We're looking for:
Why the calculus? When taking integrals, when going to first and second and third derivatives, some aspects of what happens bear a structural resemblance to some aspects of human development. Taking a slope function to compute delta, the rate of change (or improvement), makes it easier to correctly direct and change that rate of change, in a way integral to (which takes into account all relevant functions in) the situation.
Jean Piaget was the first to derive from observation and experiment the stages of development of human beings, from infancy to adulthood, and the first to make it really clear that a young child is not merely an incomplete adult, but a complete whole organism with dynamics and characteristics of his own.
Some of Piaget's most fascinating work was in the stages and dynamics of development of the human mind cognitive psychology. What we propose to explore and utilize, however, applies to the entire range of developmental areas which Piaget and Jerome Bruner and Glenn Doman and other successors have been mapping. This precis is in terms of development of the human cognition, or intellect, but applies as well to emotional development, aesthetics, ethics, etc.
We mention Jerome Bruner in part because he threw a remarkable challenge to education and educators (in his book, The Process of Education), a challenge which has never been really taken up one way or another: that any theory or idea CAN be taught, in intellectually respectable form, to any child at any stage of development, if you do so in his own cognitive (conceptual) vocabulary.
Practitioners and explorers of NLP (NeuroLinguistic Programming) talk much about useful things happening to enrich and enhance development when one "goes meta to" his own thoughts and perceptions, i.e., starts thinking about his own thoughts, about thinking itself, and looking at and studying his own perceptions and the act of perceiving as such.
Development enriches and accelerates in ways apparently integral to the nature and situation of that person. Some of that is Heisenberg Effect; some of it also bears at least a loose resemblance to acts of calculus regarding slope functions. We need to explore with a competent and creative mathematician to determine if there is a structural, scientific relationship there or merely a poetic one.
The hypothesis we're working toward, and the practical human application of all this, is via this possible project:
Devise multiple forms of self-diagnostic tests which young children can take and understand, so that they have an ongoing way of mapping, examining and studying their own strategies and phases of cognitive development, through successive forms of such tests on an ongoing basis.
More in line with conventional intention and practice of schools, it might also be interesting to see what enrichment and acceleration of intellectual (and other forms of) development might be attained with appropriate directional guidance, and to compare the long-term effects of this with those of high-integrity enrichment and acceleration of development of children in sections of the experiment free from normative pressures in this context. (Nowhere, of course, can children be isolated from normative pressures as such the comparison is with where a higher proportion of the impetus for development comes truly from within.)
The experiment would have to be very carefully designed to ensure that only benefits would result from all aspects of the intervention, for every child in whatever phase and aspect of the experiment. We can use, beyond that initial calculus-facile mathematician and beyond that initial professional well-acquainted with the work of Piaget, the help of other professionals in areas of test design and experiment design. We also need help in finding an institution able and willing to launch and sustain such a study over a half dozen or more years of tracking the human results.
If you can help in any of these ways, please reply under the subject heading of "Childrise" to Win Wenger. Thank you.
PO Box 332, Gaithersburg, MD 20884-0332