Abstract:

Four-, five-, and six-year-olds in most English-speaking countries are taught to recognize sequences of shapes and colors. This instruction, termed “patterning” has recently been shown in a series of published studies to improve children’s cognitive abilities and academic achievement.

Although it has been shown to be important in the development of reading and mathematics, there have been very few empirical studies of patterning as a cognitive development. No theory defines its place among the sequence of abilities mastered during cognitive development.
One possibility is that understanding patterns is intermediate between seriation and transitivity. In seriation items either increase or decrease in one dimension. In advanced patterning the relation is more complex; the relation might involve size, color, shape, numbers, or letters, and can be much more complicated.

Transitivity, a more advanced reasoning ability, is the understanding that if A is related to B and B is related to C on some dimension, then the relation between A and C can be deduced by comparing A to B and C to B when the relation between A and C cannot be directly observed. Both transitivity and patterning incorporate the idea that an item is defined by, and simultaneously defines, properties of items that follow or precede it. The primary difference between transitivity and patterning is that patterning does not require children to utilize the relations of A to B and C to B in deducing the relation of A to C. Transitivity does require utilization of those relations to make that deduction. Children could make use of the transitive relation or make use of the simultaneous presentation of all items and compare A to C directly to solve a patterning problem.

First-graders were tested on patterning, seriation and transitivity. Patterning was more closely related to transitivity than to seriation, although it was related to both. Effects were large and differences in correlations were significant. Hence, advances in educational achievement from mastering complex patterns may stem from advances on a seriation-patterning-transitivity continuum of cognitive development.

Keywords:

Patterning, seriation, transitivity, reading, mathematics.