If They Had A Million Dollars
Remember the hit song by the Barenaked Ladies, a Canadian alternative rock band (whose members are neither ladies nor naked — it least in public)? Here’s how it starts:
If I had a million dollar
If I had a million dollars
Well I’d buy you a house
I would buy you a house
I’d buy you furniture for your house…
Hate to sound like a million dollar spoilsport, but I sure wouldn’t pay a million for those lyrics. Not even a hundred. Still, the tune is darn catchy, and the refrain is a bit touching:
If I had a million dollars,
I’d buy your love.
Whether or not that particular commodity can be purchased at any price will not be the subject of this post, although you may wish to pursue it elsewhere.
Since the 1989 publication of my second book, If You Made a Million, I have seen countless examples of student writing that begin with the prompt, “If I had a million dollars…” They fall into three categories of roughly equal size. I’ll call the them “fulfillment,” “greed” and “charity.”
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Math-Lit for the Older Set
I got an email the other day from a parent looking for good mathematical literature to interest and challenge older children. Is there any? Which books would I recommend?
Before I describe a few of my faves, I must point out, as I did at length in my INK post of May 28, 2008, that many educators have inspired intermediate grade, middle school and even high school students with picture books, using them as age-appropriate teaching tools. I believe my most successful mathematical picture books are those that can be used on many levels. In fact, when asked the target age for How Much is a Million?, I often say, “Preschool through high school.” Actually, it’s not true. I should say. “Preschool through college,” but that answer might sound overly smug. (I have twice met college professors who use my book when teaching about Avogadro’s number, a behemoth number critically important in understanding quantitative chemistry.) That said, I will mention a few books that probably wouldn’t make it into the 2nd grade math classroom but should be a staple of math classrooms or libraries serving upper elementary, middle school and high school students.
In The Number Devil by German author Hans Magnus Enzensberger, a middle school-age boy named Robert dreams of travels through the world of mathematics under the tutelage of an impish devil whom he at first finds annoying but gradually comes to enjoy and admire. At the start of the book, Robert is a mediocre and indifferent math student — no surprise, considering that his ho-hum teacher at school gives the students mathematical busywork without the least bit of mathematical inspiration. (His uncomprehending mother is no better: she believes a son who voluntarily speaks of mathematical concepts must be ill!) But Robert and the devil are on an irrepressible romp and together they challenge each other while developing plethora of mathematical concepts and meeting a pantheon of famous mathematicians. All names are whimsically disguised — Leonhard Euler becomes “Owl” (Eule in German translates to “owl” in English) and roots (as in square roots, cube roots, etc.) are called “rutabagas” (which are literal roots) — just two of many such examples. Figuring out the conventional words for the concepts at hand just adds to the devilish fun of this 1997 book which is well on its way to becoming a classic.
Flatland is not on its way to classic status: it’s already there. Like The Number Devil, it incorporates dreams but the concepts are geometrical rather than numerical. This novella, written in 1884 by English schoolmaster Edwin A. Abbott, is a pointed satire of closed-minded, hierarchical Victorian society but it is also, as Isaac Asimov put it, “The best introduction one can find into the manner of perceiving dimensions.” The story has been developed into several short films and a 2007 feature film; there have been TV episodes, a role-playing game and sequels by other authors.
The narrator of the original Flatland is a square named – ready? — A. Square. He lives in Read more »
The Play’s The Thing
The mother of a 7th grader in Oakland, CA, tells me that morning recess at her son’s middle school has been cut from twenty minutes to ten, and the entire recess, formerly held outdoors, is now limited to an indoor space. Even the theoretical 10 minutes is often whittled down to just a few minutes or none at all because teachers respond to the disruptive in-class behavior of a few students by holding the class through recess to make up for classroom delays.
This sorry state of affairs is not limited to the United States. I am just back from speaking at primary (elementary) schools in Australia. I had a few opportunities to interact with children on the playground and I was pleased to notice Read more »
On Googols and Google, Googolplex and Infinity: The Truth About Big Numbers
When I was in high school, I read a book called Infinity: Beyond the Beyond the Beyond. I don’t remember much about it, but I’ll never forget the title. The concept of infinity in its … well, infiniteness… can keep my mind occupied for a long time. And the idea of going “beyond the beyond” — and then beyond that! — provided more delicious food for thought. I sometimes think about that title and the mind-candy of endlessness when I’m speaking at a school, as I was last week in West Chester, PA, and someone asked, “What’s the biggest number?” It’s a question I often hear. The conversation usually goes something like this:
Child: What’s the biggest number in the whole wide world?
David: Do you think there is such a thing as the biggest number?
Audience: half “Yes,” half “No”
David: Will someone please tell me what you think the biggest number is.
Children, variously: billion, trillion, quadrillion, quintillion, googol, googolplex, etc.
David: Hang on. Let’s suppose you think “quintillion” is the biggest number. Then what about “quintillion-and-one”? Isn’t that bigger? And if that’s the biggest, what about “quintillion-and-two” — even bigger, right?
This usually leads to a triumphant retort about an enormous number familiar to many children (much less familiar to their parents and teachers):
Child: Googol has to be the biggest!
David: What’s a googol?
Many children know that “googol” is the name for a very large number — a one followed by a hundred zeros. This is an exciting concept. In my book G is for Googol: A Math Alphabet Book, I tell the story of how “googol” got its name from a nine-year old boy. Surely it is tempting to call googol “the biggest number,” but that’s a non-starter.
Me: If you think googol is the biggest number, then what about googol-and-one? Or two googol? Or a googol googol?
Almost inevitably, at this point someone proffers an even bigger number, “googolplex.” It is true that the word “googolplex” was coined Read more »
Messing About in Libraries: The Delectable Art of Browsing
To many of us, it’s almost unthinkable to imagine researching anything before the advent of the internet. Discovery of information before the era of google seems as onerous as hauling water out of a well. So seduced have we been by the simplicity and effectiveness of entering a few words into the rectangle at the top of the screen and — wowza! — dozens, hundreds or thousands of “hits” come up. If none is quite right, just change the search terms a bit and try again. For researchers, it’s like winning the lottery again and again.
But. . . you knew there would be a “but”. . . are we depriving ourselves of anything worthwhile when we boil the art of research down to finding 30,000 google hits in 18 microseconds? I would maintain that we are, for several reasons, and I am going to write about one of them: browsing. Sometimes there is both pleasure and success to be found by poking around in the shelves of libraries or bookstores, just to see what we might find.A few years ago, I wrote G is for Googol: A Math Alphabet Book, a potpourri of enjoyable mathematical ideas in an ABC format. Unlike the many alphabet books written for young children, this one is directed at readers in the intermediate and middle school grades (as is its sequel, Q is for Quark: A Science Alphabet Book). So how am I going to fill 26 slots with delightful math? Many entries popped into my mind right away. “A” is going to be for “abacus” because I love the fact that proficient abacus users can calculate lengthy addition or subtraction problems faster than the fastest calculator user. “Z” is going to be for “zillion” because it’s not a number at all but people often don’t realize that Read more »
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