Designing learning materials to foster transfer of principles Lennart Schalk (schalk@ifv.gess.ethz.ch) Institute for Behavioral Sciences, ETH Zurich, Universitaetsstrasse 41, 8092 Zurich, Switzerland Henrik Saalbach (saalbach@ifv.gess.ethz.ch) Institute for Behavioral Sciences, ETH Zurich, Universitaetsstrasse 41, 8092 Zurich, Switzerland Elsbeth Stern (stern@ifv.gess.ethz.ch) Institute for Behavioral Sciences, ETH Zurich, Universitaetsstrasse 41, 8092 Zurich, Switzerland principles. However, the approaches have rarely been tested competitively and the conclusions derived from different lines of research are difficult to compare. Difficulties arise due to differences in conceptualizing and measuring transfer (Barnett & Ceci, 2002). The present research aims at evaluating the different approaches to foster transfer of principles in one research program by teaching participants the principles of propositional logic (i.e. the interpretation of propositions connected by the logic operators negation, conjunction, disjunction, conditional, and biconditional). Transfer of principles can be conceptualized as analogical reasoning (e.g., Goldstone & Son, 2005). Principles are relational structures that capture the interdependencies between various variables and are highly flexible in meaning. Theories of analogical reasoning essentially explain transfer of a relational structure from a known domain, the source, to a lesser known domain, the target (for an overview see Gentner, 2010). Of course, not all problem solving and knowledge transfer can be reduced to analogical reasoning (see Nokes, 2009, Bransford & Schwarz, 1999). However, to explain the phenomenon of transfer of principles theories of analogical reasoning provide a highly elaborated and parsimonious conceptual base. Accordingly, educators have to support their students to acquire a knowledge representation of the principle which is a useful and flexible source to solve future (target) problems. Merely teaching by analogy which means basically providing learners with a single concrete source that instantiates the principle and is grounded in everyday experience has been shown to not result in satisfying transfer performance (e.g., Duit, Roth, Komorek, & Wilbers, 2001). Several reasons may account for this failure: inferences strongly depend on the features of the source chosen (e.g., Gentner & Gentner, 1983), learners fail to spontaneously retrieve the required source (e.g., Gick & Holyoak, 1980), or learners retrieve and integrate knowledge in the reasoning process that is irrelevant for the analogy (e.g., Mather, Knight, & McCaffrey, 2005). Given the failure of “classic” analogy, several approaches have been proposed on how to teach new principles. Abstract Education aims to equip learners with knowledge about principles that can be applied across a wide range of situations but often people do not recognize structural similarity between known cases and novel problems. Several approaches for designing learning materials to foster transfer of principles have been proposed including learning a generic instantiation, comparing instantiating concrete cases, and learning multiple representations. However, these approaches have rarely been tested against each other nor have they been examined by a broad range of transfer tasks. We evaluated the transfer potential of the different approaches separately (Experiment 1) and in combination (Experiment 2) by teaching undergraduates the principles of propositional logic. Students were tested on an extensive transfer test one week after learning. The best transfer performance resulted from the simultaneous comparison of a generic instantiation with two concrete cases. We suggest this approach for designing learning materials that introduce new principles. Keywords: transfer; analogical reasoning; comparison; generic instantiation; learning by multiple representations. Introduction Transfer describes the phenomenon “how knowledge acquired in one situation applies (or fails to apply) in other situations” (Singley & Anderson, 1989, p.1). The ability to transfer knowledge is especially important when scientific principles are learned. Science often advances by the discovery of principles that cross-cut and support the cross- fertilization of superficially different domains (Goldstone & Wilensky, 2008). Thus, learning a principle gives students the possibility to understand a broad range of phenomena in different domains. For example, if students learn the principles of propositional logic this should help them to comprehend the output of combinations of logic gates in digital circuits and to evaluate the validity of philosophical arguments. Therefore, it is important that principles learned in educational settings are not restricted to the idiosynchrasies of the learning situation. Researchers have devised several approaches for designing learning materials that foster transfer of