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A child calculates with their fingers or: an arithmetic operation links objects with an operator .

When calculating the activity is logical linking of objects such as by numbers called.

While numerals or digits are used to represent numbers, the mathematical notation of the links and relationships between objects in logic , mathematics and computer science uses other symbols . The statements or formulas formulated with such mathematical symbols then correspond to sentences in a language that is more formal than natural languages .

It is not uncommon for computing aids or computing machines to be used for computing , with which algorithms can be executed, now mostly automated.


The generally accepted set of rules for calculating with numbers is called arithmetic in mathematics . In common parlance, only a part of this is meant when arithmetic means the ability to deal with the four basic arithmetic operations - including their use as fractions , percentages and the rule of three  . Mastering these elementary arithmetic operations with confidence is one of the basic skills , along with reading and writing , that children should acquire while attending primary school .

Expect both notionally possible that mental arithmetic is called, as a supporting and using concrete representations, such as with the fingers ( finger count ). Furthermore, different calculation aids have been developed, such as abacus , slide rule or pocket calculator . The arithmetic book , written in German by Adam Ries in 1518, relates to calculating on lines with an abacus.

Notches in a notch or knots in a string can be used to represent a number , even those in a knotted script with a decimal place value system . The symbols or characters used to represent numbers are called digits or numerals .


The designation by the word count , Middle High German count, rechenen , Old High German rechanon from West Germanic * rec-no meaning, put in order, rows, making directed expected 'goes to the Indo-European root word * reg- , steer, set up, conduct 'back (like Latin riga ' row 'as well as shelf , rake , right , recken and others) and stands next to the shorter subsidiary form rake ' calculate, do right '. In a further relationship are raking , working with the rake, rake 'and rake , scrape together, ridging' and computationally , rigid, stiff 'to see further reh dialect meaning, from a fork-made Plow rumps'.

Disruptions and support measures

Recent research suggests that humans and higher animal species already have a sense of numbers at birth ( Stanislas Dehaene ) or have a basic understanding of the simplest arithmetic operations, such as more / less, larger / smaller, estimating, etc.

But arithmetic is not easy for everyone. Dyscalculia and numerical illiteracy are known as disorders . By investigating brain injuries or stroke patients as well as those suffering from brain tumors, the scientists found further forms of disturbances in the recognition of numbers and in the computing power. There are also people with a mathematical giftedness or island talents , which the calculation is quite easy (eg. As Gert Mittring ).

There are also major differences within the standard in terms of speed and security in dealing with numbers. For a long time, these differences were mainly explained by the fact that they arise from the effects of practice or are based on a different innate mathematical talent . In the meantime it has been proven that the approach to arithmetic tasks plays a decisive role.

Children and adults who visualize mathematical operations and combine them with real experiences are more successful at arithmetic. You are more confident with the tasks and need less repetition until you master a calculation operation. On the other hand, those who do not leave the level of mathematical symbols often remain unsure of arithmetic despite long and persistent practice. Regular math lessons as well as tutoring and remedial lessons are therefore more effective if models for number spaces and arithmetic operations are used at work.


  • Helena Harms: Learn to count while playing. Reinhardt, Munich 2008, ISBN 978-3-497-01994-6 .
  • Elisabeth Moser Opitz: Counting - Number Concept - Arithmetic. Haupt, Bern / Stuttgart / Vienna 2001, ISBN 978-3-258-06512-0 .
  • Thomas Rießinger: Don't be afraid of algebra. From fractions to logarithms. Elsevier, Heidelberg 2007, ISBN 3-8274-1779-1 (Introduction to elementary computing techniques - with numbers and variables).

Web links

Wiktionary: arithmetic  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. calculate, verb.. In: Jacob Grimm , Wilhelm Grimm (Hrsg.): German dictionary . tape 14 : R - skewness - (VIII). S. Hirzel, Leipzig 1893 ( ).