The Calculus Concept Inventory (CCI) is a test of conceptual understanding (and only that--there is essentially no computation) of the most basic principles of differential calculus. The idea of such a test follows the Mechanics Diagnostic Test (MDT) and its successor the Force Concept Inventory (FCI) in physics, the last a test which has spawned a dramatic movement of reform in physics education and a large quantity of high quality research. The MDT and the FCI showed immediately that a high fraction of students in basic physics emerged with little or no understanding of concepts that all faculty assumed students knew at exit and that a semester of instruction made remarkably little difference. More dramatic, the preto-post test average normalized gains g on the MDT and FCI in Hake's meta-analysis showed a strong correlation with teaching methodology: the average g for "interactive engagement" (IE) courses exceeded the average g for "traditional" (T) courses by about two standard deviations. No other variable, including the pretest score, had anywhere near this correlation with the gain.