Patterns, Structure, and Algebraic Thinking

Children learn to find and use mathematical regularities and structures. Children learn to identify, duplicate, and extend sequential patterns such as ABCABCABC, but also to find regularities and structures in number and geometry.  Repeating patterning skills predicts later math knowledge even after controlling for prior math knowledge. Later levels develop early algebraic thinking. 

Practice-based Research:  Pattern and structure are at the heart of mathematics. Some people define math as the science of patterns in number and shape. Looking for a using patterns and structure is a critical math competence that should be a part of children's experience in all math topics.

Clap/kick coud be the core unit of an AB rhythmic pattern. Children benefit from participating with guidance or experiencing a model of three complete repetitions of a pattern’s core unit. Advance to other, more difficult patterns as children are able, such as toe/toe/heel, an AAB pattern. Do not perform so many AB patterns that children begin to think only that way about patterning. Then introduce complex patterns, such as toe/toe/heel/clap, an AABC pattern.

Why three complete repetitions of a pattern’s core unit? That is, why not show yellow/green as "the pattern" and instead show and say “yellow/green, yellow/green, yellow/green”? Research shows children need at least that to reliably conceptualize a pattern. Further, AB alone is misleading; AB could lead to different patterns from AB, AB, AB to ABABC, ABABC, ABABC Indeed, unless carefully defined, any beginning pattern sequence could be extended in an infinite number of ways.

Inclusive Teaching Approaches

We are working with our partners at the STEM Innovation for Inclusion in Early Education (STEMI2E2) Center to improve engagement opportunities for young children with disabilities (O-5). As we move forward, we will update this area with specific tips for engaging with a lens of equity for diverse needs. 

Accessibility for Diverse Learners

  • Almost all of the videos on our website have closed captions in English and Spanish for the deaf and hard of hearing.
  • Most of our videos can also be accessed with a voiceover describing the scene for those with vision impairments. Click on the Accessibility toggle in the bottom right corner.

Accessibility for Children

Learn how to incorporate Patterning across the whole day in Routines, and find accommodations for diverse learners of all levels of Patterning in Teaching Strategies.

We have also created new activities or updated previous activities with new features that support engagement for all children. Features of the activities include intentionally inclusive design, accommodations for specific disabilities, questions for caregiver and early interventionist reflection on development, and ideas for learning in everyday routines. We have started by developing activities for infants and toddlers, with plans to add more at the older levels in the future. New inclusive activities for Counting are linked below (and also embedded in the site, at their respective trajectory level).

Level: Intuitive Patterner Foundations

Level: Pattern Recognizer

General accommodation recommendations can be accessed in our Inclusion resources, linked here

Read more about the STEMIIEE center here at their website

Special Thanks To

Institute of Education Sciences
The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through grant numbers R305K050157, R305A120813, R305A110188, and R305A150243. to the University of Denver. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.