"I love your microworlds but is it physics? I
don't say it is not. But how can I decide?"
-- A teacher
A COMMON DISTINCTION between two ways of knowing is often expressed as "knowing-that" versus "knowing-how" or as "propositional knowledge" versus "procedural knowledge" or again as "facts" versus "skills." In this chapter we talk about some of the many kinds of knowing that cannot be reduced to either term of this dichotomy. Important examples from everyday life are knowing a person, knowing a place, and knowing one's own states of mind. In pursuit of our theme of using the computer to understand scientific knowing as rooted in personal knowing, we shall next look at ways in which scientific knowledge is more similar to knowing a person than similar to knowing a fact or having a skill. In this, we shall be doing something similar to how we used the Turtle to build bridges between formal geometry and the body geometry of the child. Here, too, our goal is to design conditions for more syntonic kinds of learning than those favored by the traditional schools. In previous chapters we have explored a paradox: Although most of our society classifies mathematics as the least accessible kind of knowledge, it is, paradoxically, the most accessible to children. In