Approaches to Foster Transfer of Formal Principles: Which Route to Take?

Enabling learners to transfer knowledge about formal principles to new problems is a major aim of science and mathematics education, which, however, is notoriously difficult to reach. Previous research advocates different approaches of how to introduce principles to foster the transfer of knowledge about formal principles. One approach suggests teaching a generic formalism of the principles. Another approach suggests presenting (at least) two concrete cases instantiating the principle. A third approach suggests presenting a generic formalism accompanied by a case. As yet, though, empirical results regarding the transfer potential of these approaches are mixed and difficult to integrate as the three approaches have rarely been tested competitively. Furthermore, the approaches have been evaluated in relation to different control conditions, and they have been assessed using varying transfer measures. In the present experiment, we introduced undergraduates to the formal principles of propositional logic with the aim to systematically compare the transfer potential of the different approaches in relation to each other and to a common control condition by using various learning and transfer tasks. Results indicate that all approaches supported successful learning and transfer of the principles, but also caused systematic differences in the magnitude of transfer. Results indicate that the combination of a generic formalism with a case was surprisingly unsuccessful while learners who compared two cases outperformed the control condition. We discuss how the simultaneous assessment of the different approaches allows to more precisely capture the underlying learning mechanisms and to advance theory on how these mechanisms contribute to transfer performance.