Drawing a picture is a problem-solving strategy widely encouraged by elementary mathematics textbooks and teachers. Indeed, drawing can be a powerful way of engaging many students, especially young ones, in representing and communicating their mathematical ideas. Children develop the ability to draw long before they learn to write, and the act and product of drawing are accessible to children of diverse cognitive, academic, cultural, and language backgrounds (children with visual impairments are an obvious exception). The power of drawing as a problem-solving strategy can be observed as young children draw solutions to problems that involve mathematical concepts beyond the level of the mathematics they have studied. The shortcoming of drawing as a problemsolving strategy is that some students favor drawing even when that strategy is the least efficient or viable for finding a solution. Although there are good reasons for asking students to draw when solving a mathematical problem, teachers must also consider what they themselves know and do not know about children's drawings and what sense they make of such representations.
Sandra M. Crespo is interested in teaching practices that engage students in thinking and reasoning mathematically.
Andreas O. Kyriakides is interested in the nature of visualization and the didactics of mathematics.
Edited by Cindy Langrall, Langrall@ilstu.edu, a professor in the mathematics department at Illinois State University, Normal, IL 61790-4520. “Research, Reflection, Practice” describes research and demonstrates its importance to practicing classroom teachers. Readers are encouraged to send manuscripts appropriate for this department by accessing tcm.msubmit.net.