Representational Choices for Problem Solving

摘要

An important aspect of teaching is enabling students to analyze and solve problems in a manner most suitable for them. Some people can quickly visualize the effects of a formula. Others may first solve problems with a hands-on model approach, a diagram, or a wordy description. In this paper, we illustrate a variety of representational choices through two familiar problems / methods: the Towers of Hanoi problem and the Bucket Sort. In a broad sense, some representations of solutions may be viewed as "extensional," while others are "intensional." Depending on the predilections of the problem-solver, either approach, in general, may be preferred We emphasize the importance of making good representational choices when attempting to solve problems. Hand in hand with the understanding of a problem, developing an algorithm for its solution, and the actual solution process and its testing, is awareness of the importance of representational choice. Such awareness is certain to enhance development of students' problem-solving skills.