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Essay Paper on Graphing Calculators

A Troubled System Students begin the study of algebra. The numbers of those who do not understand are gradually reduced. They struggle at first, and eventually most begin to understand. Or do they? Studies would suggest otherwise. A great amount of research has been done in the past decade in an attempt to find out why Americans are consistently near the bottom on international comparative studies in mathematics. The minimum requirements of most universities establish a passing high school grade in one algebra, and one geometry course, as necessary for acceptance. Failure to meet these requirements excludes thousands each year from college entrance.A significantly large percentage of those who do pass, enter college with deficiencies in mathematics. Even upon completion of “college algebra” the struggle is not over. Calculus is the final summit that looms over the prospective college graduate. Demana says, “Though college students may have had as much as 2 ½ years of algebra instruction, one of the most common complaints that we hear from our colleagues about college calculus students is that the algebra preparation for calculus is very poor. And it is our experience that this criticism is a valid one.” International Comparison American performance when compared internationally is alarmingly, but not surprisingly weak. In a recent study that compared four nations, the United States was ranked last. In most areas of relevance, Americans were three to five times behind the other countries.

The focus of much research on international mathematics competency has been the ability of the pupil to obtain a correct answer. In the study entitled “Cross National Comparison of Representational Competence”, the authors take a unique approach. Past research establishes that American students tend to utilize a visual technique in problem solving, where as Asian students demonstrated confidence, and a high level of proficiency in problem solving based on symbolic manipulation. 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.

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