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I am just back from San Antonio, where I spoke at NCTE (National Council of Teachers of English). An annual appearance at NCTM (National Council of Teachers of Mathematics) has been on my agenda since 1996 but this was my first NCTE. I started thinking about similarities and differences between the two organizations in how they encourage teachers to use literature, and I mostly came up with similarities. And then I remembered a book on my shelf at home that makes that point exactly, focusing on mathematical literature. Appropriately, the book is published jointly by NCTM and NCTE. If I could put just one resource in the hands of a teacher wanting to mine the many treasures of “math-lit” as a teaching tool for both mathematics and language arts, this would be the book.
New Visions for Linking Literature and Mathematics by David J. Whitin and Phyllis Whitin is more than a resource book about using math-related literature in the classroom. It does indeed illustrate a myriad
ways that teachers can use a wide range of quality b
ooks to support both math and literacy. But note the word “quality.” In addition to providing examples (plenty!) and illustrating how teachers have used them (impressive!), it tells you how to judge mathematical literature. That’s where New Visions differs from any other resource book I’ve seen. “Many (math-related books) seem more like workbooks than stories,” write the Whitins and I agree wholeheartedly. “Some give detailed prescriptions for reading, much like a teaching manual for a basal reader, while others mask doses of ‘skills’ with comical illustrations or popular food products…” Bottom line: not all math lit is created equal, and New Visions shows you how to evaluate. It even shows why some books just don’t make the grade, and it does name names. Harsh! But someone had to do it.
The Whitins put forth four criteria as a guide for judging mathematical literature as worthy. They then select one book as exemplary, showing how it makes the grade in all four areas. More on that later. Here are their criteria with an example of a book that stands out in each category.
1. Mathematical integrity Stories and literature have enormous value when they inspire children to apply mathematical ideas to the world around them, but for that to happen, the math in a book should be not only accurate, but should be presented in a context that is believable, not forced; it should be presented in an accessible way; and it should “promote healthy mathematical attitudes and dispositions.”
The Whitins give several examples, including Ann Whitehead Nagda’s Tiger Math: Learning to Graph from a Baby Tiger, which provides both an exciting non-fiction narrative with photographs and statistical data from the true, suspenseful story of a motherless tiger cub being raised at the Denver Zoo. Data (such as weight gain over time) is expressed in a variety of useful graphs. It’s an engaging book that connects math to the real world in a way children find spellbinding — and educators find supportive of the standards they are trying to teach.
2. Potential for Varied Response. Children’s books should not be worksheets. Instead of being didactic, they should encourage children to think mathematically and invite them to “investigate, discuss, and extend… (and to) engage in research, problem posing and problem solving.” Readers are not directed. They are invited.
Readers of the charming Grandpa’s Quilt by Betsy Franco, are easily tempted to find their own solutions the problem that faces the book’s characters. The 6-square by 6-square quilt does not cover their grandfather’s feet so they must rearrange its dimensions. Children are likely to explore factors of 36 and to get a feel for the relationship between perimeter and area. And the mathematical “invitations” go on from there.
3. An aesthetic dimension “Good books appeal to the emotions and senses of the reader, provide a fresh perspective, and free the imagination.” Here the Whitins look at how well the written language is crafted, along with the quality of the visuals and whether the book actually inspires a greater appreciation of the wonders of the world (including the human world). To earn our respect, the words and visuals of a work of mathematical literature must be just as compelling as those of any other literary genre. Claiming "It's just a math book!" doesn't cut it.
In their unique counting book, Spots: Counting Creatures from Sky to Sea, author Carolyn Lesser and illustrator Laura Regan use vivid, evocative language and stunning paintings to inspire awe and appreciation of nature — as well as the mathematics that is so often useful in describing and explaining the natural world.
4. Racial, cultural and gender inclusiveness. My first reaction to this criterion was a bit dismissive. “Doesn’t that apply to all books?” I asked. Of course it does, but we should be especially careful not to let the
mathematical component of literature that perpetuates stereotypes blind us to an unfortunate sub-text. There is a huge push now to attract women and members of ethnic minorities to careers in mathematics, science and engineering, and children’s books can help promot
e equity. There is more to it than counting boys vs. girls or white children vs. black or brown children in the illustrations. As one of several fascinating examples, the Whitins sing the praises of The History of Counting by eminent archaeologist Denise Schmandt-Besserat, a non-fiction picture book that celebrates the contributions
of many cultures over many centuries in developing diverse number systems.
New Visions for Linking Literature and Mathematics goes on to provide myriad examples of books for a wide range of ages, strategies for using them to teach math, and an outstanding annotated bibliography called “Best Books for Exploring.”
Now about that exemplary book the Whitins chose to feature in the opening chapter. I held off identifying it until now for fear of seeming self-serving, but in the interest of full-disclosure, I should say that it’s my book If You Hopped Like a Frog. I’ve written about it in earlier posts so I won’t summarize it now and it would really feel way too “me”-focused to list the ways the authors of New Visions found that it met their four criteria. Instead, I’ll close with a passage from an article published in Horn Book in 1987, quoted by the Whitins. I can think of no better summary of their feelings and mine:
“You can almost divide the nonfiction [that children] read into two categories: nonfiction that stuffs in facts, as if children were vases to be filled, and nonfiction that ignites the imagination, as if children were indeed fires to be lit.” (Jo Carr, “Filling Vases, Lighting Fires” Horn Book 63, November/December 1987.)
2 Comments on It's "Math-Lit" But Is It Good Lit?, last added: 11/25/2008
Great information, David. I'd like to traverse a bit of a tangent to recommend a new math-related game for little kids -- Long Neckers Matching and Stacking Game. It's creative and fun -- read the reviews on Amazon. [Full disclosure: a friend of mine invented it.]
My book for Spring of 2008 has a simple premise—how life would change if math and numbers were suddenly gone. What if you couldn't count, or add, or measure, or tell time…? Here’s a preview of Missing Math: A Number Mystery.
We usually see books only when they're in their pristine final form, printed in living color on coated paper (in the case of picture books, anyway.) This post will give a sense of the behind-the scenes gyrations, which took longer than usual in this case.
Version #1:The Number Cruncher was a picture book written in verse. I still like the play on words of the title. The main character ran around eating any number he saw. Some sort of monster or alien, here’s what he looked like:
The dummy is undated and my memory inexact, but it’s before I went digital for illustration around 1997 so it’s over ten years old. There are some handwritten notes, such as maybe he should be more of a robot-like character. I didn't realize it until now, but the 25 m.p.h. speed limit sign somehow endured through all the versions to appear in Missing Math. Although the specific reason this version was rejected has faded, in retrospect, consuming a few numbers here and there doesn't have enough impact.
Version #2: No More Math? Still a picture book, it had become an updated three wishes story in prose about a boy who encounters a robot alien who has crash-landed. It starts out:
A robot alien! And a spaceship! The whole scene was a shocker, but I had my sneakers on in case I had to make a quick getaway. There was nothing to worry about, because this guy could barely find the tool box, not to mention a ray gun. In return for his help, the robot offers to grant the boy three wishes, and the plot lumbers on. In rereading this, it’s so long-winded I can see why my editor suggested I try…
Version #3:The Day Math Disappeared, a chapter book version. The manuscript is dated 2001:
…Don’t ask me where he came from, I didn’t find out. It is a good question, though. Some secret government project? Anyway, once he decided I wasn’t going to dismantle him or anything, he went back to working on the ship or plane, or whatever. He called it his “ziptek,” so we can just stick with that.
My nephew Caleb read it and liked it, even if my editor ended up giving the thumbs down on it. The concept was probably too young for a chapter book.
Version #4:When Math Took a Vacation is a picture book again, with a main character named “Math.” He supervises the numbers who cheerfully perform their jobs on rulers, mailboxes, license plates, and so on. That is, until Math takes a well-deserved vacation—while the boss is away, the numbers play and havoc ensues. Another rejection, which wasn’t too surprising at this point. Here are some of the number characters at work before they run off to sip sodas at the seashore, or whatever they were doing:
Version #5: The Number Cruncher, is dated 2005 and told in first person from the viewpoint of a little boy:
Somebody ATE my money last night! And Something bit my shirt, my notebook got nibbled, my homework has holes, and my books are dripping with drool… YUCK! Something totally WEIRD is going on.
It’s in sort of a non-rhyming poetic format, which may be why my editor suggested I try it in rhyming verse. Verse? I hadn’t written anything in rhyme since 1990. Sure, why not? That ended up being the manuscript for Missing Math. It has an all-animal cast, some nonsensical angles such as not even being able to THINK of a number, and a weird machine that is being used to steal the numbers for some unknown purpose. Fortunately, there is a persistent cat detective who is determined to solve the mystery of the missing math. You can see him on my site.
So why did I persevere in the effort to get this notion into book form? Despite the setbacks, I stayed in love with the the idea of making math vanish as a way to help kids perceive how integral it is to everyday life. But credit must also go to my editor Margery Cuyler who never forgot about it for all those years, and kept asking to see the “no math” idea in some new form. Her interest motivated me to rethink it. Missing Math: A Number Mystery gets right to the point and shows how completely things fall apart. But, it would’ve been nice if it had come together just a tad more quickly!
If anyone would like more info about how I made the video preview for Missing Math, please check out The Dust of Everyday Life blog, which gives an overview of the software used. The post is titled Making a Book Preview (Trailer). Other people there have also written about making book trailers.
0 Comments on 1 Idea…Many Versions…1 Book as of 1/1/1990
I'm thrilled to be here, sharing some thoughts with you. I'm just back from Boston, where I was honored to received an award for my latest book, Where in the Wild? Camouflaged Creatures Concealed... and Revealed, which I co-authored with my wife, Yael Schy. (Our book was awarded the 2008 SB&F Prize for Excellence in Science Books in the category "Children's Science Picture Book." The award is sponsored by Subaru and the American Association for the Advancement of Science and it was shared between the two authors and photographer Dwight Kuhn.) I was planning to write about the award ceremony and the four books that received the prize in different categories (see www.sbfonline/prizes) but I have decided to save that for another day,
except to give you a glimpse of our book's cover and to share one detail about the ceremony. The sponsors of the SB&F Prize arranged to have several local children present the awards to the winning authors. The kids told the audience (and the authors) what they liked about the books. Some of them spoke with passion about questions the books had raised in their minds. To these readers, a book that raises interesting questions is a good book indeed. Then the young book reviewers shook our hands while handing us our award plaques.
The opinions and questions of children often fascinate and delight me. I get a lot of great letters from children and I would be hard-pressed to pick a favorite, but one letter that stands out in my mind came from a nine-year old girl who wondered about the accuracy of various statements in my first book. I'm going to remove her name and address to protect her privacy, but we can call her by her first name, Lisa. Here is what she wrote. I apologize that the letters are small and a little hard to read. Lisa's message is summarized in the last two sentences:
In my presentations at schools, I often tell children, "Wondering is wonderful." I find it wonderful that Lisa is wondering about the statements in my book and whether or not they are true. These musings give her "mixed up feelings," which may sound uncomfortable, but she quickly goes on to reassure us that she finds these feelings magical. Her letter ends with a sentence I find truly memorable. To Lisa, the magic in books is wondering whether the "facts" are true or not!
I wish readers of my books -- or all books -- would wonder about them the way Lisa does. Active minds read critically, questioning what they read as they blend their own experiences, knowledge and observations with the author's raw ingredients. They create a nourishing stew that is more than a bowl of information.
I have been lucky enough to see see many examples of readers extending or challenging statements in my books. The 2rd and 3rd graders of one class doubted that the average height of elementary school students was truly 4'8", as I reported in the backmatter of How Much Is a Million? I used that figure to estimate the height of a million children standing on one another's shoulders. To find out if I was right, this class set about measuring every child in their elementary school. They determined the median, the mode and the mean, and they graphed their data. Finally, they declared that the average height was only 4'4".
But they didn't quit there. They proposed several possible explanations for the discrepancy between what I had written and what they had found. For example, their school has grades from K-5. Maybe my school went up to 6th or 8th grade. If so, that could explain the difference between their answer and mine. Or, they speculated, their school might be shorter than normal... or perhaps mine was taller than normal. Or maybe I just measured a single child with a height of 4'8" and I said, "He's normal!" In a scientific paper, this section of their report would have been the "discussion" section.
I'll give just one other example of children wondering about what they have read.
In If You Made a Million, I wrote that a million dollars would be equal to "a whale's weight in quarters." A group of schoolkids wondered about that. They looked up the weight of a blue whale (60 tons) and calculated that it is the same as the weight of 10 million quarters, or 2.5 million dollars -- not one million dollars as the book said. When they wrote to me about it, I pointed out that the book did not specify a particular species of whale. And in the backmatter, where I explained the math, I showed that the weight of a million dollars in quarters is about 50,000 pounds, which is "the approximate weight of many kinds of whales, including the sperm whale." Then, as if anticipating their objection, I added that blue whales can be much heavier than that. I thought I had covered my bases and I said so (nicely) in a letter to my challengers, but they were not convinced. Here is a copy of the page that they sent back to me, bearing their comment upon the situation:
Don't you love it? I sure do. I told them they would have to take it up with the illustrator, Steven Kellogg. And I even provided his address!
To me, the point isn't who is right and who is wrong. The point is that they wondered about something they had read in a book ... and they pursued their wonders through research and mathematics. It's magical. As nine year-old Lisa said, "The magic of books is not knowing whether the facts are true or not."
0 Comments on The Magic of Books: Wondering Whether the "Facts" are True or Not as of 1/1/1990
Man! I've had some rough editors and art directors before, but something like this would probably make me shrivel up and die... were it not coming from such a big talent. This is a link to a critique by veteran comics artist Alex Toth (who died last year) on the Johnny Quest pencils and layouts of the very talented Steve Rude. Very harsh, but very accurate. Plenty of good points that we all need to be reminded of when it comes to illustrating scenes and visually telling stories. (link)
1 Comments on Critique from Hell, last added: 4/10/2007
Thank you for that link... I am so glad I was able to read it. It makes all the tedious research worthwhile and all the time it takes to set up a scene is rewarded when a great illustration is ultimately created.
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Wow, thanks. Great post. Can't wait to check this stuff out.
Great information, David. I'd like to traverse a bit of a tangent to recommend a new math-related game for little kids -- Long Neckers Matching and Stacking Game. It's creative and fun -- read the reviews on Amazon. [Full disclosure: a friend of mine invented it.]