Dayle Ann Dodds (California) has authored over 21 picture books, including three of our favourite mathematical stories: 'Full House: An Invitation to Fractions’ (2003), 'The Great Divide: A Mathematical Marathon' (2005) and 'Minnie's Diner: A Multiplying Menu' (2007), as well as a mathematical concept book, 'The Shape of Things’ (2009). These four titles are all published by Candlewick Press,
To learn more about these stories, read our reviews and find out where you can purchase them, simply click on their covers below.
We hope you enjoy reading Dayle sharing her experience of working on these incredible mathematical story projects with you!
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First thing first, can you tell us three interesting/weird facts about you :-)
How would you describe your relationship with mathematics (and mathematics learning) when you were younger? And now?
Math always made sense to me. There were clearly defined rules, and if followed correctly, predictable results. Two plus two is four. There were also equations, which are sort of like puzzles for you to solve. Ten minus “x” equals seven. I enjoyed trying to figure out the answer. I guess you could say I’m a problem-solver by nature. I love a good mystery, and math is sort of like that until you uncover the answer. I especially liked geometry because it’s visual. As a little girl, I loved learning about shapes and drawing them. One of my favorite doodling pastimes was to draw a two dimensional shape like a square, and then add lines and sides to make it a three dimensional shape.
You authored 'Minnie's Diner', 'The Great Divide', 'Full House: An Invitation to Fractions’ and 'The Shape of Things’. What inspired you to write these stories with a mathematical focus for young children?
One day I was helping out in a kindergarten class. The teacher gave each of the children a large white piece of blank drawing paper. They were free to draw whatever they wanted. Most of the kids jumped right in, creating pictures of their family or favorite pets or activities, but I noticed one little boy just sitting and staring at the blank paper. He told me he didn’t know how to draw. I knew this to not be true, as everyone can draw something, even if it’s only a wiggle or squiggle or dot. So I asked him, “Can you draw a square?” He said “Uh-huh”, and sure enough, he put a square on his paper. Then I said, “Can you draw a triangle, and put it on top of the square?” He did that also. Voila! A house! I suggested he draw a rectangle and put it in the center of the square for a door, and two more smaller squares on each side for windows. We made circles for trees, a larger circle for the sun, and on and on. Before he knew it, he had drawn an entire picture, made of shapes put together. The next day at school he ran up to me with a wonderful new picture and a big smile on this face. “Look what I made!” he shouted. Yes indeed!
As far as my other picture book stories, what I really enjoy is taking a basic math concept such as addition, subtraction, multiplication, division, etc., and then thinking of a fun way to incorporate it into a story children will enjoy. Math and mathematical concepts are all around us, and truly do make up this amazing world we live in.
On average, how long did it take you to work on each of these mathematical picturebooks?
That’s a difficult question to answer, as each book has its own journey. I’ve had stories that I’ve been able to write in two weeks, others have gone through several revisions for months and months. I would say on average it takes me about two to three months to complete a manuscript I feel is ready to submit.
Some mathematical story authors prefer to have a context and setting as closely related to children’s real-world experience as much as possible. Some prefer fantasy. In the specific context of mathematical stories, what is your preference, and why?
Both. I thoroughly enjoy the process of taking real life characters and moving them into fantastical places and experiences. It’s sort of like “The Lion, the Witch, and the Wardrobe.” Three bored kids find a door in the back of a closet, and off they go to a wonderful imaginative adventure.
What were some of the key stages that you went through in creating your maths picturebooks?
I always decide on the concept first. For example, with 'The Great Divide', I knew I wanted to do a book on division. Then I just let the ideas float in my mind for awhile, and see what comes up. Usually, for me, the next step appears as a visual image. I’ll be driving in my car, or taking a shower (warm water is great for allowing creative ideas to flow), or taking a walk, or shopping at the grocery store, and WHAM! An idea will come as a picture or pictures in my mind. I can’t explain why or how they do, they just do. It’s sort of like sending out an invitation, and eventually something interesting usually shows up.
Next, I’ll begin playing around with words, phrases, sentences. I love to write in rhyme, so I’ll see if I can figure out how to tell the story with rhyming words. That is a terrific challenge, and I thoroughly enjoy the process.
Even though I’m not an illustrator, I do work very visually when creating a book. It is often said that a picture book is a marriage between words and pictures, so making it work visually is very important to me. I see the pictures in my mind, and I need to know how or if my idea will work in a book format. I always make a dummy - which is like a “pretend” book.” I do this by getting an inexpensive drawing pad and numbering the pages. Then I paste in the words and draw pictures page by page to go with them.
When my children were young, I used to show them my new “book” by reading the dummy and having them look at my pictures. This helped me see if the concept was working and the story was something kids would enjoy.
I will insert here that once I send off the manuscript, I am super excited to see what the actual illustrator will do with the text and concept I’ve created. It’s always a great surprise, and I’ve never been disappointed.
Which of these stages did you find most challenging? Similarly, which did you find most satisfying?
For me the most challenging is also the most satisfying when I get it right. As I mentioned before, I write many of my books in rhyme. So once I have decided on my concept, see the visual picture in my mind, it’s time to start writing the story. I’ll spend hours thinking of lines that are simple, descriptive, and fun (fun is an important requirement for my stories). Sometimes these lines come out easily, such as “A square is just a square, until you add a roof, two windows and a door, and then it’s much much more.” Other times I can think and think and it may be days or weeks before just the right rhyme will appear. Sometimes I have to work at it, and other times the right words or phrases will just pop into my mind! That’s great when it happens. As far as rhyming words, I guess you could say I have a natural ability to do that. I’ll also let you in on a little secret. I have a wonderful yellow rhyming dictionary I have used for years and years. I always start writing the lines and figuring out the rhyming words first myself, but if I get stuck, I rely on my book. And did you know there are words that cannot be rhymed no matter how hard you try? See if you can find a rhyming word for “purple.” Not going to happen! That’s why it’s great to have a book to tell you it’s better to choose another word.
Did you find coming up with a storyline / context to embed your chosen mathematical concept in difficult? Where did you draw inspirations from?
It depends. Sometimes once I’ve chosen the mathematical concept, the story comes to me rather quickly. Take 'Minnie’s Diner', for example. I decided I wanted to write a book on multiplication, and I wanted it to be funny. When I was young our family had a weekend ranch in a small Northern California town. My father, a true “weekend cowboy,” would often take us kids to a wonderful diner in town that served what he called “cowboy breakfast” - eggs, pancakes with fresh berries and delicious sticky maple syrup, bacon, orange juice. That breakfast was so big, I could never finish it. I just remember there being more, and more, and more! 'Minnie’s Diner' was born from that memory. Some of the other stories I’ve written have come from experiences my own children, family, friends had. And some simply appear out of nowhere.
To what extent did you have a say in the illustrating process, particularly in relation to the visualization of mathematical concepts?
Like I mentioned earlier, I find it extremely necessary to visualise my books as I’m writing them. I need to make sure the math concept is carried through the story from beginning to end. If there is a visual component to it that I feels needs explanation, I will send along my rough dummy to help explain what I’m seeing. Generally however, I like to watch the illustrator bring his or her talents to the project. It’s so thrilling to see what different artists come up with. Often I am given thumbnail illustrations of what the pictures may be, and I appreciate that opportunity. I try to respect the artist’s process, and only comment on changes when I feel strongly about something - which luckily hasn’t happened often. In my book 'The Color Box' (non-mathematical), I wrote the story with the idea that a little boy climbed inside a box that took him to several worlds of color. The illustrator chose a blackbird for the main character, and that didn’t feel right to me. We were able to co-operate on the issue, and a monkey became the main character, which turned out great. In 'The Prince Won’t Go to Bed' (non-mathematical), the illustrator, Kyrsten Brooker, did amazing illustrations of collages using both drawings and real objects. On one page I noticed some torn bits from a newspaper as part of the collage. On further inspection, I spotted some objectionable words not meant for kids’ eyes. It was a simple oversight that went past illustrator, editor, and art director, and I was glad to have noticed it. Speaking of which, children are extremely quick and clever at spotting anything that is out of place in either text or illustrations!
How do you know whether the language used in your stories is age-appropriate for your target children? Do publishers normally have a word limit that you need to stick to?
I do this pretty intrinsically. I guess because I have a teaching background, have studied and read so many children’s books, and have been a parent for many years, I just know what words kids in my target range understand. That doesn’t mean I don’t like to throw in a word or two that they may not know. In my book “Wheel Away!” the wheel gets loose from the boy’s bicycle and rolls into town where there is a bazaar going on. That’s a new word for most kids, and it offered a new learning opportunity. As far as length, yes, picture books are generally 32 pages, with 4 pages for “front matter.” So you’re really looking at only 28 pages for text and illustrations. I have never been asked to limit the number of words per page, but I do that automatically. Picture books usually have relatively few words per page. Again, the words tell only half the story, and the pictures tell the rest. It’s part of the creative challenge to see if you can get your story across with as few words as possible.
On reflection, how would you comment on the diversity of the books’ characters in your mathematical stories Would you have done anything differently in terms of the diversity of the books’ characters?
No, I feel pretty good about that. I believe my books are written in such a way as to reach everyone. And the illustrators support that goal. The winner of the marathon race in “The Great Divide” is female. The guests at 'Full House: An Invitation to Fractions' are certainly a diverse and colorful mix of all genders and races. Also my books have been translated to many, many languages all over the world, which tells me people of all cultures are enjoying them. Language-wise, once in awhile a word might not translate, which is interesting. For 'Sing, Sophie' (non-mathematical), I needed to revise the word “jam” for the British translation, as I was told in England our American jam is called “jelly.”
Can your fans expect to read any more stories with mathematical connections from you in the soon future?
Yes! I have just finished a picture book that deals with volume and spatial relationships called 'Romney, Pack Your Bags!' It’s about a little boy who has to pack his own suitcase for the first time to go on vacation. He feels he needs to bring more and more and more, and the suitcases get bigger and bigger and bigger until…well, you’ll just have to see!
I’m also working on a fun new idea on identifying and predicting patterns of different colors and shapes.
Do you have any favourite mathematical story author(s)? If so, which one, and which aspects of their works do you particularly like?
There are many. Some of the all time favorites include 'The 500 Hats of Bartholomew Cubbins' by Dr. Seuss, 'The Little Mouse, the Red Ripe Strawberry and the Big Hungry Bear' by Audrey and Don Wood, and 'Inch by Inch' by L. Lionni. What I like about each of these books is that there is a highly entertaining story that incorporates math. That’s my favorite type of math-related book. The math concepts are woven in, but the story itself is truly enjoyable on its own.
"Mathematics and imagination can absolutely go together. Math doesn’t have to be boring, or confusing, or overwhelming. It can be fun and useful and even suspenseful at times."
What do you think are some of the key benefits of children developing their mathematical understanding through maths picturebooks?
Mathematics and imagination can absolutely go together. Math doesn’t have to be boring, or confusing, or overwhelming. It can be fun and useful and even suspenseful at times. What will happen if I do this? How can I use that information to solve this challenge or mystery? How funny is it when 500 hats appear on the same person’s head? How far away are the stars or the moon? How many makes a dozen? What is a sphere? How big is an ant? How many toes does a platypus have? How many cups of flour would you need to make the biggest birthday cake in the world? Math is part of every day, and everything we see, hear, taste, smell and touch. But it’s more than that. It conjures up amazing ideas for our imagination to explore.
What do you think are some of the key benefits of helping children to develop their mathematical understanding by encouraging them to produce their own maths picturebooks?
It’s like swimming in a lake. Yes, you can stand on the shore and look out at the peaceful blue water shimmering in the sunlight. If you’re lucky you can even see floating logs with turtles sunning themselves on top, or hear the occasional “bloop” of a big old frog jumping into the water. But in order to truly experience the lake, you need to jump in. Get your feet wet, get your whole self wet, swim around, splash a bit, squish your toes in the soft sandy bottom. Think it, sense it, and then use what you know to make it work. Math is your toolbox to help you build what you imagine. And what an incredible toolbox it is!
Do you think teaching mathematics through storytelling (particularly in the format of illustrated storybooks) could be used with secondary school students too? What would you say to secondary school teachers who are hesitant / skeptic about the use of this approach to make maths learning more accessible for their students?
I would say they have not done their research. Just because a book is in a storybook format doesn’t mean it can’t be interesting to older students also. Look at Rube Goldberg and his fantastical cause and effect machines. (My picture book 'Henry’s Amazing Machine' was partly inspired by his inventions). Or David MaCaulay’s 'The Way Things Work' books. Size, shape, depth, volume, physics, estimations and more to explore. In addition there are numerous middle grade novels to be found, where the main character faces a challenge or obstacle and must incorporate his or her knowledge of mathematical principles and concepts to save the day.
For teachers and parents who want to encourage their children to create their own maths picturebooks at school or at home, but are not sure how to guide them through the creative process, what would be your advice?
For teachers and parents who want to have a go at having their own maths picturebook published by a publisher, what would be your advice?
Well, I have taught entire courses about this. In a nutshell, I would say if possible take a course on writing for children. A lot of people think writing children’s books is easy, and they don’t realize all the many factors that are involved. In order to give yourself your best chance of success, learn all you can. If possible, join a writer’s group and be open to critiques of your work. You want to be sure your story is as ready as can be before sending it out. Research which publishers accept the type of story you’ve written, what their guidelines are, and if they accept unsolicited manuscripts (assuming you don’t have an agent). It’s a highly competitive field, so you want to put your best foot forward. Once you submit, be patient, and be persistent. All writers face rejection, but you need to keep trying. In America, I also encourage new writers to join The Society of Children’s Writers and Illustrators. They publish a wonderful newsletter that helps you keep informed on what’s happening in the world of children’s literature.
What do you think of the research that we do and the resources that we provide to teachers and parents on our MathsThroughStories.org website?
The MathsThroughStories.org website is wonderful. I especially like resources that list books and stories that incorporate mathematical themes and concepts for teachers and parents.
Illustrations copyright © 2003 by Abby Carter from Full House: An Invitation to Fractions by Dayle Ann Dodds. Candlewick Press. All Rights Reserved.
Illustrations copyright © 2007 by John Manders from Minnie's Diner: A Multiplying Menu by Dayle Ann Dodds. Candlewick Press. All Rights Reserved.
Illustrations copyright © 2007 by John Manders from Minnie's Diner: A Multiplying Menu by Dayle Ann Dodds. Candlewick Press. All Rights Reserved.