The Use of Symbols, Words, and Diagrams as Indicators of Mathematical Cognition: A Causal Model

This article reports on the results of a study that investigated the strategic representation skills of eighth-grade students while they were engaged in a set of tasks that involved applying geometric knowledge and using algebraic equations. The strategies studied were derived from Dual Coding Theory (DCT) (Paivio, 1971, 1990), and they were elicited with task-specific prompts embedded in an assessment developed for the study. The purpose of the study was to test a model that highlights strategic representation as a mediator of the effects of reading ability, spatial ability, and task presentation on problem solving. The proposed model was tested using the linear structural equations modeling approach to causal analysis and the data did not reject the model. The results showed that students' use of symbols, words, and diagrams to communicate about their ideas each contribute in different ways to solving tasks and reflect different kinds of cognitive processes invested in problem solving.