“Solving versus relating”: Pre-service teachers’ conflicting images of formulas and dynamic contexts

Researchers have identified both the affordances of engaging students in symbolization activities and students’ difficulties in meaningfully representing contexts through algebraic expressions/formulas. In a semester-long teaching experiment, two pre-service teachers demonstrated their conflicting meanings for formulas with their images of a context when engaging in a task about a dynamic geometric object. The two students could construct both normative formulas by reasoning with a context and descriptions of covariational relationships between quantities within the context, but both still struggled to relate their formulas and quantitative relationships to one another. This result highlights the importance of attending to what students’ formulas mean to them, which for the students in this study, could be either a way of “solving” or “relating” quantities.