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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"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..."

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."

Tags: education, grouping, poor, performance, teaching, school, mixed-ability, classrooms

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."

Tags: critical, design, experiment, learning, motivation, psychology, research, skinner, theory

From the Paper
"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 ... "

From the Paper
"The purpose of this research is to examine the Babylonian theory of polynomials. The plan of the research will be to set forth the historical and cultural context in which the Babylonian approach to developing equation theory emerged, and then to discuss the ways in which the theory could have evolved across ancient cultures toward modern interpretations of the authentic character and importance of equations. As appropriate, reference will be made to the assessments of the Babylonian contribution to the body of mathematical thought as it may have impacted upon subsequent mathematical theory.


One may begin a discussion of the authentic nature of Babylonian theory of polynomials--not by saying what it is but by suggesting what it is not, which is an equivalent of purely theoretical explorations of the mathematical universe that were..."

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 ..."

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)."

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 ..."