Methods developed by Newman and Casey for analyzing errors by children attempting verbal arithmetic problems are described. Emphasis is given to Newman's hierarchy of error causes. Data obtained by Newman, Casey, and Clements show a large proportion of errors by children are in categories…

The evidence suggests that students in grades 5 through 8 have difficulty relating isometric type drawings to the rectangular solids they represent. Errors made by students were analyzed and the effect of instruction in spatial visualization activities assessed. (MNS)

The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (MNS)

The literature on proportional reasoning is reviewed. After methodology is discussed, strategies used to solve proportion problems, variables that influence performance, and training studies are each considered. (MNS)