Maths
The mathetics is the science of learning .
The word “mathetics”, from the ancient Greek μάθησις mathēsis “learning” to μανθάνω manthanō “I learn, understand” and μάθημα mathēma “what has been learned”, refers to “learning”, both in the sense of a process and a sudden gain in knowledge with the similar meaning already used by Plato . In its conception, maths goes back to Jan Amos Komensky (= Johann Amos Comenius , 1592–1670) from eastern Moravia , who in his Didactica magna described didactics as " teaching art" and maths as "learning art". This means that maths is oriented towards the learner in relation to the recipient, while the didactics is sender-related to the teacher.
In its basic meaning today, maths includes any kind of learning, i.e. exploring learning both with and without a teacher. The spectrum ranges from understanding maths as “technology” to the emphasis on a “human-friendly” or “brain-friendly” orientation of learning to the needs of the learner. The knowledge of maths gained in critical pedagogy - or criticism of pedagogy - is also confirmed by modern neurosciences , the research results of which, according to the psychiatrist M. Spitzer, are in some cases not in line with traditional practices of imparting knowledge in school and at work.
Maths in school pedagogy
The concept of maths had almost been forgotten until Hartmut von Hentig brought it back from obscurity in 1983 in a report for the Free School in Frankfurt . "Maths is a necessary correction of the thoughtless absolutized principle of didactics : that learning takes place on instruction." (Von Hentig, 1985).
Mathematics looks at school learning from the perspective of the student and characterizes the relationship between teacher and student as 'symmetrical' and 'free of domination'. This means that the student and teacher are on the same level. The teacher is not the 'master' of the learner, but a learning advisor and helping educator .
Maths - understood as the antithesis to (teacher-oriented) didactics - includes the individualized teaching progress from the “preoperational” to “concrete” to “formal operating”. It relativizes the dedicated evaluation emphasized in the 'learning goal-oriented didactics' to the effect that precise 'learning goal control' is often not possible or useful.
Maths implies the 'constructivist' understanding of learning, which understands it as an active, self-organizing ( autopoietic ) process in which the individual's own 'realities' are ' constructed' by them ( constructivism ).
Maths also includes the 'holistic' perspective of the student. The concept of ' holism ', which is subject to different loads in the present context, draws on the holistic theory, which is to be understood in the sense of a humanistic personality theory. It sees every single action of the person in connection with his overall personality and recognizes all experiences that he makes with himself and his environment as comprehensive experience and integrative cooperation.
In summary , the considerations on maths speak against a technical lesson preparation and against a teacher-centered 'pulling through' the lessons by the student. She postulates to constantly change perspectives and to always look at conscious, structured teaching in the class anew, 'holistically' from the student's learning, which - as mentioned - appears to be 'constructivist'. From this it follows for the teacher to commit to a relativistic point of view and to be asked to adopt an attitude that always questions his own assessments. As a consequence, this means seeing teaching primarily as a structured, comprehensive offer to the learner, which takes place not only on the content level, but also on the relationship level . On the one hand, it includes learning itself and, on the other hand, not only addresses cognition , but also emotion , motivation and volition (will) of the learner.
Critics of the term maths point out that a counter-position to a very narrow understanding of didactics is artificially built up here. The considerations put forward under the catchphrase have therefore always been a central component of theories and models of didactics and therefore do not contain any new and specific research direction in current education or teaching-learning research: Didactics always deals with teaching and learning, where and because there are close connections between the two in the sense of the didactic triangle . A didactically not only reasonable but specific situations even more meaningful change in perspective, in the form of by psychologists exchange / barter distinct forms of teacher-centered , student-centered and socially inclusive education does the principle not diminish. It does not separate the areas of teaching and learning, but brings them together, thus forming part of a flexible, interrelated teaching method that promotes learning processes and that cannot and should not be broken up into abstract and formalistic teaching and learning. Accordingly, maths does not play a role in school pedagogy and teacher training today and is hardly taken up in scientific discussions.
Maths in professional development
More self-initiative is required for learners in professional life than for school-based learning. For an efficient transfer of knowledge at work, it would therefore be expected that in-house transfer of knowledge, customer training courses and, for example, the design of manuals and instructions for use are primarily geared towards the needs of internal and external customers. Nevertheless, the concept of maths is largely unknown in the field of professional training .
See also
literature
- Johann Amos Comenius: Mathetica. (ie learning art) In: R. Golz, W. Korthaase, E. Schäfer (Ed.): Comenius and our time, Baltmannsweiler. 1996, pp. 130-147.
- M. Anton: upbringing and self-education - teaching and learning - didactics and maths. In: learning worlds. 5, No. 2, 2003, pp. 73-76.
- Seymour Papert: Revolution in learning - children, computers, schools in a digital world. Heise, Hannover 1994, ISBN 3-88229-041-2 .
- J. Göndör, Ch. Schreger: Welt-ABC won the Austrian Multimedia State Prize 2007. Neukirchen-Vluyn, Vienna 2007. (full text ; PDF; 604 kB) - a mathematical concept
- J. Wiesemann: Learning as everyday practice - forms of learning for children at a free school. Klinkhardt Verlag, Bad Heilbrunn 2000, ISBN 3-7815-1062-X .
Web links
Individual evidence
- ↑ PO Chott: The development of the MATHETICS term and its meaning for teaching in (primary) school. In: PÄDForum. No. 4, 1998, pp. 390-396.
- ^ HG Liddell-Scott: A Greek-English Lexicon . 9th edition. Clarendon Press, Oxford 1996, ISBN 0-19-864226-1 .
- ^ W. Gemoll, K. Vretska, T. Aigner: GEMOLL. Greek-German school and manual dictionary. 10th edition. Munich 2010, p. 514.
- ^ Johann Amos Comenius : Didactica magna in Opera didactica omnia (1657)
- ↑ Hartmut Mitzlaff: Johann Amos Comenius (1592–1670) teaching pansophic things. In: A. Kaiser, D. Pech (Hrsg.): Basic knowledge of subject teaching. Volume 1: History and historical concepts of general science. Schneider Verlag Hohengehren, Baltmannsweiler 2004, ISBN 3-89676-861-1 , pp. 41-46.
- ↑ TF Gilbert: Mathetics: The Technology of Education. In: The Journal of Mathetics. No. 1, January 1962.
- ↑ Manfred Spitzer : Learning. 2007, ISBN 978-3-8274-1723-7 .
- ↑ Hartmut von Hentig: How free are free schools? Expert opinion for an administrative court. 1st edition. Klett-Cotta, Stuttgart 1985, ISBN 3-608-93340-9 (Hartmut von Hentig developed his concept of maths in this report in the administrative court proceedings for the approval of the Free School in Frankfurt).
- ↑ Reinhard Tausch, Anne-Marie Tausch: Educational Psychology. Psychological processes in education and teaching. Göttingen 1979.