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Ways pupils form concepts in Mathematics

Concepts are the ideas or abstraction formed as a result of categorizing data from several observations.
Concepts enable us to group different things that have some similarities. They allow us to organize and store similar pieces of information efficiently.

Children use their senses to learn about the universe. They form some basic mathematical concepts even before learning to add or abstract.
The following are the various ways pupils form mathematical concepts

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Discrimination
When pupils interact with their immediate environment they begin to discriminate. When they manipulate materials, they usually find out the objects bearing common properties and classify them in of their previous experiences and the fitting of their present experiences into one of these classes. To classify is to collect together our experiences on basis of observed similarities.
This helps them use past experiences to understand new ones.

Abstraction

To abstract is to extract what is common to several different situations and to disregard what is irrelevant. An abstraction is a mental representation of a mathematical object.
It is the process of formulating,
Generalized concepts of common properties by disregarding the differences. Pupils use abstraction in concept formation when they begin to abstract the (main) invariant properties of the examples presented before them.

Generalization
Having done the abstraction after the initial discrimination and classifying, the next thing the child does is to draw some general conclusions from several experiences, that is, to generalize.
Pupils begin to make generalizations when they begin to ask the question will this always work?

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