The following review of 2019 Mathical Award Winner Crash! Boom! A Math Tale was submitted by Mathical Selection Committee member Dr. Herbert Ginsburg.
This saga, as seen through the eyes of a winsome little blue elephant, shows how block building, and a children’s picture book that portrays it, can be rich in mathematical ideas. The elephant is gender-less and name-less, but I am going to call her Ellie, for ease of reference (and grammar), and because we need to see more girls playing with blocks.
At the outset, Ellie carefully begins with 1 block (a rectangular prism) and then places on it, as the text shows, “1 more.” Ellie then sets herself a measurement task, “I want it to be as tall as ME!” To achieve this goal, she asks, “2 more?”, as she places the blocks not very carefully one upon the other, until she has created what she acknowledges as “a little…wobbly” tower. When the tower is up, Ellie counts to four and is extremely happy that she has created a tower to match her own height.
To this point, the book has set out an apparently simple measurement task in which Ellie reveals her thought processes as she tries to make the tower equivalent in height to her own. Several features are notable.
First, the story involves a task and a goal familiar to young children: they love to play with blocks and they are definitely interested in their height, a concern that is likely fueled by adults’ focus on their growth.
First, the story involves a task and a goal familiar to young children: they love to play with blocks and they are definitely interested in their height, a concern that is likely fueled by adults’ focus on their growth. “Look at how tall you are now! You are a big girl!”
Second, the author “mathematizes” the story from the outset. From the first page, the text highlights the written numerals 1, 2, 3, 4, and math language, “more,” “as tall as ME!,” and “it’s up,” referring to the blocks stacked to make the tower. In the background, but not mentioned, are blocks, all rectangular prisms, of different lengths, small, medium, and large.
Third, Ellie reveals her thinking as she goes along. She sees the beginnings of the tower and wonders how many more blocks will be needed to complete the edifice. This problem is the beginning of addition. Further, by carefully counting the blocks, Ellie engages in measurement, which reveals that “It’s as tall as ME!”, meaning that the two heights, Ellie’s and the tower’s, are equivalent in length. Note too that Ellie—deliberately or not—used a common unit to measure height: all of the blocks were the same size. So much mathematics in the first several pages alone! Block play can be a rich opportunity to explore mathematical ideas.
But Ellie’s mathematical rapture is short-lived. The blocks crash down (hence the title of the book, “Crash! Boom!”), leaving Ellie feeling blue (hence her color?). Indeed, the episode leaves Ellie in tears (4 from each eye). Ellie is not happy that “It’s not tall anymore. It’s shorter than me.” In other words, Ellie realizes, and tells us very clearly, that the initial equivalence has been destroyed, resulting in an unwanted height difference. Ellie is also clear on the corrective action required: what’s “down” has to go “up” in order for the tower to be as tall as Ellie.
To restore the equivalence, Ellie needs to figure out how to make a more stable tower. Ellie’s conjecture is that If the block is placed in the up position, with the narrow part on the ground, it may be less stable than when in the flat position.
So Ellie decides to stack the blocks in the flat position, discovering that when 4 have been stacked the tower is still not tall enough. More are needed. Eventually, Ellie is again successful, having placed 8 blocks, in the flat position, in a tower the height of which is equivalent to Ellie’s. The mini math lesson is that 8 blocks in the flat position are needed to do the work of 4 identical blocks in the up position. An algebraic solution is almost visible.
But you will not be surprised to learn that disaster strikes again, this time because giddy Ellie backs into the tower, knocking it down, with another unfortunate CRASH! BOOM!
Ellie is thoughtful, wondering, “What if?” What would happen if the blocks were to be stacked in different ways? Having a eureka moment, Ellie then stacks the shortest blocks on their flat sides, followed by the identical shortest blocks in the upright position, and then the next longest blocks in the upright position, and then the very longest blocks, again in the upright position. The result is spectacular:
We see that the 8 small blocks in the flat position are matched by the 4 small identical blocks in the upright position, the 2 next tallest, and the 1 tallest. There are so many measurement ideas in this picture! All of the stacks are equivalent in height; measurement can determine equivalence by using different units, so long as all are the same; and from left to right, the number of units is always twice the number of the previous. Can you find more?
What happens next? Nothing. The author does not comment on Ellie’s construction. Is the lack of elaboration a good idea? Perhaps she was avoiding being pedantic; it would be counter-productive to turn this little gem of a book into a math lesson. On the other hand, it might have been useful to have Ellie observe, “Look, there are two of these next to one of these over here. And over here too.” Saying something like this might involve the adult reader and child in an interesting discussion about measurement. If you agree, you can pursue measurement ideas with the child when you read Crash! Boom! A Math Tale.
Crash! Boom! A Math Tale
By Robie H. Harris, illustrated by Chris Chatterton
Candlewick Press, 2018
2019 Mathical Honor Book, PreK
Dr. Herbert Ginsburg is the Jacob H. Schiff Foundation Professor Emeritus of Psychology and Education at Teachers College, Columbia University. He has conducted basic research on the development of mathematical thinking, with particular attention to young children, disadvantaged populations, and cultural similarities and differences. He has drawn on contemporary research to create mathematics activities (Big Math for Little Kids) and storybooks for young children, tests of mathematical thinking, and video workshops to enhance teachers’ understanding of students’ mathematics learning. He is now developing materials designed to help teachers and parents engage in mathematical book reading with their children.