Numbers country

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Numbersland is a didactic holistic method of teaching preschool children the basics of mathematics , especially the number range from 1 to 10. It is now implemented in many day-care centers.

history

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The concept of the land of numbers was used in textbook literature as early as 1940, at which time the G. Braun Karlsruhe publishing house published the arithmetic book Ins Numbers Land to 1000 by E. Kunzmann and colleagues. However, this textbook has nothing more in common with today's concept apart from the name "Numbersland".

Ten years later, in 1950, Hans Zoozmann published the children's book Der Nullrich - A Journey into the Land of Numbers . Hans Zoozmann is likely to be the founder of today's basic concept of numbers. In this illustrated book, the idea of ​​personifying numbers appears for the first time in children's literature: the “Nullrich” is a personified zero that becomes aware of its own meaning for the other numbers on a journey through the land of numbers. The basic numbers from 1 to 10 appear as fantasy beings.

At around the same time, the picture book by Tanja Peter and Kurt Weinert Peterlein's dream trip into the realm of numbers was published by Chronos Verlag Berlin. There, too, there are many ideas of today's number country concepts, albeit not under the title “number country”.

In the book The Children in Numbers Land , published in 1974, number fairy tales appear explicitly, although the basic numbers are not specifically addressed. In the following years, however, there are many examples where the idea of ​​personalized numbers that act as fairy tale characters emerged. Dietmar Müller reports, for example, on the “zero birthday party”, to which many guests from the realm of numbers and geometry are invited.

In Nil and Nele and the Numbers , basic numbers are finally associated with geometric shapes. It is about Nile and Nele visiting different number countries. All things there are matched to the corresponding country of numbers: In the country of one there is a tree with a sheep in a fence, in the country of two the house has two doors and two windows, etc.

Today, Gabi Preiss and Gerhard Preiss (discoveries in the land of numbers) as well as Barbara Schindelhauer, Gerhard Friedrich and Viola de Galgóczy (come with us in the land of numbers) are associated with the concept. Both concepts aim to provide holistic support for the children, but have central differences. The concept of “discoveries in the land of numbers” is firmly rooted in the pure subject didactics of mathematics, whereas the concept “come with us in the land of numbers” is based more on educational science and, in addition to a subject-didactic orientation, is strongly based on the educational concept of co-construction and meta-cognition.

Today's number country concepts are based on the most concrete possible interpretation of the term “number space”. For this number range from one to ten, a place was created according to a strictly mathematical system, in which the numbers “are at home” - the so-called number land. In this land of numbers, each number is given a fixed, geometrically represented place of residence (circle, ellipse, triangle, square, ..., decagon) and a specific character or an unmistakable identity in the form of a personified number (number animal, number puppet). Their shape is based on the individual digits and at the same time represent the number aspect of the respective number. A variety of actions are carried out with these personalized numbers.

In addition to "number gardens" (geometric shapes) and number figures, essential elements of the number land are special furnishings (number houses, number towers, everyday objects), special number fairy tales and music specially composed for this project, as well as the number line, which has also been internationally known for many decades.

The project Komm mit ins Zahlland , started in February 2003, was funded by the Ministry of Culture, Youth and Sport of the State of Baden-Württemberg and the Robert Bosch Foundation at kindergartens and day-care centers in Lahr / Black Forest .

Theoretical background

The concept of number land is based on the idea that information is best stored when it is “holistically learned”; H. presented and processed in as diverse a way as possible. “Holistic learning” can refer to both the learner (interplay of different senses such as sight, touch, hearing, balance and movement) as well as the learning object. In relation to the number range from one to ten, holistic learning includes the entire sensual experience of the variety of meanings (number aspects) of the basic numbers:

  • Cardinal number aspect : number of elements a lot (e.g. 6 apples, 3 pine cones).
  • Ordinal number aspect : Rank in an ordered set (e.g. first, third, etc.).
  • Nominal number aspect or coding aspect: designation or identification (e.g. postcodes or telephone numbers).
  • Cultural or narrative number aspect: symbolic or mythical meaning in fairy tales, rites, stories (e.g. the number 13 as the number of bad luck, the number seven as the lucky number).
  • Dimension aspect: Quantification of sizes (e.g. two minutes, five kilometers).
  • Operator aspect: In connection with a function, e.g. B. as a multiple of an action (mowing the lawn twice, shopping three times).
  • Geometric number aspect: Identification of geometric patterns (e.g. a pentagon, a triangle).
  • Calculation aspect: Result of an invoice, e.g. B. an addition (e.g. 5 = 3 + 2).

Example: The number garden of the number five is located between that of the four and that of the six (ordinal number aspect). The garden itself is constructed as a regular pentagon (geometric aspect) and can be decorated at every corner (one-to-one assignment). In the garden there is a house with five windows (cardinal number aspect) and an attachable house number (coding aspect) as well as a number tower with the help of which number decompositions (arithmetic aspect: 1 + 4 or 3 + 2) can be illustrated or constructed. In addition, the numbers are searched for in musical structures and the specific living environment of the children.

Further methodological ideas come from various areas of knowledge.

  • Neurodidactics : The material formability or changeability of the brain and learning are indissolubly related. The memory of children is mainly shaped by concrete situations and special experiences. Children also remember places where the events took place. In concrete terms, every number is given a fixed location in the country of numbers, the number gardens are always in the same order and the basic numbers become "number events".
  • Developmental psychology in connection with elementary education: Human characteristics or behaviors are assigned to non-human objects. Specifically, personalized number animals are used as didactic aids in numbers land.

The basics of mathematics are projected into an imaginative world, offer age-appropriate access to the world of numbers and are a great motivation for children.

Scientific studies

The concept of “discoveries in the land of numbers” by Preiß was scientifically examined by Düringer in 2006 with a view to its contribution to conveying the concept of numbers. The author comes to the conclusion that this concept is not able to create a basis for the development of a secure number concept. According to Düringer, this concept does nothing to convey essential insights into the development of the concept of number.

The two authors Joachim and Gronbach also come to a very negative judgment in their documentary "Mathematizing the environment and play world of preschool children with language disorders" with regard to the Preiss concept "Discoveries in the land of numbers". Above all, the “selling” of Preiss's “patent recipes” is heavily criticized: one could “get the impression that the focus here is not on teaching mathematics to children”.

Accordingly, the criticism of the “discoveries in the land of numbers” on the education and mathematics server Matheblogger reads disillusioning: “The literature [von Preiß] is limited to a single publication, his own. The feeling arises that the funding does not have a strong theoretical basis. In addition, the program has never been evaluated. The explanations on the website of the country of numbers do not even describe the framework in which the funding was tested. The commercial side seems to outweigh the scientific. "

Friedrich, Galgóczy and Schindelhauer's concept “Come with us into the land of numbers”, on the other hand, was empirically examined twice with regard to its effectiveness. A study by Friedrich and Munz from 2006 shows that the concept that Friedrich helped to develop sustainably promotes children in key school-relevant skills. The school-based precursor skills in the field of mathematics are in particular the amount and number-specific prior knowledge. These include the ability to seriate (classify an element in a given row), compare quantities (recognize that the number of a quantity is not determined by the arrangement of the elements), counting skills, simple arithmetic skills with concrete material and knowledge of the number symbols. They are an important prerequisite for successfully participating in math lessons in first grade.

As part of the “Offensive Education” project initiated by BASF, an overarching elementary pedagogical concept was developed in collaboration with recognized education experts, which was implemented across the board in all 90 Ludwigshafen day-care centers.

literature

  • J. Düringer: Critical reflection on the concept "Discoveries in the land of numbers" - presented in its contribution to conveying the concept of numbers. Publishing house for academic texts, GRIN 2006.
  • G. Friedrich: The numbers are finding their way into kindergarten. A project for mathematical early learning. In: Kindergarten Today. January 2003, pp. 34-40.
  • G. Friedrich: In the land of fairytale numbers. In: The time. Sept. 25, 2003, No. 40, 2003.
  • G. Friedrich, A. Bordihn: Spot: This is how it works - fun with numbers and math in kindergarten. (= Special issue of the magazine “kindergarten heute” ). Herder Verlag, Freiburg 2003.
  • G. Friedrich, H. Munz: With the numbers on you and you. Preschoolers discover the land of numbers. In: School magazine. Ministry of Culture, Youth and Sport BW, spring 2004, pp. 24–25.
  • G. Friedrich: General didactics and neurodidactics. (Habilitation thesis) An investigation into the importance of theories and concepts of learning, especially neurobiological, for general didactic theory formation. Peter Lang, Frankfurt am Main 2005.
  • G. Friedrich, H. Munz: Promotion of forerunner school skills through the didactic concept "Come with us in the land of numbers". In: Psychology in Education and Teaching. 2006, 53, 2006, pp. 134-146.
  • G. Friedrich, V. Galgóczy: Come with us into the land of numbers. A playful journey of discovery into the world of mathematics. 4th edition. Urania Verlag, Stuttgart 2008.
  • G. Friedrich, V. Galgóczy, B. Schindelhauer: Come with us into the land of numbers. A playful journey of discovery into the world of mathematics. Revised new edition. Herder Verlag, Freiburg 2011, ISBN 978-3-451-32420-8 .
  • G. Friedrich: Come on, let's play math. A number land action book. Herder Verlag, Freiburg 2017, ISBN 978-3-451-37650-4 .
  • U. Herrmann (Ed.): Neurodidaktik. 2nd Edition. Beltz, Weinheim 2009.
  • AM Matute: The children in the land of numbers. Bitter Verlag, Recklinghausen 1974.
  • Dietmar Müller: from 5 and 6 make 7 and 8. In: Learning and playing in primary school. Luchterhand, Neuwied 1993.
  • S. Pauen, V. Herber: From being small to Einstein. Cornelson Sriptor, Berlin 2009.
  • T. Peter, K. Weinert: Peterlein's dream journey into numbers. Chronos Verlag, Berlin around 1950.
  • G. Preiß: Guide Numbers Land 1. Numbers Land, Verlag 2004, ISBN 3-9809690-2-9 .
  • G. Preiß: Guide Numbers Country 2. Numbers Country , Verlag 2005, ISBN 3-941063-10-3 .
  • B. Schönle-Walter: "Come with us in numbers land ". A concept for everyday kindergarten life. In: KiTa aktuell BW. Issue 10, 2005, pp. 201-204.

Web links

Individual evidence

  1. ^ Hans Zoozmann: Der Nullrich - A journey into the land of numbers . Schmidt Verlag, Berlin 1950.
  2. ^ Ana María Matute : The children in the land of numbers . Bitter-Verlag, Recklinghausen 1974, ISBN 3-7903-0015-2 .
  3. ↑ Learning and playing in primary school. Luchterhand, Neuwied 1993, ISBN 3-472-00980-2 , p. 193.
  4. ↑ Wilfried Gebhard: Nil and Nele and the numbers . Ravensburger Buchverlag, Ravensburg 1997, ISBN 3-473-33372-7 .
  5. ^ Gerhard Friedrich, Horst Munz: On the project "Come with us in the land of numbers". In: Martin R. Textor, Antje Bostelmann: Das Kita-Handbuch. to: kindergartenpaedagogik.de
  6. ↑ J. Düringer: Critical reflection on the concept "Discoveries in the land of numbers" - presented in its contribution to conveying the concept of number. GRIN, 2006, p. 110.
  7. ↑ Esther Joachim, Claudia Gronbach: Mathematisation of the environment and play world of preschool children with language disorders. ( Memento from April 14, 2010 in the Internet Archive ) (= Rosi's adventures in the world of math ). April 20, 2011, p. 14.
  8. ↑ number country. ( Memento from June 1, 2009 in the Internet Archive ) on: matheblogger.de