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Universal Truths in Math, 2005.
This paper examines some theories in order to determine if there are any universal truths in mathematics.
675 words (approx. 2.7 pages), 3 sources, $ 26.95
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Abstract
The paper looks at the theories of George Lakoff and Rafael Nunez, as well as those of Keith Devlin in order to explore if there are really any universal truths in maths. Set off by an excerpt from Robert Sawyer's novel "Computing God," the paper theorizes that there really are not any universal truths, at least none that can be defined until all forms of life are themselves defined. The paper points out that this is neither the quantification nor the metaphor and symbolism that math requires and uses.
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Mathematics and Universal Truths, 2005.
This paper discusses whether mathematical thought can lead to fundamental truths and highlights the use of metaphor in mathematical thought.
675 words (approx. 2.7 pages), 3 sources, $ 26.95
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Abstract
The paper argues that fundamental truths cannot be arrived at by math. The paper is of the opinion that this is insofar as the questions we ask, the processes we use and the assumptions we make are shaped by environmental, biological and contextual factors that have little - if anything - to do with "rational" and purely objective thought. The paper places great emphasis upon the place of metaphor in the construction of mathematical thought.
From the Paper
"The question of whether there are unquestionable truths in mathematics is indeed a puzzling one. This paper will examine the matter by looking a few readings from our class notes. As will soon become apparent, there is much doubt that mathematics leads irrevocably to universal truth; indeed, in the limited space available, this paper will suggest that, because so much of mathematics is metaphorical in nature, Euclidean mathematics and other "relational" branches of math may lead us into the realm of creative metaphor and no further. In fact, as Sawyer seems to suggest, mathematical "truth" - all truth - is essentially the product of cultural epistemology and ontology."
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Question of Mathematical Truth, 2002.
Examines the concept of mathematical truth and whether it really exists.
900 words (approx. 3.6 pages), 4 sources, $ 35.95
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Abstract
In this essay, I will discuss the question of mathematical truth and attempt to decide whether there can be such a thing as an "absolute fact."
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Absolute Truth and the Relativity of Truth, 2005.
Are there absolute truths or is truth relative? A review of the philosophical concept of truth and an extended discussion of the movie, "Rashomon", to see if the question is even understandable.
5,145 words (approx. 20.6 pages), 6 sources, MLA, $ 128.95
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Abstract
This paper investigates the intelligibility of the philosophical understanding of truth as appearance and reality. After reviewing the nature of the philosophical picture of what constitutes truth, there is an extended discussion of an often-cited example of truth?s relativity in the movie, "Rashomon". There is then a discussion of some other examples, which attempt to clarify the philosophical picture, only to conclude that the philosophical posing of truth and appearance is actually not yet understandable.
From the Paper
"In Theaetetus Socrates quotes Protagoras with what is possibly the first clear statement of the relativist: that ?man is the measure of all things? and that anything ?is to me such as it appears to me, and is to you such as it appears to you?? (856, 152a) On the other hand, there is Plato?s well-known allegory of the cave in the Seventh Book of the Republic, (747- 750, 514a-518b) in which he advances the notion that there is an ultimate truth that lies beyond our interpretations or appearances of that truth. But how understandable are both the notions of relativism and of an absolute truth?"
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The Truth About Truth, 2006.
A philosophical look at the meaning of truth.
1,401 words (approx. 5.6 pages), 2 sources, MLA, $ 46.95
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Abstract
In this paper the author looks at all the aspects of truth as we understand it. He identifies truth as something which could be universal and eternal and if it is, he examines whether it should be considered eternal or absolute. The author elaborates on these points and enters a deep discussion of how absolute truth can be assessed and defined. The author concludes the paper with his belief that truth is relative and therefore it cannot be absolute as absolute truth is eternal.
From the Paper
"One common mistake made by men is to allow ourselves to be led by our senses alone. I believe our senses do not always lead to truth. Senses can be deceiving, especially when relating dreams. In a dream one may feel things or see things, and when that person wakes up has to ponder for a second whether those things were real. Of course, those things experienced in a dream were not real, but for an instant that dreamer believed those things to be true. He was fooled by his senses. Although many will agree that in this case the senses do deceive us, still some will rely solely on their senses to guide them through life."
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Concepts of Relativity and Truth: Finding Your Own Truth, 2000.
A discussion of Nietzsche's belief on deconstructing truth and the concept of relativism in terms of other thinkers.
793 words (approx. 3.2 pages), 0 sources, $ 28.95
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From the Paper
"The concept of relativism makes many ideas and concepts impossible to argue. The idea that every person and group acts and is entitled to live by their own perception of the truth allows such a difference in opinions that consilience among them seems to be impossible. Friedrich Nietszche wrote that we had to ?deconstruct? truth because we can?t allow ourselves to rely on truths that we think are absolute. To rely on an absolute truth is to put your trust into something that may prove false. John Stuart Mill wrote that an individual should be able to seek happiness and liberty, as long as that search does not encroach upon the happiness and liberty of another. In a sense, he speculated that each man has to search for his own truth. In finding his own truth, Nietszche would urge us to question those truths constantly, to make sure in ourselves that what we are believing in is true. "
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Philosophy of Mathematics, 2007.
An analysis of the universal nature of mathematics and developments in the philosophy of mathematics.
1,899 words (approx. 7.6 pages), 6 sources, APA, $ 60.95
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Abstract
This paper considers some of the major developments in the philosophy of mathematics regarding the capacity of mathematics to be universally valid and applicable. It presents some of the basic arguments and schools of thought of the philosophy of mathematics. The paper then analyzes whether, at its foundation, mathematics can have a legitimate claim to be universal.
Table of Contents:
The Problem Of The Ideal And The Real
Math As Logic
Math As Structure
Application And Universality
From the Paper
"This problem, Russell's paradox, proved to be an intractable problem for Frege which, after it was pointed out to him, he could not overcome. The impact upon the philosophy of math was major. An important attempt to boil math down to logical principles had proven unsuccessfully, and eventual efforts to rescue the project by Russell and others were unable to develop a logicism that showed math as both consistent and complete. Therefore math cannot be said to be universal by appeal to logic alone."
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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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A History of Mathematics, 2002.
This paper discusses some aspects of the history of mathematics from the earliest mathematical records to the modern era.
1,400 words (approx. 5.6 pages), 9 sources, $ 53.95
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Abstract
This paper only touches on some selected aspects of a broad and encompassing subject. The author begins by outlining some of the key developments as a whole before further subdividing into three sections: Greek mathematical developments; Chinese and Middle Eastern developments; and Western developments. The paper concludes by drawing attention to the enormous scope of the history of mathematics.
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Mathematics Pedagogy, 2005.
This paper discusses of teaching mathematics.
3,825 words (approx. 15.3 pages), 13 sources, $ 151.95
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Abstract
This paper examines issues of mathematics pedagogy and the degree of the contextualization of the subject matter in teaching mathematics. The author points out that mathematics is often presented more as a more abstract examination of numbers and measurements that appear, when mathematics really is always relevant and should be seen in the context of the real world. The paper states that mathematics pedagogy needs to develop a way present mathematics within this real world context.
From the Paper
"The issue of relevance in education is often a question of the contextualization of subject matter, meaning that the subject relates to the lives of the students because it can be seen in the context of their lives, with issues understandable because they are applicable to the real world. Mathematics is often presented more as a pure Mathematics has the dual character of being both a language (a symbol system) and an underlying model of relationships among actions with objects. As such, it fits closely with the Vygotskian description of sign-sign relationships and de-contextualized knowledge. At the same time, its development in relation to human actions on objects gives it a prominent place in Piagetian analysis. Furthermore, mathematics teaching requires the recognition of mathematics as a sociocultural achievement worthy of reproduction in new generations."
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Stephan Korner's "The Philosophy of Mathematics", 2004.
Summary and review of Stephan Korner's "The Philosophy of Mathematics: An Introductory Essay".
1,091 words (approx. 4.4 pages), 2 sources, MLA, $ 38.95
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Abstract
The first part of this paper expounds on Stephan Korner's discussion, in "The Philosophy of Mathematics, of the nature of mathematics, and the three main schools of thought relating mathematics to philosophy. The paper continues with a discussion on logicism and why it provides the clearest way to look at mathematical concepts and the best way to explain mathematical philosophy.
From the Paper
"Mathematics is an indispensable science that justifies and confirms many aspects of other scientific subject matter. Mathematics relies on conclusions not assumptions and evidence is required to confirm theoretical entities as true. Of course the debates exist as to which school of thought holds the most validity. Mathematical realism will always be different to each of these philosophical schools and arguments can be found to both support and reject each school of thought."
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Mathematics Instruction in English in Bilingual Classrooms, 2005.
Research proposal for examining the effects of mathematics instruction in English in bilingual classrooms.
2,211 words (approx. 8.8 pages), 14 sources, APA, $ 68.95
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Abstract
This paper proposes a research project that would examine the effectiveness of English instruction of mathematics on Second Grade ELL (English language learners) students as compared to the effectiveness of instruction in their native language. The proposal is in response to the controversy surrounding the issue of how best to teach mathematics to children from non-English-speaking backgrounds, since it has been found that the best way for children to learn to use mathematics to organize, understand, compare, and interpret their experiences is by making a connection between mathematics and their everyday lives. The paper examines whether ELL students should be taught how to make this connection in their native language with gradual exposure to English in language classes, or whether they should be immersed in English as early as possible. The paper includes an annotated bibliography and an observation checklist of lessons taught in class.
Introduction
Setting
Problem/Issue
Research Question
Hypothesis
Methodology
Subjects
Instrumentation
Significance of the Study
From the Paper
"Mathematics is a powerful tool for interpreting the world. Research has shown that for children to learn how to use mathematics to organize, understand, compare, and interpret their experiences, mathematics must be connected to their lives. Such connections help students to make sense of mathematics and view it as relevant. There has, however, been controversy with regard to children from non-English backgrounds and the best ways to get them to make those connections. Questions are raised regarding how to instruct these children who are referred to as English language learners (ELL?s). Should they initially be taught in their native language with gradual exposure to English in language classes, or should they be immersed in English as early as possible."
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Mathematics and Art, 2008.
A comparative analysis of the disciplines of mathematics and art.
2,332 words (approx. 9.3 pages), 10 sources, MLA, $ 71.95
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Abstract
This paper discusses how mathematics is often treated as a distant and very different discipline from the arts even though the arts make use of mathematics in a number of ways. In particular, the paper looks at how paintings, drawings, and designs can be analyzed according to mathematical principles to see ways in which the artist balances different shapes and forms according to mathematical principles or draws on mathematical theory for inspiration. The paper also examines how the art of different periods may reflect different mathematical ideas.
From the Paper
"The classical era was one in which mathematics was used quite consciously in developing artistic styles, and some of these styles have even been named with mathematical references. The artworks of a given era reflect the formalist, social, and economic realities of the period, exemplifying the prevailing artistic styles and the social and economic structures which influence the arts. In Greek art, the Geometric period was an era which produced a good deal of pottery and other geometrically regular works. The Geometric krater from the Dipylon cemetery from the eighth century B.C. (De La Croix, Tansey, and Kirkpatrick 130) exemplifies the style of the period. The Geometric period is the name given to the era between the end of the Mycenaean age and the beginning of the Classic age. "
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Language and Mathematics, 2006.
Discusses the similarities between natural human languages and mathematics.
1,350 words (approx. 5.4 pages), 3 sources, $ 53.95
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Abstract
Normally, natural human languages and mathematics are regarded as being diametrically opposed to one another. Mathematics is formal and is marked by precision; the objects of theory must be carefully defined so that the informal can be formalized. Natural human language on the other hand is flexible, and one term can denote not just multiple meanings but opposing ones as well. This paper explains that, in spite of these differences, human language and mathematics actually share common ground such as the fact that both human language and the language of mathematics actually have a precise formal structure.
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Teaching Mathematics, 2005.
This paper explores challenges in teaching advanced mathematics.
3,825 words (approx. 15.3 pages), 10 sources, $ 151.95
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Abstract
This paper discusses that studies have demonstrated that there are a minimum of seven specific forms of intelligence including mathematics. The author identifies the emergence of standards-based education within the United States and its significance for teaching, particularly in regards to high-school and pre-college mathematics education. The paper examines the effectiveness of selected teaching methods used by educators to help convey mathematics to their students.
From the Paper
"Advanced mathematics, specifically content at the algebraic level and beyond, creates challenges for many students. Learning strategies, modes of learning, and types of student intelligence all impact the method through which the student approaches mathematics and the extent to which they acquire and are able to apply learned information. Yet increases in national standards demand that students perform at specific levels of academic abilities before they are passed into the next grade, and an emphasis upon standards-based testing as a component of admission to college further demands specific performance levels from students. This combination of factors stresses a need to help students achieve certain goals within their academic careers in regards to advanced mathematics. In order to explore the challenges in teaching advanced mathematics to students, this paper will survey three specific components. First, this paper will explore types of intelligence."
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