| In this study a theoretically determined model is proposed which implies that students' representations and transformations of tasks, tasks which entail application of geometric knowledge and algebraic skills, explain the effects of reading ability and spatial orientation ability on the number of correct solutions generated. The study was designed to collect data that would test the tenability of the model, and it was expected that the results would assist in developing valid inferences about what abilities and mental skills students apply when tasks are solved correctly.;The results from testing the linear structural relationships among the measured variables did not support rejection of the model. In the context of this empirically justified model, further analysis of the data revealed that mental representation and transformation processes, derived from Dual Coding Theory (Paivio, 1971, 1991), did mediate the effects of the performance indicators. In fact, students' skills for communicating with algebraic expressions were revealed as the mediating variable most strongly associated with task performance.;Implications of the results serve to refine a general information processing model accepted by mathematics education researchers (e.g., Schoenfeld, 1992), and they suggest that (a) for most students their failure to reach correct solutions to algebra and geometry tasks is due to a lack of skill in constructing algebraic representations, (b) reading ability as measured is a broad construct contributing to all levels of representation and transformation, and (c) with well designed tasks there is no advantage to students when tasks are presented using a diagram compared to when they are presented using only text with the exception of those students with exceptionally low reading and spatial abilities. |
