Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…

How does the visual system recognize images of a novel object after a single observation despite possible variations in the viewpoint of that object relative to the observer? One possibility is comparing the image with a prototype for invariance over a relevant transformation set (e.g., translations and dilations). However, invariance over…

This seven-year longitudinal study examined how children's spontaneous focusing on numerosity (SFON), subitizing based enumeration, and counting skills assessed at five or six years predict their school mathematics achievement at 12 years. The participants were 36 Finnish children without diagnosed neurological disorders. The results, based on…

Described in the context of a computer simulation are highlights of a program of research focusing on the storage of mathematics problem solving information in young children's memory and the development of such knowledge structures in older children. Specifically discussed are the problem size effect, the network nature of the memory…

This paper reports on an experiment designed to investigate the effect of structural and linguistic variables on level of difficulty in solving arithmetic word problems. Identification of such variables is intended to assist curriculum writers in preparing exercises at a specified level of difficulty for students at various age levels. The study…