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 examines how although Florence Nightingale is mainly remembered for her compassion and work in the field of nursing. Another of her achievements was in the field of statistics and mathematics. It looks at how she succeeded in augmenting a practical application of statistics to the profession of nursing and how her graphical and statistical representations of deaths in the Crimean conflict promoted the use of sanitary reforms, which were implemented throughout the nursing profession.
From the Paper "Furthermore, she also made important contributions in the field of epidemiology. This is the study of the demographics of disease processes, including the study of epidemics, which uses statistical procedures. For example, Nightingale "... made a statistical study of sanitation in Indian rural life. She invented a diagram known as the coxcomb or polar area chart to depict changing patient outcomes in the military field hospital she managed". (Campus Program) She had become an expert statistician and in 1858 was elected the first female member of the Statistical Society. She was also made a member of the American Statistical Association. The statistical measurement and innovations used during the Crimean War not only led to a reduction of deaths but also added to her reputation as both a statistician and nurse."
Abstract This paper explains that L'Hopital, who lived during the conception of modern calculus, was taught by Bernoulli; the result of this tuition was L'Hopital's "Analyse des Infiniments Petits", which became the French reference book in the calculus for a century. The author points out that L'Hopital's name is guaranteed to survive in the memories of thousands of mathematicians because of the L'Hopital rule, which is useful when dealing with indeterminate forms. The paper relates that L'Hopital created the template by which all calculus texts would be modeled and measured against for the next three hundred years. Formulas included.
From the Paper "A natural progression from his two first works on the topic of calculus would have been a serious examination of the integral calculus. Indeed, this was a project that L'Hopital was capable of and actually began to write before his death. However, one of his contemporaries-Leibniz-made it known to L'Hopital that he also endeavored to publish a work covering the same hole in written calculus of the time. Apparently, out of respect to the mathematician who made much of his fame possible, L'Hopital abandoned the project."
Tags: derivative, calculus, Bernoulli, indeterminate, text
Abstract This paper explains that professional development is an opportunity for existing teachers already in schools to learn new teaching methods thus making them and their programs more effective. The author points out that utilizing outdated or ineffective teaching techniques or an inadequate knowledge of basic technological advances is completely unacceptable in the realm of teaching mathematics because a good knowledge of mathematics is important to all aspects of students' lives. The paper describes two models of professional development programs: (1) CATIE Mentoring Program, which is an extremely successful process for instituting technology into the realm of mathematics teaching and (2) School-within-a-School Model, developed in Canada, which is a project-based learning process strongly supported by the entire school system.
Table of Contents
Introduction
Importance
Good Teachers
Models of Professional Development
Model 1
Model 2
Conclusion
From the Paper "The program also incorporates parents who pay for students' laptop computers and a local university as a pre-service for the teachers. The program consists of bi-monthly half-day meetings conducted within the participating schools and there they review issues, concerns and topics such as cooperative learning, curriculum integration. The program also has a very effective community model that helps teachers utilize more social and culturally aware notions in the classroom. This helps the teachers teach at a level that is adequate for the various learning levels with in the classrooms."
Abstract By using "The Presocratics", edited by Philip Wheelwright, this paper mainly concentrates on Pythagorean definitions of realities. It looks at how there is a correlation between Pythagorean and modern philosophies, primarily connected to mathematical themes. It goes into depth of defining Mandelbrot sets through math and philosophy and how it connects to ancient philosophy.
From the Paper "There are many ways to define things that we perceive in our daily lives. We define them through science, art, language, and psychology as in many other ways. Most of the philosophies that exist today come from the 'bare bones' of pre-Socratics. They are the basis of different philosophies as well as studies and advances of our time such as astronomy, biology, physics, psychology, mathematics and many more. Pre-Socratics were the first to record their thoughts about the universe. Of how it originated, what made up the things surrounding us, the composition and elements used to make the universe."
Abstract This paper explains that the Veterans Health Administration uses aggregation, a process for clustering several similar products or services to group veteran types by age, priority level and enrollees type. It also shows how the VHA uses cost models to reflect the projected health care demand of the enrollees by preferred facility and to reflect the projected health care demands of enrollees by their county of residence. The author outlines the methodology used to develop the Veteran Enrollment, Health Care Utilization and Expenditure Projection Demand Models. The paper states that predictive forecasting customer demand models achieve for the VHA (1) an integrated healthcare plan including financial, capital assets and workforce needs to provide data-driven information for budgetary and legislative and regulatory negotiations with OMB, the President, and Congress; (2) a continuous feedback loop for VHA to assess performance and outcomes and (3) needed information for mandated reporting to Congress. Charts.
From the Paper "The root of most business decisions is the challenge of forecasting customer demand; this function is a difficult task because the demand for goods and services can vary greatly. External factors impact the VA's demand for healthcare. External factors that affect demand for a firm's products or services are beyond management's control. For example, it is impossible to determine how world events will unfold. Those events that impact our economy and the use of our military may have a profound impact on veterans' enrollment in our health care programs as well as expenditure projections."
Abstract This paper explains that psychologists use statistics to make sense of the human behaviors; through observation measurement and statistical inference, researchers are able to take the abstract and make it more understandable. The author points out that, in inferential statistics, researchers use probability to make generalizations about the entire population based on the results from the research sample. The paper relates that statistics can be used to dictate public policy; thereby, it is especially important that mis-measurements do not occur particularly by drawing samples from non-normative or incomplete populations; while seemingly straightforward, statistics require judicious application of ethical behavior. 2 figures. 6 tables.
Table of Contents
History
Descriptive and Inferential Statistics
Samples and Populations
Probability
Data
Measures of Central Tendency
Central Limit Theorem
Hypothesis Testing
Related Samples
Correlation of Pre and Post Test
What Does Is All Mean?
From the Paper "Some of the earliest work in statistics was done by Sir William Perry in 1532, when he began to record the number of deaths in London on a weekly basis. Later in the 1600, James Bernoilli, a Swiss mathematician, begin using probability to predict outcomes. In the 1700s, it was Thomas Bayer who gave birth to the concept of inferential statistics. The normal distribution was discovered in 1733 by a Huguenot refugee de Moivre as an approximation to the binomial distribution when the number of trials is too large. Today, not only do scientists but also many professions rely on statistics to understand behavior and ideally make predictions about what circumstances relate to or cause these behaviors."
Tags: probability, sample, normative, prediction, population
Abstract This paper explains that factor analysis analyzes the patterns of relationship among several variables, with the aim of finding something about the character of the independent variables, which influence them, even though those independent variables, called factors, were not assessed directly. The paper explains that the results gotten by factor analysis are essentially more theoretical and provisional than is true when independent variables are spotted directly. The author stresses that, in order for the factor to be analyzed, the data must be bi-linear; this implies that the row entities and the column entities must be independent of each other.
From the Paper "Factor analysis can handle over hundred variables at a time; recompense for random and meaningless mistakes, and unravel difficult interrelationships into their major and distinct reliabilities. But, factor analysis has disadvantages. It is mathematically problematic and requires varied and various relevant factors. Its technical terms include strange words like 'eigenvalues, rotate, simple structure, orthogonal, loadings, and communality'. Its product usually takes up a dozen or so pages in a given report, giving little space for a procedural foreword or clarification of terms."
Abstract This paper explains that gaps do exist between genders in the field of mathematics with females falling into the lower edge of the learning curve; however, the assumption that men are better equipped to solve mathematics equations points to a lack of equitable treatment for females and an unbalanced educational environment in public education. The paper points out that girls and boys with the same math SAT scores do not do equally well in college: Girls actually perform better on average. The paper stresses that, in the middle school, girls generally take more high-ability math courses and make better grades than boys; however, they hold less positive attitudes toward the subject because of their relatively high levels of performance anxiety, little confidence in their personal abilities and a tendency to attribute their success to luck rather than their own efforts and abilities.
From the Paper "Moreover, the number of women Ph.Ds in mathematics has increased considerably over the years, according to a study conducted by Marie A. Vitulli and Mary E. Flahive. Data collected from the 1991-95 AMS-IMS-MAA Annual Surveys on initial employment of Ph.Ds in mathematics were obtained from questionnaires distributed to math departments with follow-ups to the degree recipients. In this study the researchers focused entirely on new Ph.Ds from Group I-III departments, that is, from departments of mathematics. The high response rate to the questionnaires (95%) from Group I-III departments allowed researchers to regard it as a census. The primary result of the analysis reported that women seem to be getting their share of first jobs, no more and no less."
Abstract The purpose of this paper is to discuss forecasting methods that are used in commercial business. Competition for consumers is high and in order for businesses to survive, they all have to consider what products are needed, where and when they are needed as well as in what quantities. It looks at how a successful forecasting strategy requires selecting the appropriate forecasting technique and compares and in particular contrasts forecasting methods as they relate to an organization called United Parcel Service. It looks at how there are three types of forecasting to predict demand: judgment methods, time series analysis and causal methods.
Outline
Abstract
Introduction
Judgment Methods
Time Series Analysis
Causal Methods
Conclusion
From the Paper "Judgment methods can be defined as tools that use opinions to develop forecasts without reference to any available historical data. The basis for judgment methods is to utilize decision-makers that have sufficient experience to establish forecasts. This is a low cost method that has rapid development time. However, it is not consistently accurate and subject to bias. The judgment method would not work at the UPS billing site. Most of the forecasting is based on previous numbers and historical data collected as far back as two years ago. Plans for staffing, potential growth, and volume production are weighed in comparison with these same factors in previous years of operation especially during
their consolidation processes. "
Tags: judgment, method, time, series, analysis, causal
Abstract This paper explores why, despite being one of America's national education priorities, mathematics is a 'dreaded subject' for both teachers and students. From student anxiety to lackluster teacher, the paper explores a variety of reasons for the shortcoming. The author goes on to look at proposals for mathematics reform, concluding with his own recommendations.
From the Paper "If anxiety is one of the causes of students' inability to learn, or their lack of interest in learning, teachers need to be aware of the problems caused when math students, regardless of their age or experience, generally blame themselves for a failure to learn or to respond to the teacher's questions. Sometimes, of course, there is parental pressure to excel and succeed, and parents often have no means of helping their children become more familiar and comfortable with learning mathematics."
Abstract This paper examines the life history of Blaise Pascal, born in France in 1662 and who died at the age of 39 from stomach cancer. The paper examines some of the great contributions made by Pacale to the maths field, including the first mathematical device, the creation of "Pascale's Triangle" and his theory of probability and causes.
Paper Outline:
A Genius is Born
Pascal's Education
Acceptance by the Mathematical Community
The Development of the Adding Machine and Other Experiments
Pascal's Triangle
Conclusion
Bibliography
From the Paper "When he turned fourteen, Pascal began to accompany his father to weekly geometrical discussions with what would later become the French Academy. The geometricians at these meetings included Roberval, Mersenne, Mydorge, Carcavi, Auzout, Mylon, Desargues and other's. The meetings were held at the home of Mersenne. Mersenne was a member of a religious order called the Minims. This is important, because later in his life Pascal would abandon math to study religion for several years."
Abstract This paper summarizes the considerations and steps necessary to properly design a successful program for mathematics, science, and all content areas in the elementary classroom. It offers an overview of classroom arrangement to create a stimulating environment, evaluating materials for a content-based program, and offering a variety of assessments to evaluate student learning.
From the Paper "Evertson, Emmer, and Worsham (2003) state that the logical place for a teacher to begin his or her classroom management procedures is in arranging the classroom as it occurs prior to the beginning of the school year. Reflective teachers will arrive at the school several days before their contract calls them to so that they can assess the space to plan for the best arrangement, begin to hang posters and other personal effects, and decorate bulletin boards (Eby, Herrel, & Hicks, 2002). They go on to say that the classroom appearance makes a statement to the students and others about how much the teacher cares for the environment in which the class will learn. Whether the room is tidy or neat, colorful or drab, or filled with extra items to make it livelier will set a tone."
Abstract Marilyn Curtain-Phillips' article, "The Causes and Prevention of Math Anxiety" attempts to explain the causes of math anxiety among students young and old alike. This paper shows how the
article suggests that while math anxiety is something that is tangible and real, it is also something that can be conquered when it is approached from the right perspective.
From the Paper "Curtain-Phillips then goes on to suggest that teachers should alter the manner in which they teach math in order to help students feel more successful and realize higher levels of achievement in the classroom and out. The authors cites research conducted by Spikell in 1993 which suggests that students are more able to comprehensively learn actively rather than passively, meaning lessons should be presented in a manner that engages students actively. The article points out that lessons in math should be taught from a visual and special, logical and mathematical, body and kinesthetic, musical as well as verbal and linguistic perspective so that everyone is able to grasp information based on the manner in which they learn best."
Abstract In the world of science and history there are few great names that can match the name of Stephen William Hawking. Hawking is perhaps one of the best known physicist and mathematicians in history, or at least in modern times. This paper presents a close examination of the life and works of Stephen William Hawking. The writer explores his childhood to help determine how he became what he is today. The writer then examines his adult life, his works and his contributions to the world, as well as some of his more better-known theories and ideas.
From the Paper "Another difference between Hawking and many other scientists throughout the world is that he understands the world's need for laymen terms. Many scientists are reported to be so scientific and mathematically based that their works and words are boring and over the head of everyone but other scientists. Hawking understands the average person is not going to take time to dissect scientific jargon and he put together a book that explains many of the most mind boggling ideas in history in terms that can be understood by the non scientist."
