Quality Literature as a Springboard to Problem Solving
Ducolon, Colin K., Teaching Children Mathematics
High-quality children's literature that is captivating for both students and teachers can be used to develop process skills and essential knowledge in children. The provocative power of a "good read" is limitless. Listening to or reading a good book allows all of us, young and old, to think, reason, solve problems, compare and contrast, critique, and communicate in both old and new ways. The educational potential of a well-executed children's story can change how teachers plan their curricula.
Creating Problems from Caps for Sale
In my twenty-five years of working with pre-service teachers and young children, I have never been disappointed in the power of high-quality stories to evoke enthusiasm and interest in both the college students and the children with whom they work. This past year, several of my college students and I decided to use a well-known book, Caps for Sale (Slobodkina 1987), with children ages five through eight as a springboard for mathematical problem solving. In this story, a peddler walks through neighborhood streets and country roads selling the gray, brown, blue, and red caps that are balanced on his head. When he stops for a rest, several clever monkeys steal his caps and the peddler must find a way to trick the monkeys to retrieve them.
We often act out the caps-for-sale story with preschool children. With children in primary grades, more complex problem-solving tasks are possible. Activities that involve ordering the four colors of caps and selling the caps for fifty cents suggest several problems requiring mathematical reasoning and problem solving. Our goal was to help children connect conceptual knowledge, or understanding how and why to do something, with procedural knowledge, or knowing the rules (Payne 1990).
As we planned problems for these young children to solve, we kept in mind the extensive work done by Kamii in explaining how children must "reinvent" procedures if they are to understand them fully (Kamii 1985). Both the National Council of Teachers of Mathematics's Standards (1989) and Vermont's Framework of Standards and Learning Opportunities (1996) emphasize the importance of problem-solving skills for children to truly understand mathematics.
We developed five levels of problems for students in kindergarten through third grade. The pre-service teachers knew that the problems they developed had the potential to challenge the thinking of five- through eight-year-olds, and they encouraged the students to invent their own approaches to solving these problems. For each class, the student teacher or I read the story to, and discussed it with, the students before presenting the problems, and all work was completed in a one-hour period. The examples selected for this article are representative of each class, although some children were unable to complete the problems presented to their classes. Student teachers were able to conduct follow-up sessions with all children in subsequent class meetings. We present these examples in order of complexity rather than by grade level.
For kindergartners, we began with a simple task of patterning the caps on the peddler's head. For simplicity's sake, we restricted our choices of hat colors to red, brown, and blue and did not use gray. Evan, a child in our campus lab school kindergarten class, was eager to place the red, brown, and blue caps on the peddler's head (see fig. 1). His vertical placement of the blue-red-brown pattern, although quite simplistic, became somewhat more complex when he added the letters b for blue, r for red, and br for brown. Evan used logical reasoning to continue the blue-red-brown pattern well beyond the hats that were on the page.
Many of the kindergartners could create patterns on their own. This task required them to notice similarities and differences and to use these observations to create a repeated design. Such a skill is important for many components of mathematical thinking. …