We introduce an educational toy, called curlybot, as the basis for a new class of toys aimed at children in their early stages of development – ages four and up. curlybot is an autonomous two-wheeled vehicle with embedded electronics that can record how it has been moved on any flat surface and then play back that motion accurately and repeatedly. Children can use curlybot to develop intuitions for advanced mathematical and computational concepts, like differential geometry, through play away from a traditional computer. In our preliminary studies, we found that children learn to use curlybot quickly. They readily establish an affective and body syntonic connection with curlybot, because of its ability to remember all of the intricacies of their original gesture; every pause, acceleration, and even the shaking in their hand is recorded. Programming by example in this context makes the educational ideas implicit in the design of curlybot accessible to young children. Keywords Educati...