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Home > Topdrawer > Patterns > Good teaching > Abstraction and generalisation

Abstraction and generalisation

Good mathematics teaching starts with familiar hands-on examples of concepts and procedures.

But eventually students need to learn that these concepts and procedures are general — that is, that they apply to a wide variety of different situations including ones they have not yet encountered.

In other words, teaching should aim to encourage students to make abstractions and generalisations.

Abstractions

Students should recognise that the 'same' pattern can be found in quite different situations.

For example, many patterns can be described as 'AAB repeated'. This description is an example of an abstraction — a description of a type of pattern rather than any specific pattern.

Generalisations

Students may also find patterns that show general relationships.

For example, students may notice that the numbers in a growing pattern increase by two each time. This is an example of a generalisation — a relationship that is always true.

Abstraction of repeating patterns

When exploring repeating patterns, students should be encouraged to describe patterns in abstract terms.

Generalisation in growing patterns

When exploring growing patterns, students should identify the way in which the numbers or shapes change, and the type of shape or number at each stage.