By Ameis, Jerry A.
Teaching Children Mathematics , Vol. 8, No. 5
One important recommendation of Principles and Standards for School Mathematics (NCTM 2000) is the need to involve students in problem solving. One way to understand the term problem solving is to examine two aspects of the process: (1) teachers' creating classroom cultures that facilitate learning through problem solving and (2) children's solving mathematical problems.
Children in elementary school enjoy being read or told interesting stories (Bainbridge and Pantaleo 1999). Storytelling can be a vital part of a classroom culture of problem solving (Lewis, Long, and Mackay 1993). For example, How Many Snails? A Counting Book (Giganti 1988) can be used to engage children in learning about numerical relationships. As they listen to an interactive reading of the story, they can think about, and respond to, counting-based situations in it. In doing so, children become engaged in the important processes of reasoning and explaining as they learn about numerical relationships. In short, they are learning mathematics through problem solving.
Storytelling or story reading can introduce the second aspect of problem solving, as well. A story can provide a meaningful context that motivates children to solve problems embedded in it. Consider the following excerpt from a fantasy adventure story written by the author while researching ways to engage children in solving mathematical problems:
Cheka saw the woomer first. Her hand signals warned Plasto to be ready for trouble. Cheka spoke to the woomer, "Hello friend. How can we help you?" The woomer replied, "Who are you? What village do you come from?" Luckily, Cheka remembered seeing a village name on the map of the island. She answered, "We come from the Village of Darda. We have been looking for new hunting grounds. Now we are on our way home." The woomer became less suspicious, but it still was ant convinced. It said, "Villagers from Darda are good at solving puzzles. Solve this one."
Cheka and Plasto happily agreed. After all, any puzzle that a creature such as the woomer might know cannot be too difficult Then the woomer described it: "Draw a 6 x 6 grid on the ground. Place 12 pebbles on the grid so that each row, column, and diagonal has exactly two pebbles on it." Cheka and Plasto gasped when they heard the puzzle, but they quickly found the pebbles and drew the 6 x 6 grid. The time had come for some serious thinking.
Would a child of elementary school age want to solve the problem about the 6 x 6 grid, as well as other difficult problems? The author's work with children indicates that the answer is yes. The following description of one part of that work explains this conclusion.
Working in Difficult Conditions
The setting was an after-school day-care center, and the research involved six boys and seven girls, eight of the children being in grades 1-2 and five of them, in grades 3-4. I met with the children almost every Friday from October through April. My purpose was to investigate how children might be engaged in mathematical problem solving under difficult conditions. One reason for the research was to uncover potentially fruitful and fundamental ways to engage children in problem solving. In elementary school, children may prefer not to engage in problem solving, but they typically do so, at least partly because schooling influences them to do as the teacher expects. The day-care setting offered a way to investigate engagement in problem solving under conditions where the influence of schooling was unlikely to be a factor.
The day-care setting presented sufficiently difficult conditions. As might be expected, the children did not view 4:00 P.M. on Friday as a time for mathematics. This feeling was intensified by the fact that most of them did not like mathematics, a sentiment that became evident when I was introduced as someone who was going to do mathematics with them and when I interviewed the children individually. …