Graphical representation fosters discovery in the 2-4-6 task

Abstract

In the 2-4-6 rule discovery task, reasoners seek to discover a rule that governs the arrangement of three numbers (or triple). The to-be-discovered rule is "ascending numbers". Upon being given the triple 2-4-6 as an initial example, however, reasoners tend to formulate algebraically specific hypotheses. Traditionally, this task is conducted primarily from an internal representation of the triples and candidate hypotheses. More recently, substantial representational effects have been demonstrated wherein an external representation of the dimensions of the problem space facilitated successful rule discovery. In the two experiments reported here, an interactive graphical representation was created by concurrently plotting each triple produced by the participants. In Experiment 1, participants who performed the task with this external representation were more likely to discover the rule than were a group of control participants. Experiment 2 replicated the effect but also assessed participants' hypotheses for each triple generated. Results indicated that a graphical representation of the triples fostered the development of hypotheses that were less constrained by the implied algebraic specificity of the initial triple