This is the ability to express mathematical terms and concepts in words.

Abstract symbolization

This is the ability to understand the representation of numbers by symbols. Children with difficulty in this area will have particular problems in algebra.

Auditory-visual associations

This is the ability to identify a number with a written symbol. Children with difficulty in this skill may count well, but be unable to read numbers.

Clustering

This is the ability to discern or identify groups of objects (sets). Children with difficulty in this skill have to count objects individually.

Concrete mathematical manipulation

This is the ability to judge the size and number of actual objects, such as cubes and rods. Children with difficulty in this skill have problems when required to do hands-on manipulations involving these objects. This is often unexpected, because most people find concrete manipulations easier than abstract calculations.

Conservation of quantity

This is the ability to understand that quantity does not change with shape. For example, if liquid is poured from a short, wide container into a narrow, high one, the volume of liquid remains the same. Most children first begin to understand this during the early school years. Some older children can be shown not to have grasped this concept.

Establishment of one-to-one correspondence

The ability to deal with constant mathematical proportions. Children with difficulty in this skill may, for example, not be able to allocate three cubes to three children.

Graphic representation of numbers

This is the ability to remember and write down numbers.

Interpreting process signs

This is the ability to read and understand arithmetical symbols such as ‘+’, and ‘-’. Children with difficulty in this area may be extremely slow in working out what such a sign means when they see it written down.