Abstract This paper focuses on mathematical achievement in African-American boys versus their white counterparts. It addresses risk factors such as family income, mother's education, single-parent households and a non-English primary language. The paper discusses the works of theorists Lev Vygotsky, Jerome Bruner and John Dewey regarding this issue.
Table of Contents:
Objective
Introduction
Theoretical Framework
Limitations
Literature Review
Summary of The Literature Reviewed
From the Paper "The African American male was not expected to achieve in educational areas of management and accounting studies evidenced in the statement related in the work of Dantley and Leonard (2006) who states that a participant related that: "I only indulged myself in my studies to the degree that I was satisfied that I could do math up to multiplication and division of fractions and decimals and it was good enough for me for what was I going to do. I wasn't going to be doing any math. To be a laborer, all it's going to require is to run a piece of machinery." (p. 42) additionally a participant stated: "We don't have no industry out there and the industry that is out there, they're not targeting the Black community and saying, "If you go and get more math, then I can guarantee you this." (p. 45) and finally: "I have hopes. My expectation is that (my son) will graduate from high school. If he doesn't, it's no big deal...My expectation for him is to probably be no worse than I was. Just to pass." (p.46) (Dantley and Leonard, 2006)"
A regression analysis used to explain whether police use different standards of severity when dealing with resident versus non-resident drivers in Florida.
Abstract This paper discusses whether police use different standards of severity when dealing with resident versus non-resident drivers in Florida. The paper uses the regression analysis, which estimates the significance of the variation of the dependant phenomenon with the independent and the influence of the latter on the former. The paper explains its analysis and shows that a relationship does exist.
From the Paper "The hypothesis is tested with the confidence level of 95%, thus the allowed chance of rejecting no relationship between the variables when there is actually this relationship, is 5%. Decreasing the confidence level to 90% will give more errors in the model and the model did not result in better relationship. Having carried out this multifactor regression, the result revealed that there is no statistically significant relationship between the over speeding and the fact that the person is a resident or non resident and the gender of the person. The first problem with the model could be the very data set as out of the 536 observations in the population, only 136 were the cases when people were none residents. Thus, the results could be distorted. The R2 in the model is extremely low and reveals that very little variation in the severity of this crime could be explain by the factors in the model. P-values are low only for the intercept and none-residence factor."
Abstract This paper discusses the life of John Wilder Tukey, who was a mathematician. It describes Tukey's upbringing and his introduction to mathematics. The paper discusses Tukey's most important statistical work, which was the way he presented his evaluation of "spectra time series". It then describes the three major contributions of Tukey according to Regents of the University of Minnesota.
From the Paper "Tukey's first official school was at Brown University where he took both his Bachelor's Degree and the Master's Degree in Chemistry. Since he was interested in mathematics, he pursued his Ph.D. at Princeton University in 1937. Lefschetz supervised Tukey's research and Tukey eventually received his doctorate in 1939 with a dissertation in Denumerability in topology that was published in 1940 as Convergence and uniformity in topology (O'Connor and Robertson, 2004)."
"Tukey became a mathematics instructor at Princeton and joined other famous statisticians and mathematicians during the World War II to study the statistical mathematical problems of artilleries and weapons. This study covered the computations and calculations of how to accurately target traveling objects. In 1945, he was enlisted at AT&T Bell Laboratories in Murray Hill. By 1965, he wrote a manuscript entitled Mathematics in Computation with J. W. Cooley wherein he presented the Fourier transform algorithm."
Abstract The paper explores the connection between math and reading skills and how to improve both skills in students. The paper explains that it may be that the same areas of the brain are used for arithmetic and phonological skills. The paper discusses how the critical problem facing the adoption of new techniques, such as the use of journals in the math classroom, is that teachers do not have the support needed to continue with the new technique.
Outline:
Why is Reading Important to Math?
Strategies for Improvement
Conclusion
From the Paper "Reading and math were historically thought to be in no way connected. Much time in primary math classes are spent memorizing math facts. With the exception of the occasional word problem, reading skills were virtually ignored as a component of math success. However, the role of inquiry in mathematics is gaining importance as the role of critical thinking becomes tied to the job skills needed as an adult. The new technology paradigm requires the adult to be able to analyze complex situations and to develop solutions to the problems that they encounter."
Abstract This paper discusses the life and work of William Sealey Gosset, who was one of the leading statisticians of his time, particularly with his work on the concept of standard deviation in small samples. It gives examples of some of his achievements in the realm of statistics. The paper describes Gosset as both brilliant in his professional work as a chemist and statistician and as a loved and respected man.
From the Paper "After Gosset had worked for many years developing the practical application of his theory, he was involved in a terrible car accident in 1934 which left him incapacitated for many months. During this time, he had the opportunity to continue to work on his statistical work. He recovered enough after a year to move to London where he became the head brewer and scientist of production at a new Guinness brewery. Gosset continued to publish the results of his statistical findings while working in London. He did not hold his position there long as he died in Beaconsfield, England, on October 16, 1937 (O'Connor and Robertson)."
Abstract This paper is a research project, which uses anomaly intrusion detection to determine if there are any abnormal patterns and, hence, intrusions in the provided log files. The author stresses that a statistics approach seems to be the easiest and most straightforward approach. The paper relates that a common practice in IDS software is to incorporate different techniques to detect intrusion so that other methods such as hierarchical clustering can still be included in the system to search for suspicious/ known data patterns such as viruses. The paper includes charts, graphs and a screen-shot.
From the Paper "Since we are not building a new system, we will try to implement and base the report on existing work. Viewing sequence algorithms for intrusion detection helps to determine which patterns look like patterns of intrusion. The statistics technique is discussed but will not be programmed at this current time. We will also attempt to show manually how this algorithm will detect the patterns using previous research as it correlates to this specific data using logs provided and some data mining algorithm."
Abstract This paper discusses an intrusion detection algorithm for analyzing university web server log files. It also discusses integrating hierarchical clustering with other algorithms for an intrusion detection system. The paper proposes to use hierarchical clustering as the main back bone of the intrusion detection system and then incorporating other algorithms like statistics and support vector machines (SVM) as needed.
From the Paper "The initial plan was to use the user signatures method by Seth Freeman or the Traffic Classification technique but the first method seems more suited to an OS than for web server log files and the second seems a lot more complicated and also requires a destination IP, which is not readily available from our log files. I started out by writing a statistics based algorithm but then added hierarchical clustering based on instructor feedback. Eventually I settled on this paper based on hierarchical clustering with other methods as backup although I still like the statistics approach."
Abstract This paper provides a clear explanation of Blaise Pascal's "Wager for Sceptics." It explores, in depth, its merits and its flaws and focuses on the flaws in Pascal's reasoning that resulted in it not achieving his stated goal. This paper demonstrates that, ultimately, the arguments against the "Wager for Skeptics" all stem from the incomprehensible nature of infinity, a notion that lies at the heart of Pascal's work.
From the Paper "Emanating from his mathematical background, comes Blaise Pascal's Wager - a line of reasoning designed to lure people into the Christian faith. Pascal is acutely aware of human nature, and so bases his campaign around the reader's self-interests, rather than actual theological proofs. The Wager's basic proposition is that if a person believes in the Christian God, there is a chance of them gaining infinite reward. Conversely, if a person does not believe in God, they have no chance of gaining the reward which is on offer. This is a deceptively simple choice: one that immediately appears both enticing and convincing. However, our initial arousal begins to subside just as quickly when we realise that there are major flaws in Pascal's reasoning. Pascal attempts ardently, though unconvincingly, to quash some of the objections that might be proposed. The argument itself, however, if taken as convincing, leads to some unexpected outcomes - ones that do not align with those that Pascal intended. Ultimately, the Wager does not succeed in providing a compelling reason for believing in Pascal's God over any other form of belief."
Abstract The paper discusses the Hungarian mathematician, George Polya and relates that he is hailed by many as not only one of the greatest mathematicians, but also a great teacher of his time. The paper examines his schooling, his studies in university and the path to his career in mathematics. The paper details all his various accomplishments and promotions.
From the Paper "Polya's parents, Anna and Jakab, were both Jewish. Jakab's original surname was in fact Pollak, but he changed this for the sake of his professional goals. After his law firm failed, he worked for an international insurance company. However, Jakab's dream was to obtain a research post at a university and pursue his true interests, economics and statistics. It appears therefore that George inherited not only his father's tenacity, but also his interest in numbers. In 1882 Jakab Polya was finally appointed as Privatdozent at the University of Budapest."
Tags: numbers, combinatorics, Hurwitz, professor, university
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 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 explains that a lookback option is path dependent, based on the maximum or minimum underlying value reached during the entire life of the option. The author points out that, at the expiration date of these options, the holder may "look back" over the life of the option and exercise it, based on the optimal underlying value achieved during that period thus giving the holder the ability to buy an asset at its lowest price or sell it at its highest price achieved over the life of the option. The paper relates that, through the lookback option, the investor can achieve economic intelligence and value through the benefit of hindsight; however, lookback options carry risk and are more expensive than standard options. The paper includes several formulas.
Table of Contents
Definition of Options
Call and Put Options
Introduction to Lookback Options
Lookback Options in Greater Depth
The Model
Option Pricing
Discrete Lookback Options
Case Study of Lookback Options
From the Paper "Put options conversely involve the investor aiming for a stock price decrease. The put option, as mentioned in the introduction, allows the holder to sell an asset by a particular date for a certain price. An example demonstrated by Hull (2006) involves a European option involving an investor who buys the option to sell 100 shares with IBM for a strike price of $70. If the current stock price is $65 and the expiration date is in three months, Hull supposes for example that the option to sell one IBM share is $7. The initial investment, therefore, will be $700."
Abstract The paper defines the unit circle as a key instrument in learning about trigonometric functions, values and concepts. The paper lists the steps to making a unit circle and provides detailed examples and graphs.
Outline:
What is the Unit Circle?
How Do I Make a Unit Circle?
How To Find Coordinates
How To Find a Reference Angle
Negative Values
In Conclusion
From the Paper "Well, to first understand the Unit Circle, you must first understand basic graphing, because the Unit Circle is based off the circular graph x2 + y2 = 1. The Unit Circle is a circle whose values are counted counterclockwise starting from the point (1,0). Then the values- in degree and radian measure (don't worry all of this will be further explained later, so don't worry if your lost)- are used to solve trigonometry problems and equations. The values on the Unit Circle are used to find sine, cosine and tangent values as well as to find compliment and supplement angles. Overall, the Unit Circle is one of the most helpful things to know when doing the ever so complicated trigonometry. An easy was to think of the Unit Circle is that the Unit Circle is a box of primary colors, it's your red, blue and yellow. With this Unit Circle/primary color box you are able to make and understand all sorts of other colors and concepts."
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."
Abstract This paper discusses Godel's theorem and how it is sometimes used to imply that all machine logic can eventually become self-aware. The paper also discusses the criticisms of the theorem and its limitations. The paper then provides an allegory to explain Godel's theorem and discusses the advantages of this explanation, as well as the limitations in using an allegory to try to understand the theorem.
Table of Contents:
Allegory and Godel: Oil and Water
From the Paper "Godel recognizes that his theory in fact could not be fully described in human language and concepts and this is a fact that Hofstadter completely misses. When Godel is quoted as saying the epistemological descriptions in a given language cannot be restated in that same language, he directly disallows the use of allegory in retelling his theory. The unfortunate aspect of Hofstadter's allegory is that most readers get lost in trying to decide what the various characters represent, what is meant by the way the dialogue is spoken and, ultimately, what the Omega record player looks like. None of which, of course, has anything to do with Godel's Theorem."
