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 to mean a one followed by a googol zeros. It’s way bigger than a measly googol! Googolplex may well designate the largest number named with a single word, but of course that doesn’t make it the biggest number. In a last-ditch effort to hold onto the hope that there is indeed such a thing as the largest number…

Child: Infinity! Nothing is larger than infinity!

True enough, but there is nothing as large as infinity either: infinity is not a number. It denotes endlessness. A number designates a specific amount.

So, finally we get to a consensus: There is no such thing as the largest number. Yet numbers as large as googol or googolplex continue to tantalize, and well they should. To me the most fascinating thing about googol is how incredibly enormous it actually is. Writing those hundred zeros, while tedious, would take only a minute or two, yet the amount represented is, as I stated in G is for Googol, “more than the number of hairs on the head of everyone in the world, more than the number of blades of grass on all the lawns of the world, more than the number of grains of sand on all the beaches of the world — even more than the number of atoms in the universe.”

The estimated number of atoms is a one followed by 72 zeros (ten to the 72nd power, but I can’t do exponents in this blog). Let’s suppose the astrophysicists who estimated the number of atoms are way off. For the moment, let’s imagine that the actual (though unknowable) number of atoms is a hundred times as what they claim. So it would be a one followed by 74 zeros —still way, way, way less than a googol.

The number “googol” is, in fact, useless — except as food for a hungry mathematical mind. And it is an especially nourishing numerical treat for young hungry minds. In fact, a child possessing just such a hungry young mind corrected me when I once said, “There isn’t a googol of anything, anywhere.” The boy countered, “There are more than a googol numbers. The number of numbers is infinite.” Right he was! Now I modify the statement: “There isn’t a googol of any physical object.”

I am less enthusiastic about the point that was made by sixth graders in a class that sent me a stack of letters. All had the same basic theme, reflected by this one:

Dear Mr. Schwartz,

How do you know how many hairs are on the head of every person in the world? You probably haven’t met every person in the world. Even if you have, babies are being born every minute. People are losing hair every day!

No argument there but, unfortunately, this class didn’t seem to have a good understanding of the importance (and legitimacy) of estimation.

Now, with the ascendancy of a certain multi-billion dollar online enterprise, it is necessary for me to include in any discussion of googol the following important inequality, lest there be confusion:

It is interesting to note that the item on the right was the result of a spelling error. When Larry Page and his friends were choosing a name for a start-up company, he attempted to name it after the huge number “googol.” Instead, he committed what is probably the most famous (and lucrative) misspelling in history. Regardless, there is absolutely no doubt that both “googol” and “google” are mighty big.

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, so by discussing the difference between real numbers that end in “illion” and fake ones, I can discuss the actual meaning of number. As for what’s going to come in between A and Z, I had lots of ideas but not enough to fill out the book, so. . . let’s browse the library!

And so it was that I stumbled across Maps, Tracks and the Bridges of Königsberg: A Book About Networks by Michael Holt, a 1975 picture book that was one of many in the now sadly defunct “Young Math” series from the now sadly defunct publishing company, Thomas Y. Crowell. What fun! A great “K” word — Königsberg. I had heard about the dilemma that the residents of Königsberg, Germany, had tried to solve — to see if they could walk across each of their city’s seven bridges exactly once (all had to be crossed once and none could be re-crossed). No one could figure out a way to do it, but for centuries they were taunted by the prospect that a hidden solution eluded them. Finally the mathematician Leonhard Euler developed the postulates and theorems of a new branch of mathematics now known as graph theory or network theory in order to solve the Königsberg bridge problem. His goal was to figure out how to walk the bridges, or to prove it impossible. He succeeded not only in why the seven Königsberg bridges could not be walked once time each, but under what circumstances it could or could not be done for any network of bridges. Network theory not only proved to have many applications (useful, for example, in designing networks of cables) but it also laid the foundation for another branch of mathematics, topology. For me, as a researcher and writer, the cool thing is that I wouldn’t have thought of including the bridges of Königsberg in G is for Googol if I hadn’t bumped into them in Holt’s book on the shelves of a school library during a break between two assembly programs.

So that was an example of browsing, more-or-less aimlessly, to see what I could find and how I could tie it in. But there is another, more directed, way that browsing the shelves has proved fruitful in my research. It’s when I know what I’m looking for but neither google, for all its power, nor the library catalog nor anyone or anything else can tell me where to find it. For example. . .

Recently I have been doing research for an upcoming book called Where in the Wild? Mysteries in Nature Concealed. . . and Revealed, the next book in the series that began with Where in the Wlld? Camouflaged Creatures Concealed… and Revealed. One of the entries in What in the Wild? will be about the diggings of a star-nosed mole, a small mammal whose activities leave unwelcome mounds of soil on lawns and pastures. Moles, whether star-nosed or not, are usually not loved by landowners whose property they think of as their own.

Books and websites about moles turned out to be informative but a bit dull, focused on the minutia of their biology or harsh methods of putting an end to them and their excavations. So I wondered if I could find an interesting book with a section about moles. My initial searches in google and the public library catalog turned up no such book, probably because any that existed did not have the word “mole” in the title or subtitle or as one of the subject terms entered into the Library of Congress Cataloging-in-Publication data. Still, I figured that at least one such book must exist. I would employ a more venerable method of research.

And so it was that I found myself on hands and knees in the Rockridge branch of the Oakland Public Library, exploring the bottom shelf of the 596s just to see what I could find.

Within a few minutes, I had walked my fingers to Every Creeping Thing: True Tales of Faintly Repulsive Wildlife by Richard Conniff. The title seemed promising, and sure enough the table of contents led me to a chapter called “Notes from the Underground” — about moles. And guess what: star-nosed moles have a starring role! Conniff describes this creature in a most quotable way as a mole that “looks as if it’s got a sea anemone stuck on its snout.” And from there followed all kinds of fascinating information about the critters themselves and a colorful curmudgeon (of the human variety) who pursues them at the behest of disgruntled landowners in England. Once again, browsing trumped google!

The other day, a student at Landstuhl Elementary/Middle School on the U.S. Army base in Landstuhl, Germany, asked me the secret of success in researching books, and I told him a few things I thought of on the spot, but it didn’t occur to me at the time to tell him what I am saying here. To rewrite Kenneth Grahame’s delightful line (which, as it happens, was spoken by the character Mole in Wind in the Willows), “There is nothing—absolutely nothing—half so much worth doing as messing about in boats.” In this case, Grahame’s ode to blissful aimlessness might be rewritten for researchers as “There is nothing so delightful — or fruitful — as messing about in libraries.”

The authors of Wildlife and Plants, 3rd edition (Marshall Cavendish Reference) write that the nest tunnels are "3-7 feet long." In Water Birds of California, author Howard L. Cogswell says "3 to 6 feet (even 10)," while World Book Encyclopedia reports "4-15 feet." So which is it?

Those who read non-fiction often seem to have the impression that facts are facts. Period. The writer of non-fiction must merely learn them and report them, and that’s that. I’ve gotten this attitude often from children, egged on by the adults in their lives. "You wrote X, but we read Y in another book. Who is right and who is wrong?" Cheers for the author of truth. Jeers for the liars. But in reality, the depth of kingfisher tunnels (and many other facts) are unknowable. It might be instructive to consider how the figures above have come to light.

Over 200 or so years of American ornithological research, what percentage of kingfisher nests have been measured? I’d guess a sliver of a fraction of one percent. That alone tells us something: we don’t have a very strong sample here. And of those that have been measured, what fraction of the locations of kingfisher nests across North America have been measured? Another small fraction. Is there a wide variation in tunnel depths? It’s unlikely we know. Would different average lengths be found from Florida to Washington, from southern California to northern Maine? Possibly, but who knows? Are the tunnel lengths longer where the birds are digging into a softer material, shorter in a harder material? We don’t know. Or longer in one climate than another. It’s unlikely anyone would ever fund a study to find out, and probably for good reason.

So that’s a point: does it really matter? I can’t think of a good reason to study such a subject exhaustively. But if a question has not been studied in a statistically responsible way, we can’t really know the answer, can we? We can take a stab at it to get a general idea. So any of the above reported lengths is probably as good as any other. If someone found a nest burrow 15 feet long, it’s worth marveling at such a feat on the part of these birds. But overall it probably doesn’t make much difference whether the tunnels usually range from 3-6 feet or 4-10 feet, and whether the maximum is 10 or 15. So no one is out there doing studies to find out… and we may never find out.

My point is that facts are a much squirmier subject than many people realize, and it would be instructive for readers and thinkers to keep that in mind. One manifestation of this uncertainty is found in the common frustration at diverse and changing health recommendations. People blame science. I think they would do better to modify their expectations.

In an article called "The Fisher King," in the August-September 2009 issue of National Wildlife, respected naturalist and author Les Line describes kingfishers and their nesting habits but does not mention any measurements for how deep their nest tunnels can be. Perhaps Mr. Line is onto something. But I do find myself wanting to hang some kind of measurement on the subject. So, I am willing to accept the varied figures I do find, knowing that no definitive numbers can be stated, and savoring a certain tantalizing deliciousness in the uncertainty.

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. Lenses magnified the film onto a screen. Needless to say, it was no easy feat to find the right section and you had to watch unwanted pages whiz by, often zipping past the part you wanted. It was a pain in the . . . eyes. But who knew that such things as personal computers and internet browsers and search engines and digital archives would make the job a lot easier if only we were willing to wait a few decades?

Despite the trials of research by microfilm (and, slightly later, microfiche, a close cousin of microfilm that used flat sheets of film instead of rolls, thus avoiding the need for scrolling), it had some advantages. When you looked for an article in the New York Times about an especially popular soda fountain in Queens, as I did, you didn’t just get that article in isolation, but you got a glimpse into the world of 1951, as captured on the pages of the Times. There were other articles on the politics and culture and society and sporting events of the day, and there were advertisements that presented the tenor of the times as well as anything a journalist could have written. (In the course of reading about that Queens soda fountain, for example, I learned that big shiny luxury cars were selling for under $2,000. I reached for my credit card but then remembered that there were no credit cards back then.)

In the course of my research on soda fountains, conducted on the microfilm reader at the Wallingford (CT) Public Library, I stumbled upon a very short article, a space-filler, positioned on a back page of the New York Times of July 8, 1951. It briefly told the story of a 66-year old Swedish grandfather named Gustaf Håkansson who had just completed a 1,000-mile bicycle race despite having been barred from the race on account of his age. (How laughable that is in the context of a modern era in which athletes ten or fifteen years older than Gustaf routinely complete grueling races of many kinds — but this was the early 1950s). Hakansson had, in fact, started his personal race well ahead of the other racers and, 158 hours 20 minutes later, he finished to the rapturous cheers of thousands of fans who had turned out just to see him — the official racers weren’t due in for another day!

Gustaf’s story enchanted me, a lifelong bicycle lover, and I decided it needed to be told in its stereotype-bashing entirety. First, of course, I had to find out the story in its entirety.

Using The Reader’s Guide to Periodic Literature, an index that was then a staple on the reference shelves of libraries, I was able to find a more lengthy article about Gustaf in a long-defunct magazine called Lifetime Living. The article filled in some of the details, but I thought I’d need even more if I wanted to get into the mind of Gustaf and the psyche of his adoring fans. I hoped to see why he is, even to this day, remembered as a hero in Sweden.

Luckily, I had a Swedish friend living in the States who was getting ready to visit her family over the holidays. She offered to look in old Swedish newspapers for articles on the bushy-bearded bicyclist. She found several good ones and actually translated them into English for me. Another friend, studying at the University of Lund in Sweden, did further research with the help of a librarian friend.

The result was my picture book Supergrandpa, illustrated by Bert Dodson, later republished as Super Grandpa (with an audio CD of me reading the story with Swedish fiddle music in the background). In telling Gustaf’s story, I decided to “embroider” the actual facts to add to the dramatic tension, but in a page of back matter, I explained what actually happened.

To me, the most provocative lesson of this story is not about a bicycle ride in Sweden more than half a century ago. It is about differences in research methods between the internet era and the microfilm era. I’ll take the enormous power of the internet over the squinting inefficiency of microfilm readers any day. But let us not forget that sometimes the forgotten ways had their own power. Had I not been seduced by the charm of an old newspaper, the story of Gustaf Håkansson would probably still be buried in the back pages of a paper published on July 8th, 1951, and hardly noticed after July 9th.

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 on the publishing world, I will dish up a few scoops as I pay tribute to Tricycle Press. I do not know how, or if, things will change at Tricycle, but from the perspective of an author, I do know what I loved about the old Tricycle Press. I’ll share these thoughts by answering the kinds of questions I have heard from teachers who are curious about authors interacting with publishers.

“Do you get to choose your illustrators?”

— Answer for most publishers: No. End of story.

— Answer for Tricycle Press: No… and yes. Of course Tricycle gets the final decision. But I have had major input. When Tricycle bought my manuscript G Is for Googol: A Math Alphabet Book, editor-in-chief Nicole Geiger asked if I had any thoughts about the illustrator. (To be consulted on such a decision was in itself remarkable.) I admired Marissa Moss’s light-hearted but detailed illustrations, so I suggested that Nicole consider Marissa, who had already published several books with Tricycle. A week later, Marissa was offered the job, and she accepted. When the sequel to Googol, called Q Is for Quark: A Science Alphabet Book, was ready for publication and Marissa was busy with other things, I introduced Nicole to Kim Doner. I had just met Kim in Tulsa and I thought that the bold humor in her illustrations would be perfect for my book. She was little known outside of Oklahoma but I felt she deserved much wider recognition. Nicole sent her a “trial assignment” (an invitation to illustrate one small section of the book for the editors’ perusal) and sure enough, Kim made the grade. Her pictures add immeasurably to my book, and she has since illustrated a number of titles by other authors for Tricycle.

“Do you get to work with the illustrator while he/she is working on your book?”

— Answer for most publishers: Not really. I sometimes get to see sketches and make comments that may or may not be conveyed to the illustrator.

— Answer for Tricycle Press: While I don’t work with the illustrator (i.e., I do not visit his or her studio and talk about the work in progress), I get to see the art at various stages in its production and my comments, relayed through the editor, are taken seriously. When Kim was doing Quark, I was looking at her work almost daily and made many suggestions to keep it true to the science behind my text. She and I both appreciated the process and the final result.

“How hard is it to get an editor to read your manuscript?”

— Answer for most publishers: Very. Some will not read a manuscript unless it has been submitted by an agent. Regardless, it takes a long time to get an answer. Publishers typically say it takes 6-8 weeks but I believe that’s wishful thinking. Two to six months is more typical and I have sent in many manuscripts that have never generated a response.

— Answer for Tricycle Press: All publishers are inundated by manuscripts these days, so I cannot promise you will get the same treatment I got, but consider my story: I sent G Is for Googol to Tricycle on a Monday. On Tuesday, my answering machine had a message from Nicole: “I like it a lot.” On Wednesday, we had a phone conversation in which she conveyed her enthusiasm but told me that she still had to send it around to various readers for their opinions. About two weeks later, we were negotiating a contract. Sometimes it takes longer, but usually I can send a simple email to find out when I can expect an answer.

“Do the publicity people at a publishing house really help get your book known?”

— Answer for most publishers: Maybe — but mainly if your book has blockbuster potential, or if it’s already a blockbuster. Then they’re really happy to promote it!

— Answer for Tricycle Press: As a small publisher, the original Tricycle did not have a large budget for marketing, but they had  good ideas and a willingness to consider anything. I have always felt that my marketing suggestions have been taken seriously. When I suggested a classroom contest for activities based on Q Is for Quark, they set it up and publicized it. The prize was a free visit to the school by Kim and me. When I requested a poster as a promotional piece for Googol, and I pointed out my busy upcoming school speaking schedule, Tricycle agreed that a poster was a good idea even though they had originally wanted to do a bookmark (less expensive, but less durable).

“Who has the last word on the many decisions that must be made in producing a book?”

— Answer for most publishers: The publisher. It’s in the contract. No ifs, ands or buts.

— Answer for Tricycle Press: The publisher. It’s in the contract. But there are ifs, ands and buts. In producing four books with Tricycle, every time we’ve struggled over a sticky issue related to my text, we have resolved the disagreement in a most agreeable way. After I tried to see it the editor’s way (and failed) and the editor tried to see it my way (and failed), I have always been told, “You are the author. You get the final word.” The contract says the publisher gets the final word and I am certain that Nicole would have exercised her ultimate authority if necessary, but she has thus far always let me have my way . . . and my say. In the end, we always found a solution that made everyone happy. The book was a collaborative effort — exactly as it should be!

And so, I close my paean to Tricycle Press with hopes for its future. Nicole Geiger is still Tricycle’s editor-in-chief and the editorial offices are still in Berkeley, close to my home in Oakland. I don’t know what the future will bring but I’m trying to be optimistic. Perhaps Random House will allow this small imprint to maintain autonomy while effectively directing some of its vast marketing resources to selling my books. I hope to be a happy little fish in a very large pond.

As an author of non-fiction children’s books, I receive many letters from young readers. One that stands out came from a nine-year old girl named Lisa who wondered about the accuracy of various statements in my first book, How Much Is a Million? I was thrilled to receive her letter, for I am always happy to learn that my books are being read critically.

Lisa wondered about the truth of my book’s claim that counting from one to one billion (saying each number individually) would take 95 years. After questioning a few other statements in my book, she closed her letter:

“I had mixed up feelings about your book. That’s where the magic comes from the world of books. The magic of books is not knowing whether the facts are true or not.”

In my presentations at schools, I often tell children, “Wondering is wonderful.” I find it wonderful that Lisa is wondering about the truth of statements in my books.

I wish more readers of my books—of all books—would wonder about them the way Lisa does. Active minds read critically, questioning what they have read as the reader blends his or her own experiences, knowledge and observations with the author’s raw ingredients. Critical readers ingest a nourishing stew that is more than a bowl of information.

I feel privileged to have seen many examples of readers extending or challenging statements in my books. The members of a 2nd/3rd grade class doubted that the average height of elementary school students is 4′8″ (142 cm), as reported in the backmatter of How Much Is a Million? Using 4’8” as the average height, I had figured that average shoulder height would be about 4’, and I multiplied 4’ by 1,000,000 to estimate the height of a one-million child tower, which came out to about 757 miles (1,218 km): “If one million children climbed onto one another’s shoulders,” the book begins, “they would be taller than the tallest buildings, higher than the highest mountains, and farther up than airplanes can fly.”

The members of this particular class doubted that the average elementary school student is only 4’8” tall, and to prove me wrong, they measured every child in the school. They found the median, mode, and mean, and they graphed their data in several ways. Finally, they declared that the average height is only 4′4″ (132 cm).

But they didn’t quit there. Like a journal article by professional scientists, the report included a section devoted to reflecting upon their results. Scientists would call it the “Discussion” section. In it, the students wondered aloud if there were a legitimate explanation for the four-inch discrepancy between the average height I reported and what they found. They proposed some possibilities: Their school stopped at Grade 5. Maybe I used data from an elementary school that went up to Grade 6 or 8. That might explain why my average height was higher than theirs. Alternatively, their school could have been shorter than normal… or perhaps mine was taller than normal. Or maybe I just measured a single child and declared him or her to be normal! “He’s 4’8” and he looks normal,” I might have said, “so that’s the average. Done!” I find their out of-the-box thinking quite impressive.

In If You Made a Million, my book on money (using United States currency), I write that one million dollars would be equal to “a whale’s weight in quarters.” A group of children wondered if a whale really did weigh the same as four million U.S. 25-cent pieces. They looked up the weight of a blue whale (appx. 60 tons or 54,400 kg) and calculated that the blue whale’s 60 tons is the weight of about 10 million quarters or $2.5 million— not $1 million, as my book says! They wrote to tell me their results, and in my reply I pointed out that the book does not name a particular species of whale. It simply says a million dollars is equal to “a whale’s weigh in quarters.” And in the back of the book, where I provide the calculations, I specifically note that the weight of a million dollars in quarters (about 50,000 pounds or 22,680 kg), is “the approximate weight of many kinds of whales, including the sperm whale.” Then, as if anticipating their objection, I had added the fact that blue whales can be much heavier.

I thought my arguments had absolved me of error in their minds, but these students were not convinced. They sent me a color copy of the illustration in the book, with an arrow pointing to the blue-tinted caricature of a whale. Handwritten in thick block letters were their final words on the matter:“This is a blue whale!”

After recovering from laughter, I wrote back to suggest that they take it up with the illustrator, Steven Kellogg.

To me, the point isn’t who is right and who is wrong. Often it’s a matter of interpreta-tion, as in the case of the whale. The point is that wonderful things happen when children wonder about what they have read. They can pursue their wonders through research and, if appropriate, mathematical calculations or estimations. As nine year-old Lisa wrote, “The magic of books is not knowing whether the facts are true or not.”

It truly is magical.

For years I’ve been using popcorn to demonstrate various math concepts as I act out the plot, if you can call it that, of On Beyond a Million, my powers-of-ten counting book. The popcorn almost never fails to excite children from grades K to 5 or 6, whether they are urban or rural, rich or poor, white or black, X or Y.  On several occasions I dropped the popcorn from my presentation, but I had to put it back because it’s so popular. 

The fact that 21st century children go wild over popcorn as a math prop encourages me wildly. Why? Because popcorn is so simple. It isn’t a coveted, rare treat that they hardly ever get to see (or taste). They haven’t been barraged by commercials touting its pleasures. There’s nothing high-tech about my bags of popcorn, and no special effects. There isn’t even an on/off switch. Yet kids love it because of the way the bags’ growth in size appeals to their senses and their emotions.

Much has been written recently about the current plugged-in generation that can’t have fun without electric outlets at hand and electronic devices in hand. Richard Louv’s best-selling book, Last Child in the Woods: Saving Our Children from Nature Deficit Disorder, sounds an alarm that children who are alienated from nature suffer in many psychological and physiological ways. Elementary school curricula may teach students all about the Amazon rain forest’s endangered species but do not encourage them to interact with the natural world outside their classroom, says Louv. That interaction, when it does occur, has a wealth of salubrious effects.

I am encouraged by the popcorn. If kids can get so excited about something as simple as my popcorn, then there is hope. For instance, if adults simply expose children to “nature play,” they will drink in the benefits.

Something else without an on-off switch comes to mind: books. In recent years, pundits have predicted death knells for the paper-and-ink variety of reading material but I don’t see it coming. Like big bags of popcorn, books are too much fun to hold and behold. They’re going to stick around for a while. Furthermore, as an author, I find the popcorn factor instructive. It says I can stick with the basics. By basics, I don’t mean what that word has come to mean in the politicized world of education and testing. I mean the basic and universal emotions and responses in children (shared by adults who haven’t lost the basics). One of the most valuable pieces of advice I ever got from an editor was in reference to a fiction manuscripts, Super Grandpa, but I think it applies to non-fiction as well. This editor told me to “cut to the emotional core of the story.” The emotional core of powers of ten is that every time you add a zero to a number, it gets ten times bigger and that’s WAAAAAAAAAY bigger. “WAAAAAAAAAY bigger” is the emotional core. It’s exciting. If I can get to that in my readers  (or audience members),  I’ve reached them. Just pop up some corn and you’ll see what I mean.

Children love to guess. The opportunity to figure out something or to find objects hidden in illustrations, combined with a chance to show off what they have already learned, gets kids jumping (sometimes literally) with knowledge and joy. If an author can present good factual material in an enjoyable format that allows to children to take guesses, the author might have a popular book on his or her hands. It’s happened to me 25 times, with number 26 on its way.

In the late ‘90s, I wrote two dozen science books in the series “Look Once, Look Again.” They came out in two batches of 12 – the first oriented around habitats and the second around anatomical features of animals and plants. The publisher, Creative Teaching Press, predicted they would be in print for five or six years but it’s now been almost a dozen since the first series came out, and the “LOLA” books (as photographer Dwight Kuhn and I fondly call them) are still going strong.

There was nothing special about the idea, other than the interactive possibilities that come from children using both visual and textual clues to identify plants and animals. First they see a close-up photograph of an organism that gives a magnified view of part of its exterior (the plates of a turtle’s carapace, for example, or the kernels of an ear of corn). The text hints at the organism’s identity (“These are plates but you wouldn’t want to eat from them. What animal has hard plates on its back?” or “What has ears but cannot hear?”). And the child is on his or her way. Kids tear through these books and reach for more. With so many colorful covers, I long ago began to call them “book candy.” Unlike mouth candy, this kind of confection allows kids to think and have no-calorie fun at the same time, while expanding their knowledge of the natural world and, in a subtle way, encouraging them think like a naturalist — in terms of a creature’s characteristics.

As an author who visits schools, I have had the most fun when I’ve seen class projects derived from mybooks, including class-created books based on “Look Once, Look Again.” Typically, first or second graders have drawn close-ups of animal or plant parts and written clues about the identity, followed by drawings of the complete animal or plant and further explanation. In one school, the students went beyond modeling their work after the LOLA books. They invented fantastical animals that combined characteristics of various real creatures. It reminded me of one of my favoite Dr. Seuss books, On Beyond Zebra, which I first encountered on the shelf of one of my biology professors at Cornell.

Late last year, I published (with co-author Yael Schy, who is also my wife) a book of poems that hint about the identity of well-camouflaged animals found (if you can spot them) in the photographs (also by Dwight Kuhn). The challenge is to find the animal hidden in the picture and identify it from the poem. We adopted a unique design element in which the gate-fold pages open up to reveal another version of the same photo; the difference is that now the background is faded (thanks to the miracle of PhotoShop) to allow the hidden animal to stand out. Then come prose “naturalist notes,” identifying the animal and offering more info about its life history, its use of camouflage, and a few more photos.

Many readers, both young and older, have suggested that Where In the Wild? reminds them of I Spy and Where’s Waldo?. Our book hasn’t yet enjoyed quite the success of those (their illustrations are not limited by the true arrangements of objects in the world), but it has captured the attention of many readers and reviewers (and, I’m pleased to say, award committees–most recently the Animal Behavior Society, which just honored it with its 2008 Outstanding Children’s Book Award). Again, I think the hook is the guessing game format.

With great anticipation, I am waiting to see student projects based on Where In the Wild? Teachers and home schoolers: this is your chance to combine science with poetry. Please show me what you come up with by sending an email to (you know how to turn that into an email address). And all INK blog readers can post some of your favorite non-fiction books that use a guessing-game format. Why limit ourselves to science? How about history, geography, grammar, philosophy, math — there’s no limit! Aspiriing authors of non-fiction: it’s better than plastics.

Super Grandpa tells the true story of a Swedish grandfather who, in 1951 at age 66, rode his bicycle about 1,000 miles in the Sverige Loppet (Tour of Sweden), despite having been barred from entering the race on account of his age. As an unofficial entrant, he finished the course in six days and became a national hero, remembered to this day. End of story. Or is it? The story has many numbers that can generate math problems. To take a simple example, Gustaf, our hardy grandpa, rides his bicycle 600 miles to the starting line because he has no other way to get there. Then he begins the 1,000 mile race. Obvious question to ask a reader: how many miles all together did he ride? Less obvious questions: was the race itself twice as long as the distance he rode to get there? More than twice? Less than twice? By how much? More difficult question: The book says he rode the 1,000 miles in six days. On average, how many miles per day did he ride? Research question: if a 1,000 mile race started in our city, where might it end? Get out the map. Use the scale. Find several points that are 1,000 miles away. Note the distance between as-the-crow-flies miles and actual road miles. How about a circuit that starts and ends here. What are some of the cities it could pass through? Christina Nugent, mentor teacher and math supervisor for Dubuque Public Schools in Iowa, has written two mathematical lesson plans for Super Grandpa (for primary and intermediate grades), which can be downloaded at the publisher’s website. Here’s a caveat: don’t forget to let the story be a story. Read it and enjoy it. Then mine its math.

Ladybug, along with eleven other titles in the “Life Cycles” series, are nature books, not math books. Right? Not exactly. I’d agree that Ladybug is a nature book but, as in so many nature books, you can find plenty of mathematical learning opportunities. One of the photographs shows about 20 bright orange ladybugs on a bed of vegetation. Their spots can be seen and counted, and the number of spots per beetle ranges from zero to a dozen or so.

Along comes Patty Brown, an elementary school math coach from Freso, CA. Patty gives first graders orange cardboard cut-outs resembling the backs of ladybugs, each divided into two “wings” (actually elytra, a beetle’s hardened wing cases). The first graders also get ten yellow cardboard circles representing spots. They are asked to arrange the ten spots on the backs of their ladybugs. Every child in the class arrives at the same solution: five spots on each side. “Can we arrange them any other way?” Patty asks. No one budges. “Is five and five the only way to make ten?” The children resist admitting to any other possibilities. “How about this?” Patty picks up a lady bug back and puts six spots on one side, four on the other. The kids get it but they’re not happy about it. The symmetry, which they see as “fairness,” of five and five has a very strong pull on them, but eventually they come to discover and accept all the other combinations of numbers whose sum is ten. Patty writes each combination as an equation. Everyone is happy and an important first grade math concept has been learned.

In the Forest is one of 24 titles in my “Look Once, Look Again” series. In these books, readers look at a close-up photo of an animal and they read text hinting at its identity. Turning the page reveals the full animal and more information about it. One section shows a close up view of one antenna of a cecropia moth. The text that accompanies the “reveal” photo of the whole moth explains that its two antennae are its nose – a nose sensitive enough to allow a male moth to smell females three miles away. The second graders of Judy Baker in Vacaville, CA, found this interesting and a class discussion showed their teacher that they had no idea of the distance defined by a mile. And so began an extensive classroom project Judy called “How Much is a Mile?” in which 15 students taped together the paper yardsticks they had made earlier in the year to create a long strip of paper which they dubbed “Longie.”

At first they thought Longie would be a mile but they figured out it was only 45 feet long, and a little research told them that a mile was 5,280 feet. This led them to wonder aloud, “How many Longies make a mile?” They sought the answer by repeatedly adding 45 + 45, etc., but Ms. Baker saw a teachable moment and used the project as an opportunity to teach hows and whys of multiplication by ten. Excitement grew as they approached the ultimate answer. “It was time for lunch,” Judy wrote in an email to me, “but they had such momentum, they didn’t want to go to lunch!”

Building on Judy’s classroom experiences and adding some new technology, another 2nd grade teacher, Laura Bush, in Andover, CT, went online to pull up a high-resolution map of the local area on an interactive whiteboard. Placing the school in the middle of the map, she asked her students to imagine a male moth at the school, and to plot several points three miles from the school in order to see how far the moth could smell. Referring to the scale of miles, they entered points on the map; as more and more points appeared on the screen, a magical thing emerged: a circle. What an opportunity to teach the vocabulary of circles: radius, diameter, circumference, area, and so forth, and to make it relevant and meaningful.

To think that all that math started with a nature book.