when confronted with the history of school math, education can adopt two approaches. the traditional approach accepts school math and attempts often with a great struggle - to teach math the computer; computers are used by some teachers for this purpose. consequently, force feeding unwelcome and unpopular material left over from the pre-computer age has become-alas-the most common use of the computer in education. on the other hand, the computer has a totally different use in turtle geometry. there, the fans of turtle geometry maintain, the computer is used as a so-called mathematically expressive medium, one that frees teachers to design meaningful and coherent and easily learnable math topics for children. Now, instead of the educational problem being put as "how to teach the existing school math" it is posed as " reconstructing knowledge in such a way that no large effort is needed to teach it