Upper Secondary School Teacher Training in Descriptive Geometry

We will teach you to see

Master's degree programme, full-time study mode, double-subject, Czech, 2 years 
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The graduates of this study programme obtain the qualification for teaching descriptive geometry at secondary schools - they can teach geometry, visualization methods, and areas of computational geometry and graphics. The aim of the studies is to train secondary school teachers of descriptive geometry. This follow-up Master's degree programme educates students in many disciplines of geometry, descriptive geometry with applications, computational geometry, and also provides the necessary methodical, didactic, and other general knowledge and abilities defining the qualification of a secondary school teacher of descriptive geometry. Elective courses provide a broad overview of many disciplines in geometry.

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After successfully completing his/her studies the graduate is able to:

  • teach secondary school descriptive geometry at the proper professional level and employ the appropriate methodical and didactic methods
  • apply experience with professional spatial imagination and creative approach to work
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The graduates of this study programme obtain qualification for teaching descriptive geometry at secondary schools - they can teach geometry, visualization methods, and areas of computational geometry and graphics.

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The follow-up Master's degree programme of the Upper Secondary School Teacher Training in Descriptive Geometry can be completed only in combination with the follow-up Master's degree programme of the Upper Secondary School Teacher Training in Mathematics. These studies are available to students who have completed the Bachelor's studies of Mathematics or Mathematics with a view to Education.

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Two practical training courses in descriptive geometry, each worth 2 credits, form a part of the studies. The teacher training in descriptive geometry 1 must be performed by students at selected secondary schools in Brno, and the teacher training in descriptive geometry 2 can be completed at secondary schools of their choice. The students receive their teacher training from experienced secondary school teachers. Teacher training includes also sitting in on classes, class presentations, and active involvement in the running of the school.

Since the studies are necessarily double-subject, students are required to complete the teacher training of the same extent also in the second study programme.

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The final state examination consists of the Master's thesis defence and the state examination.

Characteristics of the Master's thesis and its defence

In the Master's thesis students demonstrates their knowledge in the area of the theme of the thesis and the ability to work under supervision. During the defence of the Master's thesis the understanding of the topic and level of presentation are assessed.

Characteristics of the state examination

The purpose of the examination is to verify whether the student is familiar with the theory of imaging techniques, and knows sufficiently well the practical constructions of the individual imaging methods - Monge imaging method, axonometry, central projection, linear perspective, and others. The final state examination consists of written and oral parts. In the written part, students will demonstrate on specific tasks the practical knowledge of structures in various imaging methods. In the oral part they should demonstrate the adequate understanding of the theoretical foundations of imaging methods.

Defining the scope of questions for the oral examination

Descriptive Geometry

Parallel Projection, Pohlke's Theorem

Monge Imaging Method, Quetelet-Dandelin's Theorem

Axonometry, Skuherský Method, Sobotka Method

Central Imaging Methods

Linear Perspective

Developable Surfaces

Warped Surfaces

Surfaces of Revolution

Generalized Helicoids

Lighting

The Use of Imaging Techniques in Cartography

Didactics of Descriptive Geometry

Focal Properties of Conic Sections

Free Parallel Projection

Positional Problems in Stereometry

Metric Problems in Stereometry

Axial Affinity and Collineation

Monge Projection

Positional Problems in Monge Projection

Metric Problems in Monge Projection

Displaying Polyhedra in Monge Projection

Displaying Round Bodies in Monge Projection

Sections and Intersections of Solids in Monge Projection

Dimensioned Projection in Teaching Descriptive Geometry at Secondary Schools

Axonometry in Teaching Descriptive Geometry at Secondary Schools

Geometry of Triangle

History of Descriptive Geometry

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After completion of the Master's degree programme the graduates may progress to the doctoral degree programmes. The most suitable programme is General Problems of Mathematics.

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Students
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Field of study specifications

Field of Study: Upper Secondary School Teacher Training in Descriptive Geometry
Abbreviation: UDG
Code: 7504T045
Type: Master's degree programme (following the Bachelor's one)
Degree: Mgr.
Accreditation: to 31/12/2024
Programme: N1101 N-MA Mathematics
Faculty of Science
Field of study guaranteed by:
Faculty of Science
Field guarantor:
doc. PhDr. Bohumíra Lazarová, Ph.D.
Field guarantor:
prof. RNDr. Josef Janyška, DSc.