From the Paper "A History of Mathematics in America before 1900
A History of Mathematics in America before 1900 was written by David Eugene Smith and Jekuthiel Ginsburg and published by The Mathematical Association of America in cooperation with The Open Court Publishing Company in 1934. It is one of a series of monographs entitled, The Carus Mathematical Monographs.
The book is organized historically, covering the uses of mathematics, the development of mathematics instruction and research, and discussion of the important names in mathematics in America from the earliest settlement to the year 1900. The book is divided into four chapters, each chapter dealing with a particular time period in chronological order. The authors closely relate the development of mathematics in this country to the development of education and instruction of math, with ..."
Research proposal for teaching math skills in Saudi Arabia to children at the same grade level, but at variable degrees of proficiency, using individualized instruction.
2,700 words (approx. 10.8 pages), 11 sources, 1993, $ 95.95
From the Paper "Teaching Mathematics to Elementary Children in Saudi Arabia With the Use of Individualized Instruction
Background of the Problem
While Christian Europe was slumbering through the darkness of the Middle Ages, the Middle East experienced its own renaissance of the arts and sciences, including mathematics. It is, after all, the Arabs who invented the concept of zero, along with Arabic numerals, and developed a sophisticated system of mathematics before the scientific revolution entered the European continent. This scientific outpouring did not last, however, and much of the Middle Eastern civilization that developed during the early Islamic period declined into quiescence (Nyrop, 1977)."
Ancient Greece to 1990s. Major figures & discoveries of mathematics. Looks at principles, calculus, physics, specialization and algebra. Compares the attitude differences between U.S and Japan.
3,600 words (approx. 14.4 pages), 16 sources, 1993, $ 127.95
From the Paper " The Evolution of Mathematics:
The American and Japanese Perspectives
Elementary forms of mathematics have probably been with man throughout his evolution. As human societies advanced, so too did mathematics. From the 1500s to the present, a long lineage of mathematicians have revolutionized the field. These men were often of European origin. Only in the last century has the United States and Japan emerged as dominant mathematical forces. At present, either of these nations could lead the field into the future.
The first systems of numeration were invented by the Greeks and the Romans (Struik, 1987, p. 80.81). Later, the Western merchant, Leonardo of Pisa, introduced the Hindu.Arabic system of numeration into Western Europe. Europeans came to accept these.."
From the Paper "Leonhard Euler (1707-1783) published his first mathematical work in 1726, one year before Isaac Newton's death. Euler's enormous gifts and broad interests were ideally suited to this slot in history. In pure mathematics and mathematical physics, his work elaborated that of his predecessors, such as Newton and Leibniz, and exerted an enormous influence on those who followed him. Euler also systematized, standardized, and generally cleared the way for mathematical applications in numerous fields. In the course of his long and productive career, Euler "worthily united the ages of Newton and Gauss" (Morgan 133).
Euler was the most prolific mathematician in history. During his career, he published around 560 books and articles, and still left a backlog of over 300 works at his death. The St. Petersburg Academy did not finish publishing his "literary ..."
Abstract This paper discusses the life and work of Isaac Newton and how his laws and discoveries have ensured that his name is imprinted in the history of science. The author illustrates how Newton is not only one of the greatest scientists but also one of the most influential scientific personalities.
From the Paper "Isaac Newton was the greatest and the most influential scientist of all times. Born in Woolsthrope, England on a Christmas day in 1642 Newton was a bright child with an incredible mechanical aptitude. Newton entered the Cambridge University when he was eighteen years of age and soon he mastered the science and mathematical concepts of his time and went on to continue his independent research. It was during this period that Newton laid the foundation for the subsequent discoveries that were to revolutionize the scientific world. Newton was conferred the honorable Fellow of Royal Society of London in 1671."
Abstract This paper aims to provide information on generalization of existence and uniqueness theorem for ordinary differential equations (ODE). This contains mathematical definitions, notations, symbolisms, formulas, graphics, and equations of the theorems mentioned. A few examples were also provided to illustrate and prove the definitions of the theorems.
From the Paper The fundamental theorem of Existence and Uniqueness answer the questions does a solution exists and is it unique. If at least one solution can be determined for a given problem, a solution to that problem is said to exist. Frequently, mathematicians seek to prove the existence of solutions (by means of a so-called existence theorem) and then investigate their uniqueness (by means of a so-called uniqueness theorem). The solutions to an ordinary differential equation (frequently abbreviated as ODE) satisfy the existence and uniqueness properties.
The foundation of the theory of differential equations is the theorem on the existence of solutions for the initial value problem
x = f ( x ), x ( t o ) = x o
for a function x: R - Rn and f: Rn - Rn The main tool that we will use in developing our theory is the reformation of the differential equation as an integral equation. Suppose that both x(t) and f(x) are continuous functions. Then we can formally integrate both sides with respect to t to obtain:
x ( t ) = x o + ....
Abstract This paper discusses the lives of Archimedes and Carl Friedrich Gauss, two of the greatest mathematicians of all time. The paper provides a point by point comparison of their childhood and education, outlines each of their mathematical contributions and examines the influence their work continues to have on the science of mathematics.
From the Paper "Far more details survive about the life of Archimedes than about any other ancient scientist, but scholars disagree on which details are fact and which are anecdotal. The most famous Archimedes story centers on how he determined the proportion of gold and silver in a crown made for Hieron through measuring water displacement. Since he supposedly made the discovery while in the bathtub, the excited Archimedes ran naked through the streets of Syracuse shouting ?Eureka!? (Muir 20)."
Abstract This paper examines the question of how to reverse the trend of lack of educational progress, specifically in the world of mathematics. This is considered through an evaluation of three elementary schools' stated mathematics curriculum, and how they compare to the standards of the National Council of Teachers of Mathematics published standards. The process of this evaluation is a point by point comparison between the NCTM standards and the printed curriculum guidelines for these schools. Specific points which are supportive, and which may fail to reach the guidelines are identified and discussed for each school. The purpose of this evaluation is not to approve or reject these curricula, but rather to identify specific applications which can be either improved through change, or strengthened by building upon existing positive initiatives.
Introduction
Discussion of the NCTM Standards
West New York Public Schools, West MY
Bogota Public Schools, Bogota, NJ
North Bergen Public School System, North Bergen, NJ
Bibliography
From the Paper "According to national statistics, the mathematical educational progress of American elementary students has failed to keep progress with the rest of the world. This stinging indictment of the educational system of the most technologically advanced culture in the world has caused a serious evaluation of the standards and goals of the elementary system. According to the National Council of Teachers of Mathematics, there are knowledgeable teachers in the system. The teaching staff has adequate support and resources. In a society which depends daily on mathematics, there is opportunity for students to learn and apply math principles and facts. There also is an abundance of access to technology to support the educational process. Finally, if students are considering careers, those in math related fields, such as engineering, financial planning, accounting and many others are some of the highest paying positions in our current job market."
Abstract This paper examines the bove book which discusses every imponderable imaginable right from the mundane ones such as lottery odds, predicting a child's height, baseball arithmetic, to more complex ones including Windchill equivalent temperature, carbon dating, Newton's relativity theory and synchronous satellites. It shows how the book improves one's problem solving skills by making them think about imponderables and also aids one's understanding of mathematical concepts and sheds light on their useful application in our everyday lives. It evaluates how the book is also an attempt to improve numeracy among American public by making them more aware of the usefulness of mathematics in their lives.
From the Paper "The book begins with calculation of distance between one particular point and the horizon. Brookhart gives a simple geometric formula to predict the approximate distance. A casual look at these formulas in the beginning of the book prepares the reader for what comes later. However the very simple tone of the book is what arouses skepticism in readers. Some have even pointed out the errors they found in the book. For example the rejection of Goldbach's well-known assumption that "no one has ever found a number greater than 2 that could not be expressed as the sum of two prime numbers" is one such error."
This paper looks at the cases of John Nash and Anais Nin who both grew up in troubled households and later developed severe emotional and psychological problems.
Abstract This paper examines the emotional scarring that children undergo as a result of abusive or neglectful parents. It follows with a look at their lives and it concludes with specific examples of parental abuse and its impact on the children's lives as adults.
From the Paper "Anais Nin on the other hand went through different though equally disturbing experiences as a child, revealed in her book, Dairy of Anais Nin. She, like Nash, grew up in a family where father was the culprit. Her parents had an abusive relationship and fighting was a regular feature of their troubled marriage. He proved to be anything but a good father when he would openly make sexual advances to Anais and would regularly spank the children. Despite occasional periods of apparent tranquility, the family hardly ever felt harmony and real peace because Anais' parents would argue incessantly. This had a bad impact on Anais who it is believed developed psychological problems, as she often experienced bouts of depression, which she was able to overcome with the passage of time. Though her personal journals and dairies were received well by the public, she was nonetheless accused of lying in her diaries by some of her critics."
Abstract Matthew Rabin's model of fairness is based on Geanakoplos, Pearce and Stacchetti's (1989) notion of "psychological game", in which payoffs depend on actions and on beliefs about actions. The paper describes how Rabin's model shows how fairness expectations lead to different results than standard theory and demonstrates some general implications of fairness on game theory and economics. This paper contains a short description of Rabin's model, gives some examples, propositions, proofs and critique.
From the Paper "Suppose that (a1,a2) is a mutual-max outcome. Then both f1 and f2 must be nonnegative, thus reflect a positive regard for each other.
If each player chooses a strategy which maximizes both his own material well-being and the well-being of the other player this must maximize his own utility. In a case of mutual min outcome the f1 and f2 is non positive, thus, f~j(bj,ci)[1+fi(a1,bj)] is non negative. If each player is choosing a strategy which maximizes his own material well-being , this must maximize his utility."
Abstract This paper explores the general perceptions of Horace Barlow, reflected in his paper "The Exploitation of Regularities in the Environment by the Brain", pertaining to the role of evolutionary internalized regularities, especially as they occur in theories of vision. The focus lies principally on issues relevant to the ecological validity of Shepard's kinematic geometry constraint in ordinary motion perception perspective. This paper also establishes the thought for two individual sets of assertions; perception of apparent motion modeled as kinematic geometry theory and internalization of the like.
From the Paper "The limitations of kinematic geometry proposed in Barlow's paper have been recognized, however kinematic geometry being a model for perception of apparent motion in my opinion is an idea that can expand into new dimensions. However internalization of kinematic geometry does project reservations about being a possibility. As indicated by Barlow, internalized principle of object observation gives way to the perception of apparent motion. The human brain's support for a percept is purged from an external stimulus. Conforming to the putative universals are the preferred perceptual solutions. "
Abstract This paper begins by providing a history of the evolution of zero and discusses the origin of the symbol. It then discusses the origins of the concept of "zero" and how this was perceived differently by various ancient cultures such as the Egyptians, the Mayans and the Babylonians. It then focuses specifically on the "Babylonian zero" and how this differed in concept from other figures at the time. The paper includes several diagrams and pictures.
From the Paper "The symbol zero evolved into its present form after quite a number of transformations. The idea of how the symbol was devised also harbors a few contradictory ideas. Opinions range from it being a dot originally, replaced by a circle with a dot in the center and then maturing to the current form, an oval shape that we all are familiar with. (Pearce, I., 2002). The Egyptian zero that evolved has also been equated with the hieroglyph for beauty, and that of the human windpipe, heart and lungs. (Williams, S. W., 2002)"
Abstract Details the current teaching and testing methodologies in high school mathematics classes. Also discusses some alternative strategies for teaching math that have been employed at the secondary school level.
Outline
Current Teaching and Testing Methodologies in High School Mathematics
Classes
Alternative Strategies for Teaching Math Employed at the Secondary
School Level
Learning Concepts and Mathematics Education
The High School Environment: Putting it all Together
Conclusion
From the Paper "As I have stated, the perceived general needs of the high school can be seen as duo-fold: to provide an education that encourages excellence to exceptional students, and to provide an education that encourages competency to average students. Based on the size, location and level of heterogeneity at any particular school, these needs attract varying degrees of attention."
Abstract This paper considers the problem of low math scores for American elementary students and looks at how there are considerable differences between Chinese and American teachers and how these differences account for the poor performance of American students. It also analyzes how the problem goes beyond the teachers themselves, with the base cause being the American approach to mathematics.
Outline
Possible Explanations for Low Math Scores
Comparing Elementary Mathematics Teachers
The Problem with American Mathematics
Conclusion
From the Paper "Ma argues that the American approach to teaching mathematics is based on teaching procedurally, not conceptually. According to Ma mathematics is approached as a collection of facts and rules where mathematics means following set procedures step-by-step to arrive at answers. This American approach appears to be a correct definition of how mathematics is seen. Unlike subjects like English and geography, the emphasis is not on understanding, but on remembering. Students do not have to know why a certain number is the area of a shape. Instead, all they have to do is remember the formula for calculating the area."
