The first line of the programme, TO CIRCLE, tells the Turtle that you are about to teach it a new word, which will be called CIRCLE. The second line, REPEAT 360 (FORWARD 1 RIGHT 1), teaches it the meaning of the word CIRCLE. The third line, END, tells the Turtle that you have finished defining the new word. Now, when you want a circle, you simply type CIRCLE.

      The Logo language invites students into a microworld. By exploring this microworld, they can discover certain principles underlying the real world. One textbook, Turtle Geometry [Abelson & diSessa 1987], takes the student from his first few tentative Turtle steps through Euclidian geometry and Newtonian physics to Einstein's theory of relativity.

      Whereas the first vision is too outside-in, this second vision is too inside-out. It is a step in the right direction, since it shifts emphasis from the secondary process of outside-in conditioning to the primary process of inside-out growing. However, a further step is necessary. The theoretical basis of outside-in teaching is behaviourism, with its emphasis on conditioning from the outside; the theoretical basis of inside-out teaching is humanism, with its emphasis on growing from the inside. We all know, of course, that we are simultaneously growing from the inside out and being conditioned from the outside in. The behaviouristic thesis and the humanistic antithesis, therefore, require a synthesis. The interactionism of Jean Piaget, based on a long lifetime of brilliant research in developmental psychology, provides a theoretical basis for an optimal orchestration of inside-out growing and outside-in learning. This brings us to my third vision of the use of computers in education.

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