Qualification targets Teaching program for Gymnasium (102 ECTS)
The study of Mathematics as an advanced subject within the teacher training programme for upper secondary schools provides, in particular:
- Subject-specific expertise in differential and integral calculus in Rⁿ, ordinary differential equations, function theory, linear algebra, algebra, number theory, stochastics, geometry and applied mathematics,
- subject-specific teaching skills in mathematics,
- an understanding of the diversity of mathematics, its subjects and tools,
- insight, gained through examples, into the benefits of interlinking ideas and methods from different areas of mathematics,
- skills in the use of mathematical tools, particularly new technologies,
- the ability to reflect on the appropriateness of using mathematical tools,
- the capacity for abstraction and precision in analytical thinking,
- a proven ability to structure complex relationships,
- a well-founded ability to apply mathematical methods independently to specific problems,
- an understanding of internal mathematical relationships, various sub-fields of mathematics, and an understanding of interdisciplinary relationships,
- Perseverance in solving difficult problems and problem-solving skills,
- the ability to carry out advanced independent academic work.
Scientific qualification
| Learning Outcome | Implementation | Achievement of Learning Outcome | |
|---|---|---|---|
| Graduates are familiar with the working methods and technical terminology of mathematics and have mastered the methods of mathematical reasoning and proof. | Basic mathematical concepts and methods of proof, reasoning and writing in mathematics, compulsory modules in analysis and linear algebra | Small-group exercises, compulsory exercises, ungraded written tests, individual oral examinations | |
| Graduates possess fundamental knowledge of stochastics and at least one other area of applied mathematics and are able to apply the methods of these areas with confidence. | Compulsory and compulsory-elective modules | Exercises, written examination and individual oral examination | |
| Graduates possess fundamental knowledge of selected areas of pure mathematics and are familiar with the basic methods of proof in these areas. | Compulsory and compulsory-elective modules | Exercises, written examination and individual oral examination | |
| Graduates are trained in analytical thinking, possess a high capacity for abstraction, universally applicable problem-solving skills and the ability to structure complex relationships. | Lectures with tutorials, seminars where applicable, and final dissertation | Exercises, written examinations, individual oral examinations, presentations, final dissertation | |
| Graduates are able to familiarise themselves independently with further areas of mathematics with the aid of specialist literature. | Lectures with tutorials, seminars where applicable, and final dissertation | Exercises, written examinations, individual oral examinations, presentations, final dissertation | |
| Graduates are able to present their knowledge, ideas and problem-solving approaches clearly. | Seminars, tutorials | Presentations, presentation of solutions to tutorial exercises | |
| Graduates possess the basic knowledge, ways of thinking and working, and methodological skills required for further study, in particular at Master’s level. | Lectures, tutorials, seminars, final thesis | Exercises, individual oral examinations, presentations, final thesis | |
| Graduates are familiar with the rules of good academic practice and are able to apply them in their own work. | Where applicable, seminars and final thesis | Where applicable, seminars and final thesis | |
| Graduates are able to interpret and apply concepts, principles, methods and evidence-based findings from the field of mathematics education. | Lectures with exercises, seminars, placements, final dissertation where applicable | Written examinations, presentations, placement report where applicable, portfolio, final dissertation | |
| Graduates are able to reflect, on a scientifically sound basis, on the use of media in mathematics teaching and the supervision of pupils in selected teaching and learning situations. | Seminars and final dissertation (where applicable) | Presentations, portfolio and final dissertation (where applicable) |
Ability to take up employment
| Learning Outcome | Implementation | Achievement | |
|---|---|---|---|
| Graduates are trained in analytical thinking, possess a high capacity for abstraction, universally applicable problem-solving skills and the ability to structure complex relationships. | Lectures with tutorials, seminars where applicable, and a final dissertation | Tutorial assignments, written examinations, individual oral examinations, presentations where applicable, and a final dissertation | |
| Graduates are able to formulate and present their knowledge, ideas and problem-solving approaches in a clear and accessible manner tailored to the target audience. | Seminars, tutorials, tutoring and marking | Presentations, presentation of solutions to tutorial exercises, supervision of a tutorial group under guidance | |
| Graduates are able to identify, structure and model specific problems from other fields, and develop solutions using mathematical methods. | Lectures and exercises, possibly seminars and final thesis | Exercises, possibly presentations and final thesis | |
| Graduates possess a strong capacity for perseverance when solving complex problems. | Exercises, possibly a final thesis | Exercise problems, possibly a final thesis | |
| Graduates are able to work constructively and goal-orientedly in teams. | Practical sessions, seminars, work placements | Various practical session formats involving group work, practical exercises, teaching and learning situations | |
| Graduates are able to explore further areas of knowledge independently, efficiently and systematically. | Seminars, if applicable, final dissertation | Lectures, final dissertation | |
| Graduates are familiar with the use of digital media in mathematics teaching and can make effective use of mathematical software in teaching and learning situations. | Lectures with tutorials, practicals, possibly seminars and final dissertation | Exams, presentations, possibly a practical placement report, portfolio, final dissertation | |
| Graduates possess the ability to play a creative role in interdisciplinary teams. | Practical placements, seminars | Presentations, practical placement report (where applicable), portfolio | |
| Graduates apply concepts, principles, methods and evidence-based findings from the field of mathematics education in mathematics lessons. | Lectures with tutorials, practical placements, seminars where applicable, and final dissertation | Exams, presentations, practical placement report where applicable, portfolio, final dissertation |
Personality development
| Learning Outcome | Implementation | Achievement | |
|---|---|---|---|
| Graduates are trained in analytical thinking, possess a high capacity for abstraction, universally applicable problem-solving skills and the ability to structure complex relationships. | Lectures with tutorials, seminars where applicable, and a final dissertation | Tutorial assignments, written examinations, individual oral examinations, presentations where applicable, and a final dissertation | |
| Graduates are able to critically reflect upon and evaluate social, economic, historical, subject-specific didactic and practical school developments and processes. | Lectures with tutorials, placements, seminars where applicable, and final dissertation | Written examinations, presentations, placement report where applicable, portfolio, final dissertation | |
| Graduates are able to play a creative role in participatory processes. | Involvement in the student council and other student organisations, participation in committees and bodies. | Committee work and meetings | |
| Graduates possess a strong capacity for perseverance when solving complex problems. | Exercises, thesis where applicable | Exercise tasks, thesis where applicable | |
| Graduates are able to identify, implement and present ideas and proposed solutions in a way that is generally understandable and tailored to the target audience. | Lectures with exercises, practical placements, seminars where applicable, and final dissertation | Exams, presentations, practical placement report where applicable, portfolio, final dissertation |
