The influence of learner-generated domain representations on learning combinatorics and probability theory.

The aim of the current study was to examine the effects of providing support in the form of tools for constructing representations, and in particular the differential effects of the representational format of these tools (conceptual, arithmetical, or textual) in terms of perceived affordances and learning outcomes. The domain involved was combinatorics and probability theory. A between-subjects pre-test–post-test design was applied with secondary education students randomly distributed over four conditions. Participants completed the same tasks in a simulation-based learning environment. Participants in three experimental conditions were provided with a representational tool that could be used to construct a domain representation. The experimental manipulation concerned the format of the tool (conceptual, arithmetical, or textual). Participants in a control condition did not have access to a representational tool. Data from 127 students were analyzed. It was found that the construction of a domain representation significantly improved learning outcomes. The format in which students constructed a representation did not directly affect learning outcomes or the quality of the created domain representations. The arithmetical format, however, was the least stimulating for students to engage in externalizing their knowledge

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

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