Mapping principles and worked examples for structural learning: effects of content complexity

Drawing connections between principles and worked examples is an approach to learning and instruction, but it is poorly understood. This study investigated the effects of principle and example complexity on learners’ ability to map principles and worked examples. The complexity of a principle or example was determined based on the number of concepts and relationships involved. 138 college students were randomly assigned to one of the mapping conditions: principle–simple example, principle–complex example, simple example–simple example, simple example–complex example, and complex example–complex example. The participants studied related materials and completed a free-mapping and a guided-mapping task for a simple and a complex probability principle. The effects of the mapping activities were measured in terms of gains in structural and conceptual knowledge. For the simple principle, principle–example mapping led to fewer nonrelational comparisons (standalone concepts) than did example–example mapping and an equal number of relational comparisons (interconnected concepts). For the complex principle, principle–example mapping led to fewer nonrelational but more relational comparisons than example–example mapping did. Principle–example mapping of corresponding content was more difficult than example–example mapping was. However, principle–example mapping of noncorresponding content was as easy as or easier than example–example mapping. The two forms of mapping resulted in equivalent gains in structural and conceptual knowledge. The findings of this study expand the understanding of analogical reasoning and learning through mapping and comparison of abstract and concrete content. The findings indicate that principle–example mapping enables learners to overcome the obstacles of comprehending abstract or general information and to identify the interrelationships of the individual concepts in formal structures.