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 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

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Arithmetickled You Pink