An Ordinal Scale for Transitive Reasoning by Means of a Deductive Strategy

Abstract

Transitivity tasks with either equality or inequality relations between three, four, or five objects were presented by means of a successive and a simultaneous presentation procedure to 124 third-grade primary schoolchildren. Equality tasks were easier than inequality tasks. Inequality tasks were more difficult when presented successively than simultaneously. Difficulty of equality tasks was not affected by presentation procedure. These findings were interpreted in terms of the Fuzzy Trace Theory. Successively presented inequality tasks induced more deductive reasoning strategies, and simultaneously presented tasks induced both positional and reductional strategies. As perceptual differences between objects increased, more visual strategies were used. These conclusions were used to construct a series of nine tasks geared at inducing transitive reasoning by means of a deductive strategy. Mokken scale analysis was used to construct an ordinal scale for transitive reasoning. Data were collected from 417 second- through fourth-grade primary school children. The scale score correlated highly with arithmetic skills and insight into the quantity concept. Possibilities for future transitivity research, supported by advanced psychometric methods, are discussed.