Automated Feedback on Student Attempts to Produce a Set of Dimensionless Power Products from a Set of Physical Quantities that Describe a Physical Problem

Abstract

Formative feedback is important in learning. Automating the provision of specific, objective, constructive feedback to large cohorts requires complex algorithms that most teachers do not have time to develop, suggesting that a community effort is needed to create a library of specialised algorithms. We present an exemplar algorithm for a class of tasks in ‘dimensional analysis’ relating to the Buckingham Pi theorem. The challenge arises because there are infinitely many valid and invalid answers, but any valid answer is sufficient to complete a task. We present an algorithm that, given one valid reference answer, can evaluate any response to a task. The algorithm uses a vector-space formulation of the Pi theorem. Deployment across seven tasks for 380 students provided feedback 3,090 times, including stating why a response is invalid. The most common reason was that a student-proposed set was not dimensionless, but other educationally relevant reasons were also identified.