This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, "task-based interviews" were held with eight student…

Reports discriminate analyses using data from several National Longitudinal Study of Mathematical Abilities (NLSMA) measures for two groups from the NLSMA Y-population, high and low geometry achievers. The analysis correctly classified from 75 percent to 95 percent of the groups, depending on the measure used. (JP)

Accumulating evidence, particularly from research using the disorientation technique, demonstrates early sensitivity to geometric properties of space. However, it is not known whether children can use geometric cues to interpret a map. The current study examined how 3- to 6-year-olds use geometric features of layouts in solving mapping tasks.…