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John von Neumann, 2007.
An analysis of the mathematical and scientific contributions of John von Neumann.
2,009 words (approx. 8.0 pages), 6 sources, MLA, $ 63.95
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Abstract
This paper discusses John von Neumann's contributions to the fields of quantum physics, functional analysis, set theory, economics, computer science, numerical analysis, hydrodynamics, statistics and other mathematical fields. The paper also discusses his contribution to the creation of the hydrogen bomb. It goes on to describe some of his most influential achievements.
From the Paper
"John Von Neumann inarguably contributed a wealth of knowledge to the development of computers, and without his contributions the face of technology today would be primitively underdeveloped. However, Neumann may have canceled out the "good" he did in an act of self-fulfilling equivalent exchange with his work in the realms of math and science with the contributions he made to warfare and massive weaponry. The name Von Neumann is associated as much with the Atomic Bomb as it is with computer programs (Wilson), and Neumann may have had even more devastating projects on the horizon at the time of his unexpected death from cancer. During the Second World War, von Neumann worked as a consulted to both armed forces and civilian agencies that were involved in wartime projects. Neumann's genius was in high demand, and he was able to design an implosion method for bringing nuclear fuel to explosion, as well as playing an integral part in the development of the hydrogen bomb. (Cabrera) According to one of Neumann's biographers, "It has been stated that von Neumann's electronic computer hastened the hydrogen bomb explosion on November 1, 1952." (Bochner)"
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The Statistical Lie, 2007.
This paper explores how statistics can often be misleading and delusional.
1,065 words (approx. 4.3 pages), 3 sources, MLA, $ 37.95
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Abstract
The paper relates that one of man's greatest fears is that of the power of numbers. The paper demonstrates how statistics are used to misrepresent, under-represent or over-represent an event, occurrence, situation or phenomenon. The paper defines statistics as a set of numeric values obtained by way of a measurement process. This process can be either one of observation or direct testing. The paper reveals that the most widely used means whereby researchers lie is with statistics, usually for increased profits and sensationalism. The paper illustrates how companies can use a self-selecting population for survey results, or they use obscure definitions and data sets that mislead consumers.
From the Paper
"For most people numbers are nothing more than a hodgepodge of digits that are bewildering and oftentimes meaningless. As a result individuals often prefer to judge events, occurrences, phenomena, and situations from a traditionalist point of view wherein reason, conclusion, and inferences are made on the basis of past experiences rather than on best practices policies. Justification for historical acceptance is usually based on a fear of numbers and a lack of willingness to extract meaningful information from them. For those accepting of the alternatives, statistical tools have been devised wherein it is possible to extract meaningful information from data and interpret whatever the data holds as its' secret."
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Josiah Willard Gibbs, 2007.
This paper looks at the life and achievements of American scientist, Josiah Willard Gibbs.
1,544 words (approx. 6.2 pages), 9 sources, MLA, $ 50.95
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Abstract
In this article, the writer studies the character of Josiah Willard Gibbs, a mathematician and physicist. The writer discusses that he managed to achieve great things during his lifetime and lead the world on to greater and better scientific discoveries. The writer points out that Josiah Willard Gibbs has been recognized as one of the greatest American scientists of the nineteenth century. Further the writer notes that it is Gibbs who managed to provide a sound thermodynamic foundation to physical chemistry, to America and to the entire world.
From the Paper
"The second work that Gibbons published in the same year was "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces". From the years from 1876 to 1878, Gibbs published two memoirs, which were later to be combined into one work, entitled, "On the Equilibrium of Heterogeneous Substances". Added to this, Josiah Willard Gibbs has contributed to various other spheres, like for example, crystallography, the determination of planetary and comet orbits, and also to electromagnetic theory. The most interesting phenomenon that Gibbs managed to achieve was that he made the practical side of science appealing and fascinating. Gibbs was also recognized as a 'theoretical physicist' of international stature, and he received a patent in the year 1866 for an improved type of railroad brake."
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Dyscalculia, 2006.
A discussion regarding the academic developmental disorder, dyscalculia.
1,683 words (approx. 6.7 pages), 11 sources, MLA, $ 54.95
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Abstract
This paper reviews dyscalculia, an academic developmental disorder that is believed to affect about 3 to 6 percent of the population. According to the paper, an individual with dyscalculia may struggle with a number of different issues such as, linguistic skills, perceptual skills, attention skills and mathematical skills.
From the Paper
"Dyscalculic individuals can usually learn the sequence of counting words, but can have trouble moving back and forth, especially in twos, threes or more. Estimating numbers is also more of an issue in comparison to others their age. With dyscalculia, the lack of understanding number magnitudes, which is typical of children in the age group of 7 to 11, is absent. Math vocabulary may also to lead to problems for students, especially when they have to use several different words at a time, such as "add," "plus," and "combine" that can be used interchangeably. Other terms, such as "hypotenuse" and "to factor" do not occur in normal discussions and must be learned specifically for mathematics. At times, an individual may understand the underlying concept but not how to use a specific term correctly."
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Logging On, 2007.
This paper discusses the effects of web-based instruction on mathematics achievement and attitudes of 6th grade students.
2,615 words (approx. 10.5 pages), 15 sources, MLA, $ 78.95
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Abstract
In this article, the writer conducts a mixed methods research in order to measure the effect of the utilization of a computer-assisted instruction (CAI) program. The writer explores the web-based Study Island program on the student's reference competency test mathematical scores. In addition, the research focuses on how the students involved in the study related to the interactive program. The writer concludes that CAI, when combined with traditional instruction, has been shown to significantly increase standardized test scores for students in mathematics testing. Further the writer points out that research has indicated that the use of computers in schools both supports learning and is useful in the development of higher order skills such as critical thinking and scientific inquiry, because the students are engaged in complex tasks in a collaborative learning environment.
Outline:
Objective
Introduction
Background and Significance of Problem
Purpose of the Study
Importance of the Study
Research Questions
Literature Review
Summary of Literature Review
Methodology
Research Design
Data Collection/Analysis
Bibliography
From the Paper
"The Study Island program was designed for the purpose of assisting students in their mastery of the content of the New Jersey Core Curriculum Content Standards for Mathematics. The interface of this program is user-friendly allowing students to go through the program by steps. This program can be used by students at any location with Internet access. Further, this program is inclusive of questions that are styled just as the New Jersey GEPA providing an accurate assessment of student progress as the school year progresses. Students are able to learn at their own pace using this program and the student is able to choose from several different formats of learning. The beauty of this program is that statistics are kept in the program which can be viewed by educators throughout the year which allows assessment of individual student's learning and the program itself as the year progresses."
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Computerized Mathematics Testing, 2007.
This paper describes a study on the use of computer-based testing to assess the mathematical skills of high school students.
3,032 words (approx. 12.1 pages), 30 sources, APA, $ 89.95
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Abstract
This study analyzes results of the Virginia Standards of Learning tests. The author contrasts one group of high school students who used online computerized methods of testing versus the second group, who were tested with the traditional "paper-pencil" method. The author argues that computer-based testing is in its preliminary phases. This study, therefore, is intended to let scholars research the dependability of these tests. This research begins to fill this gap and offer future direction for additional research to be carried out.
Outline:
Abstract
Statement of Problem
Rationale of Study
Research Objectives
Literature Review
Hypothesis
Methodology
Participants
Measures
Procedure
Implications and Conclusion
References
From the Paper
"The control of computers is the seeming dominant feature at the closing stages of the twentieth century. In the 1970s computers operated behind closed doors to tally books, record paychecks, organize weather newscasts, and perform whichever errands whose qualities frequently incorporated repellent recurring processes. The 1980s saw a transformation. Computers took a permanent position in the forefront of firms and businesses. Soon after, the computers replaced the human employees in the department of customer services. Personal computers with telecommunication were more common. Nowadays, the computers handle far more complicated procedures than what they did before. "Machine intelligence", "Inference engines", and "Expert Systems" are expressions that are gradually growing in trend. "
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Teaching and Assessing Mathematics using Maple, 2007.
This paper describes the use of specific technological tools that assist students in the development of their mathematical skills.
19,371 words (approx. 77.5 pages), 41 sources, APA, $ 249.95
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Abstract
This extensive paper describes the use of Computer Algebra Systems (CAS) in helping students develop their mathematical skills. The research contained in this report addresses the use of CAS in the mathematics classroom. It also addresses the attitudes shared by teachers and students alike as it relates to the use of this technology. In particular, the Maple CAS system is evaluated. The author states that the purpose of this research is to take a systematic approach to the design and evaluation of the teaching, learning and assessing mathematics courses using the CAS Maple. The focus of the evaluation are first year service mathematics courses at a university. The effectiveness of different ways of incorporating Maple activities into such courses is also examined.
Table of Contents
Introduction and Statement of the Research Questions
Literature Review
How People Learn Mathematics and the Role of Technology
Review of Studies Related to the Use of Technology in the Classroom
Utilizing Computer Algebra Systems
CAS in the Classroom
Survey Papers
The Research Methodology of the Study
Conclusion
From the Paper
"The purpose of this research is to take a systematic approach to the design and evaluation of the teaching, learning and assessing mathematics courses using the CAS Maple. Of particular interest are first year service mathematics courses at RMIT University. The effectiveness of different ways of incorporating Maple activities into such courses will also be examined.
The investigation will be conducted as a research and development activity through which Maple activities are designed and evaluated in a feedback cycle and we follow an Action Research methodology. Initially, examples from the literature and relevant theories concerning mathematical understanding were sought in order to inform the development of new resources. Student's responses to the first cycle of activities in 2003 were obtained. The conclusions drawn are informing the development of resources for the next cycle. This process will continue over the course of six semesters. The research methods utilized are observations of classes, analysis of student's work, responses to specially designed test instruments, use of feedback questionnaires and structured interviews. Some use will be made of video will also be utilized to record and analyse methodology to evaluate the teaching and learning of mathematics using Maple in a computer lab."
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Technology as Teacher, 2007.
This paper examines research about the effects of computer-based programs on the teaching of mathematics.
2,985 words (approx. 11.9 pages), 17 sources, MLA, $ 88.95
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Abstract
The paper explores the Study Island computer-based mathematics program that was developed and designed to help children learn mathematical skills and to increase standardized math test scores. The paper looks at research that measured the effects of the utilization of this web-based program on the students' reference competency test mathematics scores. The paper relates that the research showed that students who were enrolled in a class where Study Island was used did better on a standardized test than other students. The paper concludes that computer-aided instruction has more advantages than disadvantages and suggests students use the Study Island mathematics program for the next state standardized test.
Outline:
Introduction
What is Study Island?
Research Study
Background and Significance of the Problem
To What Extent Did Computer Assisted Instruction Increase Standardized Mathematics Achievement Scores?
What Benefits and Advantages Emerged When Using Computer Aided Instruction With Sixth Grade?
How Can the Web-Based Mathematical Instruction Study Island Program Influence Student's Perception of Leaning?
Conclusion
From the Paper
"Mathematics is one area that is being affected by the use of such technology. There have been several computer-based mathematics programs developed and designed to help children learn mathematic skills and to increase standardized math test scores. One such program is called Study Island. Study Island was developed in 2000 and offers practical and web-based instruction for students in all grade levels. The program is based around state standards so that students can use this program to prepare for state standardized testing and increase overall testing scores. Study Island is currently being used in over 6000 schools around the nation and is helping over two million students."
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High School Calculus, 2006.
A review of the literature 'Understanding the Concepts of Limit and Continuity in Calculus Courses at the High School and/or Early College Level'.
4,037 words (approx. 16.1 pages), 13 sources, MLA, $ 109.95
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Abstract
This paper reviews and discusses the literature 'Understanding the Concepts of Limit and Continuity in Calculus Courses at the High School and/or Early College Level'. According to the paper, the ten fastest growing career fields include five that are computer-related which rely heavily on the knowledge of mathematics.
Outline:
Background and Overview
Studies in the Concept of Limit and Continuity in High School and Early College-Level Calculus Courses
Interactions of Methods and Questions for Further Study
From the Paper
"Clearly, then, just going through the motions and mechanics of calculus may serve to help familiarize these young learners with the basic steps involved. There are a number of studies to date, though, that have confirmed that these students typically experience a number of problems in understanding key calculus concepts that adversely affect their ability to master them (Bezuidenhout, 2001). To help facilitate the process, just as handheld calculators have been introduced into some early mathematics classes to facilitate routine calculations to allow more time for instruction, Heid (1988) suggested early on that computers could likewise be used to help beginning calculus students learn more by automating the algorithmic functions required. Although there is clearly a trade-off involved in such an approach, this author maintains that this approach would allow more class time for development of higher mathematics concepts."
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Pythagoras, 2006.
This paper discusses Pythagoras, one of the greatest men of the Ancient Greek civilization.
2,455 words (approx. 9.8 pages), 5 sources, MLA, $ 74.95
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Abstract
This paper explains that Pythagoras left no written works; what is known about him and about his school is from a book written by the Pythagorean, Philolaus of Tarentum, which influenced Plato's philosophy. The author points out that Pythagoras considered himself a philosopher, which is clearly mentioned in Diogenes Laertios' letters, and the dialogues of Cicero, inspired by the Greek Iore. The paper states that the Pythagorean philosophy is related with the theory of numbers, which are not only the symbols of reality but the very substance of real things.
From the Paper
"The theory of numbers is strongly connected with the harmony of spheres, this way, number ten being the perfect one has a body under the earth moving parallel with it and which is invisible to us. The five planets, the sun, the moon, and the earth with its counter-earth, moving from west to east at rates of speed proportionate to the distance of each from the central fire, produce eight tones which give an octave, and, therefore, a harmony. In their psychology and their ethics the Pythagoreans used the idea of harmony and the notion of number as the explanation of the mind and its states."
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The Relationship Between Board Games and Mathematics, 2006.
An analysis of the relationship between board games in adulthood and remembering feeling confident/able/successful in math classes as a child.
1,418 words (approx. 5.7 pages), 3 sources, APA, $ 47.95
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Abstract
This brief review of literature explores the integral connections between mathematics and board games so that the subject matter at hand will be fully understood. Extrapolations are then made as to why these connections may not necessarily mean that there is a connection between enjoyment of board games and math class success.
Table of Contents:
Introduction
Literature Review
Methodology
Questionnaire
From the Paper
"According to Heather Jenkins (2004), the mathematical omnipresence in the world is undeniable. However, many people completely overlook the fact that "math forms the basis of many forms of entertainment (and perhaps addictions)." (Jenkins 2004) The very field of probability was born of games of chance which have been played for a very long time, when a dice player became curious about betting outcomes and consulted with the mathematicians Pascal and Fermat. Mathematics is not just an "academic" occurrence. Since the game of dice was played before the field of probability was born, even though probability is the mathematical drive behind the game, it can be extrapolated that an understanding or enjoyment of the study of mathematics itself is not necessary in order to enjoy and excel at activities which are based on math."
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Measurement of Angles, 2006.
This paper provides an analysis of why angles are measured in degrees, minutes and seconds.
885 words (approx. 3.5 pages), 3 sources, MLA, $ 31.95
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Abstract
In this article, the writer discusses the notion of the 24-hour period used in the day/night cycle. The writer explains that this cycle began in ancient Egypt, while the sixty divisions of degrees, minutes and seconds is derived from the number system based on sixty (sexagesimal) of the Mesopotamians. The writer examines this approach to dividing the day and night into like segments. Further, the writer looks at ancient peoples' observations about the motion of the sun and discusses how this ultimately results in the system that is used to measure angles today.
From the Paper
"Given its ancient origins, the reason angles are measured in degrees, minutes and seconds today has likewise been forgotten by many modern observers. In fact, the basis for this method was developed almost five thousand years ago in Sumeria based on their use of sundials to track time. In her book, Time's Pendulum: The Quest to Capture Time -- from Sundials to Atomic Clocks, Jo Ellen Barnett reports that the convention of the 24-hour period used in the day/night cycle began in ancient Egypt, while the sixty divisions of degrees, minutes and seconds is derived from the number system based on sixty (sexagesimal) of the Mesopotamians; because the Mesopotamians had not yet invented fractional numbers, they preferred whole numbers which could be divided in several different ways, and the number 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30."
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