Opinion or result that is inconsistent with reality; a mistake.

In mathematics, errors can occur at various levels, such as when a concept is being learned, when a concept is being applied, when calculations are being carried out, when a situation is being represented, etc. Therefore, there are calculation errors, measurement errors, errors in the translation of a situation into its graphical or schematic representation, errors in the choice of tools or formal models used to translate or solve situational problems, etc. These types of errors are part of mathematical activities and must be taken into account.

Historical Note

The concept of errors and how to avoid them was already of great interest to the Ancient Greeks. In geometry, for example, Euclid’s Elements served as a model for more than two thousand years, creating abstractions using objects from the real world to show how errors can be avoided. Since the late 19th century, elementary algebra, arithmetic, algebra, probabilities, etc., began to be presented in a standardized way using similar models.
Descartes was convinced that error was not a result of reasoning itself, but of humans trying to judge things that are beyond their understanding.

Educational Notes

Errors are an integral part of any learning process. They should not be seen as a hindrance but rather as a driving force behind the learning process. While revealing wrong paths, errors can also present new directions. In most cases, errors observed during the learning process do not occur by chance; they are the manifestations of obstacles encountered by students or of concepts that were poorly assimilated because they were poorly understood at the start. Various studies have demonstrated the role of errors and their effect on the learning process.

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