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John Paolos' "Innumeracy: Mathematical Illiteracy and Its Consequences", 1991.
This paper is a critical review of John Paolos' "Innumeracy: Mathematical Illiteracy and Its Consequences".
1,350 words (approx. 5.4 pages), 1 source, $ 47.95
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"In his book, Innumeracy: Mathematical Illiteracy and Its Consequences, John Allen Paulos uses the term, "innumeracy" in the same way that the term illiteracy is used: to represent an unfamiliarity and ignorance in terms of numbers and mathematics. Besides being well written and entertaining, the book is also informative in explaining common instances of mathematics in everyday life.
Paulos does not confine his discussion only to one aspect of numbers and mathematics. His book is replete with examples of statistics, probability and mathematics. He suggests, for example, that we develop a "safety index" for certain activities or events which would provide the populace as a whole with a quantitative way to evaluate their activities. While such an idea may seem farfetched, it illustrates an idea which occurs .. "
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"The History of Calculus" by Carl B. Boyer, 1991.
This paper reviews "The History of Calculus" by Carl B. Boyer, the evolution and philosophy of this mathematical discipline.
2,925 words (approx. 11.7 pages), 1 source, $ 103.95
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"The purpose of this research is to examine "The History of Calculus" by Carl B. Boyer. The plan of the research will be to set forth the general ideas in the book, and then to explore details contained in the book that summarize the concepts of calculus that Boyer wants to emphasize.
Boyer's The History of the Calculus is put forward as one of the few histories of how the discipline of calculus evolved, apart from an explanation of how to use it mathematically. It is by positioning the ideas of mathematics and philosophy that influenced calculus that Boyer gradually moves toward an explanation of how calculus can actually be used and applied. The background of Boyer's approach appears to be the idea that a richer understanding of how calculus came to "be" in the world of ideas can lead to an understanding of how it can be employed in ... "
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Statistical Analysis Applied to Unemployment Problems, 1990.
This paper explains the application of statistical procedures to the solution of a realistic problem; in this paper, the U.S. unemployment problem.
1,800 words (approx. 7.2 pages), 6 sources, $ 63.95
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'The purpose of this research is to explain the application of statistical procedures to the solution of a realistic problem. In this instance, the problem is related to the domestic economy of the United States.
THE PROBLEM
The level of unemployment is a matter of significant concern to both the general public and political leaders. In order to develop effective policies to address the unemployment issue, it is necessary to understand how the unemployment rate is related to other factors. It is this problem which is addressed in this research.
HYPOTHESES
A total of six hypotheses were formulated for, and tested in ... "
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Mathematics In Bilingual and Bicultural Areas, 1980.
This paper analyzes the study of mathematics in bilingual and bicultural environments including cultural and teaching impact., particularly in the Mexican-American communities.: games, cooking, telling time, bookkeeping number stories.
1,575 words (approx. 6.3 pages), 10 sources, $ 55.95
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"The purpose of this research is to examine and analyze the uses of mathematics in bilingual/bicultural environments, with specific applications as well as in specific communities.
Because of the Supreme Court decision (1974 Lau vs. Nichols) bilingual education is now mandatory (McNichols 111-15). Mathematics is an ever present, recurring part of daily life. This provides an excellent opportunity for the inclusion of bilingual/bicultural aspects in mathematics.
Because of this decision it now becomes essential to train bilingual teachers in all academic subjects and at all academic levels, including preschool. The states of California, New Mexico, Florida, Pennsylvania, Alaska, Arizona, Illinois, New York, Maine, Connecticut, and Colorado are "working toward ... "
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Behavior Analysis, 2002.
An analysis of an article by Davison, McCarthy, and Jensen, ?Component Probability and Component Reinforcer Rate as Biasers of Free ? Operant Detection", focusing on the issue of behavior analysis.
1,221 words (approx. 4.9 pages), 9 sources, MLA, $ 41.95
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Abstract
This paper is a written summary, including a discussion of the article ?Component Probability and Component Reinforcer Rate as Biasers of Free ? Operant Detection? by Michael Davison, Diane McCarthy, and Chris Jensen. The paper outlines the article, which is a series of experiments relating to behavior analysis in general, specifically the matching law and signal detection theory. The paper presents and summarizes the series of experiments designed by McCarthy et al., including all observations, results, and conclusions.
From the Paper
"This series of experiments was designed to test the applicability of the signal ? detection model of Davison and Tustin (1978) in free operant detection under two biasing manipulations. The first was variation of component frequency (The probability of presenting S1, a bright light, over S2, a dim light), which was varied in experiments 1a and 2a. The second manipulation was variation of the within-component reinforcer rates (reinforcement schedules one each key) in experiments 1b and 2b. Each variable was varied while holding the others constant."
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On the Right Track, 2002.
An analysis of the arguments against tracking of low-ability math students.
2,810 words (approx. 11.2 pages), 5 sources, MLA, $ 83.95
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Abstract
This paper examines a crucial problem in American education, poor student performance, specifically in math and science. The paper focuses on the method of tracking or grouping, and provides arguments against this method. The paper proposes a study in order to find a successful solution to the problem. The proposed study is outlined, including the desired outcome.
From the Paper
"Poor student performance is one of the most pressing problems in American education today. In particular, math and science scores lag behind those of other developed nations. Without a proper understanding of math, and mathematical concepts, today?s students will find themselves unable to compete in an increasingly technological world. They will not be able to find jobs, nor will American industry be able to compete successfully against its foreign counterparts. Though an essential part of the educational process, the how-to of improving students? mathematical skills remains problematic. Numerous approaches have been tried, but not all have been successful. It is for this reason, that the following study is being proposed."
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Higher Mathematics, 2000.
An examination of the major concerns, a public view of, practical applications, examples, probability theory and number theory.
1,575 words (approx. 6.3 pages), 11 sources, $ 55.95
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"Higher mathematics is a subject that has always seemed completely inaccessible to all but the select few who could breathe in the rarefied atmosphere of the intellectual plane where it lives. Just as mathematics seems to be beyond most people's intellectual grasp, however, it also seemed to make absolutely no difference to the great majority of the population. Number theory, probability theory, mathematical modeling, the mysterious math used in computer technology, and even statistics and mathematical reasoning seemed to have little to do with daily life, work, or anything that was of much interest to the average man, woman, or child. When a mathematician somewhere in Great Britain announced a few years ago that he had solved the problem of Fermat's Last Theorem the news made no difference to the vast majority of people, while a few, vaguely remembering the story of..."
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Sir Isaac Newton, 2000.
The impact of the discoveries and writings of the English mathematician on the evolution of scientific thought and practice.
1,575 words (approx. 6.3 pages), 8 sources, $ 55.95
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" Sir Isaac Newton (1642-1727) was one of the greatest scientists in history and, after an initial period of resistance, his discoveries, theories, and methods proved to be a major force in the emergence of modern science. Newton became the best-known scientist in the world and, even though most of the eighteenth-century public understood little of his work, his fame eventually provided the impetus to elevate scientific research to a new level of respectability. Other seventeenth- and eighteenth-century scientists participated in the general move away from the Aristotelian paradigm of science that had dominated the Western world for two millennia. But Newton's inspired work resulted in what has justly been called the Newtonian Revolution in science. Ironically, however, Newton's progress in mathematizing science and opening it up to the full play of scientific method meant..."
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Teaching Math, 1999.
Examines problems, evolving theories and techniques, examples, problem-centered instruction, curriculum, measuring performance, teaching standards and proposes a field trip to encourage problem solving.
3,150 words (approx. 12.6 pages), 15 sources, $ 111.95
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Abstract
In response to unacceptable levels of mathematics achievement in the United States many groups with an interest in the teaching of mathematics have called for reform (Niemi, 1996). The calls for reform are based on recent advances in cognitive theory that call for a more constructivist view of learning (Wood & Sellers, 1996).
From the Paper
"In response to unacceptable levels of mathematics achievement in the United States many groups with an interest in the teaching of mathematics have called for reform (Niemi, 1996). The calls for reform are based on recent advances in cognitive theory that call for a more constructivist view of learning (Wood & Sellers, 1996). Traditionally, mathematics instruction in the primary grades has consisted of teaching computational skills, drills, and simple word problems. Concepts now included in mathematics curricula are being changed to stress problem-solving skills, but the resources and teaching methods available to primary grade teachers are not keeping current with the new standards. In 1989, the National Council of Teachers of Mathematics (NCTM) began emphasizing the teaching of mathematical concepts and problem solving at all grade levels. In the years ..."
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Airline Competition & Game Theory, 1999.
Applies game theory to airlines' fare-setting. Description of economic & mathematical theory, modeling & strategies, yield management, zero-sum.
2,925 words (approx. 11.7 pages), 11 sources, $ 103.95
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"ABSTRACT
One research question was addressed in this study. That question is as follows: ?Can the competitive behavior of air transportation companies in the United States market in relation to setting fares be explained as an application of game theory??
Game theory, as applied in the airfare wars. forecasts how competitors will respond when confronted with certain competitive situations. When formulating business strategy, no company can afford to ignore how competitors will behave. Game theory is based on the premise that in any competitive situation there are factors at work which lend themselves to mathematical representation and analysis. In turn, these representations and analyses will help explain how a result will occur.
The findings of this research indicate that the airfares competition gives the appear.."
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Math and Achievement of Girls, 1997.
Examines causes & effects of gender gap in learning math, social sterotypes & teacher bias, anxiety & self-image, examples, cultural support and solutions.
3,150 words (approx. 12.6 pages), 20 sources, $ 111.95
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"The purpose of this review of literature is to examine factors that contribute to the under-achievement of girls in mathematics and projects and programs which have been used to remediate the situation. The review begins with a brief description of the problem, and ends with the formulation of conclusions regarding factors producing the problem and interventions that will reduce and or eradicate the problem.
Description of the Problem
In general, at both elementary and high school levels, boys tend to have higher achievement levels in mathematics than do girls; moreover, girls tend to have significantly more negative attitudes toward mathematics than boys (Froebe, 1996). In ..."
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Chaos Theory & Art, 1997.
Describes scientific theory of unpredictability of life & its relation to modern art (Picasso, Pollock, computer effects).
2,700 words (approx. 10.8 pages), 11 sources, $ 95.95
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"This paper is a study of the relationship between the relatively recent scientific development of chaos theory and art. Chaos theory recognizes and attempts to analyze the points at which regularity becomes unpredictable, form turns into formlessness, Euclidean geometry yields to pandemonium. This apparent abandonment of established order also describes the dramatic changes that inspired impressionistic art and most of what are now termed modern arts - wild breaks with traditional approaches to the representation of human beings and nature, even to the point of choosing nontraditional subject matter or no apparent subject matter at all. Just as the chaos scientists upset the establishment by ignoring disciplinary boundaries and ways of examining a problem, so too did .."
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Goals in Math Education, 1997.
Examines five goals of National Council of Teachers of Mathematics & ways to achieve them.
1,125 words (approx. 4.5 pages), 6 sources, $ 39.95
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"The National Council of Teachers of Mathematics has produced a list of five goals which students in a well-taught classroom should achieve. This paper will outline how these five goals can be attained by students in a fourth-grade classroom using the Saxon text, Math 54: An Incremental Development (Hake & Saxon, 1996). Examples of how to incorporate each goal individually into the class's lessons will follow.
A good mathematics curriculum will help a teacher instill these goals in students. The best method of disseminating these goals to students is within the context of mathematics study and through opportunities for cross-disciplinary teaching; the five goals cannot be effectively taught in isolation from one another or from other subjects.
The five goals can be summarized as follows: .."
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Quantitative Decision Making, 1997.
Examines process of decision making about probable future occurrences based on objective data & subjective insight, using Bayesian statical analysis.
2,250 words (approx. 9.0 pages), 8 sources, $ 79.95
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"INTUITION, EXPERIENCE, AND QUANTITATIVE DECISION-MAKING
Introduction
Quantitative decision-making is thought of most often as an objective exercise based only on the cold analysis of verifiable hard facts. Intuition and even experience tends to be excluded from quantitative decision-making on the grounds that such information is subjective in character, and, thus, has no role in quantitative analysis.
Quantitative decision-making is based in large part on the ability of decision-makers to make inferences about the probabilities of occurrence of future events from the analyses of objective data (Markowitz and Xu 60-69). One means of improving probability estimates in such predictions, however, is the application of Bayes? Theorem (Peebles 17-19). Classical .."
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Econometrics, 1997.
A mathematical analysis of economic problems. Discusses advantages, goals, methods, models, applications and limitations.
1,350 words (approx. 5.4 pages), 5 sources, $ 47.95
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"APPLICATION OF MATHEMATICAL METHODS IN ECONOMIC ANALYSIS
When mathematical methods and statistical techniques are applied to the analysis of economic problems and issues, the term usually applied to the process of applied economics is econometrics (Ekelund & H?bert, 1991, p. 372). The goal of econometrics is the development of valid, reliable, and value free predictive models of economic phenomena.
Alan Greenspan (1991, p. 52), Chairman of the Federal Reserve Board, stressed the importance of econometric models as a means of providing a clear understanding of economic events. He argued that the greatest advantage of a "fully articulated model is that it helps the forecaster keep track of the interrelationships among the primary variables of interest" (Greenspan, 1991, p. 53). Within the context of this argument, he ..."
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