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 a two-dimensional world, Flatland, but dreams of visiting a one-dimensional world, Lineland, where he tries to convince the ignorant monarch of a second dimension but fails to open the ruler’s eyes to a universe beyond his familiar straight line domain. He also goes to one-dimensional Pointland inhabited by a monarch who is the sole inhabitant and, in fact, is the entire universe in and of himself! (He perceives any attempts at communication from the outside world to be his own thoughts.) Later, our narrator is visited be a three-dimensional sphere, which he finds incomprehensible until he accompanies Sphere to Spaceland. From there, the two discover that the leaders of Flatland know about Spaceland and a third dimension, but they prohibit their subjects from acknowledging it, under penalty of death or imprisonment. Square tries to convince Sphere of the possibility of fourth and fifth dimensions, but the notion is soundly rejected and Square is sent home in disgrace. It’s not a happy story but fascinating and uplifting in its own way, and, like the subject matter, the book has many dimensions.

Mathematics: A Human Endeavor by Harold R. Jacobs is a wide-ranging mathematics textbook so deliciously fun and fascinating that kids actually want to read it. Even more astonishing, their parents and teachers can’t put it down either. As a college senior, I discovered its first edition (it’s now it its third) while volunteering as an enrichment provider to a select group of very sharp fifth graders, and I was hooked. Jacobs covers the breadth of high school mathematics with an emphasis on the beauty and power and real-life relevance of each subject. Aptly-chosen cartoons made me and my students laugh outloud, and we immediately saw that the cartoons weren’t included just for the guffaws. “An improvement over the square wheel,” pronounces B.C in the caption of one drawing as he flaunts his great invention: a triangular wheel. “It eliminates one bump!”Jacobs shows how B.C.’s thinking is dead wrong, and in so doing, he develops principles of polygons and the mathematical concept of limit: as the number of sides grows and approaches infinity, the polygon approaches a circle — the “wheel” with no bumps (road surface willing!).

In lucid prose, the subjects range from algebra and geometry to probability, topology, statistics and more. Jacobs often shows how the math being taught is found not only in books but in life. This book has become a staple among alternative high schools and homeschoolers, but I find it so readable that it doesn’t have to be thought of as a textbook at all. Just the same, a teacher’s guide is available.

A major step down from the literary giants I’ve just described is my own picture book targeted at upper-elementary and middle school age children. G Is for Googol: A Math Alphabet Book is a potpourri of topics from “A is for Abacus” (proficient abacus users outcompete calculator users every time) to “Z is for Zillion” (not actually number, which provides an excuse to talk about what makes a number a number). Math-loving kids of all ages have found respite in its pages, and math teachers sometimes read from it to provide literary snacks on special days. It has spawned many a student-created alphabet-book as class projects. A 6th grade class in Colorado called theirs An Algabet Anthology by “The Awesome Accelerated Academics.” At first I thought the title had a typo but I later realized that “algabet” is just a play on “algebra.” Sixth grade humor. The word play continues to the final page:

THE END

We Hope This Book

Arithmetickled You Pink

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.

My friend Merri Rudd, a contra dance caller from Albuquerque, sent me this picture. Some of you “dog people” might like it — and who knows, maybe it will inspire some folks to love the book as much as LuckyDog does. (More about Merri and LuckyDog)

Since I mentioned that Merri is a contra dance caller, I should say that I am an avid contra dancer. I can hear you asking, “What is contra dance?” I could answer, “It’s a bit like square dance except that it’s done in lines instead of squares,” but that wouldn’t be a very satisfying explanation because contra dancing is really VERY different from square dancing and not just because of the geometry. Contra dancers get asked about their dance form so often that some have posted definitions and explanations on the web. Here’s a site with several long and one short explanation.

But no collection of words can really explain a dance form, and words certainly can’t capture the terrific music (which is always live at contra dances), so why don’t you just come out and join me on the dance floor?! Most contra dances are kid-friendly, though they are not usually kid-oriented. More about dances in your area.

Now… did you think I was going to sign off without a math connection? Contra dance abounds with “math moments.” Here is one I just experienced at “Labor Day Dance Away,” a fabulous weekend of dancing that took place in the San Bernardino Mountains of southern California. In a contra dance, the dancers start out standing in lines, but as they move through different figures the geometry changes. In one of the dances last weekend, groups of four dancers formed circles, and our caller, Cis Hinkle from Atlanta, told us to rotate the circle to the left “three-quarters of the way around and a little bit more.” What a delightful, kinesthetic way for a child to learn fractions, I thought to myself. I can just imagine the discussion that might grow out of a question like, “What fraction is a little bit more than three-quarters of the way around but still less than all the way around?” A contra dancer I know, Bernie Scanlon, a math instructor at Bakersfield College, gives workshops for teachers in using dance to teach math. And check out this Science News article for another take on the math-contra dance connection.

See you on the dance floor!

DMS