There has been a recent call for the use of more systematic thought experiments when investigating learning. This paper presents a storyboarding method for capturing and sharing initial ideas and their evolution in the design of a mathematics learning task. The storyboards produced can be considered as "virtual data" created by thought experiments that provided an audit trail of evolving design ideas and enabled peer feedback to be sought. The outcomes were a diagnostic computer-based task for investigating mathematical thinking and the development and analysis of the storyboarding method itself. It is argued that storyboarding offers an opportunity for systematising thought experiments and peer feedback towards more robust learning task designs and theoretical conjectures. (Contains 7 figures and 1 table.)