This paper explores the nature of students' quantitative reasoning and conceptions of functions supporting their ability to symbolize quadratic function rules, and the meanings students make of these rules. We analyzed middle school students' problem solving activity during a small group teaching experiment (n = 6) emphasizing quadratic growth through covarying quantities. Results indicate four modes of reasoning supportive of students' symbolization of quadratic function rules: (a) correspondence, (b) variation and correspondence, (c) covariation, (d) flexible covariation and correspondence. We discuss implications for research on learning vis-à-vis students' representational fluency, as well as design principles to support quantitative reasoning. [For the complete proceedings, see ED583608.]