The underlying philosophical principle is exposed by Michael Polanyi's argument that all knowledge is personal. An adequate model for learning science and mathematics must recognize that learning is a personal endeavor. The theme of connectedness of knowledge weaves through our entire discussion, in confirmation of Whitehead's position cited earlier. In the practice of science, the fundamental connection is between theory and experiment, between mathematical model and empirical data. Connections among the natural sciences, as well as those between mathematics and science, serve to reinforce motivation and enhance student learning.
Connections imply a frame of reference in which ideas can be examined, tested, and put to work.
C ompetence in modes of inquiry and in writing does not develop in a vacuum. Thinking is always about something, and therefore it is inextricably grounded in content. These qualities will meet the test of diffusibility. They can be created anywhere, not just at liberal arts colleges. That is our message.