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Manipulatives in Mathematics Curriculum, 2006.
This paper discusses mathematics education in early education programs.
875 words (approx. 3.5 pages), 5 sources, APA, $ 31.95
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Abstract
In this article, the writer explains that manipulatives are defined as materials that are physically handled by students in order to help them see actual examples of mathematical principles at work. The writer notes that manipulatives are incorporated into curriculum with the aim of helping the student understand mathematics, rather than increasing efficiency in calculation. The writer maintains that manipulatives are very useful especially in early education. The writer notes that there is a wide array of math manipulatives on the Internet. Some may be bought while others can be enjoyed for free on the web. The writer provides examples and pictures and discusses how it would be possible to use them in teaching children.
Outline:
What are Manipulatives?
References
From the Paper
"Manipulatives are incorporated into curriculum with the aim of helping the student understand mathematics, rather than increasing efficiency in calculation. Manipulatives are very useful especially in early education. Moreover, its use is not exclusive to teachers and schools, parents who would choose to help their children with school lessons can also employ them to help their children understand math concepts. Most students dislike math because they think it is very complicated. This prejudice towards this subject result to poor performance of students in math subjects. The development of this negative mind set on the subject may have started when in their childhood. Traditional ways of teaching may have bored them and cause them to dislike the subject, which they will carry to adulthood. That is why it is important that at a young age, kids should learn to enjoy math. And the use of manipulatives can help them enjoy and appreciate it. Manipulatives come in colorful packages that attract children, their interactive design also allows children to play with them as they learn. There is a wide array of math manipulatives in the Internet."
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Mathematics Curriculum Review, 2002.
A comprehensive analysis of the problems in the elementary school's mathematics curriculum.
3,545 words (approx. 14.2 pages), 6 sources, APA, $ 99.95
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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."
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Manipulatives, 2007.
This paper researches the use of manipulatives in the field of mathematics.
3,446 words (approx. 13.8 pages), 37 sources, MLA, $ 97.95
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Abstract
In this article, the writer researches hands-on manipulatives use in mathematics. This work explores the historical perspective, the effects on education and the supporting theories. In addition, the writer looks at what research has been thus far conducted. Finally, this work researches the special benefits of using algebra tiles. The writer maintains that it is significant to note that algebraic functions are mathematical processes involving abstract or symbolic representation. The writer concludes that it is quite difficult for the beginning algebra student to conceptualize the processes and functions of algebra; however, the use of manipulatives has been shown to assist in this area, making their use in algebra instruction particularly effective in classroom instruction.
Outline:
Objective
Introduction
What are Math Manipulatives?
Why Use Math Manipulatives?
How Should a Teacher Use Math Munipulatives?
Summary
What
Why
How
From the Paper
"Today's mathematics teacher has many resources that are available in assisting the development of appropriate curricula that meets the content standards of the NCTM. Not only are standard tools available but the Internet also offers several web-based learning activities that assist mathematics learning and instruction. Before this development, the teacher often would contact businesses in the community in order to obtain 'real-world' manipulatives for use in the classroom. The work of Shield holds that web-based tools motivate students in learning mathematics content but also the delivery of the information is interesting to the student."
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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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Conceptual and Procedural Knowledge in Mathematics, 2002.
A look at how theoretical difference can be extended to the understanding and solving of actual mathematical problems.
650 words (approx. 2.6 pages), 4 sources, $ 26.95
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Abstract
This paper is written on conceptual and procedural knowledge in mathematics. Procedural knowledge-or more appropriately skills-refers to the ability to physically solve a problem through the manipulation of mathematical skills: with pencil and paper, calculator, computer, etc. There is thus, in a theoretical sense, a difference between conceptual and procedural knowledge in mathematics.
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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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Aboriginal Culture and Mathematics, 2005.
A discussion regarding contemporary issues in Australian education.
1,350 words (approx. 5.4 pages), 6 sources, $ 53.95
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Abstract
This paper discusses the issues surrounding the mathematics curriculum in Australian schools. According to this paper, the needs of the Aboriginal students differ from what the Westernized education system teaches. The Australian school system fails to integrate these two cultures.
From the Paper
"For mathematics teachers working in Australia, few issues are as pressing as creating a useful curriculum that integrates the needs of Aboriginal students with the demands of a Westernized education system. Because of the sometimes-vast cultural differences that exist between Aboriginal groups, individuals, and cultures, Western education is often seen to "fail" these students, especially in mathematics. This is largely the result of the system's inability to account for the cultural differences that exist between these groups. After all, mathematics is a socially constructed discipline and should be considered within the confines of culture (Owens 2001, p. 166). While there may be some transcultural aspects to mathematics, to be truly effective mathematical pedagogy in Australia must consider the cultural differences that exist between Western schools and Aboriginal cultures."
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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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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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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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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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Mathematics Education Dissertations, 2005.
This paper describes two distinct mathematics education dissertations.
2,250 words (approx. 9.0 pages), 2 sources, $ 89.95
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Abstract
This paper explains that the field of mathematics education provides considerable support for a variety of perspectives, which include new and innovative ideas and concepts. The author points out that graduate-level mathematics students are typically required to develop and submit a comprehensive dissertation to demonstrate their knowledge and skills. The paper presents two distinct mathematics education dissertations in greater detail, emphasizing the key strengths and weaknesses of each argument and the supporting literature reviews.
From the Paper
"The field of mathematics education provides considerable support for a variety of perspectives, which include new and innovative ideas and concepts that provide valuable contributions to the subject. It is evident that today's mathematics educators provide valuable knowledge, information and skills to mathematics students of all ages, and that there is a wide body of research that exists regarding mathematics education that is critical to the field. Graduate-level mathematics students are typically required to develop and submit a comprehensive dissertation to their respective schools in order to demonstrate their knowledge and skills in order to earn a graduate degree. The following discussion evaluates two dissertations written in the field of mathematics education, promoting different concepts in unique ways. A comparison and contrast is introduced, along with an evaluation of the key strengths and weaknesses of each dissertation."
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Mathematics Education, 2005.
This paper analyzes if it is possible to test the understanding of mathematics.
3,600 words (approx. 14.4 pages), 10 sources, $ 142.95
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Abstract
This paper is a report on a questionnaire given out to students in college to test their understanding of mathematics. The author points out that this research investigates the difference between knowledge and understanding and seeks the way to assess understanding. The paper concludes that the questionnaire derived from the GED in mathematics is a way to test understanding of high school mathematics for students who have graduated from high school.
From the Paper
"The purpose of this analysis is to see if it is possible to test understanding, specifically the understanding of mathematics. Such an analysis tests both mathematics teaching and mathematics learning, though at this preliminary stage it is not clear whether the teaching method is what is most important or the learning style of the student. Testing understanding is different from testing knowledge, for the latter shows that the student has assimilated ideas and even processes, while the former shows that the student has learned the underlying theory and can apply it in different situations. In mathematics, testing understanding is perhaps more common in normal testing than would be the case in certain other disciplines where simple facts are more common. In mathematics, of necessity the student must show an understanding of theory in order to apply mathematical concepts to written problems and arrive at the correct answer."
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