Elementary Grades Students' Capacity for Functional Thinking

This is a study of how urban elementary grades students develop and express functions. Data were analyzed according to the forms of representations students used, the progression in students' mathematical language and the operations they employed, and how they attended to one or more varying quantities. Findings indicate that students are capable of functional thinking at grades earlier than perhaps thought. In particular, data suggest that students can engage in covariational thinking as early as kindergarten and are able to describe how quantities correspond as early as 1st-grade. Although pattern finding in single variable data sets is common in elementary curricula, we conclude that elementary grades mathematics should extend further to include functional thinking as well. [For complete proceedings, see ED489632.]