Scaling Continuous Covariation: Supporting Middle School Students' Algebraic Reasoning

Middle school is a critical time when students begin formal study of functional relationships in algebra. However, many students struggle in understanding functions as relationships between quantities that change according to a dependency relationship. We report on the influence of Scaling Continuous Covariation in fostering productive ideas about graphical relationships and rates of change. Scaling Continuous Covariation entails the ability to imagine a re-scaling to any increment for "x" and coordinate that scaling with associated values for "y." We present findings from two students, one who reasoned with Scaling Continuous Covariation and one who did not, and report on how Scaling Continuous Covariation supported students' reasoning in three ways: (a) sense making about graphs, (b) forming constant rates of change, and (c) understanding constantly-changing rates of change. [For the complete proceedings, see ED606531.]