Assume we wish to ultimately restructure all K-12 and college mathematics courses to be computer-based math, to the extent possible.
Would the most effective approach to such long-term adoption of computer-based math curricula be to
start with elementary courses for young children and gradually expand to ever-more advanced and sophisticated classes for older students, or instead
start with advanced classes for older students and gradually expand to ever-more elementary and basic classes?
There seem to be good reasons for each of these tactics. Which would be most effective?
Now that several responses have appeared, let me voice my view on my question.
Indeed, both approaches have their strengths and weaknesses, but I overall I favor starting with "senior" or advanced courses and then moving towards earlier classes. Why? One of the key insights and motivations for computer-based math curricula is the importance of expressing a problem, such as a real-world problem, into the language of mathematics and only then turning the crank of computer-based calculation. Older students will have a body of facts and knowledge from real-world disciplines such as physics, biology, chemistry and possibly even economics and business. This will allow them to concentrate on the asking of sophisticated questions and casting such questions into mathematical form. I think it would be more difficult to teach to young student both the real-world content and the techniques of expressing problems in mathematical form. Moreover, advanced students are more likely to have developed some expertise in programming, thereby avoiding some of the educational burden in the mechanics and basic concepts of computation (recursion, iteration, ...). I imagine that the pedagogical "lessons learned" from computer-based math at senior levels would expand and become incorporated to earlier classes over the course of several years.
These are just my current views. I would be quite open to changing them in light of carefully constructed educational experiments.
