From traditional exams to closed-ended quizzes: an exploration towards an effective assessment in mathematics at university level

The pandemic emergency has almost forced the transition from face-to-face to remote evaluation. Starting from the results of the research in Mathematics Education, this exploratory work focuses on how to design effective closed-ended questions of different types, capable of reliably assessing mathematical learning outcomes, especially in terms of the involved competencies. We also investigate how to aggregate the questions into Moodle quizzes able to effectively replace the traditional open written exam. We propose a three-dimensional theoretical model, which takes into account the various types of questions, expected learning outcomes, and mathematical arguments, to shed light on the problems of validity, reliability, balance, and correctness of closed-ended quizzes. We discuss the results of the first implementation of the model within a Linear Algebra course for engineering freshmen.