Abstract This paper discusses the life and discoveries of Galileo. It specifically discusses the conflict of Galileo's discoveries with the Catholic Church. It looks at his work in the sciences of astronomy, physics and mathematics and his adoption of the Copernican astronomical theory. The paper also looks at the Catholic Church's reactions to his views.
From the Paper "In the end, Galileo forever changed the the sciences of astronomy, physics and mathematics. Despite the attempts by the Church to silence his revolutionary work, Galileo continued. His work, was evaluated and validated by observers across Europe, in England, German and France. And, it would be Galileo's work that would encourage experimentation in physics, to test mathematical and physical laws. Sadly, it wouldn't be until more than 300 years later that the Church would recant their views, with Cardinal Paul Poupard, the head of an investigation by the church into Galileo's theory, statement in 1992 that said, "We today know that Galileo was right in adopting the Copernican astronomical theory" (qtd. Brauchli )."
Abstract This paper offers a brief biography of Pythagoras and a discussion on the mathematical theorem that is associated with him. The paper explains the Pythagorean theorem's relationship to the area of a circle.
Outline:
Abstract
Biography of Pythagoras
History of the Pythagorean Theorem
The Pythagorean Theorem's Relation to the Area of Circles
From the Paper "Pythagoras was a Greek sage of the 6th century B.C.. He was born on the Greek island of Samos, off the coast of Asia Minor. Pythagoras was introduced to mathematics by Thales of Miletus and his pupil Anaximander, according Iamblichus, the Syrian historian. He traveled to Egypt, around 535 B.C., to continue his studies, but was captured by Cambyses II of Persia, in 535 B.C., and was taken to Babylon ("Pythagorean", 2007). Eventually, Pythagoras emigrated to the Greek colonial city-state of Croton, in Southern Italy (Mourelatos, 2007; "Pythagoras", 2007)."
Abstract This paper discusses the relationship between literacy and mathematics and how children who struggle with literacy generally struggle with maths too. It describes and examines five lessons plans for a mathematics class, in terms of ability to integrate math and literacy skills. The paper contains the original sources for the five lesson plans.
Table of Contents:
Lesson Plan #1: Teach Your Friends Polynomials
Aim of the Lesson
Literacy Elements Incorporated
How, When Why, Where and for Whom they were Used
Compare Quality from Beginning to End
Lesson Plan #2: Graphing Population Studies
Aim of the Lesson
Literacy Elements Incorporated
How, When Why, Where and for Whom they were Used
Compare Quality from Beginning to End
Lesson Plan #3: Adding Fun Game
Aim of the Lesson
Literacy Elements Incorporated
How, When Why, Where and for Whom they were Used
Compare Quality from Beginning to End
Lesson Plan #4: Word Problems and Technology
Aim of the Lesson
Literacy Elements Incorporated
How, When Why, Where and for Whom they were Used
Compare Quality from Beginning to End
Lesson Plan #5: Sorting Through Life
Aim of the Lesson
Literacy Elements Incorporated
How, When Why, Where and for Whom they were Used
Compare Quality from Beginning to End
From the Paper "The students must have the necessary skills to search for and read information found on the Internet to be included in their presentation. The students must be able to organize text and present it in a concise, coherent fashion. The students must have sufficient keyboarding and software skills to be able to make the final presentation."
"Teaching others is a great way to master skills. This lesson allows students to become the teacher. They must master the skills in order to be able to teach them. The students create a tutorial for their classmates, which forces them to research and learn the material thoroughly before preparing the presentation."
Abstract The paper discusses how Sir Isaac Newton was one of the greatest mathematicians and physicists of all times with achievements in other domains such as alchemy, chemistry and even religion or philosophy. The paper looks at Newton's work "Optiks," a study which best emphasizes his work on light and color, and his work "The Principia" that explains Newton's three laws and his definition of gravity.
From the Paper "Sir Isaac Newton is one of the greatest mathematicians and physicists of all times; usually presented by the historical documents of science as the academician who discovered the Law of Gravity, Newton also had great achievements in domains such as optics, mathematics, mechanics, alchemy, chemistry and even religion or philosophy. He was born in 1642 at Woolsthorpe, near Grantham in Lincolnshire, where he started his education. In 1661 he became a student of the Cambridge University and in 1667 a Fellow of the Trinity College, when he discovered his passion for mathematics. He later on became a professor of the university, this period of his life being mainly dedicated to studying mathematics, physics and alchemy. Moreover, he made his first public scientific achievement, the invention, design and construction of a reflecting telescope and he also wrote "Principia", a study of mathematical principles applied on natural philosophy, which was only published in 1687 ."
Abstract The paper explains Abraham Maslow's hierarchy of needs theory, which holds that individuals must be offered an opportunity to experience learning in a unique way, to fulfill their need of self-actualization. The paper then goes on to discuss how to achieve this goal of creativity in the mathematics classroom.
From the Paper "Abraham Maslow is most well known for what has become known by most as, Maslow's Hierarchy of Needs. Maslow theorized that people must achieve certain needs before being able to fully experience needs of a higher order. So, in other words those who are barred from higher thought by an inability to achieve shelter and obtain enough food to eat, or basic perceived security are likely to become stunted in their ability to perform abstract thought processes and achieve more abstract personal goals. At the pinnacle of this hierarchy Maslow placed self-actualization, an ability to place one's self in an abstract position and understand lofty concepts such as justice, equality and truth. (Roeckelein, 1998, p. 318) In the context of education it is fair to say that the development of Maslow's hierarchy as well as many other contributing concepts and the real lag that is seen by those who for many reasons lack the abilty to achieve basic needs, have done much to explain why some people develop and learn, accessing higher order thoughts and concepts and others do not."
An analysis of a study entitled "The Effect of Movie Portrayals on Audience Attitudes About Non-traditional Families and Sexual Orientation" conducted by M.A. Mazur and T.M Emmers-Sommer.
Abstract This paper discusses the usefulness of statistical significance testing in psychology through a critical examination of a study entitled "The Effect of Movie Portrayals on Audience Attitudes About Non-traditional Families and Sexual Orientation", conducted by Mazur and Emmers-Sommer. The paper explains that the critical analysis of the article demonstrates a number of the criticisms regarding the use of statistics in the field of psychology and that it makes clear that a great deal of improvement is necessary in the field's use of statistics. The paper concludes that if psychology is ever to become a recognized natural science, researchers within the field must become more cognizant of the proper and practical application of statistical methods.
From the Paper "The study "employed an experimental pre-test / post-test control group design" which randomly assigned participants to one of two groups (Mazur & Emmers-Sommer, 2002, 164). Individuals placed in the treatment group watched Object of My Affection, which featured a non-traditional family and a gay male couple within the storyline. The control group watched Father of the Bride II, which displayed no forms of non-traditional families and no inter-racial, gay or lesbian relationships. Immediately prior, to and following the viewing of the movies, each group completed Lye and Biblarz's Attitudes Toward Gender Roles and Family Life Scale, Herek's Attitudes Toward Lesbians and Gay Men (ATLG) scale and a demographics questionnaire. Lye and Biblarz's scale consisted of eleven items rated on a 7 point Likert-type scale while the ATLG was abridged from its original version on both gay men and lesbians to include only the 10 items on gay men, and was rated on a 9 point Likert-type scale. "
Abstract This paper explains that Florence Nightingale was born of wealthy parents and could have lived an idle, sheltered existence, typical of women during the Victorian era who did not attend universities or pursue professional careers. Although she is best known for her role in the nursing profession, the paper relates that she also left her mark on the fields of mathematics and computer science. The paper describes her illustrious career, which overcame the social obstacles for women during the Victorian era and led to her being the founder of modern nursing and the first woman to be elected a member of the Royal Statistical Society.
From the Paper "As a young adult, Florence became interested in hospitals and nursing, but her parents refused to allow her to become a nurse as in the mid-nineteenth century it was not considered a suitable profession for a woman of Nightingale's social stature. While traveling with friends, she visited Pastor Theodor Fliedner's hospital and school for deaconesses at Kaiserswerth, near Dusseldorf, Germany and would later return to the school for nursing training. Her first job after training was Superintendent of the Establishment for Gentlewomen during illness at No. 1 Harley Street, London in 1853."
Tags: crimea, descriptive statistics, polar-area diagram, sanitary reform, data visualization
Abstract This paper examines how grounded theory is utilized in performing a qualitative research and how it recognizes and allows the subjectivity of its participants, but attempts to still be objective and avoids researcher and participant biases. The paper also looks at how there are three basic elements of grounded theory: concepts, categories, and propositions. In addition, the paper looks at the advantages and disadvantages of the theory as well as its relevance to nursing research.
Outline:
Description of Grounded Theory
The Advantages and Disadvantages of Grounded Theory
Relevance of Grounded Theory to Nursing Research
From the Paper "There are three basic elements of grounded theory: concepts, categories, and propositions (Pandit, 1996). A theoretical concept is not the data itself, but it unifies these small data into one phenomenon. Small data are recognized as codes. A concept determines if a certain data is encountered is relevant to the subject being studied. A concept is a little bit more abstract than data collected. Concrete ideas such as "taking pain relievers" or "sleeping" may be considered as activities to "removing pain". The second element of grounded theory is the use of categories. Grounded theory makes use of more abstract labels, or categories, to organize data. As more seemingly random concepts arise, a relationship among them can be found. "
Abstract Two kinds of errors can occur in significance testing. These are type I and type II errors. This paper provides an exploration of type I and type II errors and looks at how to determine if they occur as well as how they can be prevented. The paper attempts to show that the prevention of these errors will allow students and researchers of nursing to perform more accurate hypothesis tests, as well as help them understand the reliability of statistical testing.
From the Paper "A Type II error occurs when a false null hypothesis is not rejected. In other words, the false statement that there is no relationship between the variables has failed to be rejected. This case is not as serious as a Type I error for the simple statistical rule that causation does not equal correlation. Because rejecting the null hypothesis does not suggest that a relationship exists between the variables, but only that the null hypothesis is incorrect, a failure to reject the null hypothesis makes no conclusions (Lane 2008). The difference between Type I and Type II errors in terms of seriousness, therefore, is rather pronounced. A Type I error is seen as a serious error because it is stating that something is true--that the null hypothesis is false when it is actually true--while a Type II error makes no such claims, but only results in a failure to reject the null hypothesis. "
Abstract This paper talks about dividend growth models, in particular the Gordon Growth model and the assumptions that one needs to take in the calculations. The paper includes the characteristics and limitations of dividend growth models and talks about CAPM, or the capital asset pricing model, which is based on three main parameters: the risk - free rate, the stock's beta coefficient and the expected rate of return for the market as a whole, used to calculate the market risk premium. The author compares the two models and explains why the modern portfolio theory is base on CAPM notions.
From the Paper "On the other hand, the CAPM is an easy to use and implement model, based on three main parameters: the risk - free rate, the stock's beta coefficient and the expected rate of return for the market as a whole, used to calculate the market risk premium. The model has a large applicability, mainly because it does not use dividend estimates for the future and thus works for organizations that do not pay regular dividends, but also because information on the three variables mentioned are usually public and thus one does not need to make additional estimates on the variables used. "
Tags: dividend growth models. growth rates, Modern Portfolio Theory
A research paper that examines educators' perceptions of changes in reform-related practices in mathematics instruction since the implementation of state wide testing.
Abstract The paper examines the effects of mathematics reform on teacher practices and determines the perceptions of educators regarding it's effects on student achievement since the implementation of high stakes testing. The paper identifies reform-related practices in mathematics instruction that have increased, decreased, or not changed since the implementation of high stakes testing, based on educators' perceptions and determines educators' perceptions of the effects of reform-related practices on improving student achievement since the implementation of high stakes testing. The paper also addresses a significant number of research questions regarding the perceptions of educators, both generally and demographically, regarding the changes that have occurred within the classroom for students since the implementation of outcomes based testing.
Outline:
Abstract
Acknowledgements
List of Tables
Chapter 1
Introduction
Statement of the Problem
Purpose of the Study
Research Question
Significance of the Study
Proposed Methods and Procedures
Definitions of Terms
Literature Review
Introduction
Components of MERA
Perspectives of Educators Regarding Standardized Education Reforms Standards and Assessments
Changes in Curriculum and Modes of Instruction
The Effects of Accountability Systems on Individual Teachers
The Effects of Accountability Systems on a School's Capacity
The Effects of Accountability Systems on Student Learning
Alignment of Curricula and Instruction
Conclusion and Final Thoughts
Theoretical and Conceptual Frameworks
Methodology
Research Design
Sample Description
Survey Permission and Procedures for Human Subject
Protection Survey
Distribution
Survey Returns
Instruments, Measures, and Validity
Data Analysis
Specific Data Analysis Plan for Each Research
Question
Limitations
Results
Research Question One
Research Question Two
Research Question Three
Research Question Four
Research Question Five
Research Question Six
Research Question Seven
Summary and Discussion
Connecting the Theoretical Framework
Discussion
Implications of the Outcome of the Data Conclusion
Implications for Future Research
From the Paper "Another informative aspect of reform and a clear guide for future research will be real test scores, beyond marginal improvements. To accept reform as positive teachers and other educators must be shown more than marginal improvements on test scores, and they must also see real improvement for remedial as well as advanced and "normal" students. Student participation in creative solutions can and likely will play a part in these improvements, regardless of early concerns regarding issues of teachers "teaching to the test." Real world mathematics applications, performance based assessment for daily, weekly and quarterly personal improvement needs as well as many other teacher based creative reforms will likely continue to play a significant role in change."
An argument against the views of Harold Bloom regarding William Shakespeare's influence in Lewis Carroll's "Alice's Adventures in Wonderland," as expressed in his work, "Shakespeare: The Invention of the Human."
Abstract This paper examines mathematics and logic versus the influence of William Shakespeare in Lewis Carroll's "Alice's Adventures In Wonderland." The paper specifically analyzes Harold Bloom's work, "Shakespeare: The Invention of the Human" and his views on Shakespeare's influence in Carroll's book. The paper argues against Bloom's view and aims to find not only references to Shakespeare, but also much grander references to Carroll's own discipline of mathematics and logic.
Table of Contents:
Epigraph
Preface
Introduction
Bloom's Argument of Shakespearean Influence
Testing Bloom's Premise: Shakespeare's Influence
Mathematical Influence
Conclusion
From the Paper "By discovering that Wonderland is indeed grounded by the same logical, predictable, mathematical basis as the real world, Alice is saved from the fate of losing faith in her knowledge and reasoning abilities, and hence from the madness which afflicts Wonderland. Similarly, she encounters this logic as she comes into contact with a variety of creatures that she does not understand or whom seem strange to her. The creatures' use of logic allows her to understand how the logic that might make sense to her seems completely illogical to them. Thus, Carroll not only manages to use logic in order to prove both the logic and the illogical, but also, he uses this logic and mathematics to emphasizes his two mains themes, that Alice is saved from the world of the illogical by logical concepts like mathematics and that what one person thinks is logical may be illogical to another and vice versa, the dichotomy of the strangers."
Abstract This paper provides an overview and a background concerning the Fibonacci series and the Golden Ratio, followed by an examination of how it is manifested throughout nature. In addition, a discussion of how the Fibonacci series is found in various human endeavors is followed by a series of representative mathematics problems based on the Fibonacci series that can be used in a wide range of classroom settings to help introduce these concepts to young learners. Finally, a summary of the research and salient findings are presented in the conclusion. Several tables and diagrams are included with the paper.
Outline:
Review and Discussion
Background and Overview
Fibonacci Series in Nature
Fibonacci Series in Human Endeavors
Math Problems Using the Fibonacci Series
Conclusion
From the Paper "The continuing emphasis on the Fibonacci series is based on the fact that this series generates the most famous proportion in the history of art and architecture: the Euclidean golden section or golden ratio (shorthand phi). The ratio between any two values in the series results in the so-called "golden number" to increasing levels of accuracy the higher the numbers in the series. Therefore, for instance, 3:5 = 1:1.666, 21:34 = 1:1.61904, 55:89 produces 1.61818, which is an approximate of the actual golden section number of 1.618034 ... . In this regard, Batten (2000) reports that, "One thing to note is that the Fibonacci sequence has many interesting properties in itself. For example, the sum of any two numbers in the sequence equals the next number in the sequence. 1 plus 1 equals 2, 1 plus 2 equals 3, 2 plus 3 equals 5, 3 plus 5 equals 8, and so on to infinity". Likewise, and more importantly, the ratio of any two numbers in the sequence approaches 1.618, or its inverse, 0.618, after the first few pairs of numbers; the ratio of any number taken to the next higher number, known as "phi," is approximately 0.618 to 1 and to the next lower number is about 1.618. The higher the numbers in the sequence, the more close to 0.618 and 1.618 are the ratios between the numbers. As Cromer points out, "Phi = (1 + 5)/2 = 1.618 . . . is one of the two solutions of the quadratic equation x2 - x - 1 = 0. Starting with any two numbers, say 3 and 7, a Fibonacci sequence is obtained by making each new term equal to the sum of the last two terms. "
Abstract The paper reveals that the result of inquiries into the efficacy of the No Child Left Behind (NCLB) Act are virtually unanimous in their characterization of the NCLB concept as a failure and as a tremendous waste of valuable resources. The paper examines the four essential elements of the Act and outlines the many conceptual problems with this approach to education. The writer relates that he is opposed to the NCLB approach because it contradicts so much of the various philosophies underlying modern educational theory. The writer goes on to relates his personal philosophy of education.
Outline:
Background and History of the No Child Left Behind Act
Educational Reform Under the No Child Left Behind Act
Conceptual Problems with the No Child Left Behind Approach to Education
Specific Issue Analysis -- Contemporary Learning Theory and the NCLB Approach
Conclusion
From the Paper "Education reform in the United States is not a new idea. In 1965, President Lyndon Johnson enacted the Elementary and Secondary Education Act and during the administration of George H. Bush, the first President Bush promised, among other things, that by the turn of the century, all American school-aged children would have the benefit of comprehensive quality educational programming and improved nutritional and healthcare access to facilitate their learning in school. President G.H. Bush went so far as to promise that improved focus on American education would go so far by then as to also provide the training necessary for the parents of preschoolers to fulfill their role at home as their children's "first teacher"."
This paper looks at the controversy over who discovered calculus and provides an explanation of why the honor should go to Isaac Newton over the claim of Gottfried Leibniz.
Abstract In considering the great controversy as to who discovered the calculus, either Newton or Leibniz, this essay argues that the accolade should go to Newton. The decision is made on the ground as to who conducted himself most honorably in the affair. There is no doubt that both scientists come to independent discovery and formulation of the calculus. The essay is at pains to point out the greatness of Leibniz, as philosopher, scientist and mathematician. It even acknowledges that Leibniz's formulation of the calculus is superior, and that this superiority derives from his related philosophy of monadology. But Leibniz certainly acts suspiciously during the controversy. The writer maintains that in contrast, Newton at all times displays magnanimity and selflessness. The writer concludes that Newton does not need accolades for his contributions to shine, and yet they shine on their own merits.
From the Paper "Calculus to Newton was merely a tool that he required to come to his universal theory of gravitation and motion, and not something that should be flouted separately. He was even reluctant to publish the revolutionary Principia, and did so only after the prodding of Edmund Halley.
"Leibniz, on the other hand, was eager to publish and propagate his findings. While we admit to his originality to a large extent, the conduct of Leibniz is highly suspicious in the proceedings. He makes no defense of his integrity, as Newton does, but instead seem entirely intent on pushing the evidence alone, as if defending himself in a court of law, and this makes us feel that he is hiding something. Subsequent scholarship does indeed reveal that he manipulated documents before being released."
