From Cake to Calculus
If academic rigor in a play-based pre-kindergarten program sounds as if it is an oxymoron, read on. If you are the parent of an older child and you wonder what such a story could possibly tell you about a school’s math program for students in grades one through eight,
It is discovery time in the pre-kindergarten. Various activities are available for exploration while the teachers move about the classroom assessing and shaping student participation.
A student is “playing with” a set of wooden cakes. Each cake has a number emblazoned on it and corresponding holes for wooden peg birthday candles. The teacher approaches the student and asks how many candles there would be if we combine the candles on the number 2 cake with the candles on the number 8 cake. “10,” the student says proudly.
The teacher follows up with several other pairs and discerns that the student knows the single-digit addition facts well. Then she says, how many total candles would there be if we combine the 8 cake, the 2 cake, and the 10 cake. The student is excited but at a loss. The teacher suggests supposing we take the 8 and 2 pair. The student affirms, “10.” Now can you add the 10? “20,” the student proclaims.
The student then wonders how many candles there are all together. “What if we use the strategy we used for adding three cakes?” the teacher suggests. She shows him the 8 and the 2 make 10. What goes with the 7 to make 10? What about the 6? In short order, the student has all the cakes save the 5 cake in a pair with a sum of 10. The teacher asks if the student can count by tens. “I can!” the student says. 10, 20, 30, 40, 50 and five left over—55!
In this lesson, the teacher has caused her student to practice scores of addition facts but just as important, she has expanded this child’s understanding of the concept of addition, introduced a strategy of pairing quantities, harkened to the role of place value, enriched (in a way that will catch on with other students) the use of mathematics manipulatives in the classroom. In short, pushed open the door to a world filled with quantitative relationships and allowed the student to recognize that the student had some tools for understanding that complex and beautiful world.
When I tell you that second grade students revel in the invention of mental math strategies to reach predetermined “numbers of the day;” or third graders to write equations that serve as shortcuts for figuring out how many toothpicks it takes to construct a row of 100 polygons (where each polygon shares one side with the next polygon in the row); or for fifth graders to determine how addition works in a 20 or base 2 number system—you will understand that the understanding of, and appreciation for, the idea that mathematics is an exquisite language we use to understand situations of quantity in the world begins with cake in pre-kindergarten.
If you wonder what the implications of this tale are for the teaching of all disciplines please come to visit, I would love to speak with you.