Word Problems- A Bit of History

Now that the kids are back in school, The Cat and the Fiddle would like to dish out some thoughts about word problems.

When doing research for a historical project some time ago I stumbled across this one, dating from 1581:

“A drunkard drinketh a barrel of beer in the space of 14 days, and when his wife drinks with him then they drink it out within ten days. In what space will his wife drink that barrel alone?”

(from Elizabeth’s London: Everyday Life in Elizabethan London by Liza Picard)

Hopefully the scholars were sober whilst they tried to figure it out. Eager to know more math history, I read Susan Gerofsky’s fascinating A Man Left Albuquerque Heading East: Word Problems as Genre in Mathematics and learned that word problems are as old as the earliest human records (they show up on 4000 year old Babylonian cuneiform tablets) and have been employed continuously ever since. Some of the old chestnuts are even included, with alterations, in textbooks today. An Italian Renaissance math textbook contains an early version of the “two trains crossing” problem, using couriers dispatched from both the Holy Father in Rome and a certain Signora of Venice.

In her book Gerofsky analyzes and critiques word problems and makes recommendations for how to improve them. Hallelujah! Gary Larson spoke for most of us with his legendary cartoon that depicts a library in hell stocked with books like "Story Problems Galore.” Why did we dread them when we were in school? For their often preposterous scenarios. For their two dimensional characters. Who really cared about the number of fabric squares Jane needed for her quilt, or the length of the shadows cast by those flagpoles? Nobody did. Everyone knew word problems were cheap instructional set-ups, math not even thinly disguised as story.

Why is this my business? Because I’ve worked, as a substitute teacher, with hundreds of students in elementary classrooms. I’ve felt their pain. And I say, along with Gerofsky, that word problems don’t have to be lifeless. We can do better. Together, we can build exciting story problems for tomorrow’s children. Or at least we can have fun with them on this blog.



As I was going to St. Ives,
I met a man with seven wives,
Each wife had seven sacks,
Each sack had seven cats.
Each cat had seven kits.
Kits, cats, sacks and wives,
how many were there going to St. Ives?





Elsewhere, in Tyrannosaurus related news: "Fossil Identified as mini-T-rex" What a story! Anastasia Suen featured Tyrannosaurus Math as a Picture Book of the Day, and it's now part of the 2010 California Collection by California Readers. Roar!

Booksigning at Chevalier's

Sending out a group hug to supporters who came out yesterday to encourage Tyrannosaurus Math as he took his first lurching steps out into the public! It was great fun dedicating books for you in the sunlit window of Chevalier's.

I'm 4tunate 2 have fan who are gr8 writers, 1derful teachers, steadfast friends-

and thank you from the bottom of my prehistoric heart.

We're planning to serve freshly baked dinosaur cookies at the inaugural book signing for TYRANNOSAURUS MATH

Saturday, September 12
11 am - 1 pm

Chevalier's Books
126 N. Larchmont Blvd.
Los Angeles CA 90004

(323) 465-1334.

A big thanks to gracious blog hostess Tina Nichols Coury for posting our Q and A on her site.

In other news, I taped an exclusive TV interview with dino host Rex Green! I nearly got my fingers nibbled off, but I'm hoping it's a good career move.

So here at The Cat and The Fiddle thoughts drift to the end of summer, of summer fruit, and fresh fruit pies. Which brings back memories of EACH PEACH PEAR PLUM by Janet and Allan Ahlberg (Viking), a perfect confection of a children’s book.

My daughters and I loved the sweet and humorous illustrations, the little poems, the hunt for the hidden nursery rhyme and fairy tale characters, and the comforting ending where the whole gang eats their wedge of plum pie together on a checkered tablecloth under the fruit trees. (What a classic last scene, characters communing over food...)

I’m a fan of fairy tale retellings, (including fresh POVs), but this book revealed how characters behave in their down time, when they’re not busy resolving conflict in their narratives. It was a surprise, for me, that Robin Hood, Cinderella, The Three Bears, Mother Hubbard, Tom Thumb, Jack and Jill, Baby Bunting and even the Wicked Witch were all part of the same social network. I suspect I’m not alone in wanting to know more about the secret lives of these beloved characters. Who’s eating tarts with whom. “Behind the Nursery Rhymes” if you will.

And while we’re on the subject, why don’t we hire these kid lit celebrities to liven up some “story problems” in the classroom. If Cinderella arrives at the ball at 10:15, how much time will she have before her coach turns back into a pumpkin?

More on story and math, later. I’m going out for one last piece of peach pie, before summer's over.

So you've pointed your mouse to The Cat and The Fiddle, where I'll be serving assorted thoughts on children's books, writing, and teaching.

Today the specialty of the house is:

ROARRR! My new book Tyrannosaurus Math, illustrated by Doug Cushman (Tricycle Press/Random House.)

We've got five fresh copies of T-Math to offer in a book giveaway, courtesy of my publisher.

To enter the contest, blog about this post and send me the link, OR
post a comment to this thread, recommending your top five trade math books for kids published within the last five years. Use only a valid email address! Winners will be selected at random in two weeks.

To get you up to speed about the book, here's most of the review from SLJ:


From the moment Tyrannosaurus Math (T-Math for short) is hatched, he views the world in mathematical terms. He begins with simple addition (how many siblings have also hatched) and proceeds through such skills as grouping (counting a herd of triceratops, though he’s not yet old enough to consume them), ordering and comparing (who ate the most dragonflies), and geometric shapes (is that meteor a sphere or a cube?). In all, 15 concepts are demonstrated with clear, logical, and amusing examples...

Markel never misses an opportunity to weave math into the lively text: “At his full size, nothing was scarier than the sight of T-Math thundering through the forest, chewing on a problem in his head.” Cushman’s acrylic cartoons, with their clean lines and vibrant colors, add considerably to readers’ enjoyment....This is a clever addition to the growing number of books that make a sometimes daunting subject both more understandable and just plain fun.





The book is riddled with puns, and I love how other reviewers have gotten into the spirit:

"T-Math's enthusiasm for numbers and solutions to real-world problems makes this a title that math teachers can sink their teeth into." -Kirkus

"Roaring, rampaging, and arithmetic. Markel uses a perennial favorite—dinosaurs—to introduce basic mathematical concepts through word problems featuring a young T. rex with a head for numbers." -Booklist


I'm delighted to share this interview with Doug Cushman, my wonderful illustrator.

What kind of research did you do for Tyrannosaurus Math?

When I was working on the sketches for this book, I had already planned a trip to London so I took the opportunity to go to the Natural Science Museum there and go through their extensive research library. I was mainly concerned about foliage, plant life, different kinds of insects, etc during the late Cretaceous era (where you set your story & I know how particular you were about all of that, rightly so). I always like to add special detail and asides in the pictures. And of course I took photos of the T-Rex automaton they have on display there.



What was the most challenging aspect of illustrating the text? The most fun?

Just drawing and painting all those wonderful dinos was a kick. I confess I especially enjoyed the spread during the hurricane. The painting style I used was fairly new for me, I’d only used it twice before. But the bright colors and shapes seemed appropriate for your text. It was fun painting again in a different way. I’m no math scholar so trying to figure out a good way to illustrate simple math concepts was a real challenge. The hardest was designing those groups of triceratops. T-Math was a little kid so how to show the four groups of five but keep the size relationships real? It took weeks before I finally hit upon the idea of standing T-Math on a cliff overlooking the herds. Duh!

How do you decide what chunks of a manuscript to illustrate? Which ones will be 2-page spreads?

Pacing a picture book is the most important part of the process in my opinion. You want to make each page flow naturally into the next one but be true to the pace of the text as well. Your text was fairly easy as each page illustrated a single math idea. It was actually an easy manuscript to pace out. The challenge was to clearly present the math.

What was the role of the art director?

I worked mainly with the editor on this book. The AD is responsible for the whole look and feel of the book, choosing the font for the text, etc. She let me hand-letter the display type and the speech bubbles which was more work for me but I wanted to do it; it made the look of the book more fun (at least I hope it did). She also sent me the final layouts so I could design my illustrations with a better idea where she was going to place the text. A book is really a team effort!

If T-Math was your guest in Paris, what spot would you take him to?

Paris is a carnivore's paradise, lots of meat-eaters. I have a great little restaurant I go to every Thursday that serves an entrecote pour deux, a rib steak for two (though we'd probably have to order a couple extra). T math would be able to figure out the bill and the tip...he'd be the perfect dining partner!

More later!