A Learning Trajectory in Young Children’s Understanding of Generalizing Functional Relationships

• In Event: Mathematics Learning in the Early Grades

Abstract

The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children’s understanding of functions. This paper identifies an empirically developed learning trajectory in grades K–2 children’s understanding of generalizing functional relationships. The study reported here employs a design research methodology, and data are analyzed qualitatively to characterize levels of sophistication in children’s thinking about functional relationships. Findings suggest that, as early as Kindergarten, children can learn to think in quite sophisticated and generalized ways about how two quantities co-vary, thus challenging the typical curricular approach in which children consider only variation in a single sequence of numerical values or geometric objects.

Authors

• Maria Blanton, TERC

• Barbara M. Brizuela, Tufts University