Coupling representations for sense-making of sinusoidal function parameters: constraining as a resource?

We report a design-based case study on grade 11 students’ sense-making of sinusoidal parameters in a GeoGebra environment that dynamically couples the unit circle and the Cartesian graph. Drawing on Ainsworth’s DeFT framework, the coupling was designed to serve a constraining function while students predicted and justified graphs associated with transformed motions (e.g., phase shift, reversed rotation). Analyses of small-group discourse and interviews reveal that the constraint can serve as a resource, supporting students’ monitoring and self-correction; however, it can also be interpreted in locally plausible ways that hinder the intended coordination across representations.