Abstract This paper examines why it is necessary to learn algebra. It shows its everyday uses and importance. It uses some basic examples such as calculating the miles per gallon of a car, and solving a calendar riddle.
From the paper:
"Algebra is simply the branch of mathematics in which the operations and procedures of addition and multiplication are applied to variables rather than specific numbers. It is also probably the subject about which schoolchildren are most likely to ask the question: What good will this ever do me when I get out of school. This paper puts forth three different answers to that eternal question of what good will algebra do me?"
Abstract Diophantus is referred to more often than not as the "Father of Algebra", although algebra predated Diophantus. His contributions to the study of algebra, however, have led to this attribution. This paper reviews his life, his mathematics, his place in the history of mathematics and the relevance of his work in the 21st century. The review is presented in discussions of his life, his work, his place in mathematics history and the contemporary relevance of his contributions.
From the Paper "Diophantus lived in the third century A.D. The best estimates of his birth and death years are 200 A.D. and 284 A.D. Other conjectures of these data range from 150 B.C. to 350 A.D. Exactly when he lived, however, is not nearly as relevant to contemporary society as is what he accomplished while he lived. What is generally agreed upon about Diophantus is that he was a normal man who married, had children, and lived a normal but scholarly life. Not all of his work has survived, at least not in a recorded form that may be attributed directly to him. That work which has survived and which can be directly attributed to him, however, has established him as mathematics theoretician of worthy note (Heath (Vol. I) 15-16)."
Tags: mathematics, numbers, equation, Arithmetica, formula
Abstract This paper explains that the Extensible Markup Language or XML was created to help allow users to share and pass documents, which were richly structured, over the Web in an easy, cost effective manner. The author points out that a markup language is a methodology of identifying the inherent structure of a document, and therefore, XML is a critical aspect of the World Wide Web because it helps explain the way to add markup to all documents. The paper relates that the Internet is based on a foundation of distributed hypertext, which could be regarded as a large distributed database where there are million to billions of queries processed daily.
Table of Contents
Introduction
Background
History
Governing Bodies
XML PAT Algebra Operators
Conclusion
From the Paper "One such body is the American National Standards Institute or ANSI which is a non-profit private organization that surprisingly institutes standards the industry accepts voluntarily. Other influential standards organizations include the Institute of Electrical and Electronic Engineers or IEEE and the Organization for Standardization or ISO. The IEEE was the organization that defined LAN standards in the Project 802 or the 802 series. These projects could be the blueprints that could be used to make XML more effective by using PAT Algebra Operators for query needs."
Abstract This paper explains that any tool, such as a graphing calculator, which can help students gain an improved mastery of the fundamental skills required to complete algebraic problems, must be viewed as educators as a "Good Thing"; but a consistent theme is the need to keep the material relevant in order to maintain student interest. The author points out that, although students should have the experience of entering the program commands themselves, an alternative approach is for the teacher to write the relevant on one calculator and then distribute it to students' calculators by using their linking capabilities. The paper relates that teachers can adapt the material for use with Texas Instruments (TI), Casio, Hewlett-Packard and Sharp graphing calculators.
From the Paper "The use of graphing calculators in a comprehensive algebra curriculum has been advocated by a number of educators. For example, some currently teach their students how to solve and graph linear equations manually, give them a test on it that is worth 50 points where no calculators are allowed during the test, classwork, or homework. Afterwards, they teach students how to solve the same or similar problems using a calculator. Then they give them another test of the same topic as during which problems are to be solved only by using calculators. During chapter tests and exams, students have the freedom to choose whether to use a calculator or not. "
Abstract This paper uses a problem from everyday life and sets up an algebraic equation to solve it. It then solves the problem. In this case the problem is a plane flying from San Francisco to Hawaii which experiences an emergency and it is necessary to determine at what point on the flight it is faster to continue to Hawaii than return to San Francisco, given the air speed, the tail wind factor and the distance between San Francisco and Hawaii.
From the Paper " A plane is flying miles from San Francisco to Hawaii. It is flying at a speed of mph and there is a tailwind blowing at mph. Problem How many hours after take off would it be faster to keep on flying to Hawaii than to turn around and fly back to San ..."
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."
Abstract This paper reviews findings in literature stating that hands-on manipulatives are effective in the middle school mathematics classroom. The paper then reports that the findings are of limitations in the use of manipulatives and, specifically, in the misuse of the manipulatives in the classroom. The paper further emphasizes that teachers must be well-educated and trained in the use of manipulatives, whether concrete material or virtual manipulatives for use on the computer and the Web. The paper concludes that it is clear that the use of manipulatives in mathematical instruction and learning in combination with cooperative learning is the best practice for instructional methods in today's mathematics classroom.
Outline:
Objective
Introduction
Historical Perspective
Theories
Research Studies
Virtual Manipulatives
Limitations
Static and Dynamic
Algebra Manipulatives
Summary
From the Paper "The slide-rule is a manipulative that was used in early education in providing students with a hands-on application in mathematics. Hands-on manipulatives such as blocks, rods, bean sticks and other manipulatives have been historically used in the math classroom as an aid in teaching mathematics. The work of Clements (1999) entitled; 'Concrete Manipulatives, Concrete Ideas" published in the Journal of Contemporary Issues in Early Childhood states that: "The notion of 'concrete' from concrete manipulatives to pedagogical sequences such as 'concrete to abstract' is embedded in educational theories, research and practice, especially in mathematics education."
Abstract This paper explains the importance of a summer mathematic program is because of new requirements in Michigan, which will immediately endanger the graduation track of students who struggle early in their ninth grade Algebra course. The author presents the rational for a summer support algebra program and reviews the literature upon which to develop the project. The paper summarizes this literature by stating the need for new innovative methods of teaching specifically relevant to the instruction of Algebra. In addition, the author states that the traditional algebra instruction methods have left a generation of students who not only see no practical need for algebra but also view it as a frivolous waste of academic time and resources.
Table of Contents:
Introduction
Problem Statement
Importance and Rationale of the Project
Background of the Project
Statement of Purpose
Research Objectives
Limitations of the Project
Literature Review
Mathematics Curricula
Computer-Assisted Instruction (CAI) Programs
Instructional Process Programs
Summary
From the Paper "Another program used in addressing student achievement in Algebra is 'The Algebra Online Program' as reported by the Louisiana Department of Education - Center for Educational Technology. This program involved a team of planners all of whom are certified in teaching mathematics who met to discuss, design, format, supplementary textbook selection and implementation of the course. This is a distance-learning curriculum."
Tags: alternative, personal curriculum, college-level tutorial collaborative
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."
An analysis of James Baldwin's short story, "Sonny's Blues", as a study in the relationship between two brothers and how they come to terms with their radically different philosophies of life.
2,546 words (approx. 10.2 pages), 5 sources, 1999, $ 77.95
From the Paper "James Baldwin's short story, ?Sonny's Blues,? (1957) is a study in the relationship between two brothers and how they come to terms with their radically different philosophiesof life and the different "lifestyle"choices they have made. Both Sonny, the younger brother and the unnamed narrator of the story, the older brother, have markedly different ideas on what constitutes vocation, on the dangers of drugs, on the life of the African American in a predominantly white society, and on music and its meaning in life."
From the Paper " James Baldwin's "Sonny's Blues" is the story about the clash of sensibilities between two brothers. The unnamed narrator is an algebra teacher, and he is a man who has survived his Harlem upbringing and seeks out a normal life with traditional middle-class values in America. His brother, Sonny, has become a jazz piano player and also a drug user.
The two brothers are clearly very different, yet they have a blood tie and the story explores how the two of them reconcile (or try to reconcile) their differences. In dealing with the story, it would be good to start with a focus on the symbolism of ice and water throughout the story.
When the narrator finds out that Sonny has been picked up in a raid for peddling and using heroin, he becomes extremely tense. ?A great (...)"
From the Paper "James Baldwin's short story "Sonny's Blues" is concerned with the reconciliation of two brothers. One of the brothers, Sonny, is a carefree jazz musician who has a problem with heroin addiction. The other brother, the narrator who does not reveal his own name, is a conservative algebra teacher who has trouble accepting Sonny's way of life. One important theme in the story is that music has redemptive power in its ability to express the pain and suffering that all people share. In the words of Williams, "Sonny's Blues" shows that "music is the medium through which the musician achieves enough understanding and strength to deal with the past and present hurt" (147). Another important theme in the story is that there is a common bond between people in dealing with their mutual suffering. Thus, when the narrator finally accepts Sonny and his lifestyle, by extension he accepts..."
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.."
Abstract Using the developmental theories of Piaget, Erikson, Kohlberg, and Skinner, this paper explains how to use them with high school math, English, algebra, and science.
Abstract This paper presents an overview of the life of Omar Khayyam, born on 18 May 1048 at Nishapur, the provincial capital of Khurasan. The writer explores all aspects of his amazing life, as painter, mathematician, musician, writer and philosopher. The paper begins with his early life in Persia through to his death in Nishapur on 4th December 1131. The writer believes that Omar Khayyam was an outstanding astronomer and astrologer and his contributions to this field are invaluable still today. The paper includes a number of drawings of the man and examples of his writing.
From the Paper "Omar Khayyam was well known as a poet, philosopher, mathematician, astronomer and physician. His full name was Ghiyath al-Din Abu?l-Fath Omar ibn Ibrahim Al-Nishapuri al-Khayyami. A literal translation of the name al-Khayyami means "tent maker" which maybe derived from his father's trade or he may have practiced this skill at one time. Khayyam played on the meaning of his own name when he wrote; ?Khayyam, who stitched the tents of science, Has fallen in grief's furnace and been suddenly burned, The shears of Fate have cut the tent ropes of his life, And the broker of Hope has sold him for nothing!?."
