Fig. 1.
Performance in the lines intuitions test. Percentage of planar responses to questions that call for the same answer or distinct answers in the plane and sphere subtests (labels same or dis on the x axis). Perfect mathematical understanding calls for 100% planar responses, except for the distinct answer questions on the sphere, where there should be 0% planar responses (last bar; shown in white). The results partially conform to this pattern but with a strong bias to planar responses.