Math class

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Arithmetic lessons in a first class (Berlin, 1949)

Mathematics instruction refers to the institutionalized imparting of subject-specific knowledge as well as skills and abilities in the area of mathematics to students by a mostly specifically trained teacher, both in school in the form of a school subject , in the university and in adult education . The lessons are usually based on a lesson planning , draws on knowledge of mathematics didactics as subject didactics , implements this practically with the help of teaching and learning methods and has to take curricular requirements into account. Mathematics is in Germany to the High School at all general schools in all grades mandatory school subject and is due to its share of the timetable major.

Educational value and legitimation of a math lesson

Hans Werner Heymann answers the questions about the educational value and the legitimation of a mathematics lesson by deriving the following seven mathematics lesson tasks from the relationship between mathematics and general education on the basis of educational theory .

  • Life preparation
  • Cultural Coherence Foundation
  • World orientation
  • Instructions for the critical use of reason
  • Developing willingness to take responsibility
  • Practice in understanding and cooperation
  • Strengthening the student self

Heymann particularly emphasizes the tool character of the subject, which helps to find one's way in everyday life and to orient oneself. He also sees mathematics as a communication medium. For example, the use of symbols and graphic representations as well as the ability to estimate and classify sizes that can be seen as material qualifications for future life can be experienced especially in mathematics lessons. By converting real models into mathematical models , it is important to gain insights into relationships and to critically and scientifically reflect on application situations instead of just accepting them. The ability to think is particularly trained and self-esteem is promoted. Heymann places the handling of elementary, geometric shapes and numbers as well as the mastery of elementary operations with numbers in addition to the mastery of the mother tongue as a form of cultural tradition with a cross-generational and reform-resistant character. Heymann also points out the historically-oriented internationality and universality that flow into mathematics lessons as the history of mathematics through the presentation of, for example, previously developed doctrines and is therefore culture-creating. Furthermore, mathematics is part of many training and study courses and here the subject of examination as well as aptitude tests and therefore has a qualification contribution for professional maturity. Heymann admits that not all tasks for mathematics lessons have the same weight and that other subjects such as religion and German tackled some tasks more directly, but in a "networked complex of human knowledge and ability [...] the specific contribution of mathematics lessons through no other subject can be compensated. "

Heymann's main positions on establishing mathematics as a general educational subject can also be found in the more recent writings by Hans-Joachim Vollrath and Jürgen Roth, in the statements made by Alexander Israel Wittenberg as early as 1963 and in UNESCO resolution 29 C / DR 126 of 1997.

Lothar Profke takes a different position . Under the question: "Do we need mathematics lessons", he pleads for dispensability as a contribution to general education. He suggests that if there is a mathematics lesson, it should be considered an optional subject for interested students with well-trained teachers from a certain grade onwards . He justifies this with the fact that schools do not have to prepare for certain professions and that basic qualities such as spatial imagination can also be taught in other subjects such as art. Compared to Heymann, Profke notes that a qualification in the application subjects such as economics, medicine or law must first be acquired before the content can be mathematized. In general, a legitimation of mathematics lessons cannot simply be derived from the content such as the Pythagorean theorem or quadratic equations . Rather, the decisive factor is the teaching culture in which teachers and students interacted with one another.

Model scheme for math lessons

Model scheme for mathematics lessons according to Zech

Friedrich Zech presents a model scheme for mathematics lessons based on teaching and learning theory . Lessons are embedded in their preparation and follow-up . As a framework, Zech is based on the anthropogenic and socio-cultural factors of the Berlin model . With regard to the learning goals , he differentiates between interdisciplinary and general goals of the subject, whereby Zech sees the goal of actively dealing with problems in which finding solutions plays a central role. In this regard, essential objectives at Zech can also be found in the operators for the subject of mathematics, which are intended as concrete instructions for teaching. Zech pays special attention to the development of mathematical thinking according to the operational principle and the learning phases , especially the phase of motivation and the transfer of mathematical learning . Furthermore, Zech generates a new classification of learner types in mathematical learning, which is less based on the learning style or the learning strategy of the learner, but is based on the technical-didactic position. Particular attention is paid to the learning types conceptual learning, rule learning and problem solving . Regardless of the curricular requirements, Zech also presents a checklist for the selection of mathematical lesson content, which is based, among other things, on the explanations of Heinrich Winter , who demands that mathematics lessons should enable the following three basic experiences:

  • Perceiving and understanding phenomena of the world around us, which concern or should concern us all, from nature, society and culture, in a specific way.
  • Get to know and understand mathematical objects and facts, represented in language, symbols, images and formulas, as intellectual creations, as a deductively ordered world of its own.
  • In dealing with tasks, acquire problem-solving skills that go beyond mathematics ( heuristic skills).

Of the criteria of teaching and class management, student orientation and cognitive activation , the latter is considered a predictor of learning success, whereby the student orientation increases motivation and the first criterion simply creates the conditions for mathematical learning as a whole. In contrast, Wittenberg emphasizes the content-related component "Mathematics lessons should do justice to what mathematics really is."

In addition to these fundamental considerations relating to mathematics teaching, the TIMSS study adds the aspect of the effectiveness and thus the quality assurance of mathematics teaching. This is where the discussion about the acquisition of significant quality features and the concrete implementation of mathematical-didactic findings play a role. Tasks, understood as an invitation to learn to act, can be seen as a decisive tool in mathematics lessons, the quality of which could be based on the criteria of authenticity , significance, relevance, openness and the nature of a challenge.

Consequences of the mathematics educational standards

The educational standards for mathematics set nationwide for the subject of mathematics in 2003 by the Conference of Ministers of Education and Cultural Affairs aim to make teaching processes transparent and to optimize them with regard to quality assurance in education , and to achieve greater sustainability in knowledge acquisition. In this regard, on the one hand, process-related competencies were generated in the form of six general mathematical competencies, each of which can be differentiated into three requirement areas, and on the other hand, subject-related competencies were designed as so-called five main ideas for mathematics lessons. Instead of the traditional achievement of learning objectives, the achievement of competence becomes the yardstick for successful teaching, so-called competence-oriented teaching. In addition to the two areas of competence mentioned, personal and social skills should also be taken into account in the classroom. As a consequence of the definition of the educational standards, it is important to construct teaching materials, especially exercises, according to these specifications. When planning lessons, the teacher is faced with questions such as: "How should tasks and lessons for sustainable competence acquisition look like?", "How can one support the development of self-control competence when learning mathematics?" Or also "How do you learn mathematics?" something about the competencies of pupils in class work? ”Among other things, this is problematic because the educational standards only describe what the learner should be able to do at the end of certain macro-sequences, but do not give any indications as to how specifically they should learn. In addition, certain areas such as the formation of mathematical terms are not included at all. The artificial separation of competencies that do not exist in the learning process also complicate the work of the math teacher.

Social evaluation

The actual encounter with mathematics takes place within the framework of mathematics lessons. For most people, school experiences made there largely determine their image of mathematics. The question arises as to how and to what extent mathematics lessons represent mathematics. Due to the fixation on textbooks and the tendency towards the questioning-developing style of teaching, mathematics is presented as a system of finished, completed, historically based knowledge that appears to be objective, incorruptible and strict. In comparison, mathematics lessons make high demands on the learners. Discussions about the role of math lessons are often emotional due to the personal concern of most people. Lietzmann already points to the polarizing effect of the subject and refers to survey results from 1923 and 1956. Even in current surveys, mathematics ranks first when it comes to the most popular and the least popular subject. Overall, math is more popular as a subject among boys than girls. The subject is positively assigned its logic and objectivability, its uniqueness with regard to correct and incorrect solution results and the international validity of mathematical statements, which leads to a performance evaluation that is perceived by students as fair. In maths sayings (on postcards) the opposite attitude to math lessons becomes clear, such as: "Math is an asshole", "Dear math book, please grow up and solve your problems alone from now on", "Better a five in Math as no personal touch at all ”. The reason for this negative attitude could be the relevant reduction of mathematics to arithmetic. The framework curricula are structured in such a way that there is no time for realistic applications, interesting stories and exciting puzzles. If the parents' generation is not very successful in arithmetic, this “math phobia” can have a significant impact on the child's attitude pattern. Therefore, Günter Ziegler advocates a change in the image of the subject. The Luxembourg physicist and science journalist Ranga Yogeshwar criticizes that mathematics lessons are too far from reality and that only very few students help them in their future lives. In his opinion, math is "misused for exam purposes" in school. “We release people into life who never want to know anything about math again after their last exam. Many even have a real trauma, ”he criticizes. He calls for the students to be “excited” about the beauty of mathematics in class.

Influencing factor: math teacher

Under the heading “What are math teachers actually doing wrong” in the magazine of the Süddeutsche Zeitung , it is pointed out that especially in math lessons, students would suffer from a lack of pedagogical appreciation of their teachers. Furthermore, a lack of internal differentiation among students whose learning pace is slower and who need more practice time would practically prevent learning success, which also has a negative effect on professional prospects because of the poor grades.

In comparative studies, a connection can be established between the quality or the availability of specialist pedagogical training, one's own professional competence and didactic competence as a mathematics teacher. In this regard, Profke points to the sometimes very suboptimal training of math teachers, but also emphasizes that individual colleagues are making efforts to make the lessons appealing. Erich Wittmann has already drawn attention to this component : "For a math teacher who really feels called to work, private engagement with technical issues should be perceived as a personal enrichment and should be part of a meaningful leisure activity."

literature

  • Werner Blum: Educational standards in mathematics: concrete . Cornelsen Verlag, Berlin 2006, ISBN 3-589-22321-9 .
  • Hans Werner Heymann: General education and mathematics . Beltz publishing group, Weinheim 1996, ISBN 3-407-34099-0 .
  • Regina Bruder, Timo Leuders, Andreas Büchter: Developing mathematics lessons . Building blocks for competence-oriented teaching . 2nd Edition. Cornelsen Verlag, Berlin 2012, ISBN 978-3-589-22569-9 .

Web links

Commons : Mathematics Didactics  - collection of pictures, videos and audio files

Individual evidence

  1. ↑ Hans-Joachim Vollrath, Jürgen Roth: Fundamentals of mathematics teaching in secondary school . 2nd Edition. Spektrum Verlag, Heidelberg 2012, ISBN 978-3-8274-2854-7 , p. 1 ( limited preview in Google Book search).
  2. ^ Hans Werner Heymann: General education and mathematics . Beltz Verlag, Weinheim, Basel 1996, ISBN 3-407-34099-0 , p. 64 f., 79 f .
  3. ^ Hans Werner Heymann: General education and mathematics . Beltz Verlag, Weinheim, Basel 1996, ISBN 3-407-34099-0 , p. 89 f., 183 ff .
  4. ^ Hans Werner Heymann: General education and mathematics . Beltz Verlag, Weinheim, Basel 1996, ISBN 3-407-34099-0 , p. 71 .
  5. ^ Hans Werner Heymann: General education and mathematics . Beltz Verlag, Weinheim, Basel 1996, ISBN 3-407-34099-0 , p. 154 f .
  6. ^ Hans Werner Heymann: General education and mathematics . Beltz Verlag, Weinheim, Basel 1996, ISBN 3-407-34099-0 , p. 146 .
  7. ^ Hans Werner Heymann: General education and mathematics . Beltz Verlag, Weinheim / Basel 1996, ISBN 3-407-34099-0 , p. 133 .
  8. ↑ Hans-Joachim Vollrath, Jürgen Roth: Fundamentals of mathematics teaching in secondary school . 2nd Edition. Spektrum Verlag, Heidelberg 2012, ISBN 978-3-8274-2854-7 , p. 10 ff . ( limited preview in Google Book search).
  9. ↑ Alexander Israel Wittenberg: Education and Mathematics. Mathematics as an exemplary high school subject . 2nd Edition. Klett Verlag, Stuttgart 1990, ISBN 3-12-983410-9 .
  10. ^ European Mathematical Society: resolution. (No longer available online.) Archived from the original on December 27, 2014 ; accessed on December 23, 2014 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.mathematics-in-europe.eu
  11. ↑ Lothar Profke: Do we need mathematics lessons ? In: Mathematics in School 33 . 1995, ISSN  0465-3750 , p. 129-136 .
  12. ^ Friedrich Zech: Basic course in mathematics didactics . 7th edition. Beltz, Weinheim / Basel 1992, ISBN 3-407-25100-9 , pp. 18 .
  13. ^ Friedrich Zech: Basic course in mathematics didactics . 7th edition. Beltz, Weinheim / Basel 1992, ISBN 3-407-25100-9 , pp. 51 .
  14. ↑ Kultusministerkonferenz: Operators for the subject of mathematics. (PDF) (No longer available online.) Archived from the original on September 19, 2014 ; Retrieved December 26, 2012 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.kmk.org
  15. ^ Friedrich Zech: Basic course in mathematics didactics . 7th edition. Beltz, Weinheim / Basel 1992, ISBN 3-407-25100-9 , pp. 168 f .
  16. ^ Friedrich Zech: Basic course in mathematics didactics . 7th edition. Beltz, Weinheim / Basel 1992, ISBN 3-407-25100-9 , pp. 59 .
  17. ^ Heinrich Winter: Mathematics lessons and general education. (PDF; 152 kB) Accessed July 10, 2013 .
  18. ↑ Kristina Reiss , Christoph Hammer: Fundamentals of mathematics didactics . Springer, Basel 2013, ISBN 978-3-0346-0141-2 , pp. 16 f .
  19. ↑ Alexander Israel Wittenberg: Education and Mathematics. Mathematics as an exemplary high school subject . 2nd Edition. Klett Verlag, Stuttgart 1990, ISBN 3-12-983410-9 , p. 50 .
  20. ↑ Timo Leuders: Quality in mathematics lessons at secondary level 1 and 2 . Cornelsen Scriptor, Berlin 2001, ISBN 3-589-21425-2 , pp. 8 .
  21. ^ Regina brother, Timo Leuders, Andreas Büchter: Develop mathematics lessons . Building blocks for competence-oriented teaching . 2nd Edition. Cornelsen Verlag, Berlin 2012, ISBN 978-3-589-22569-9 , pp. 18th f .
  22. ↑ Timo Leuders: Quality in mathematics lessons at secondary level 1 and 2 . Cornelsen Scriptor, Berlin 2001, ISBN 3-589-21425-2 , pp. 99 .
  23. ↑ Werner Blum , Christina Drüke-Noe, Ralph Hartung, Olaf Köller (eds.): Educational standards mathematics: concrete . Secondary level I: example exercises, suggestions for lessons, ideas for further training . Cornelsen Verlag, Berlin 2006, ISBN 3-589-22321-9 , pp. 9 .
  24. ^ Regina brother, Timo Leuders, Andreas Büchter: Develop mathematics lessons . Building blocks for competence-oriented teaching . 2nd Edition. Cornelsen Verlag, Berlin 2012, ISBN 978-3-589-22569-9 , pp. 11 f .
  25. ^ Regina brother, Timo Leuders, Andreas Büchter: Develop mathematics lessons . Building blocks for competence-oriented teaching . 2nd Edition. Cornelsen Verlag, Berlin 2012, ISBN 978-3-589-22569-9 , pp. 17 .
  26. ^ Regina brother, Timo Leuders, Andreas Büchter: Develop mathematics lessons . Building blocks for competence-oriented teaching . 2nd Edition. Cornelsen Verlag, Berlin 2012, ISBN 978-3-589-22569-9 , pp. 15 .
  27. ^ Hans Werner Heymann: General education and mathematics . Beltz Verlag, Weinheim, Basel 1996, ISBN 3-407-34099-0 , p. 254 .
  28. ^ Hans Werner Heymann: General education and mathematics . Beltz Verlag, Weinheim, Basel 1996, ISBN 3-407-34099-0 , p. 254 .
  29. ↑ Hans-Joachim Vollrath, Jürgen Roth: Fundamentals of mathematics teaching in the secondary level . 2nd Edition. Spektrum Verlag, Heidelberg 2012, ISBN 978-3-8274-2854-7 , p. 1 f . ( limited preview in Google Book search).
  30. ^ Walther Lietzmann: Funny and strange things about numbers and shapes . 11th edition. Vandenhoeck & Ruprecht, Göttingen 1982, ISBN 3-525-39112-9 , pp. 11 f .
  31. ↑ Andrea Hennis: Maths is the Germans' favorite subject. In: Focus Online. February 25, 2010, accessed December 11, 2014 .
  32. ^ German Association for the Promotion of Mathematical and Natural Science Education V .: Mathematics as a favorite subject. (No longer available online.) Archived from the original on December 26, 2014 ; Retrieved December 20, 2014 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.mnu.de
  33. ↑ Postcard - "Math is an asshole". Retrieved December 20, 2014 .
  34. ↑ Postcard “Dear math, finally grow up and solve your own problems ...”. Accessed December 20, 2014 .
  35. ↑ Andrea Hennis: Math needs a new image. In: Focus Online. December 5, 2007, accessed December 20, 2014 .
  36. ↑ a b c Ranga Yogeshwar: "Mathematics from school is of no use to us in life". July 2, 2019, accessed November 12, 2019 .
  37. ↑ Susanne Klein: School - "Math is misused for exam purposes". Retrieved November 12, 2019 .
  38. ↑ Karoline Amon: What do math teachers actually do wrong? Retrieved December 21, 2014 .
  39. ↑ Christoph Titz: Pädagogen-Pisa: Woe if the math teacher has to calculate. In: Spiegel Online. Retrieved December 21, 2014 .
  40. ↑ Lothar Profke: Do we need mathematics lessons . In: Mathematics in School 33 . 1995, ISSN  0465-3750 , p. 134 .
  41. ↑ Erich Wittmann: Basic questions of mathematics lessons . 6th edition. Vieweg Verlag, Braunschweig 1983, ISBN 3-528-58332-0 , p. 177 .