Constrained sketching on a grid : a lens for online assessment of derivative sketching
In this study we aim to characterize the challenge related to sketching functions by constrained sketching on a grid. Our research question is as follows: What are the characteristics of sketching graphs by dragging points vertically in assessment e-tasks? Specifically, which functionality does this design support? Towards this goal we explore how students construct a sketch of f'(x) based on a given graphic representation of f(x), and vice versa, how they construct a sketch of a function based on the graphic representation of its derivative. The analysis of 114 submissions of high-school students, support the formation of assessment tasks’ design principles for drawing a sketch. The sketch that students construct makes it possible to characterize each submission with respect to the actions the students took at critical or non-critical points; to whether they attend to certain points separately or to domain and to conjecture about various concept images.