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Defining Mathematics Education *REDUCED*

Defining Mathematics Education

The Seventy-fifth Yearbook is a celebration and reflection of the history of the NCTM yearbooks, and is a great resource on the key issues of mathematics education through the years.

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Home > Topdrawer > Patterns > Good teaching > Concrete to abstract

Concrete to abstract

Patterns become more and more abstract between the Foundation year and year 3.

In the Foundation year students are only expected to explore patterns with objects.

In year 1 skip counting leads to simple number sequences.

By year 2 students are expected to be able to skip count from an arbitrary starting number and to investigate other number sequences.

In year 3 the possibility of sequences formed by subtraction is included.


It is important that such abstract number sequences are related to previous concrete experiences with patterns.

For example, skip counting from zero should always be related to repeating patterns, number lines and rectangular grids.

Skip counting from an arbitrary starting number is best related to jumps on a number line.

Students should be encouraged to verbalise their thinking at every opportunity.


Beware of asking students to continue a number pattern or to find missing numbers without any context or stated rule.

A pattern of numbers can be continued in an infinite number of ways if there is no reason to prefer a particular type of pattern.