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This entry is from Winter semester 2022/23 and might be obsolete. You can find a current equivalent here.

Mathematics Education: Teaching Geometry
(dt. Didaktik der Geometrie)

Level, degree of commitment Advanced module, depends on importing study program
Forms of teaching and learning,
workload		 Lecture (2 SWS) or seminar (2 SWS),
90 hours (attendance in den Lehrveranstaltungen 30 h, 50 h preparation and follow-up inklusive Studienleistungen, 10 h Vorbereitung and Ablegen von Prüfungsleistungen)
Credit points,
formal requirements		 3 CP
Course requirement(s): Depending on the type of course, two of the following three course requirements are offered and must be passed for admission to the module examination: (1) Successful completion of at least 50 % of the exercises, (2) presentation, or (3) written test.
Examination type: Written examination (90 min.) or term paper (15-20 p.)
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program LAaG Mathematics. In the event of failure, a total of 4 attempts are available for the examination.
Origin LAaG Mathematics
Duration,
frequency		 One semester,
Jedes Studienjahr
Person in charge of the module's outline Prof. Dr. Thomas Bauer, Dr. Roland Weber

Contents

Different types of knowledge formation in geometry and their development are described, corresponding didactic guidelines are identified and suggestions for teaching method are given. The use of dynamic geometry software is also taken into account. Possible main topics of the module are in the following content areas:

Figures and illustrations:

Topics are covered that are related to geometric shapes, congruence and similarity with the corresponding geometric maps.

Dimensions and functions in high school geomety:

Topics are covered that are related to measuring geometric quantities such as lengths, areas, volumes, and angles.

Space and form:

Topics concerning geometric objects and forms are dealt with, i.e. properties and relations of plane figures and spatial forms are investigated. Description, components and didactic functions of construction problems, proof problems, and problem solving tasks are dealt with.


Qualification Goals

Competences:

The students

  • understand the study of geometric maps and shapes as a foundation for conceptualizing mathematically space and forms and for developing appropriate mental models and intutions.
  • experience geometric content theory as a classical topic of mathematics teaching, which can show the fruitful connection of theory formation and application in an elementary context,
  • understand which mental techniques of mathematical knowledge formation (abstraction, mental ordering and structuring, formalisation) are necessary for understanding,
  • know a multi-faceted spectrum of different approaches, mediating ideas and paradigmatic examples,
  • acquire the ability to flexibly alternate between levels of conceptual rigor and precision on a topic-related basis,
  • know topic-specific learning obstacles and sources of error,
  • know the associated results and considerations of didactic research and examples of practical implementation in teaching.

Qualification goals:

The students have a basic knowledge of mathematics and didactics for teaching geometry in the secondary level. This includes in particular the knowledge of approaches, forms of representation, paradigmatic examples and learning obstacles concerning geometric maps and shapes as well as in geometric content theory.


Prerequisites

The following modules are required: Geometry, Analysis I, Analysis II, Linear Algebra incl. Foundations of Mathematics.


Applicability

The module can be attended at FB12 in study program(s)

  • LAaG Mathematics

When studying LAaG Mathematics, this module must be completed in the study area Advanced Modules.


Recommended Reading

(not specified)



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2022/23. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.