problem solving, where as Asian students demonstrated confidence, and a high level of proficiency in problem solving based on symbolic manipulation (Silver, Leung, Cai 1995). The new study design would evaluate students on how well they solved a problem using a variety of methods in a controlled environment, instead of allowing them to choose for them selves. The intent was to isolate the method used for a specified problem. They hypothesized that American students would do better, relative to past performance, when solving problems that required visual methodology. In contrast the null hypothesis was rejected. Chinese pupils outscored American students in all methods, with a score three times higher on visually based problems. This left researchers to conclude that American students were not as competent with visual representations as previously believed. Due to the flexibility of other nations in using a variety of methods, evidence was also found in support of existing research showing that flexibility in using a variety of representations correlates to success in problem solving (Dreyfus & Eisenburg, 1996). Lesh, Post and Behr (1987) stated, "Good problem solvers tend to be sufficiently flexible in their use of a variety of relevant representational systems that they instinctively switch to the most convenient representation to emphasize at any given point in the solution process (p.38)." Based on these and other similar studies (Beaton, 1996; McKnight, 1987; Mullis, 1997; Peak, 1996; Stevenson & Lee, 1990), we can conclude that there is a need for curriculum reform in the United States. If there are deficiencies at the secondary level, then we must assume that these same deficiencies exist at all levels, due to the inter-relation of mathematics. These studies are relevant in establishing the need for reform, and in the case of Brenner, Herman, Hsiu-Zu Ho, and Zimmer (1999), constituting what type of reform will be m...