|CBC Features Vol. 46, No. 2 Summer-Fall 1993
The Children's Book Council
Playing with Math
by Bruce McMillan
When I was in school, math was a tool - a tool to be enjoyed as I learned how to use it. I enjoyed the logic of mathematics. It made so much sense. But it didn't seem like the kind of thing one would chat about with others, so I didn't. I still don't chat about math. But I've made math a part of my work. Of the thirty children's books I've written and photo-illustrated, five are math related.
What I try to bring to my math-related concept books is what appealed to me during my early experiences with math-a fun time with logic. For example, I once thought about doing a book introducing the concept of the simplest number set of all-the pair. The story line of this book, One, Two, One Pair! (Scholastic), is the anticipation and joy of going ice skating. As with most of my concept books, I decided on a visual narrative approach. Early in the story I provide a subtle clue to the surprise ending. What appears to be one person putting on a pair of socks, mittens, skates, laces, and so on is actually a pair of people-twins.
Before photographing this book, I contacted a respected teacher from the largest school district in Maine and asked for a list of their K-6 teaching objectives for math. I was interested in which math skills students were expected to know at each grade level. Since my books are often used as teaching tools, in effect I'm a teacher as well as an author.
The list of math objectives stimulated a new book idea: cooking fractions. I like to cook. I first thought of doing this book for grade levels 3-6, based on the age levels in the list of objectives. I planned to show additive fractional units as children cooked something sumptuous and then subtractive fractional units as they ate it. However, I couldn't sell the idea to a publisher. They decided that this age group, grades 3-6, was too old for a picture book. So, I simplified my idea and refocused it for grades K-3. The result, Eating Fractions (Scholastic), is about a meal. Two children divide and share what they eat as fractional units. Each fractional unit is displayed on the left page in a photograph, graphic, and text, while the visual story line appears on the facing right page. The story progresses from halves to thirds to fourths. Then, to reinforce learning this concept, the story continues and repeats the progression of halves, thirds, and fourths, followed by a visual surprise - plus recipes - at the end.
Obviously, the list of teaching objectives was informative in pointing out what teachers are teaching. But it also showed me that the corresponding age levels aren't written in stone. When autographing this book at schools, bookstores, and libraries, I've noticed that the readers I'm autographing for range from kindergartners to fifth-graders. My approach served as an introduction to fractions for younger students and at the same time reinforced the concept for older readers.
While I made Eating Fractions for children to enjoy as a story, as well as to help them learn a new concept, the overwhelming positive response from teachers has been gratifying. Thanks to them, it has become one of my biggest-selling books. I thought it would do well, but not quite this well. Teachers have told me one of the reasons why. Repeatedly, I heard, "There aren't any quality books about fractions. And we all teach fractions." Eating Fractions filled a void.
Teachers have also told me how Eating Fractions has led to hands-on learning. That's why I included the recipes. I'm a hands-on learner, and when I was planning this book I could foresee children dividing food, looking forward to eating it, and actually learning along the way.
There was another reason besides math for doing One, Two, One Pair! and Eating Fractions. I'd just completed my own twelve-year hands-on project - my house. Though I recently traveled far away to photograph a forthcoming book, Penguins at Home: Gentoos of Antarctica (Houghton Mifflin), I didn't have to go far at all to photograph the math concept books-my newly finished home was the perfect setting for both.
Geometry is a subject that lends itself to a visual approach. I selected the "vehicle" to tell this story. Recalling my childhood field trips to a fire station in Bangor, Maine, I remembered the thrill of stepping out into a void, grabbing hold of the fire pole, and sliding down to the floor below where the fire engines were parked and ready to go. So began Fire Engine Shapes (Lothrop). It takes a graphic look at the geometric shapes found on parts of a fire engine, but I also included a game because I like to play. The little girl exploring the fire engine can be found in every photo, but it takes careful observation to do so. I thought the idea of looking for shapes while looking for the little girl would engage the minds of young readers. Had I foreseen how popular this phenomenon would become-looking for a person hidden in the illustration of a book-I might have titled this book Where's Stephanie? Waldo had not yet made his debut.
When I'm out speaking at schools I always like to bring along some surprises and props. I wish that my tricycle, the "star" of The Remarkable Riderless Runaway Tricycle (Apple Island Books), could collect frequent-flyer miles, as it often accompanies me on trips. On a few special occasions I've brought along a very large prop. In some of Maine's elementary schools, I've introduced students to "My 'star'... waiting outside by the playground - too big to come inside." When we go outside we find Engine 5, the very same one photographed in Fire Engine Shapes. It's a treat to see a whole school, class by class, walking around the actual fire engine, and picking out the geometric shapes.
The first numbers that children often utilize are related to time. When I began work on Time To... (Lothrop) I had to consider a variety of clocks. I settled on a traditional-looking clock face, but there was a dilemma. A few years ago this wouldn't have applied but now it does: digital clock faces. So, in addition to using the traditional clock face, I also included the time in digital format on the same page.
In Time To... the progression of a child's day is seen in the photo on the right page, and the photo on the left page features a clock on the young boy's wall. What readers may not be aware of is that, although it appears the clock wall photos were taken in the boy's room, they weren't. I used extra wallpaper on a propped up sheet of wallboard to make a false wall set and placed it in my new living room, twenty miles away. This way I could control the lighting in order to show the progression of time throughout the day.
I teach a children's picture book course, open to the public, at the University of Southern Maine and the University of New Hampshire (2001 addendum - now only at UNH). Time To... provided me with an example to use in my children's book classes of how two artists, working independently and having never met nor exchanged correspondence, can approach a theme and concept in a similar manner. It's fortunate that my book, Time To... and Mordicai Gerstein's book, A Sun's Day (HarperCollins), were published at about the same time because it's uncanny how similar they are. The identical details in each book both amuse and amaze me.
My college degree is in biology and so when I began work on my first math concept book, Counting Wildflowers (Lothrop), it was also a taxonomy lesson. My editor and I agreed that children would be interested in wildflowers rather than garden flowers. It was a search for wildflowers, which blossom at various times throughout the season. Every species of flower has its own biological clock. That's why I couldn't photograph dandelions-they had already blossomed and gone to seed by the time I began shooting.
Counting Wildflowers concludes with a photo of maiden pinks. After counting from one to twenty wildflowers, the reader finds a photograph filled with a profusion of delicate pink blossoms. What the reader doesn't know is that the photo was taken of flowers growing on very fertile ground - my septic field. Once again, I was photographing a math concept at home.
The profusion of flowers in that particular photo inspired a comment from a teacher which led me to a concept that may be what I focus on in my next math-related book. When I spoke at last year's annual Math Their Way Conference I floated this idea by some of the teachers. They all said, "That's great, we need a book on that." The topic? You'll just have to wait to find out. But I can tell you one thing. Though it's a math concept book, unlike four of my previous math concept books, it probably won't be photographed at my home - but you never know.
(2001 Addendum. That book became Jelly Beans for Sale, Scholastic 1996. It demonstrate the basics of making change using a jelly bean stand as the vehicle. I photographed it where we set up our jelly bean stand in my neighbor's field.)
Bruce McMillan is a writer, photo-illustrator, speaker, and teacher. He photographs and writes both concept books and science/nature books for children. His math concept books have been distinguished with honors including ALA Notable Books, Parenting magazine's Certificate of Excellence, Parent's Magazine Best Kids' Books, and many starred reviews. His 1993 titles are Mouse Views, What the Class Pet Saw (Holiday House), and A Beach for the Birds and Penguins at Home: Gentoos of Antarctica (both Houghton Mifflin).
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