Algebraic Thinking and Pictorial Growth Patterns

Principles and Standards for School Mathematics advocates exploring algebraic ideas beginning in prekindergarten and continuing through the high school mathematics curriculum. In particular, algebraic thinking emphasizes analyzing change, generalizing relationships among quantities, and representing these mathematical relationships in various ways. Here, Billings et al explore how analyzing and extending pictorial growth patterns can promote algebraic thinking in young children, ultimately helping them to extend their numerical reasoning to think more generally about relationships. They conclude that the children's thinking reported here illustrates that analyzing and extending pictorial growth patterns provides a meaningful context for young children to think algebraically as they analyze change and think more generally about the relationships inherent in a pattern.