Department of Mathematics
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Teaching Subject Mathematics
(Teacher training for primary, secondary and grammar schools)

according to the modularized version of the Lehramtsprüfungsordnung I of 13.03.2008

Since the winter semester 2010/11, the Ludwig-Maximilians-University of Munich has been implementing the modularized version of the Teacher Examination Regulations I of 13.03.2008 in all teacher training programs. On this page you will first find general information about the study of mathematics at the LMU Munich for the teaching profession at elementary, secondary and grammar schools, regardless of the type of school chosen. The subsequent pages then contain more specific information on the

Study contents

In addition to subject didactics, the study of mathematics as a teaching subject for primary, secondary and grammar school teachers covers the following three subject areas:

Within the framework of the Fundamentals of Mathematics, on the one hand, some concepts central to all areas of mathematics, such as sets and figures, as well as important working methods and procedures, especially proof principles, are introduced and the classical number ranges from natural numbers to complex numbers are considered; on the other hand, selected questions from elementary number theory, elementary stochastics and elementary geometry are treated, which are not only of independent importance, but also promote the understanding of the fundamental concepts or form the basis for further areas of mathematics.

Linear Algebra and Analytical Geometry examines the structure of (real) vector spaces as well as the properties of their linear mappings and applies the results obtained in this way to the treatment of geometric problems. The considerations are based on the systematic consideration of linear systems of equations with the development of an algorithm for determining the solution behavior and for determining the solution set and can often be formulated with the help of matrices. The mostly abstract objects of linear algebra then find their illustration in the context of analytical geometry.

The basic concept of differential and integral calculus is convergence, i.e. the existence of limit values, which is illuminated by sequences and series as well as by functions of one and more real variables; this allows the study of continuity, differentiation and integration of functions as well as the construction of elementary functions like exponential function and logarithm. Special types of ordinary differential equations are considered as applications, which play a central role in the description of the temporal course of quantities.

The subject didactics of mathematics deals with the teaching and learning of mathematics. It represents the link between subject science and the disciplines of teaching-learning research. It is of central importance for the profession of mathematics teacher, because the reflection of mathematical learning processes and the design of profitable learning opportunities are the focus of interest. Topics of mathematics didactic research include models of mathematical thought processes of learners and experts as well as characteristics of high-quality mathematics teaching.

Ideal Profile

The pleasure of dealing with mathematical objects and questions as well as a certain talent in this field form the indispensable basis for a successful study of mathematics. In particular, this includes the ability to think logically and abstractly, as well as exact working methods and perseverance in dealing with tasks; special knowledge of school mathematics is not required.

However, there must be the willingness to think your way into an abstract system of definitions, sentences and proofs, which is illuminated and illustrated by meaningful examples and counter-examples. In addition to regular attendance of the lectures, which serves to impart the necessary knowledge and skills, active participation in the exercises and tutorials offered in parallel is urgently required, as these form the indispensable basis for familiarizing oneself with the contents of the lecture and achieving familiarity with the material.

Students of the teaching profession acquire sound professional knowledge that should enable them to reflect on the subject matter from a higher perspective. On this subject-related basis, they learn theories of mathematical thinking and learning and relate them to interdisciplinary psychological and pedagogical ideas. In addition, students studying to become teachers should be prepared to critically question and further develop the image of mathematics teaching they have acquired in their own school years.

In doing so, it is necessary to get involved in typical social and educational science working methods, such as dealing with the results of empirical research, and to concretize findings from the reference sciences in mathematical content. A prerequisite for acting in the later professional field is the willingness to take pedagogical responsibility for students and to treat people from different social and cultural backgrounds as well as different talents and abilities with respect.

 

Structure of the courses

The study of each subject includes both scientific and didactic components; while the teaching of mathematics in didactics is differentiated according to the type of school chosen (elementary school, Hauptschule or Realschule), the scientific content of mathematics is the same at all three types of school, so that students also attend joint courses.

The Institute of Mathematics at the LMU Munich follows the concept of special courses in the subject area, which has been tried and tested for many years. These courses are tailored to the content requirements of the Teacher Examination Regulations I for the subject Mathematics. However, these courses require the beginning of a winter semester; in the weeks before the start of the lecture period, various introductory and information events are offered, such as the Teacher Training Day of the Munich Center for Teacher Education (Münchener Zentrum für Lehrerbildung MZL), der Bridge Course Mathematics (as a subject) or the orientation phase of the Mathematics Student Council.