We report on an empirical study grounded in our sustained implementation over ten years of a sequence of three-term undergraduate core mathematics courses centred on microworlds. The survey study investigates students' views on 15 competencies potentially developed as they, individually or in pairs, create 12 Exploratory Objects, i.e., microworld-type environments, on diverse mathematical topics as part of their workload. Results suggest that students develop further the competencies as they repeat designing, programming, and using microworlds to learn and do mathematics, and that original projects in which students start by selecting their own topic, is key to the development of these competencies. No gender differences were found. [For the complete proceedings, see ED597799.]