For more than 20 years educators and scientists have expressed surprise and dismay when viewing the video A Private Universe (Schnepps and Sadler 1989). Surprise comes from observing obviously bright people who failed to learn seemingly simple science concepts that have traditionally been taught at the upper-elementary and
middle-school level. Dismay comes from the realization that people who impress us with their abilities to solve complex mathematical problems may not have even a rudimentary understanding of the concepts that underlie the problems they are solving.