ALFANUMROOTS

OUR ALFANUMERIC ROOTS "The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but surpressing none of them." Henri Poincére (mathematician who -- a year before Einstein's "Relativity" paper -- described Relativity at "The Saint Louis World's Fair" which Judy Garland and her family visited at end of the 1944 film, Meet Me in St. Louis).

THESIS: Humans best appreciate the value of some artifact by interactively going through the stages to its development. If children interactively work through our "alphanumeric roots", they may better understand and appreciate the shortcuts of our Alphabet and NUMERATION.
ALPHA ROOTS
Children should be shown a chart of the stages from crude drawings to an alphabet, and keep it posted on wall during all sessions.

pictograms (icons of concrete or abstract ideas; first appeared on cavewalls)
ideograms: combinations of pictograms, but often run together; example, Chinese ideograms for ëye"and "water"to represent "tear"; also in Mesopotamian cuneiform inscriptions, Egyptian hieroglyphics, & all Chinese characters are logograms
logograms: ideograms separated into words; may be partially sound-referenced as in the Sumerian language to represent people's names
syllabary: symbols represent syllables, not words; apparently first developed by Semites & Phoenicians circa 1700 BC; adapted in Old Hebrew, Cypriote, & Persian scripts. (A syllabary for the Cherokee language was developed in the late 19th century by Sequoia.)
alphabet: symbols represent phonemes (units of spoken sound); thus American English has about 44 phonemes; first came consonants, then vowels later; first fully alphabetic language was Greek
NUMERIC ROOTS

Children should be shown a chart of the stages from tallies to an Hindu-Arabic Decimal Numeration, and keep it posted on wall during all sessions.

To count, our ancestors used such material representations of quantities as tally cuts in bone or ivory or stone; clay tokens; tally sticks; knots in cords, pebbles in bags; marks on walls; wooden beads on a wire; etc.
Tallying is apparently the earliest form of writing. A wolf bone found in Europe, dating from the period of 30,000-25,000 B. C., shows fifty-five cuts in groups of five. Certainly, tallies provided the earliest form of bookkeeping.

In later Neolithic times appeared tokens: clay representations of types of countable of products of agriculture or craft.. From these were abstracted signs for words, another instance of writing deriving from primitive mathematics.

Different numeric systems developed in various cultures. The Greek numerals spread with the Empire of Alexander the Great. But these were often replaced with Roman Numerals with the extension of The Roman Empire.

The Hindus began developing the precursors of the numeric symbols we presently use, circa 3rd century BC. These numerals were absorbed and modified in the extension of Islamic rule. But Hindu-Arabic numerals were resisted in Europe for some time. Any merchant found with these inscriptions was liable to charges of religious heresy or political intrigue. Yet one would have to go to the best universities in Italy to multiply with Roman numerals, and only at the University of Bologna would you learn how to divide with Roman numerals.

Leonardo of Pisa (a.k.a. Fibonacci) (1175?-1250?) introduced them into Europe in 1201 with his arithmetic book, Liber Abacci. They "caught on" by facilitating the great periods of Trade and Navigation.
Repeating: If children interactively work through our "alphanumeric roots", they may better understand and appreciate the shortcuts of our Alphabet and NUMERATION.