Patterns: a gateway to mathematics in preelementary school

Abstract

How can we stimulate an interest in mathematics from an early age? In early childhood education, children are often asked to create or complete patterns, such as threading a yellow bead, then a red one, then a yellow, then a red, and so on, on a necklace. These activities are sometimes seen as exercises to develop fine motor skills, writing, or artistic expression. However, we demonstrate that they are primarily a powerful stimulus for the development of mathematical skills, particularly in geometry and logic.

Indeed, the study of patterns leads children to form numerical and geometric abstractions that they can transfer from one domain to another. Recognizing the same pattern in a sequence of musical notes and in a row of beads draws the child’s attention to the abstract properties of numbers, symmetries, rules, and written notations. This is why we propose making pattern-based activities more systematic in early childhood and the early years of primary education, and we present a hierarchy of activities that can be used in the classroom.

Written by Lorenzo Ciccione and Stanislas Dehaene

Key takeaways

Patterns are sequences of items (objects, numbers, sounds…) in which we recognize an order, regularity, and therefore predictability.
Many early childhood and primary school teachers propose exercises based on the recognition and use of patterns to improve fine motor skills and writing, without necessarily perceiving their mathematical dimension.
Scientific research suggests (without definitively proving) that school activities with patterns can improve mathematical skills, as they constitute an excellent example of proto-mathematical abstraction.
During their development, children progressively identify increasingly complex regularities that allow them to understand, extend, and transpose patterns.
To emphasize the abstract nature of the rules underlying patterns, we suggest presenting them in different ways: the same ABABAB pattern can be presented to students in the form of sounds, beads, letters, numbers, etc.
Beyond simple ABABAB alternations, preelementary school students should be confronted with more complex regularities, for example, repetitions (AABBAABB…), increasing series (ABAABBAAABBB…), or involving more than two elements (ABCDABCD…; AABBCC…).
We advise teachers to propose different tasks to their students: copying a pattern, extending and prolonging it, finding the intruder in a sequence, completing a figure with its symmetrical image, completing a series of numbers…
Games and exercises with geometric figures are an excellent way to implicitly introduce important mathematical concepts (symmetry, half, pair, set, fraction…).
The playful, creative, and artistic nature of exercises with patterns could be favorable to mathematical development in both boys and girls, reducing the stereotypes associated with this discipline.
We suggest that teachers value the multiple abstract formulations that students can propose for a pattern, but always guide them explicitly in understanding the underlying mathematical concepts, to which patterns are only a first intuitive approach