Children's book author, educator, math & science lover
In case you missed it, March 14th was an important international holiday. Every year, math enthusiasts worldwide celebrate the date as Pi Day. March 14th. 3/14. 3.14. Pi. Get it? If you’d like a higher degree of accuracy, you can celebrate Pi Minute at 1:59 on that date (as in 3.14159). Or why not Pi Second at 26 seconds into the Pi Minute (3.1415926)?
“It’s crazy! It’s irrational!” [Read more…]
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.”
[Read more…]
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 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…]
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…]
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…]
Way back a few centuries ago in the mid-1980s, long before anyone had ever heard the word “internet,” I was assigned to write an article for Smithsonian magazine on the decline of a once-loved American institution, the drug store soda fountain. The research for my story led me to seek newspaper and magazine articles from the heyday of soda fountains in the early- and mid-20th century.
If you are of a certain age, you will understand what I mean when I say that this endeavor resulted in my spending many hours in a public library squinting through a gargantuan, eye-straining machine known as a microfilm reader. If you are younger than that, herewith a brief explanation: to make back issues of certain magazines and newspapers accessible for years to come, a few companies were in the business of photographing the publications, page by page, and printing them onto acetate film in a much reduced size.
The film was called microfilm and in order to actually read it, a researcher could put the film into a machine called a microfilm reader and turn a cranking device (later replaced by an electric motor) in order to scroll to the section being sought. [Read more…]
Today is Memorial Day and I am in the mood to memorialize a publisher. Not a publisher that has died, fortunately (though many worthy ones have), but a publisher that is in transition. I don’t know whether the transition will transform it, but I know what I like about the way it used to be and I’m going to celebrate that here.
Why would I use this forum to talk about a publisher? Because I often meet educators with a passionate interest in children’s literature and I have found that many want to understand the relationship between author and publisher. (Actually, I know plenty of authors who would like to understand the relationship between their publishers and themselves!) Whereas children ask authors, “Where do you get your ideas?” and “How old are you?” their teachers tend to ask, “Do you get to choose your illustrators?” or “How hard is it to get an editor to read your manuscript?”
My six publishers come in three sizes: small, medium and large. About two months ago, one of the small ones, Ten Speed Press of Berkeley, CA, was bought by one of the world’s largest media conglomerates. Ten Speed Press and its children’s book division, Tricycle Press, are now part of Random House of New York, a division of Bertelsmann AG of Germany. So, for those who are interested in the inside scoop [Read more…]
“Where do y
ou get your ideas?” This is a question I often hear from children, along with “How old are you?” and “How much money do you make?” I like to tell them that ideas are everywhere. “You just have to keep your eyes open, your ears open and your mind open.”
As a child, I was filled with awe as I contemplated ordinary things. With their enormous numbers, sizes and distances, the stars amazed me. One day, visiting a museum with my parents, I focused on much closer, much smaller objects, looking through a microscope at hairs from my head and tiny creatures in a drop of pond water. I wondered how many hundreds or thousands of them would be as big as a flea! My mother and father were not scientists or mathematicians, but they encouraged me to ask questions like these, to find math everywhere.
Now, as a math author and educator, I have traveled the world speaking to children, teachers and parents. I’ve noticed that the kids who are successful in math are often those whose parents have helped them find mathematics at home and in family activities. These families know that it only takes a moment to make math meaningful.
– David Schwartz
Costumes … pumpkins … candy … math! All can be part of Halloween fun. With their hard-earned loot spread on the kitchen table, children see caloric pleasure, but parents can look at the same piles of sweets and see Math Moments.
The brightly wrapped candies can become “manipulatives,” or math props that parents can serve to their children as calorie-free math learning treats.
Children usually need no prompting for the math to begin. The first thing they usually do, after admiring their pillage, is to sort the jumble of candies into those they like and those they could live without. Parents can encourage other kinds of sorting by asking them to group candy by various characteristics. Sorting is an important early math skill that involves seeing similarities and differences, and classifying things according to characteristics – a mode of thinking used in higher-level math.
At age 3, Chaney Grover can find the square and round candies in his heap and sort them into two piles. By next year’s Halloween, he may be able to add a few more shapes to his sorting vocabulary – rectangles, ovals and cones, perhaps – and a year or two later, he’ll start to sort by multiple characteristics: “Do we have any candy that is round and brown?” his parents might ask. Or, “Can you find something cone-shaped and silver?” Or, even harder,“What is yellow, but not round?” The many characteristics of packaged candy can lead to impromptu games. “How are these two candies similar? Different?” Parents can invent a 20
Questions-type game: Parent: “I’m thinking of a candy. Find out
which one.”
Child: “Is it a square?”
Parent:“No.”
Child: “Is it orange?”
Parent:“Yes.”
And so on.Then switch roles.
Of course, children will probably
be more concerned with quantity
than qualities, which can lead
to counting and computation.
Chaney can count to 10 but,
like many 3-year-olds, when he
counts objects, he doesn’t always
start at one. Using candies, his
mom Meliss helps him get the idea.
She puts down three candies and
Chaney tells her how many. She
adds two more and Chaney starts
the count over again from one.
With practice, he will see short
cuts, like “counting on” (starting
from the previous total). Later, he will
simply add: three candies plus two candies
make five candies.
Children do not learn these math
basics by memorizing rules. Practice gives
them the chance to discover for themselves
how numbers work, and discovery
means understanding.
When more than one sibling is counting
his or her own sweet treasure, comparisons
(and boasts) are inevitable: “I
have nine Butterfingers™, and you have
only four!” Don’t let such an opportunity
get away without a Math Moment:“So
how many more do you have?”
If that’s too easy, try phrasing it another
way:“How many more would Sabrina
need to have as many as you?” It may seem obvious that the two questions are
equivalent, but children can draw blanks
when a simple question is posed in an
unfamiliar way.
Munchy Manipulatives
Daniel Pascal, 5, is very good at
adding small sums, and he has decided to
view his haul by lining up each kind of
candy in a separate column, like a bar
graph. He thinks this will make it easier
to compare quantities, but he soon sees
that a taller column doesn’t necessarily
mean more candy.The height of the column
depends on the size of the package,
not just the number of pieces, so he
pairs the candies side-by-side across the
columns. Now it’s easy to see that there
are more Dove™ chocolates than
Snickers™ bars, even though the line of
Snickers bars is taller.
Though Daniel can count to 100, he’s
a little shaky on some of the larger number
names. His dad, Steven, sees a chance
to give him some practice:“How many
candies do you think you have?” Daniel’s
guess is 33.
“OK, let’s count.” With a little help on
the harder transitions (49 to 50, 59 to
60) he completes the count.There are 70.
His father takes it one step further:“If
you can eat two a day, how long will it take
to eat all of these?” To answer the question,
the candies can be used as manipulatives,
taking two at a time to represent a
day’s ration. It’s a challenging problem for a
5-year-old, but Steven Pascal has always
challenged his kids with math.
Five years earlier, when Daniel’s older
sister Emily was 6, Steven took her to
inspect a new wing of their house, then
under construction. Referring to the
architect’s plans, they used a measuring
tape to find the future location of doors
and windows. Steven remembers telling
Emily that the doorknob would be
halfway up the door. He asked her to
mark the exact location of the doorknob.
Having been nurtured on a steady diet
of real-life math, Emily has excelled in the
subject at school. Last summer, she participated
in an intensive four-week math and
science program for middle school girls.
Math with Jack
You can find Halloween Math
Moments even before the first treat falls
into your child’s sack. Pumpkin-carving
gives children a chance to guess (and then
measure) their pumpkin’s weight and
dimensions. One mother asked her three
kids to cut a piece of string just long
enough to go around the pumpkin at its
widest place. All three kids cut strings
that were way too short. (Try it with any
spherical or cylindrical object.) This led to
a discussion of circumference,
the distance around a circle or
sphere.
She also had the children
guess how many seeds were in
their pumpkins, and once the
seeds had been scooped out,
they refined their guesses.They
divided the seeds scooped
from each pumpkin into four
equal piles, counted the number
of seeds in one- fourth of
a pumpkin, and used that
amount to estimate the total.
Then the 10-year-old wondered
aloud, “Does a heavier
pumpkin always have more
seeds than a lighter one?”
They got out the scale and weighed
their pumpkins and try to answer the
question with data they’d collected.They
were not only thinking mathematically, but
acting scientifically. And it all began with a
few simple Math Moments.
Click here to submit your Math Moments