The effects of different modes of representation on the solution of one-step additive problems

This study investigated the role of different modes of representation, i.e., verbal description, decorative pictures, informational pictures and number line, in solving additive change problems. Data were collected from 1447 students in Grades 1, 2, and 3. Structural equations modelling affirmed the existence of four first-order representation-specific factors indicating the differential effects of the representations and a second-order factor representing the general mathematical problem-solving ability. It also provided support for the invariance of this structure across the three age groups. Rating scale analysis showed the interaction of the representational affiliation and the mathematical structure of the problems in their hierarchical ordering. (c) 2007 Elsevier Ltd. All rights reserved.