Patterns: The building blocks for mathematical thinking

Recent early childhood research has found that the ability to make and understand patterns is a critical skill for future mathematical understandings. Studies have found that an understanding of patterning can lead to the development of analogical reasoning and the ability to identify, extend, and generalise patterns is important to inductive reasoning. The studies have found that a child can learn these skills at a very young age.

Papic and Mulligan (2007) found that teaching the "unit of repeat" is the key concept. The unit of repeat is the element that constantly reoccurs. For example, in a pattern that goes: Blue, Yellow, Blue, Yellow, Blue Yellow. The unit of repeat is "Blue, Yellow". If the pattern was changed to : Blue, Yellow, Red, Blue, Yellow, Red. The unit of repeat would be blue, yellow, red. It can also be any other representation e.g. square, circle; rectangle, circle, triangle.

Joanne Mulligan when she lectured us about the findings was so particular about the finding to the point that if the unit of repeat was not completed e.g. red, blue, red, blue, red. We should not label it a pattern at all as it doesn't demonstrate a understanding of the unit of repeat. However, the child can be scaffolded and asked "what needs to be done to finish the pattern?" and if they are able to suggest the addition of "blue" then they are on the way to understanding mathematical patterning. A sound understanding of the "unit of repeat" concept was the key to future mathematical development.

Those of you who are familiar with mathematics will see that this "unit of repeat" concept is identical to the algebra concepts. E.g. a+cd. This is why the study also recommended a focus on the 'structural features' of the pattern rather than the colours - as a focus on the colours of led to a over simplification of the pattern that was occurring.

Overall, the study has opened a new direction in mathematical practices and understanding in the early years. So when you next look at a child's building or construction ask yourself:

•  Is there are unit of repeat happening here?
• How can I draw attention to it?
• What scaffolding do I need to provide to build on this child's understanding?
• How can I discuss the concept but in a different way? e.g. drawing it, building it etc
• How can I model (or demonstrate) the unit of repeat in everyday practice? For example, setting the table has a unit of repeat, everyone has a pair of shoes and so on.

What are your thoughts??