Since the appearance of the 1980 Yearbook of the National Council of Teachers of Mathematics (Krulik, 1980) and the more recent appearance of the National Research Council's Adding It Up: Helping Children Learn Mathematics, problem solving has been viewed as an essential focus of mathematics learning. Yet the chances are good that two people talking about problem solving are not talking about the same thing. All too frequently, problem solving is understood to be activities that apply computational skills that have been taught in a textbook. For the most part, textbook problem-solving exercises are just that: routine exercises. In this view, problem solving is "problem solving as context," as described by Stanic and Kilpatrick (1988). It is intended to relate mathematics to real-world situations, provide motivation, and provide additional practice. A second definition of problem solving that emerged in the 1980s is that of "problem solving as skill" (Stanic and Kilpatrick, 1988), which acknowledges that problem solving is a worthwhile goal in itself and that students can become proficient in this skill by mastering a set of strategies that are taught and practiced as individual skills. Many current mathematics textbooks introduce a set of such strategies, devoting one lesson per grade level to explaining the surface features of each strategy. For example, the strategies shown in Figure 1 represent a useful and robust set of strategies to introduce for middle-school and intermediate students. A third view of problem solving, "problem solving as art" (Stanic and Kilpatrick, 1988), is that problem solving is a highly creative process. In this view, problems are not repetitious, do require some thought and perseverance, and often include missteps by the problem solver. Problems in this sense often lend themselves to more than one method of solution and may require more than one strategy if they are to be solved successfully.