The influence of representational format on learner-generated domain representations and mathematical achievement

The purpose of this study was (a) to assess the effects of learner-generated domain representations on understanding combinatorics and probability theory and (b) to investigate the effects of the format (graphical, arithmetical, or textual) in which learners create their domain representation. A pretest-posttest design was applied in which four conditions were compared: three experimental conditions in which learners constructed a personal representation of the domain in a graphical, arithmetical, or textual format, and a control condition in which learners did not have to construct a representation. It was found that the construction of a domain representation significantly increases learning outcomes. Furthermore, it was found that the format in which learners express their knowledge does not directly affect learning outcomes or the quality of the created domain representations. However, the arithmetical format prevents most learners from engaging and succeeding in externalizing their knowledge.