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The current study investigated the effects of different external representational formats on learning combinatorics and probability theory in an inquiry based learning environment. Five conditions were compared in a pre-test post-test design: three conditions each using a single external representational format (Diagram, Arithmetic, or Text), and two conditions using multiple representations (Text + Arithmetic or Diagram + Arithmetic). The major finding of the study is that a format that combines text and arithmetics was most beneficial for learning, in particular with regard to procedural knowledge, that is the ability to execute action sequences to solve problems. Diagrams were found to negatively affect learning and to increase cognitive load. Combining diagrams with arithmetical representations reduced cognitive load, but did not improve learning outcomes.

The effects of representational format on learning combinatorics from an interactive computer simulation