For many decades, the amount of geometry curriculum worldwide has been cut, mathematics curricula have lacked diversity of geometrical phenomena, and geometry teaching has been reduced to a somewhat eclectic mix of activities. Recently, new trends have begun to counteract these tendencies by framing new curricula around fundamental ideas. The goals of this paper are threefold: (a) to present the structural elements of a coherent geometry curriculum through the lens of fundamental ideas, (b) to develop an analytical tool to determine the fundamental ideas of geometry in children's drawings, and (c) to provide insight into the images primary grade students have of geometry. The results are discussed not only with regard to the latter of these goals, but also with regard to their theoretical and practical implications.