This study presents partial results from the project "A Study of perceptual apprehensive, operative apprehensive, sequential apprehensive, and discursive apprehensive for elementary school students (POSD)", which was undertaken to explore gender differences and passing rate of van Hiele's geometric thinking level. The participants were 5,581 elementary school students randomly selected from 23 counties/cities in Taiwan. The conclusions drawn from this study were: (a) evidence supporting the hierarchy of the van Hiele levels, (b) students at different levels have different concepts of basic figures, and (c) for elementary school students, the passing rates of boys and girls have no significant differences in van Hiele's geometric thinking level.