary Number Theory 10-M-ELZT-152-m01 Institute of 6 numerical grade 1 semester undergraduate Introduction to fundamental techniques in mathematics. Approach to the number as a basic theme in mathematics, basic topics in elementary number theory and the structure of the number system. The student knows the basic ways of thinking and working in mathematics, as well as the fundamental mathematical proof methods. He/She is able to apply these skills to basic problems in the fields of number theory and the structure of the number system. V (4) + Ü (2) Written examination (approx. 60 to 90 minutes If announced by the lecturer at the beginning of the course, the written examination may be replaced by an oral examination of one candidate each (approx. 20 minutes) or an oral examination in groups of 2 candidates (approx. 15 minutes per candidate) and written exercises (approx. 12 exercise sheets, approx. 3 exercises per sheet). 51 I Nr. 3 (2015) page 9 / 135

10 Elementary Stochastics 10-M-ELST-152-m01 Institute of 5 numerical grade 1 semester undergraduate Fundamental topics in elementary stochastics: descriptive statistics, probability theory, combinatorics, inferential statistics, stochastic modelling, introduction to basic mathematical techniques. The student knows the basic ways of thinking and working in mathematics, as well as the fundamental mathematical proof methods. He/She is able to apply these skills to basic problems in stochastics. V (3) + Ü (1) Written examination (approx. 60 to 90 minutes If announced by the lecturer at the beginning of the course, the written examination may be replaced by an oral examination of one candidate each (approx. 20 minutes) or an oral examination in groups of 2 candidates (approx. 15 minutes per candidate) and written exercises (approx. 12 exercise sheets, approx. 3 exercises per sheet). 51 I Nr. 3 (2015) page 10 / 135

11 Basic Linear Analysis 10-M-GRLA-152-m01 Institute of 9 numerical grade 1 semester undergraduate Basics in linear algebra: groups, rings, fields, systems of linear equations, vector spaces, matrices and determinants, linear maps, examples and applications. The student is aquainted with the basic methods and concepts of linear algebra. He/She is able to comprehend the central proof methods, can perform easy mathematical arguments and present them in written form. He/She can analyse basic mathematical problems and employ methods of linear algebra to solve them. V (4) + Ü (2) Written examination (approx. 60 to 90 minutes). If announced by the lecturer at the beginning of the course, the written examination may be replaced by an oral examination of one candidate each (approx. 20 minutes) or an oral examination in groups of 2 candidates (approx. 15 minutes per candidate). creditable for bonus 51 I Nr. 2 (2015) page 11 / 135

12 Basic Analysis 10-M-GRAN-152-m01 Institute of 12 numerical grade 2 semester undergraduate Convergence and divergence of sequences and series, functions, continuity, differentiation and integration (Riemann integral), Taylor approximation and power series, functions in several variables, total and partial differentiability, inverse and implicit function theorem, curves in R^n, curve integrals, integration theorems in higher dimensions (Fubini's theorem, transformation rule), examples and applications. The student is aquainted with methods and concepts in analysis of one and several variables. He/She is able to comprehend the central proof methods, can perform easy mathematical arguments and present them in written form. He/She can analyse basic mathematical problems and employ methods of analysis in one and several variables to solve them. V (4) + Ü (2) + V (2) + Ü (2) Written examination (approx. 60 to 120 minutes). If announced by the lecturer at the beginning of the course, the written examination may be replaced by an oral examination of one candidate each (approx. 20 minutes) or an oral examination in groups of 2 candidates (approx. 15 minutes per candidate). creditable for bonus 51 I Nr. 1 (2015) page 12 / 135

13 Elementary Geometry 10-M-ELGE-152-m01 Institute of 6 numerical grade 1 semester undergraduate Fundamental topics in elementary and Euclidean geometry: axiomatic foundations of Euclidean geometry, congruence geometry, imaging geometry, similarity geometry, basics in analytic geometry in R^3, introduction to basic mathematical techniques. The student knows the basic ways of thinking and working in mathematics, as well as the fundamental mathematical proof methods. He/She is able to apply these skills to basic problems in Euclidean geometry. V (4) + Ü (2) Written examination (approx. 60 to 90 minutes If announced by the lecturer at the beginning of the course, the written examination may be replaced by an oral examination of one candidate each (approx. 20 minutes) or an oral examination in groups of 2 candidates (approx. 15 minutes per candidate) and written exercises (approx. 12 exercise sheets, approx. 3 exercises per sheet). 51 I Nr. 3 (2015) page 13 / 135

14 Analytic Geometry 10-M-ANGE-152-m01 Institute of 6 numerical grade 1 semester undergraduate Applications of linear algebra to analytic geometry: quadrics, characterisation of affine maps and isometries, discussion of Euclidean spaces (scalar products, arcs, orthonormal bases). The students is acquainted with advanced methods, concepts and results in linear algebra and analytic geometry. He/She is able to comprehend the central proof methods, can perform easy mathematical arguments and present them orally and in written form. He/She can analyse basic mathematical problems and employ methods of linear algebra and analytic geometry to solve them. V (4) + Ü (2) Written examination (approx. 60 to 90 minutes). If announced by the lecturer at the beginning of the course, the written examination may be replaced by an oral examination of one candidate each (approx. 20 minutes) or an oral examination in groups of 2 candidates (approx. 15 minutes per candidate). creditable for bonus 51 I Nr. 2 (2015) page 14 / 135

15 Basic Differential Equations 10-M-GRDG-152-m01 Institute of 5 numerical grade 1 semester undergraduate Examples and natural appearances of ordinary differential equations, existence and uniqueness theorems (Picard-Lindelöf, Peano), systems of linear differential equations, applications and examples. The student is aquainted with methods and concepts of ordinary differential equations. He/She is able to comprehend the central proof methods, can perform easy mathematical arguments and present them in written form. He/She can analyse basic mathematical problems and employ methods of differential equations to solve them. V (3) + Ü (2) Written examination (approx. 60 to 90 minutes). If announced by the lecturer at the beginning of the course, the written examination may be replaced by an oral examination of one candidate each (approx. 20 minutes) or an oral examination in groups of 2 candidates (approx. 15 minutes per candidate). creditable for bonus 51 I Nr. 1 (2015) page 15 / 135

16 Review Course (German Grundschule/Mittelschule/Realschule) 10-M-M3GMR-152-m01 Institute of 5 (not) successfully completed 1 semester undergraduate Revision and consolidation of the topics in analysis, ordinary differential equations, linear algebra and analytic geometry by completing exercises and answering past state examination questions. The student has advanced knowledge in the topics stated in LPO I (examination regulations for teaching degree programmes), 51 (2) 1, 2, and is able to apply them on the level of the state examination. Ü (4) a) talk (approx. 45 minutes) or b) project (10 to 15 pages) 51 special branch of science without assignment (2015) page 16 / 135

17 Teaching ( ECTS credits) (2015) page 17 / 135

18 Compulsory Courses ( ECTS credits) (2015) page 18 / 135

19 Didactics of - Geometry (German Grundschule) 10-M-DGGS1-152-m01 Institute of 5 numerical grade 1 semester undergraduate In-depth discussion of topics in teaching geometry in Grundschule, taking didactic aspects into account (aims of geometry, spatial visualisation ability, planar figures, symmetries, 3-dimensional solids, geometric drawing). Possibilities of implementation in the classroom and employment of materials and media, including modern technologies. The student knows about the objectives of teaching geometry in elementary school, basics in developmental psychology and didactics of mathematics, fundamentals in elementary school mathematics, as well as important models, presentations and media which can be employed in elementary school teaching of mathematics. She/he knows about common difficulties and problems of pupils in the acquisition of mathematical skills, and can employ and assess didactical principles and teaching and learning strategies. V (2) + Ü (2) Written examination (approx. 60 to 90 minutes). If announced by the lecturer at the beginning of the course, the written examination may be replaced by an oral examination of one candidate each (approx. 20 minutes) or an oral examination in groups of 2 candidates (approx. 15 minutes per candidate). creditable for bonus 51 I Nr. 4 (2015) page 19 / 135

20 Didactics of - Arithmetics and Application of (German Grundschule) Institute of 7 numerical grade 2 semester undergraduate 10-M-DGGS2-152-m01 In-depth discussion of topics in teaching arithmetics and application-oriented mathematics in Grundschule, taking didactic aspects into account (aims of teaching arithmetics, didactic principles, sets, numbers, positional notations, arithmetic models, elementary arithmetic, mental calculation, half-written and written calculations, aims of teaching applications of mathematics, treatment of quantities, representation of data, possibilities of teaching application-oriented mathematics, heuristic principles, strategies and tools, modelling, mappings, typical difficulties in solving text problems, possibilities of promoting competences in applied calculation). Possibilities of implementation in the classroom and employment of materials and media, including modern technologies. The student knows about the objectives of teaching mathematics in elementary school, basics in developmental psychology and didactics of mathematics, fundamentals in elementary school mathematics, as well as important models, presentations and media which can be employed in elementary school teaching of mathematics. She/he knows about common difficulties and problems of pupils in the acquisition of mathematical skills, and can employ and assess didactical principles and teaching and learning strategies. V (2) + Ü (1) + V (2) + Ü (2) a) oral examination of one candidate each (approx. 30 minutes) or b) oral examination in groups (groups of 2, approx. 15 minutes per candidate) or c) written examination (approx. 60 to 120 minutes) 51 I Nr. 4 (2015) page 20 / 135

21 Extra Skills ( ECTS credits) (2015) page 21 / 135

22 ( ECTS credits) (2015) page 22 / 135

23 Selected Topics in Didactics of 1 (German Grundschule) 10-M-DAGS1-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Discussion of basic topics in mathematics didactics with a focus on didactic aspects (e. g. dyscalculia, evaluation of teaching materials for mathematics in Grundschule, using computers for teaching mathematics in Grundschule, selected topics and research results in modern mathematics didactics, theoretical foundations of mathematics didactics, dealing with heterogeneity in the classroom, organising substantial learning environments). The student is acquainted with theoretical concepts in the didactics of mathematics, knows important aspects of planning and analysing teaching of mathematics, masters different strategies for teaching and learning und can assess and employ them. S (2) a) talk (approx. 45 minutes) or b) term paper (5 to 10 pages) or c) project (10 to 15 pages) Assessment offered: Every two years, winter semester 22 II Nr. 1 h) (2015) page 23 / 135

24 Methodology of Teaching in 1 (German Grundschule) 10-M-DMGS1-152-m01 Institute of 3 (not) successfully completed 1 semester undergraduate Discussion of topics in the methodology of teaching mathematics; e. g. support for pupils who are particularly weak or particularly strong in mathematics, dealing with heterogeneity in the classroom, organisation of substantial learning environments as well as possibilities of implementation in the classroom, also including modern technologies. The student knows about possibilities to promote mathematical skills, criteria für assessing media and their use in teaching mathematics and important aspects in planning and analysing the teaching of mathematics. He/She is acquainted with learning and teaching strategies and can employ and assess them. S (2) a) talk (approx. 45 minutes) or b) term paper (5 to 10 pages) or c) project (10 to 15 pages) Assessment offered: Every two years, winter semester 22 II Nr. 1 h) (2015) page 24 / 135

25 Selected Topics in Didactics of 2 (German Grundschule) 10-M-DAGS2-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Discussion of basic topics in mathematics didactics with a focus on didactic aspects (e. g. dyscalculia, evaluation of teaching materials for mathematics in Grundschule, using computers for teaching mathematics in Grundschule, selected topics and research results in modern mathematics didactics, theoretical foundations of mathematics didactics, dealing with heterogeneity in the classroom, organising substantial learning environments). The student is acquainted with theoretical concepts in the didactics of mathematics, knows important aspects of planning and analysing teaching of mathematics, masters different strategies for teaching and learning und can assess and employ them. S (2) a) talk (approx. 45 minutes) or b) term paper (5 to 10 pages) or c) project (10 to 15 pages) Assessment offered: Every two years, summer semester 22 II Nr. 1 h) (2015) page 25 / 135

26 Methodology of Teaching in 2 (German Grundschule) 10-M-DMGS2-152-m01 Institute of 3 (not) successfully completed 1 semester undergraduate Discussion of topics in the methodology of teaching mathematics; e. g. support for pupils who are particularly weak or particularly strong in mathematics, dealing with heterogeneity in the classroom, organisation of substantial learning environments as well as possibilities of implementation in the classroom, also including modern technologies. The student knows about possibilities to promote mathematical skills, criteria für assessing media and their use in teaching mathematics and important aspects in planning and analysing the teaching of mathematics. He/She is acquainted with learning and teaching strategies and can employ and assess them. S (2) a) talk (approx. 45 minutes) or b) term paper (5 to 10 pages) or c) project (10 to 15 pages) Assessment offered: Every two years, summer semester 22 II Nr. 1 h) (2015) page 26 / 135

27 E-Learning and Blended Learning in Mathematical Teaching (virtual Course) 10-M-DVHB-152-m01 Institute of 3 (not) successfully completed 1 semester undergraduate In a course offered by Virtuelle Hochschule Bayern (vhb), the student becomes acquainted with and reflects on techniques in e-learning and blended learning for teaching mathematics. The student is acquainted with basic methods of e-learning and blended learning in teaching methematics, as well as their potentials and limitations. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, winter semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 27 / 135

28 Basics in Arithmetics (virtual course) 10-M-VHBAri-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Basic topics on teaching arithmetics in school, e. g. divisability theory, prime numbers, set theory. The student learns basic topics in the teaching of arithmetics and the related mathematical backgrounds and proofs. He/She is acquainted with the employment of new technologies for teaching arithmetic in school. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, winter semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 28 / 135

29 Basics in School Geometry (virtual course) 10-M-VHBGeo-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Revision and consolidation of the fundamental topics in elementary geometry that are prerequisites for the subject-specific and didactic courses (in particular teaching degrees Grundschule, Hauptschule, Realschule) in geometry. The student has basic knowledge of school geometry, as required for the study of mathematics and its didactics.he/she is acquainted with the employment of new technologies for teaching geometry in school. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, summer semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 29 / 135

30 Stochastics in Sekundarstufe I (virtual course) 10-M-VHBSto-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Revision and consolidation of the fundamental topics in stochastics that are prerequisites for the subject-specific and didactic courses in stochastics. The student has basic knowledge of stochastics, as required for the study of mathematics and its didactics.he/she is acquainted with the employment of new technologies for teaching stochastics in school. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, winter semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 30 / 135

31 in grade 10 (virtual course) 10-M-VHBM m01 Institute of 2 (not) successfully completed 1 semester undergraduate Basic topics on teaching mathematics in tenth grade in Hauptschule, Realschule and Gymnasium. The student learns basic topics in the teaching of mathematics in tenth form at German Mittelschule and Realschule, as well as the related mathematical backgrounds and proofs. He/She is acquainted with the employment of new technologies for teaching mathematics in tenth form. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, summer semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 31 / 135

32 Basics of für German Grundschule 1: Arithmetics and Orders of Magnitude (virtual course) Institute of 2 (not) successfully completed 1 semester undergraduate 10-M-VHBAuG-152-m01 Fundamental topics in teaching arithmetics in Grundschule, e. g. positional notation, elementary arithmetics, arithmetic laws, divisibility. Additional selected topics in application-oriented mathematics on the quantities covered in Grundschule. The students know the subject-related contents in arithmetic in elementary school, and are able to structure the notions and methods within a conceptual map. They know the subject-related contents in application-oriented mathematics related to quantities, and are able to structure the notions and methods within a conceptual map. They know strategies for development of understanding of the central notions of arithmetic in elementary school. They are able to assess and value the importance of digital technology with respect to todays and future design of instruction. They know various fields of application of arithmetic concepts, and are able to perform modelling independently. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, winter semester 22 II Nr. 1 h) (2015) page 32 / 135

33 Basics of für German Grundschule 2: Geometry and Stochastics (virtual course) Institute of 2 (not) successfully completed 1 semester undergraduate 10-M-VHBGuS-152-m01 Fundamental topics in teaching geometry (planar figures, solids, congruence and symmetry) and application-oriented mathematics (statistics, probability and combinatorics) in Grundschule. The students know the subject-related contents in geometry in elementary school, and are able to structure the notions and methods within a conceptual map. They know the subject-related contents in application-oriented mathematics related to statistics, probability and combinatorics, and are able to structure the notions and methods within a conceptual map. They know strategies for development of understanding of the central notions of geometry and application-oriented mathematics in elementary school. They are able to assess and value the importance of digital technology with respect to todays and future design of instruction. They know various fields of application of geometry and application-oriented mathematics concepts, and are able to perform modelling independently. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, summer semester 22 II Nr. 1 h) (2015) page 33 / 135

34 Basic Notions and Methods of Mathematical Reasoning 10-M-GBM-152-m01 Institute of 2 (not) successfully completed undergraduate Introduction to the basic notions and proof techniques in mathematics: approach to sets, formal logic and maps. The student gets acquainted with the basic working techniques which are prerequisites for the further courses in the Bachelor's degree study programme. V (1) + Ü (1) Project (10 to 15 pages) Language of assessment: German and/or English 22 II Nr. 1 h), 22 II Nr. 2 f) (2015) page 34 / 135

35 Didactics of Geometry (virtual course) 10-M-VHBDG-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Geometry didactics is about learning and teaching geometry. This course focuses on topics which are central and important for all of geometry and mathematics, namely proving and problem solving. It also addresses topics which are usually discussed only briefly or not at all in university lectures and in the literature. Among these are chapters on space geometry, trigonometry and similarity geometry. The students are acquainted with the subject-specific contents of school geometry, and are able to structure the notions and methods within a conceptual map. They know strategies of short, middle and long term development of understanding of the central concepts of geometry in teaching mathematics. They are able to develop and justify learning units and learning sequences for the important topics in school geometry independently. They are able to assess and value the importance of digital technology with respect to todays and future design of instruction. They know various fields of application of geometric concepts, and are able to perform modelling (in the sense of modelling cycles) independently. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, summer semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 35 / 135

36 Didactics of Algebra (virtual course) 10-M-VHBDA-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Algebra didactics is about learning and teaching algebra. This course focuses on the central and important topics in school algebra: extensions of number domains, variables and terms, equations and functions. The students are acquainted with the subject-specific contents of school algebra, and are able to structure the notions and methods within a conceptual map. They know strategies of short, middle and long term development of understanding of the central concepts of algebra in teaching mathematics. They are able to develop and justify learning units and learning sequences for the important topics in school algebra independently. They are able to assess and value the importance of digital technology with respect to todays and future design of instruction. They know various fields of application of algebraic concepts, and are able to perform modelling (in the sense of modelling cycles) independently. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, winter semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 36 / 135

37 Exam Tutorial Didactics of (virtual course) 10-M-VHBEx-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Revision of basics (definitions of mathematical notions, formulation and proving of theorems) in preparation for the Erstes Staatsexamen für Lehramt Gymnasium (first state examination for teaching at a Gymnasium) as well as basic guidelines for answering exam questions (with a special focus on the state examination in Bavaria). The student learns about the structure of the state exams and different methods for solving the exam problems. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Once a year, winter semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 37 / 135

38 1 (virtual course) 10-M-VHBMa1-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Discussion of basic topics on teaching mathematics in a Gymnasium, in particular verbal and subject-specific fundamentals concerning the organisation of classes. The student is able to discuss selected topics and questions on teaching mathematics at German Gymnasium, considering both subject-related and methodical aspects. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Every two years, winter semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 38 / 135

39 2 (virtual course) 10-M-VHBMa2-152-m01 Institute of 2 (not) successfully completed 1 semester undergraduate Discussion of central topics on teaching mathematics in a Gymnasium, in particular didactic analyses and possibilities of implementation in the classroom. The student is able to discuss and analyse selected topics and questions on teaching mathematics at German Gymnasium from a didactical point of view. Ü (2) Course type: elearning, mostly Virtuelle Hochschule Bayern (vhb) Project (web-based, 15 to 20 hours) Assessment offered: Every two years, summer semester 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 39 / 135

40 Methods and Media in Teaching 1 (German Grundschule) 10-M-MMMG1-152-m01 Institute of 3 (not) successfully completed 1 semester undergraduate Topics in the methodology of teaching mathematics (e. g. support for pupils who are particularly strong or particularly weak in mathematics, dealing with heterogeneity in the classroom, organisation of substantial learning environments) and the use of media in the classroom (e. g. real objects, the use of computers) are discussed with a focus on practical implementation in the classroom. The student knows the possibilities, limitations, advantages and disadvantages of methods and media for employment in teaching mathematics. S (2) a) talk (approx. 45 minutes) or b) term paper (5 to 10 pages) or c) project (10 to 15 pages) Assessment offered: Every two years, winter semester 22 II Nr. 1 h) (2015) page 40 / 135

41 Methods and Media in Teaching 2 (German Grundschule) 10-M-MMMG2-152-m01 Institute of 3 (not) successfully completed 1 semester undergraduate Further topics in the methodology of teaching mathematics (e. g. learning materials, in-depth employment of media in the classroom) are discussed and tested in practice. The student knows the possibilities, limitations, advantages and disadvantages of comprehensive methods and media for employment in teaching mathematics. S (2) a) talk (approx. 45 minutes) or b) term paper (5 to 10 pages) or c) project (10 to 15 pages) Assessment offered: Every two years, summer semester 22 II Nr. 1 h) (2015) page 41 / 135

42 School from a Higher Perspective 10-M-SCH-152-m01 Institute of 5 (not) successfully completed 1 semester undergraduate Discussion of selected topics in school mathematics with respect to their integration into wider theories and their didactic implementation at both school and university levels. By means of selected examples, the student gains insight into the interrealtion between school mathematics and advanced mathematical theories. He/She is able to discuss these under mathematical, didactical and methodical aspect. V (2) + Ü (2) a) talk (approx. 45 minutes) or b) term paper (10 to 15 pages) or c) project (15 to 25 hours) Assessment offered: In the semester in which the course is offered and in the subsequent semester Language of assessment: German and/or English 22 II Nr. 1 h), 22 II Nr. 2 f), 22 II Nr. 3 f) (2015) page 42 / 135

43 A comparison of Education Systems 43-LA-BildsysEx-152-m01 Centre for Teacher Training and Educational Research (ZfL) 2 (not) successfully completed 1 semester undergraduate The modul functions as the preparation for the subsequent excursion to schools in different European countries. The course includes facts about the history, culture, society, and other aspects of the target culture. Furthermore, students will acquire knowledge about the structure of teacher training, schools and higher education systems of the respective country in order to compare them to the German educational system. Additionally, students are prepared in an intercultural way for the respective country. This will form the basis for the mutual exchange Students are able to reflect upon and discuss about similarities and differences of international educational systems in comparison with the German educational system. They can discuss different aspects of educational systems in respect to migration and intercultural learning. They recognize and can assess historic, social, cultural and political effects on educational systems. S (2) a) presentation (approx. 20 minutes) or b) term paper (approx. 10 pages) or c) portfolio (approx. 30 hours total) 30 places. Should the number of applications exceed the number of available places, places will be allocated as follows: Option 1: (1) Places will be allocated by lot. (2) A waiting list will be maintained and places re-allocated as they become available. Option 2: (1) Places will be allocated according to the number of subject semesters. (2) A waiting list will be maintained and places re-allocated as they become available. (2015) page 43 / 135

44 Employing media and interactive methods at school and in classrooms 43-LA-MedUnt-152-m01 Centre for Teacher Training and Educational Research (ZfL) 3 (not) successfully completed 1 semester undergraduate Basics of communication at school / educational work; task specification of a teacher; introduction to various (interactive) media and medial methods; their use and purposeful usage in the classroom; production of learning objects for the classroom. The students know a broad variety of media and medial methods and are able to use them in the classroom purposefully. Through the use of interactive media they can lead the students to self-organized and independent learning and working. They can prepare their lessons effectively and support them with objects for learning in an optimal way. S (2) Presentation (approx. 10 minutes, approx. 15 pages) 27 places. Should the number of applications exceed the number of available places, places will be allocated as follows: Option 1: (1) Places will be allocated by lot. (2) A waiting list will be maintained and places re-allocated as they become available. Option 2: (1) Places will be allocated according to the number of subject semesters. (2) A waiting list will be maintained and places re-allocated as they become available. (2015) page 44 / 135

45 Learning through the arts - Learning theories and classroom experience 43-LA-LTTA-Lernprax-152-m01 Centre for Teacher Training and Educational Research (ZfL) 3 (not) successfully completed 1 semester undergraduate "Learning through the arts" can be used at all types of schools and with all kinds of pupils. In the seminar, interconnections with the Bavarian curricula and own lesson plans for the major subjects will be worked out. Areas of the sciences of teaching and learning, learning theories, and results of brain research form a focal point of the theoretical part. Artist-teacher-cooperation leads to a changed understanding of learning culture. Besides insights into practical work, there will also be an elucidation about educational successes. In the seminar, students will get to know the work of LTTA at our schools and in other countries, while also analyzing and reflecting upon it. The participants of the seminar can also take part in events by LTTA, such as artists' training, teachers' further education, as well as in teaching examples at our project schools. Students gained knowledge about teaching theories, are able to do immersed curricular work, to reprocess lessons methodically and can transfer the artistic experiences choreographically, sculpturally, musically etc to their subject area. They can confidently work in a team. Furthermore, through their own practical implementation, they have experienced a furthering of their teaching personality with an increased feeling of security when using artistic elements for the purpose of achieving cognitive curricular goals. Moreover, they gained knowledge about classroom teaching research and are able implement and analyze their own units and surveys. S (2) a) oral presentation (approx. 20 minutes) with written elaboration (approx. 6 pages) or b) designing a seminar (approx. 45 minutes) with written elaboration (approx. 3 pages) 30 places. Should the number of applications exceed the number of available places, places will be allocated as follows: Option 1: (1) Places will be allocated by lot. (2) A waiting list will be maintained and places re-allocated as they become available. Option 2: (1) Places will be allocated according to the number of subject semesters. (2) A waiting list will be maintained and places re-allocated as they become available. (2015) page 45 / 135

46 Self-assessment and career planning 43-LA-Self-152-m01 Centre for Teacher Training and Educational Research (ZfL) 3 (not) successfully completed 1 semester undergraduate Based on a number of working steps, students' own ideas and wishes concerning their careers and plans for their professional future are made more transparent. Besides contributions by the seminar supervisors, topics will be treated in depth via role playing games as well as group and individual work which focuses on determining individual strengths and weaknesses, self-presentation (replication of their self-perception and how others perceive them), and definition of goals (in life as well as their career, and the compatibility of both). The students learn to grasp and specify their skill profile. This includes a critical self-reflection in reference of their own goals. A comparison of their self-perception and how they are perceived by others enables the students to make their first steps towards improving their skills. These include their self-presentation as well as raising awareness for a possible correction in their career planning. The seminar prompts the students to take meaningful steps towards an implementation of their career plans. S (2) Seminar paper (approx. 10 pages) 15 places. Should the number of applications exceed the number of available places, places will be allocated as follows: Option 1: (1) Places will be allocated by lot. (2) A waiting list will be maintained and places re-allocated as they become available. Option 2: (1) Places will be allocated according to the number of subject semesters. (2) A waiting list will be maintained and places re-allocated as they become available. (2015) page 46 / 135

47 Communicative competence and teaching competence 43-LA-Komm-152-m01 Centre for Teacher Training and Educational Research (ZfL) 3 (not) successfully completed 1 semester undergraduate Reflection upon their own role as a teacher trainee and future teacher; Self- and time-management; Image of the self and the other; goal-oriented use of media; theme-centered use of teaching methods. Students are able to reflect about their own role and to constructively include difference between their image of themselves and the image of the other. They command over a basic know-how and repertoire of methods. In the interplay of their role, the image of themselves and of the other as well as an appropriate repertoire of media and methods, students are able to didactically process acquired contents of their discipline while taking into consideration the addressee S (2) a) presentation (approx. 45 minutes) or b) term paper (approx. 10 pages) 15 places. Should the number of applications exceed the number of available places, places will be allocated as follows: Option 1: (1) Places will be allocated by lot. (2) A waiting list will be maintained and places re-allocated as they become available. Option 2: (1) Places will be allocated according to the number of subject semesters. (2) A waiting list will be maintained and places re-allocated as they become available. (2015) page 47 / 135

48 Practical work experience in the classroom 1 43-LAPraxUnt1-152-m01 Centre for Teacher Training and Educational Research (ZfL) 3 (not) successfully completed 1 semester undergraduate The students gain an insight into teaching practice. The focus lies on the conveyance of teaching methods and methods for individual advancement in the classroom. Through observations, coaching projects, internships or purposeful assignments inside or outside the classroom, the students have their own practical education and teaching experiences. The students learn about various kinds of teaching methods and methods for individual advancement and differentiation. They are familiar with concepts about professional action in the classroom and about dealing with heterogeneity and difference. The acquired knowledge about teaching can already be applied in some cases. S (2) Report (approx. 10 pages) 15 places. Should the number of applications exceed the number of available places, places will be allocated as follows: Option 1: (1) Places will be allocated by lot. (2) A waiting list will be maintained and places re-allocated as they become available. Option 2: (1) Places will be allocated according to the number of subject semesters. (2) A waiting list will be maintained and places re-allocated as they become available. (2015) page 48 / 135

49 School social work: various fields of activity 43-SchulSozTF-152-m01 Centre for Teacher Training and Educational Research (ZfL) 3 (not) successfully completed 1 semester undergraduate As a means of help for young people at school the youth welfare services offer fast and unbureaucratic help and/ or cooperation with other areas. It is aimed at young people with severe social and pedagogical problems, who are dependent on support to overcome disadvantages or individual impairments. The module offers an insight into the tasks, structures and contents of an active youth or social school work. In various areas of occupation, such as the "fostering of psychosocial competence" or the diverse tasks of networking the tasks of social school work are presented in their different aspects Students have gained insights into the diverse areas of responsibility of social school work. Because of their focus on "psychosocial competences" they are experienced in the application of psychosocial methods of the social school workers and are able to choose and apply them adequately, reflect upon them critically and broaden them independently. Alternatively, with the focus on "networking", the students have basic knowledge about institutions and some experience in committees, and are familiar with tasks, competence and procedures in social school work and are thus able to coordinate the different requirements. R (2) a) project report (approx. 10 pages) or b) interview (approx. 30 minutes) with log (approx. 5 pages) or c) portfolio (approx. 45 hours) 10 places. Should the number of applications exceed the number of available places, places will be allocated as follows: Option 1: (1) Places will be allocated by lot. (2) A waiting list will be maintained and places re-allocated as they become available. Option 2: (1) Places will be allocated according to the number of subject semesters. (2) A waiting list will be maintained and places re-allocated as they become available. (2015) page 49 / 135

50 School social work: focus on projects 43-SchulSozPro-152-m01 Centre for Teacher Training and Educational Research (ZfL) 3 (not) successfully completed 1 semester undergraduate As a means of help for young people at school the youth welfare services offer fast and unbureaucratic help and/ or cooperation with other areas. It is aimed at young people with severe social and pedagogical problems, who are dependent on support to overcome disadvantages or individual impairments. The module offers an insight into the tasks, structures and contents of an active youth or school social work and gives the students the opportunity to participate in the concrete pedagogical work with a professional focus on "projects", or to bring their own small projects to fruition. The students have gained an insight into the diverse task areas of a teacher at the elvel of lower secondary education. They are experienced in carrying out projects of social school work and are able to use those as a basis for the development of their own pedagogical projects. They have furthered their own methodic competence and are able to use it purposefully, reflect upon it critically and broaden it independently. R (2) a) project report (approx. 10 pages) or b) interview (approx. 30 minutes) with log (approx. 5 pages) or c) portfolio (approx. 45 hours) 15 places. Should the number of applications exceed the number of available places, places will be allocated as follows: Option 1: (1) Places will be allocated by lot. (2) A waiting list will be maintained and places re-allocated as they become available. Option 2: (1) Places will be allocated according to the number of subject semesters. (2) A waiting list will be maintained and places re-allocated as they become available. (2015) page 50 / 135