Evidence was also sought of any interaction between the strategy and the students' mathematical ability. A significant main effect favoring a rational over a random sequence was found at the formal level- the interaction effect was not significant at either level of attainment. This study investigated the effects of spatial training upon calculus achievement, spatial visualization ability, and the use of visualization in solving problems on solids of revolution. Multivariate analyses of covariance revealed no treatment effect on calculus achievement or spatial visualization ability, but there were significant sex differences favoring women in calculus achievement and favoring men in spatial visualization ability. Spatial training may benefit performance in certain areas of calculus for women more than for men.
Kindergartners appear to differ in their readiness to use a concrete strategy.
Many children persisted in counting all with objects. The most common sequence of mental counting strategies was counting all starting with the first addend, counting all starting with the larger addend, and then counting on from the larger addend. A knowledge of commutative does not appear to be necessary to invent counting strategies that disregard addend order.