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The Pie Chart, 2005.
Examines the use of the pie chart as a tool for data visualization in business.
811 words (approx. 3.2 pages), 3 sources, APA, £ 17.95
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Abstract
Data visualization is the use of interactive, sensory representations, typically visual, of abstract data to reinforce cognition. That, in itself, is a method or technique of decision-making. To further break it down, the most popular and widely used tool of data visualization is the pie chart. This paper presents an introduction of the pie chart and it's most common applications. It explains when it should and should not be used and provides examples in color.
From the Paper
"Pie charts work well when the values of the percentages of the whole differ greatly from each other. In other words, you do not want your pie values to be within one or two digits from each other, which would be indistinguishable on the chart to the naked eye. Another moniker for pie charts is: do not use a pie chart when there are more than six parts to the whole. Having too many values for comparison on the chart will distract from the clear simplistic message and instead offer a complex confusing assortment of data."
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Teaching Algebra Comprehension, 2005.
This paper discusses the use of graphing calculators to improve algebra comprehension in high school.
1,830 words (approx. 7.3 pages), 9 sources, APA, £ 35.95
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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. "
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Sir Isaac Newton, 2005.
This paper discusses the life and works of one of the most instrumental contributors to mathematical and scientific theory in the last few centuries, Sir Isaac Newton.
2,535 words (approx. 10.1 pages), 6 sources, APA, £ 46.95
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Abstract
This paper explains that Sir Isaac Newton advanced a whole new system of mathematics, including systems of physics and calculus, which were revolutionary during his time and continued to be
observed long after his death. The author points out that one of Newton's most significant contributions is his basic laws of motion often call Newton's Laws. The paper relates Isaac Newton would never have described himself as a 'scientist' because the word was not coined until more than a century after his death; he was a reclusive Hebrew scholar and Classicist who wrote more about alchemy and theology than the natural world, and his posthumous reputation is riddled with contradictions.
Table of Contents
Introduction
Life of Mathematician
Significant Contributions
Comparison to Present System
Conclusion
From the Paper
"Newton's laws of motion can generally be described through example and demonstration and represent a continuation of thought and inquiry into questions of physics. For example, many scientists before Newton could think of explanations for the continuation of movement of a given object due to force and velocity, but could not demonstrate it in a scientific way in the same way that Newton could with his laws of
motion. Using force and velocity, Newton made important mathematical relations that showed up in real world examples. For example, if someone was riding on a horse, they were going the same speed as the horse, then their velocity remained constant, but if something changed their velocity, it would differ from the velocity of the horse, and they
may change velocity in direction of proportionate force. Newton also contributed the commonly repeated maxim that each and every force (action) has an equal and opposite force (reaction). This is a very significant contribution because it represents a basic precept of modern physics."
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Chinese-Taiwanese Relations, 2005.
This paper uses an algebraic model in conjunction with an extended strategy game to prove that the passage of Chinese Anti-Secession bill was empirically and scientifically sound.
1,812 words (approx. 7.2 pages), 5 sources, APA, £ 35.95
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Abstract
This paper explains the dynamic history of the China-Taiwan relationship especially the controversial Chinese Anti-Secession bill, particularly Article 8, which states that, after exhausting all other avenues, China reserves the right to use military force or embargo to bring the situation with Taiwan to a close, conditional on Taiwan actually declaring independence. The author creates a game with nominal payoffs (a, b,c) creating a situation where China, assumed to be a rational actor, would most prefer, for example, say "c" but could risk getting a payoff of "b". The paper relates that, after computing the minimum threshold using expected utility formulas, arriving at a non-numerical solution, a probability value shows that China was rational in its decision to pass the bill since it saw its chances of being reprimanded by the international community as being much lower than is seen by the international community. Graphy. Formula.
From the Paper
"Those supporting Taiwan in this conflict are the US and Japan, and from this US alliance we could see countries like New Zealand and Australia come to Taiwan's aide if the US decides to invoke the conditions of the ANZUS treaty signed in 1951 . Among those supporting China's position are countries like Pakistan , North Korea, and Russia . If the bill was interpreted as a hostile war bill instead of a "fence-mending" bill as China claims it to be, the global community could formally and militarily become involved in the conflict. Setting aside this possible military threat, China must also weigh the economic consequences, with reaction from the global community that could include sanctions."
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Teaching Effectiveness, 2005.
An assessment of the avenues open to New York schools in terms of training mathematics and science instructors effectively so that there is true communication between the faculty and the students.
3,353 words (approx. 13.4 pages), 6 sources, APA, £ 58.95
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Abstract
This paper looks at aspects of teacher training and instructional quality in the instruction of mathematics and sciences in New York State schools, concentrating primarily on students in the 7-12 grade range and ways in which teacher training and instructional quality can interact in a planned program. This program is designed to train math and science teachers in more effective uses of pedagogy and the student-centered classroom in New York schools and focuses on the implementation of technology in the classroom as related to these subjects. It begins with a literature review in which instructional methods for mathematics and science teachers are assessed. Current policy is then analyzed, including training programs in other states that have been shown to be effective in teacher training. It advocates a system in which technology in the classroom, combined with more effective teacher-student interaction and subject application, can be introduced into the educational system.
Outline
Introduction
Literature Review
Current Policy
Recommendations
Short-Term and Long-Term Benefits
Conclusion
Bibliography
From the Paper
"Teachers can act as advocates of technology by acknowledging their own place in the school's inherent duty to empower students and help them improve their situation in terms of heightened achievements. To help the school fulfill its mission to truly help students and enable them to overcome their disadvantages, a new paradigm of instruction is sought. This new paradigm is based on the integration of computer assisted instruction into schools, and the goal is to improve conditions and monitor achievement through the implementation of teacher-led pilot programs. Computer assisted learning can help children learn to read, learn basic mathematics, and participate purposefully in their own
educational development."
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"The Problems of Philosophy", 2004.
An analysis of Bertrand Russell's "The Problems of Philosophy" and how his theory is a plausible account of representative realism.
1,430 words (approx. 5.7 pages), 5 sources, APA, £ 28.95
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Abstract
In chapter V of his book, "The Problems of Philosophy," originally published 1912, Bertrand Russell examined how mere humans perceived the world and how this perception occurred. This paper provides a brief biography of Russell. This is followed by a review and discussion of his analysis in "The Problems of Philosophy" to identify how he distinguishes between 'Knowledge by Acquaintance' and 'Knowledge by Description'. The paper also identifies how Russell's theory presents a plausible account of representative realism. A summary of the research is provided in the conclusion.
From the Paper
"To help elaborate on this component of his view, Russell says, "We shall say that we have acquaintance with anything of which we are directly aware, without the intermediary of any process of inference or any knowledge of truths." According to Russell, only the objects of immediate experience are known by acquaintance, through our direct awareness of them. Other things are known only by description, through the mediation of our apprehension of true propositions about them. For instance: "I am in a state of hunger now" may be known through acquaintance, but "Eating a pizza will relieve the state of hunger" can be known only by description. In spite of this apparently narrow extent, Bertrand maintains that knowledge by acquaintance provides the foundation for further knowledge by description, discussed further below. "
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Concepts of Beauty, 2003.
Examines why fashion models are admired in society today.
2,024 words (approx. 8.1 pages), 6 sources, APA, £ 39.95
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Abstract
Notwithstanding the adage, "Beauty is in the eye of the beholder," to explain why some humans appear more attractive than others, this paper provides a review of the relevant literature to identify what scientific basis there is for making determinations of beauty and how this can be applied to fashion models today. A discussion of the criticisms being directed against beauty pageants and their directors is followed by a summary of the research in the conclusion.
From the Paper
"We have all seen it: the New Miss America proudly walking down the runway, tears streaming down her humble face as she displays her crown and scepter -- showing the whole world exactly what it takes to be considered "beautiful." Some researchers, though, say the swimsuit-and-scholarship competition promotes an "ideal of female undernutrition" by crowning ever-skinnier contestants. A member of the staff at Johns Hopkins School of Public Health said, "Clearly there is a trend toward undernourished winners." In a recent analysis published in the Journal of the American Medical Association, scientists examined the decline in body mass index (BMI) scores among contest winners since first Miss America won the title in 1921. The winner of that contest had a BMI of 20.4. The "BMI reflects a person's weight divided by height to arrive at a number indicative of weight-related health" (Vergano, 2002, n. pag.)."
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Inferential Statistics vs. Single Case Designs, 2004.
This paper compares inferential statistics to single case designs and comments on the usefulness of each of these techniques for the practitioner.
1,117 words (approx. 4.5 pages), 5 sources, MLA, £ 23.95
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Abstract
The current paper comments on a quote by J.M Johnson and H.S Pennypacker that compares inferential statistics to single case designs. It discusses how the statement in question calls to account psychology as a science to abandon a traditional reliance on inferential statistics and group design research and to support its practical focus on the individual with reliance on more individually focused research.
From the Paper
"Inferential statistics is a branch of statistics that consists of generalizing from samples to populations, performing hypothesis testing, determining relationships among variables, and making predictions (Tabachnick & Fidell, 2001). This type of research is the most widely used in psychology, with the majority of published studies in this field relying solely on the use of group comparisons. The major argument for the use of inferential statistics is that it increases the external validity of the study and increases the likelihood of the results generalising to other people. These results are gathered by statistical inference where various methods of calculation are used to find a central tendency within a group. The variability of the results between subjects are often explained by measurement error or extraneous variability because well conducted group research introduces the only variability deliberately as an intervention designed to examine and measure its effect(s) on subjects (Hayes, Barlow & Nelson-Gray, 1999)."
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The Approaches to Studying Questionnaire (ASQ), 2004.
An explanation of how to conduct a factor analysis using Richardson's ASQ as an example.
2,848 words (approx. 11.4 pages), 5 sources, MLA, £ 51.95
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Abstract
This paper examines the results of a factor analysis conducted on Richardson?s short version of the ASQ with data obtained from 187 university students. This paper defines factor analysis and describes each step in the factor analysis process, giving a clear explanation for each decision made.
Outline
The ASQ
Factor Analysis Defined
Sample Size
Data Screening & Preliminary Analysis
Descriptives
KMO and Bartlett?s Test of Sphericity
Factor Extraction
Factor Rotation
Conclusion
From the Paper
"Richardson (1990) developed a short version of the ASQ in an attempt to examine the reliability and replicability of this version, which contained eight subscales of meaning orientation and reproducing orientation. Richardson concluded that this new questionnaire can be used in examining meaning orientation and reproducing orientation in research on student learning, with a factor analysis successfully retrieving these two primary approaches to learning. Richardson did warn however that the validity of the constituent subscales was still rather unclear."
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Statistics in Everyday Life, 2004.
Describes ways in which statistics are applied in everyday life and how they are used and abused.
1,437 words (approx. 5.7 pages), 6 sources, APA, £ 28.95
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Abstract
Statistics are a valuable aspect of scientific research. This paper demonstrates many different ways in which scientific data is used in everyday life. By the same token, statistics may also be abused to reach a false conclusion, and this is also illustrated through several cases.
From the Paper
"Just as statistics help in prosecution and defense of cases, they may also be abused when different experts in the same field offer different evidence and conclusions from examining the same data. Another way in which statistics may be abused is through corruption; in this case the police investigators may take DNA sample from a suspect and introduce it to a crime scene."
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Tracking System in Mathematics, 2004.
A study of the effectiveness of using tracking as a means of testing a student's abilities in mathematics.
2,922 words (approx. 11.7 pages), 9 sources, MLA, £ 52.95
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Abstract
This paper explains that tracking is an extremely common and widespread system whereby students are divided up among different classes and teachers according to their abilities. The paper uses a group of 20 students, with varying ranges of abilities in mathematics, and they are divided into 3 groups according to the tracking system. The paper lists the results of the study and summarizes the benefits and failures of the system. The paper ends with the results of the study, student-by-student, with statistical analysis as well.
From the Paper
"Poor student performance is one of the most pressing problems in American education today. In particular, math scores lag behind those of other developed nations. (Kodrzycki, 2002) Without a proper understanding of math, and mathematical concepts, today?s students will find themselves unable to compete in an increasingly technological world. They will not be able to find jobs, nor will American industry be able to compete successfully against its foreign counterparts. Though it is an essential part of the educational process, the how-to of improving students? mathematical skills remains problematic. (Stotsky, 2000, p. 44) Numerous approaches have been tried, but not all have been successful. One of the most popular methods is that known as Tracking ? an extremely common and widespread system whereby students are divided up among different classes and teachers according to their abilities. Tracking is rare until the Middle School Level, after which it becomes the norm."
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Prime Numbers, 2004.
This paper discusses the history and theories relating to prime numbers.
1,625 words (approx. 6.5 pages), 6 sources, MLA, £ 31.95
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Abstract
This paper explains that prime numbers have upset humanity for the last 2,300 years, ever since Euclid proved that there was infinity. The paper presents Euclid's proof. The author points out that, in the 19th century, the Russian, Tchebychef ,made significant contributions to the study of prime numbers by concluding that if the B(x) from Legendre's equation had a limit, then that limit had to be 1. The paper relates that Bernhardt Riemann, in 1859, continued Euler's work on series of numbers and made fundamental new discoveries within the prime numbers domain.
From the Paper
"Let x be a positive real number and let us define ? (x) as the number of primes less or than equal to x. ? (x) is a function and will be studied as such. For small values of x, we can intuit the values for ? (x). Thus, for example, if x is 10, then the primes less then 10 are 2, 3, 5 and 7, so that ? (10) is 4. Similarly, ? (24) = 9. Our concern is for very large values of x."
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"The Foundations of Arithmetic", 2004.
A review of Gottlob Frege's much-discussed book, "The Foundations of Arithmetic".
1,522 words (approx. 6.1 pages), 3 sources, MLA, £ 30.95
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Abstract
This paper explains how Frege's book is an influential and valuable insight into the philosophy of mathematics. It shows how Frege delves deeply into, not only an understanding of numbers, but also looks into much larger questions surrounding meaning and truth. Frege argues against the idea that arithmetic is based on psychology and, instead, notes that logic is the main underpinning of arithmetic.
From the Paper
"Friedrich Ludwig Gottlob Frege was born in Germany in 1848. He got his doctoral degree in G?ttingen, and quickly wrote his post-doctoral thesis, and became a university professor. During his long and fruitful academic career, the tireless Frege worked extensively to build up the philosophical foundations of mathematics and science. Among his important contributions is the invention of an artificial language called Begriffsschrift, which was based on logical notation (Frege Biography). Frege wrote extensively, publishing a number of other influential papers during his lengthy career, including Grundgesetze der Arithmetik, Volume I (1893), Logic (1897), Sources of Knowledge of Mathematics and the Mathematical Natural Sciences (1924/5), A Brief Survey of my Logical Doctrines (1906), and Thought (1918) (Frege Biography)."
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Problems in Statistics Education, 2004.
Critical analysis of a current problem in the field of statistics education.
2,681 words (approx. 10.7 pages), 20 sources, MLA, £ 48.95
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Abstract
This paper examines some of the ways to teach statistics that will best overcome some of the main problems that students encounter while learning statistics and offers solutions to these problems.
From the Paper
"Students do not normally encounter statistics until they are in college--at least not on any kind of practicable level--unless they are in extremely advanced mathematics classes at their high school. Even so, not every high school offers statistics as a course, while almost every college does. Teaching and learning statistics is problematic for most college students and teachers because to learn and understand statistics, it is necessary to first have a grasp of some of the properties and features of higher mathematics. Many college students do not have these skills upon entering college, and many professors assume that they do have these skills when beginning to teach a statistics course."
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