(I created the terms "conek, loconek, hiconek", as special forms of what I call "THE CHARLOTTE-CONNECTION" (named for the spider in E. B. White's Charlotte's Web). My special labelling conforms with my FIRST LAW OF MEASUREMENT: LET ALL YOUR NAMES BE UNIVALENT -- SPEAK WITH ONE VOICE OR MEANING!) In other words, "concept" is too noisy for me.

Have you ever planted an African violet cutting? If so, and if you have a green thumb (or, at least, not a gangrene thumb), then the cutting may have put down roots and may have begun to grow. Later, it may have put forth flowers.

The key-words (for representing my model) are CUTTING, ROOT, FLOWER. The "cutting" models "conek": essential concept or procedure. The "roots" model "loconek": a conek's primitive beginnings in daily life or some stage in human history. The "flower" models "hiconek": conek's extension to important applications in "hitech".

What better conek can we consider than number? For we possess many number-loconeks, showing the beginnings, in prehistory or in the practices of more contemporary "primitive" peoples, of the number-concept.

We can tell children about a wolf bone dating from around 30,000-25,000 BC -- a bone displaying 55 cuts across the bone, collected in groups of 5. This bone must have recorded the count of something important for some prehistoric ancestor. And, as I show elsewhere, we can guide children through the simulation of various stages of human development of the NUMBER CONEK.

For example, as I describe elsewhere (based on an article of Charles Dickens), the use (only a few hundred years ago) of tally sticks to inventory the number of gold or silver pieces in the British "Treasury". I mention also the use of pebbles in a bag; knots in string; etc. And we know of peoples who could only count the equivalent of "One, two, many", and we know that the word "three" derives from the Latin word "trans" for "beyond two". These and other loconeks will help children understand the development of the number-conek.

In particular, the logician-mathematician-philosopher, Bertrand Russell (x-y), said "It must taken eons for humans to realize that a brace of partriges and a couple of days are both instances of the number two." Kids can be shown that one word was used for a number of this and a different word for the same number of that and still a different word for the same number of something else. Etc. So the general number-conek was slow to develop.

Elsewhere, I also show the "flowering" of the NUMBER CONEK in various hiconeks of different number-systems; of limits in calculus; of vectors and multivectors; and, in general, into the rich hiconeks of The Arithmetic of Clifford Numbers, which encompasses 25 or more vast systems of mathematics. From such primitive beginnings -- highly HICONEK!

I argue: ALL CONCEPTS AND PROCEDURES ESSENTIAL TO EDUCATING OUR CHILDREN AND YOUNG PEOPLE SHOULD BE PROCESSED AS CONEKS, ALONG WITH THEIR LOCONEKS AND HICONEKS.

We plant seeds or cuttings and give them time to root and flower. Why not this for educating our young?

I conceived this many years ago. But now a second opinion.

A report (11/20/96) by the U. S. Dept. of Education -- "the largest international study of how American students perform in math and science" -- rates American students 17th in science and 28th in math! (The "leaders" were Singapore, Japan, and Korea.)

The report finds that American students spend more class time on math and are assigned more homework than students of leading countries in the survey. (The American math text shown on TV was 4 times as thick as the comparable Japanese text.)

But "the study contends that American math teachers often emphasize basic mathematical formulas rather than helping students understand the deeper concepts behind them, and try to accomplish too much too soon in class."

It was found that, Japan, "teachers devoted more than 80%of the time to developing the concepts, not merely stating them. In Germany, teachers developed about 75% of the math topics. But, in America, "teachers develop only 20% of their lessons and only briefly address the rest of them."

Exactly what I'm promoting here, except that I've a program for "developing concepts", which can be tested and improved. In terms of ideas elsewhere, the effective way may emphsize STRATEGY-OVER-TACTICS, versus the American TACTICS-AT-EXPENSE-OF-STRATEGY. For, I've long advocated division of math class time into days devoted to the STRATEGY OF PROBLEM-SOLVING (when calculators or computers are allowed to that students don't get lost in the wilds of calculation while learning strategy) and other days devoted to the TACTICS OF PROBLEM-SOLVING (when students must work with pencil and paper).

I argue that what we practice in American schools (in all subjects!) is JITED -- JUST-IN-TIME EDUCATION -- treating our children and young people like unfinished products on an assembly-line. Put a kid on the line. Sand her/him with this concept. Stamp him/her in that procedure. Solder this whatsis onto her/him. Glue that on. Etc. When the student comes off the assembly-line, we inspect and ACCEPT or REJECT the "product". Great quality control experts, such as W. Edwards Deming and Joseph Juran, taught us that this regimen doesn't provide good quality in the factories. And it doesn't work in the schools, either!

CHALLENGE: HELP ME COLLECT CONEKS, LOCONEKS, HICONEKS!