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)."
Abstract This paper discusses the WRAT3, which has been used for many years as a screening device to help pinpoint students who may need extra instruction or academic support. The paper describes the make up of the WRAT3 test, outlining its three academic subtests - reading, spelling, and arithmetic. The writer claims the importance of this specific test being part of a battery of tests in order to achieve the most accurate reading.
From the Paper "This test was normed using students age 5 to 19 in grades kindergarten through 12th grade. The test can be administered to anyone aged 5 to 75 (Overton, 2000), making it a screening tool with wide application. It has been noted in the marketing information for this test that wider claims are made for its use. Both the publisher and some distributors have made claims suggesting that the WRAT3 may represent complete testing. The Stoelting Company, one marketer for the test, says
?Useful in determining a person's level of performance in relation to age peers, WRAT3 can be used to determine appropriate instructional levels, and in diagnosing learning disabilities in reading, spelling, and arithmetic.? (Wllkinson, 2000). This seems an exaggerated claim unless the tester realizes that the WRAT3 should be one part of a test battery when diagnosing significant learning problems. As noted later in the paper, the reading subtest is markedly limited, and the test does not measure written expression at all, even though that is one area where a student can be found to be learning disabled."
Abstract This paper relates the deplorable state of education in the U.S, which ranks at the very bottom of 19 industrial nations in reading, writing and arithmetic, disastrous for a country that has bet its future on an information-driven economy. The author stresses that, if the philosophy of education is to be reformed and rethought, the beginning is with the educators themselves. The paper states that the first step in reforming the American school system is to retain some of the traditionalist values, such as teaching the basics of reading, writing and arithmetic; however, the methods and environment in which these skills are taught needs to be approached using a progressive viewpoint.
Table of Contents
The State of Education Today
Identifying Goals of Formal Education
Towards A Better Education
A Personal Philosophy
From the Paper "Part of the problem lies in the somewhat dismal salaries being paid to educators. Granted, this is in itself is a sad commentary on educators, but it is a fact of life, the economy and the rising costs of goods and services. As a result, because educators feel they are not being fairly compensated, the students ultimately suffer from neglect and/or lower standards of education. In a way, we can look at it as the classic case of the domino effect - to borrow a phrase from the Cold War era. Because the economy is suffering, educators' salaries are negatively impacted. Because educators' salaries are negatively impacted, their lack of dedication and motivation is dramatically affected, and at the end of the domino effect are the students."
Abstract This paper attempts to show that the world is changing at too fast a pace and that in order to give students the opportunity they deserve to develop all the skills needed to survive in the world, the classroom must be expanded and the support and cooperation of parents and the community organizations must be solicited.The author of this paper claims that a student confined to the traditional classroom will certainly not make it in society.
From the paper:
"Schools typically started out in very early days as a one-room, barn-like building, where all the children who lived anywhere nearby came to be taught how to read and write. There was usually one teacher for the whole school. Schools and education today is a far cry from this type of schoolhouse. With the growth in the population and the fast paced growing technology, education has had to develop to what is now very advanced systems and techniques. Schools are now large buildings housing hundreds of students, with a wide variety of specialty teachers, and modern equipment. Since schools have had to produce citizens to work in the organizations and companies which are moving so fast along, teaching has had to expand rapidly beyond mere reading, writing and arithmetic".
Abstract This paper examines the bove book which discusses every imponderable imaginable right from the mundane ones such as lottery odds, predicting a child's height, baseball arithmetic, to more complex ones including Windchill equivalent temperature, carbon dating, Newton's relativity theory and synchronous satellites. It shows how the book improves one's problem solving skills by making them think about imponderables and also aids one's understanding of mathematical concepts and sheds light on their useful application in our everyday lives. It evaluates how the book is also an attempt to improve numeracy among American public by making them more aware of the usefulness of mathematics in their lives.
From the Paper "The book begins with calculation of distance between one particular point and the horizon. Brookhart gives a simple geometric formula to predict the approximate distance. A casual look at these formulas in the beginning of the book prepares the reader for what comes later. However the very simple tone of the book is what arouses skepticism in readers. Some have even pointed out the errors they found in the book. For example the rejection of Goldbach's well-known assumption that "no one has ever found a number greater than 2 that could not be expressed as the sum of two prime numbers" is one such error."
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."
Abstract This paper explains that, because of the difficult of diagnosing accurately mental retardation in very young children, these children are often placed in early intervention programs without their final diagnoses having been completed. The author points out that the treatment should involve helping the person gain basic academic skills, such as reading, writing and arithmetic, which will support functional life skills, appropriate social skills and behavior management techniques for any inappropriate behavior. The paper relates that mentally retarded students may benefit from inclusion programs when younger; but, when older, it may have more negative effects unless the non-handicapped students are supportive of the program.
Table of Contents
Early Signs of Mental Retardation
Causes
Assessment
Treatment
Inclusion with Mental Retardation
From the Paper "While low IQ as measured on a good cognitive test is a cornerstone for the diagnosis of mental retardation, functional and adaptive skills must also be evaluated. A person who scores low on an IQ test but who functions adequately in life, for instance using public transportation, handling money adequately and living independently does not function as a retarded person and should not be diagnosed as such. A medical evaluation can look at developmental milestone and rule out causes such as deafness."
Abstract This paper explains that, from Robert Sternberg to Charles Spearman, psychologists over the last hundred years have attempted to shed light on the popular idea of intelligence and turn its nebulous concept into one of concrete measured understanding. The author points out that, by examining the cognitive process of young children, Piaget found that intelligence was an evolving process of a certain adaptation to the outside world. The paper relates that Charles Spearman was the first to develop techniques, which measured inter-correlations between different tests of intelligence, and postulated the existence of a general intellectual ability factor, which is tapped by all other mental abilities such as linguistic, mechanical and arithmetic abilities.
From the Paper "Robert Sternberg was the first of the set to research intelligence as something discernible by a definitive standard and comparable to its lay interpretation. Using supermarket shoppers, newspaper readers, commuters, students, and strangers, he asked nearly five hundred people to associate behaviors associated with ideas of "intelligence," "academic intelligence," "everyday intelligence, and "unintelligence." These associations led Sternberg to develop a list of characteristic behaviors each ideal which he then delivered to a group of 140 intelligence-psychologists for further analysis."
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 Godel's theorem and its lack of proof, absolute or otherwise, that machines do or may in the future experience self-awareness of one type or another. It discusses the assertions of the theory and the problems with it. The paper then provides a personal response, by the writer, to the issue of the present and future self-consciousness of machines.
Table of Contents:
Discussion
Response
From the Paper "Free will is a concept that cannot be even remotely defined with any degree of consensus. Talking about free will with religious groups results in completely different concepts of free will than when talking with political groups or academic groups or any number of different types of groups. Conversely, arithmetic calculations are easy to quantify and easy to define within the confines of the overall system. Somehow Smullyan would like his readers to believe that defining free will is as self-apparent as 2 plus 2 or similar arithmetic equation. Some researchers have described Godel's Theorem as being some type of alternate description of a value system: "The system of values could be part of the program the computer followed in making its choices. The computer system would then appear to have those values, and be guided by them (Machina 3). Thus Smullyan's entire argument regarding free will is based on a number of unfounded and unproven assertions that have no basis except in extreme positives or negatives. These equate to a world that is either black or white and all decisions are, ultimately, yes or no questions."
