Essay Paper on Graphing Calculators

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.

Lesh, Post and Behr 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.” Based on these and other similar studies, 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, constituting what type of reform will be most effective. Curriculums that focus on multiple strategies in problem solving are necessary for the improvement of mathematics achievement.

Studies indicating an epidemic of American incompetence in mathematics are not a revelation, but rather a confirmation of past research. The varieties of conclusions are related by one simple theme: The United States while tentatively the only superpower is not a superpower in mathematics. Our communist threat, China leads in mathematics supremacy.

What Is Algebra? The very center of mathematics comprehension, and problem solving is the function. The algebraic function (i.e., equation) is the most central concept taught to all students studying pre-calculus mathematics, and is the foundation for all subsequent course work in mathematics and many other disciplines. It is a dynamic concept that relates numbers to real life situations.

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