Young children should have maximum access to interactive computation so that they can use the machine as a tool for mathematical thinking of the most general kind. And, if children are given an understanding of the theoretical capabilities of machine computation, they might use it for more effective study of their own thinking about the world. With these as goals, we produced an experimental course for teaching computer programming concepts to children who had no previous experience with a computer. This paper discusses the results of that experiment and what they suggest about how children react to different programming languages and problems, and programmable devices. We provide details of the curricula and remarks on the students' experiences.