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by Mark Wahl
Where did the symbol "7" come from? When and where was long division a university subject? Did you know that centimeters were born in a revolution? Which country was the first to use "x" to mean an unknown amount and soon after became a world mathematical champion? Which country had been the previous champion? Exploration of historical questions like these will enhance math interest and involvement in those math students with active interpersonal intelligence.
As many know, Howard Gardner delineated the intrapersonal intelligence as one of eight intelligences in which people can have a "high IQ." Those strong in interpersonal are good resolvers of personal conflicts, are magnets for friends, and are fascinated by the personal dramas that gave rise to objects and situations around them. These same students may, like everyone else, yawn during a world civilization class full of abstract facts and dates, but they will eat up the fascinating personalized historical connections that gave rise to the well known math concepts they've all heard of. That gives you a chance to entertain a dual purpose as you teach: use historical highlights to help kids appreciate math and to befriend history.
A very good example of a historical connection is our amazing number system. It is a great vitalizer and motivator in almost any math class. Introduce this topic dramatically, when the board has several numbers written on it, and ask, "How many numbers are on the board?" Suppose "2306" and "37" are the only numbers written. Some will say "two" (Answer, "No."), others say "six," counting the number of digits ("Answer, "No.") and others have some kind of different take on it, like "five, because zero isn't really a number." ("No, again.").
They may give up. Answer "There are NO numbers on the board!" They'll feel like you're tricking them. Then write "8" and say, "Is this the number 8?" They usually say "yes." Draw a horizontal line splitting the 8 symbol in half and reply, "Then half of 8 is zero." Draw a vertical line splitting the 8 in half again and quip, "And half of eight is also 3." By then they're beginning to get the idea, but add, "Then what is this?" and write "VIII" on the board. They'll say "eight." Ask how VIII and 8 can both be eight when the two look nothing alike.
By then they're looking for a resolution of this confusion. It occurs when you make the distinction between numbers and symbols for numbers, called numerals. That is, "eight" truly exists only in our heads, not on boards; it is a concept. We can symbolize eight in any number of ways. From there you can go, if you have researched it, into the invention and evolution of specific systems of numerals. The Chinese, Babylonians, and Mayans had good written systems (having bases 10, 60, and 20 respectively), and each is worthy of fifteen minutes of time during enrichment intervals in your lesson plans. But none of them hold a candle to our current system which has a unique feature that it not only records numerals beautifully but allows calculation with the symbols as well.
This system arrived relatively late on our Eurocentric scene, having stabilized in Europe in the 1600s, replacing Roman numerals. It's likely that the Italian-Spaniard Christopher Columbus had heard of it but was probably not personally using its symbols yet, though it was being used in southern Spain. But where did this system come from? Students have many wild guesses. I quip, "No, Bill Gates didn't invent them!" In fact, they were not invented in the U.S. or Europe. Europeans were still computing their totals with the abacus and with rocks in trays, recording these with Roman numerals, when our current elegant number system was being used for centuries in other parts of the world.
The wealthy, intellectually and artistically advanced city whose inhabitants skillfully used these numbers in the fourteenth century, way before the Europeans, was the same city that is now capital of an impoverished international outcast country ruled by a tyrant. That country is Iraq and the city is Baghdad. It was the hub of the giant Moslem Empire that reached from India across northern Africa to southern Spain (whose west became a home to Christopher Columbus).
But the Moslems didn't invent these numbers either; they just used them very well and improved them as they spread them from country to country. The inventors were the Hindu priests of India in the first through seventh centuries. The Moslems conquered part of India in the seventh century (the Moslems and Hindus still struggle over temple sites in India today because of this) and, appreciating the fantastic beauty of this system, the Moslems "stole" it and proceeded to use it in trade and commerce.
Because Europe spent many decades conducting crusades against the Moslem "infidels," they missed out on their number system. With peace developing in the 1100s there arose the gradual importation (requiring over two centuries) of this valuable tool into England, France and Italy. One "importer" was the brilliant Leonardo Fibonacci of Pisa (after whom the ubiquitous Fibonacci Numbers are named). He helped Italy become such an important player in the new system of "ciphers" that only Italian universities were advanced enough to offer courses on long division in the 1500s (while other universities felt only competent to teach multiplication).
We have come to know that numeral system, our inherited system, as the Hindu-Arabic number system. Here's a research topic: when did this system reach the young America, where early colonies were coexistent with the system's spread in Europe?
But what's the fuss about these lowly numbers? They're just squiggles on paper – big deal! It was a very big deal in the history of thought to be able to write 111 and mean over a hundred instead of just three. It was a further breakthrough to write 101 and mean over a hundred even though only two 1s were written and one of the digits means "nothing." Each 1 in 111 means a different thing because of its place in the number and in 101 a place is held by a 0, meaning no 10's are present. This is the miracle of place value that the brilliant Egyptians and Greeks completely overlooked in their number systems. These simple concepts are so obvious they took centuries to invent! This system was so good that no culture has been able to substantially improve on it in two millennia and today it is virtually a world language.
Each 1 in 11,111 means something ten times less than the 1 just left of it. It wasn't until the 1500s that a Dutch quartermaster named Stevens (and a few others) said, "Why stop this downward progression at the end ones unit? Put a dot/marker then continue with another 1 that means something ten times smaller than one, i.e., 1/10. And so on to 1/100, etc. writing 11111.111. Thus the decimal system came into existence after Christopher Columbus sailed to the New World.
This is an expanded example of how historical data can be made friendly, relevant, interesting, and motivating to math learning. There are equally engaging stories of how France originated algebra and became "world math champion" in the 1600s, and how, just before 1800, centimeters were born during the French Revolution ("when rich people were beheaded"). My book A Mathematical Mystery Tour has several historical and cross cultural (as well as scientific and artistic) connections for those interpersonally intelligent kids of yours, and my other book Math for Humans: Teaching Math Through 8 Intelligences gives many suggestions for relating math to all the intelligences.
Mark Wahl is the author of Math for Humans: Teaching Math Through 8 Intelligences (LivnLern Press, 1999)., and Math Nuggets: 80 Thoughtful One-Page Activities for Pleasure, Insight, and Challenge (LivnLern Press, 1997).
You can order either book by calling LivnLern Press at 1-360-221-8842.
You can reach Mark Wahl at mathman@markwahl.com or visit his website at markwahl.com .
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