Sacramento Homeschool Math By Hand

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A Year in the Life: Ambient Math Wins the Race to the Top!

March 10th, 2014 · No Comments · Homeschool Math Curriculum

Day 66

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math.  Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”  And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.”

Why ambient?  A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.  Because the Common Core Grade 1 Math Standards address addition and subtraction exclusively, they will not appear here until math blocks 3 and 4: the 4 Processes.  Math blocks 1 and 2 focus on meeting the numbers up close and personal, through stories, movement, art, and hands-on activities like making real numbers.  (Note that Grade 1 math could be divided into three blocks of 20 days each: Number Forms/Real Numbers/4 Processes & Practice, or four blocks of 15 days each: Number Forms/Real Numbers/4 Processes/4 Processes Practice.)

It could be said that we take zero for granted, as if it has been with us forever (ho-hum), but nothing could be further from the truth.  Zero is a relatively new concept, adopted from the Hindus, then the Muslims.  Bringing zero to the west was a truly revolutionary act, and took some time to take root, against all odds.  It, along with the Arabic numerals, was roundly condemned as blasphemous and nothing short of “the work of the devil.”  Here is a wonderfully told version of the story.

These are excerpts from Neatorama’s blog post, “Thanks for Nothing, The Story of Zero,” posted with permission from Uncle John’s 25th Anniversary Bathroom Reader(!)  Here is Neatorama’s web address (sorry if this isn’t a live link, I’m not yet sure of how to paste links into the blog):!zg6L8

Aristotle didn’t have it. Neither did Pythagoras or Euclid or other ancient mathematicians. We’re talking about zero, which may sound like nothing, but, as it turns out, is a really big something. Here’s the story.

Sometime in the early ninth century, a mathematician named Muhammad ibn al-Khwarizmi (circa 780-850 AD) gained a key piece of knowledge that would eventually earn him the nickname “The Father of Algebra.” What he discovered would also speed up mathematical calculation many times over and, eventually, make a host of amazing technological advances possible, up to and including cars, computers, space travel, and robots.

What was it? The Hindu number system (developed in India). The system intrigued al-Khwarizmi because it used nine different symbols to represent numbers, plus a small circle around empty space to represent sunya- “nothingness.” To keep from having to use more and more symbols for larger numbers, the Hindu system was aplace system. The value of a number could be determined by its place in a row of numbers: There was a row for 1s, a row for 10s, 100s, 1000s, and so on. If nine numerals and a circle to represent “nothing” sounds familiar, it should. Thanks to al-Khwarizmi, the Hindu number system (known in the West as “Arabic numerals”) is the system used in most of the world today . . .

“The tenth figure in the shape of a circle,” al-Khwarizmi wrote, would help prevent confusion when it came to balancing household accounts or parceling out a widow’s dowry. The circle was the key: If no numeral fell into a particular column, the circle served as a placeholder, as al-Khwarizmi put it, “to keep the rows straight.” A merchant (or mathematician) could run his finger down each column starting from the right and be confident that the ones, tens, hundreds, and so on, were in the correct place.

If this seems less than earth-shaking, consider this: The Hindu system was based on the abacus, a counting device that some scholars say goes back to 3,000 BC. The earliest versions used pebbles lined up in columns to represent 1s, 10s, 100s, 1000s, etc. Later version used beads strung on a wire inside a frame. With this type of abacus, when you counted past nine, you flipped one bead in the 10s column and pushed the beads in the 1s column back to nothing. British mathematician Lancelot Hogben succinctly explained what was so amazing about the Hindu circle: “The invention of sunya (zero) liberated the human intellect from the prison bars of the counting frame. Once there was a sign for the empty column, “carrying over” on a slate or paper was just as easy as carrying over on an abacus …and it could stretch as far as necessary in either direction.”

Al-Khwarizmi’s books became popular throughout the Persian Empire, and not just with mathematicians. Storekeepers, bankers, builders, architects, and anyone who needed math to do their jobs made use of Hindu numbers and al-Khwarizmi’s algebra. But it would take a surprisingly long time before his concepts spread beyond the Muslim world and into Europe . . .

Introduc(ing) Arabic numerals into the Church, replacing those unwieldy Roman numerals (was a) bad idea: using Arabic “squiggles” to do math was, to many, a suspicious indication that Sylvester II had gone over to the Dark Side. Rumors spread that while in Spain the future pope had either learned the “magic” we call math from his teacher’s secret book of magic or studied with the Devil himself . . .

Arabic numerals (and zero) made their next significant appearance in Western civilization . . . courtesy of Leonardo Fibonacci. Born in Pisa to a wealthy Italian merchant around 1170, Leonardo is said to have been the best Western mathematician of the Middle Ages (not that he had a lot of competition). Leonardo was raised in northern Africa where his father oversaw Italy’s coastal trading outposts and made sure his son was schooled in the math he would need to become an accountant. Leonardo’s Arab teachers showed him al-Khwarizmi’s Hindu-Arabic number system. “When I had been introduced to the art of the Indian’s nine symbols, knowledge of the art very soon pleased me above all else,” he later wrote . . .

That didn’t end the push back against Arabic numerals. In 1259, an edict came from Florence forbidding bankers to use “the infidel symbols” and, in 1348, the University of Padua insisted that book prices be listed using “plain” letters (Roman numerals), not “ciphers” (al-Khwarizmi’s sifr). Though Fibonacci’s book is credited with bringing zero (as well as its buddies, 1 to 9) to Europe, it took another 300 years for the system to spread beyond Italy. Why? For one thing, Fibonacci lived in the days before printing, so his books were hand written. If someone wanted a copy, it had to be copied by hand. In time, Fibonacci’s book would be translated, plagiarized, and used as inspiration for books in many other languages. The first one in English was The Craft of Nombrynge, published around 1350 . . .

Zero finally came into its own in Europe during the Renaissance when it showed up in a variety of books, including Robert Recordes’s popular math textbook Ground of Arts (1543). That book may have been read by one William Shakespeare, the first writer known to have used the Arabic zero in literature. In King Lear, the Fool tells Lear, “Thou are a 0 without a figure. I am better than thou art now, I am a Fool, thou art nothing.”

Lest we forget, advanced knowledge also developed in the New World, independently of Old World thought. The zero appears on a Mayan stela (a stone monument) carved sometime between 292 and 372 AD. That’s 400 to 500 years before al-Khwarizmi “discovered” it.

So goes the story of zero.  Such a monumental milestone in human history should not be just inserted in an everyday lesson without fanfare!  Shouldn’t every child know zero’s rightful history?  Wouldn’t it be empowering for a 7 year old just learning numbers to know this?  It should not be told exactly as recounted above of course, as it’s too abstractly adult for little ears, hearts, and minds.  But it is important for you the teacher to know zero’s history and then recount it to your child(ren) in a child-sized version.

Tune in tomorrow for a child-sized version, the story of Zero as told in the Math By Hand Grade 1 Daily Lesson Plans book, with its accompanying drawings!  Remember that knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.

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