There was a 1973 study by Mark Lepper, David Greene, and Richard Nisbett which sought to measure the effect of extrinsic reward on intrinsic interests. There were 51 subjects (known to already be highly interested in drawing) selected from a nursery school, their ages ranging from a little over 3 years to 5 years old.
Once selected the children were separated into 3 groups, one in which they were promised a star as reward for their participation in a drawing activity, one in which they were promised nothing but received a surprise reward at the end, and the last who were left to draw for its own enjoyment. After the activity the students were monitored to see how they spent their free choice time, and those who received no reward or an unexpected reward spent significantly more time, over double, drawing than those who were motivated extrinsically in the activity. The act of using a “carrot” to push the children in a desired direction actually undermined their intrinsic interest to do it.