Who's Behind the Fence? Creating a Rich Learning Environment with a Nontraditional Problem

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When a teacher encourages a classroom environment in which students share various solution strategies with each other in written, oral, and visual forms, excellent opportunities arise for students to learn from their peers. Equally important, the teacher is able to develop an understanding of the students' thinking and to use that knowledge to drive the curriculum. This classroom environment is as important at the preschool and kindergarten levels as at other grade levels. However, finding appropriate problem-solving activities at the preschool and primary grades may be more challenging because of the limited knowledge, experiential background, and writing skills of younger students. However, the following scenario illustrates that kindergarten classrooms can become rich environments to develop each student's mathematical power (NCTM 1991).

A problem-solving environment can grow out of contextual situations. If a student does not have a seat, the situation becomes a problem-solving activity with the question, "How can you solve that?" If a student cannot reach the light switch, the same question is asked. In these situations, many solutions are usually suggested, and students soon realize that they must think and that their thinking is valued. Problem-solving activities that focus on mathematical ideas can be word problems centering on classroom routines, such as the distribution of drawing paper or division of crackers at snack time; games requiring the player to find a solution to move a game piece forward (Kamii 1985); and situations involving nontraditional word problems that cannot be solved algorithmically. The animal problem that follows is an example of the latter problem type.

There are some animals behind the fence. You can see four heads sticking out from the top of …