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Division by Zero Mathematics Term Paper

… Also, since any number times zero will equal zero, there is no one unique solution for the answer. Example problems such as 2x0 = 0 and 1450 x 0 = 0 show that a number times zero equals zero. However, at the same time, zero times itself does not equal the number multiplied by zero. The answers cannot be duplicated when the reverse operation is performed (Knifong 1980,-page 179). Even 0 x 0 = 0 is problematic in that zero divided can be divided by itself and multiplied by itself an infinite number of times.

In higher mathematics, such as calculus, the question of division by zero becomes even more complicated. Asymptotes, for example, are lines which correspond to the zeroes of the denominator of…. [read more]

Art and Mathematics Are Related Research Paper

… ¶ … art and mathematics are related and that this relation could be used to the advantage of educators to overcome student anxiety regarding mathematics and, in particular, difficult geometry concepts

Outline the basic topics to be covered in the study

What is hyperbolic geometry?

Who is MC Escher?

How does Escher's work relate to hyperbolic geometry?

How to design an appropriate, useful, and successful class project that integrates art and mathematics

What Is Hyperbolic Geometry?

Explain the historical development of hyperbolic geometry.

Explain what a Poincare disk is.

Explain how distance is illustrated in Euclidean geometry.

Explain how distance is handled in non-Euclidean geometry

Context: Who Is M.C. Escher?

Provide simple biographical information about M.C. Escher.

Draw a relationship between a Poincare disk and…. [read more]

Operations Essay

… d.).

As the first step, solving an equation requires combining like terms for the two expressions within the equation. In this case, like terms are those containing the same variable or group of variables that are raised to the same exponent despite of their numerical co-efficient. The second step is to isolate terms that contain the variable, which means getting terms containing that variable on one side of the equation while the other variables and constants are moved on the opposite side of the equation.

This is followed by isolating the variable to solve for that can result in obtaining a numerical coefficient. When a numerical coefficient of one is obtained following isolating the terms containing the variable to solve for, the variable was automatically…. [read more]

Teaching Strategies Problems Long Division Essay

… Ratio Proportion Percentages

In order to solve the problem that involve ratio, rate or proportion student needs to develop an understanding of ratio, and standard conventions are used to write ratios, rates, and the methods of solving such problems. Teachers have used number of representations to guide students in understanding percentages, which includes pie charts, decimal, fraction and different geometric shapes with portion shaded. There are two methods that are commonly used to numerically solve percent problems, the equation/mathematical sentence (4n=12) or using ratio proportion set up (3/5 = ?/100) (Handley, 2010; Archer & Hughes, 2011; Montague & Jitendra, 2006). In order to develop an understanding of ratio, proportion, and percent pupils should be given activities like model situations for example "there are three red…. [read more]

Mathematics Core Curriculum for Grades Essay

… New York State Education Department Standards for Grades 1-5

Each state has its own educational standards that are meant to guide teachers and establish core curriculum goals for each grade level. The New York State Education Department is no different. The state standards of the curriculum based on grade levels one to five is not only to establish particular learning achievements to prepare students for more complex lessons in the future, but it is also meant to engage them within the curriculum in order to allow them to learn more from the material and use it in an applicable way in real life situations. The Mathematics core curriculum established by the New York State Education Department is no different. In its basest form it established…. [read more]

Scientific Notation, Its Uses Research Paper

… (All nonzero digits are considered to be significant digits, also any digits that express the precision of a measurement instead of its magnitude.) This is the coefficient.

2. Find the exponent by counting the number of places from the decimal to the end of the number. Numbers smaller than 1 will have a negative exponent.

Using scientific notation not only gives a way of writing very large and very small numbers, it also makes it easier to do calculations as well. The rule for multiplication is: To multiply numbers with scientific notation, multiply the coefficients together and add the exponents. The base remains 10.

The rule for division is: To divide numbers with scientific notation, divide the coefficients and subtract the exponents. The base remains…. [read more]

Multiplicative Number Theory Term Paper

… All integers are divisors of 0. All integers 'a' are divisible by and If a has any other divisors, then it is called a composite. Otherwise, it is called a prime, unless which are called units. Of the positive integers not greater than 20, the composite numbers are

The prime numbers less than 20 are

Primality testing and factorization

The problem of an algorithm determining that all the divisors of a given integer are prime is very old. Yet no solution has been found. A number with 100 digits can be proven to be prime or composite on the computer within a matter of seconds. Through this it can be shown that a number a is composite without actually displaying two factors b and c,…. [read more]

Examples in Excellence: Jaime Escalante Teaching Calculus Essay

… Retrieved March 20, 2008, from the Midcontinent Research for Education and Learning [Web]. Retrieved

Berkas, N., & Pattison, C. (2007, November). Manipulatives: More than a special education intervention. NCTM News Bulletin. Retrieved March 20, 2008, from the National Council of Teachers of Mathematics [Web] Retreived

Jesness, J. (July 2002). Stand and Deliver revisited. Reason. Retreived

Marzell, T.L. (2012). Chalkboard Champions: Twelve Remarkable Teachers Who Educated America's Disenfranchised Students, Tucson, AZ: Wheatmark. Retrieved



Menendez, R. And Musca, T. (1988). Stand and Deliver. [Film} Warner Bros.

Schraff, A.E. (2008). Jaime Escalante: Inspirational Math Teacher, Enslow Publishers, Inc., p. 12. Retrieved

Steedly, K., Dragoo, K., Arefeh, S. And Luke, S.D. (2008, 2012). Effective Mathematics Instruction. Evidence for Education, III (I). Retrieved…. [read more]

Base Ten Number System Essay

… g. 7 groups of ten, rather than count each object or chip individually. This will also aid their mental math skills and enable them to solve complex problems quickly and easily. The use of constant multiplication in a calculator on the other hand is another quick way to learn about place-value (Ryan & Williams, 2007).

Conclusion and Key Learnings

A good grasp of place value relationships is very important to the development of a child's mind. The quicker they learn this, the better. A good number sense not only enables children to think of numbers in different ways and aids in calculation and manipulation of numbers. Teachers should be wary that place value is learnt gradually and through trial and error and in order to…. [read more]

Teaching Math Concepts to Improve Test Scores Term Paper

… Elementary Measurement: Area, Perimeter, Volume

In an era of increased demands for teacher and student accountability, identifying better ways of delivering educational services represents a timely and worthwhile endeavor. There are some significant constraints involved in teaching young learners about mathematics concepts, though, that must be taken into account in devising such approaches. Nevertheless, the mandate is clear and state-level high-stakes testing regimens across the country currently require that all students achieve minimum performance standards on reading and mathematics tests in order to be promoted to the next grade. In this environment, identifying what works best and what does not is an important first step, and these issues are discussed further below.

Problem Statement and Needs Analysis

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Bulling and Academic Performance Term Paper

… Woodsa, S. & Wolkeb, D. "Direct and relational bullying among primary schoolchildren and academic achievement"

Article Review of Paper by Woodsa & Wolkeb

School bullying is a truly international issue; in Japan there are thousands of children refusing to go to school to avoid terrible bullying while in America children have been known to commit mass murder when pushed too far by bullies. Many pop-psychology theories exist among students and parents as to why bullying takes place. This article by Sarah Woodsa and Dieter Wolkeb, titled "Direct and relational bullying among primary school children and academic achievement," looks carefully at a British primary school's system of bullying and analyze within it the popular idea that bullies are so cruel because of their own inferiority complexes.…. [read more]

Mayan History and Culture Term Paper

… Mayan History And Culture

The ancient Mayan civilization had advanced systems of astronomy and mathematics, an accurate calendar system, extensive trade routes, and a religion dominated by blood sacrifices (Jaguar pp). Although they did not have the benefit of metal tools, beasts of burden, or even the wheel, the people of this ancient civilization were still masters of architecture who built elaborate pyramids and sprawling cities (Jaguar pp). Although the collapse of these great cities led to the near extinction of the Mayan, the survivors of this culture are heralding into the new millennium (Jaguar pp). The Mayans built incredibly sophisticated urban centers, an astronomical science and mathematics among the most sophisticated in the pre-modern world, and the most developed and complex system of writing…. [read more]

Antigua Guatemala Coffee Business Plan

… Any well-funded and large company, where capital is not an issue might be potential entrants because they have a solid brand image in the business sector (Blackwell, 2011).

Rivalry: in this market segment, there are many big players. With the high number of small-scale coffee shops, big players must battle with small players across the market segments. With customers increasingly taking coffee home, it provides the convenience, which is the main factor for players. There is an intense competition in this industry, as companies must battle each other to increase their customer base.

Bargaining power of suppliers: there is a high bargaining power for suppliers. The developments in technological innovations like the automated coffee machines and espresso machines have made them bargain over the industry.…. [read more]

Pedagogic Model: Teaching Technology in Special Education Dissertation

… " (Dougiamas, 1998) Such trivial constructivism, though, is the bedrock from which Glaserfelds more radical constructivism springs. He continues to state that because knowledge is constructed by the learner, and because no two learners are the same, knowledge itself is not absolute. There is a degree to which knowledge is an illusion, and every individual constructs their own conception of reality which (while susceptible to the demands of "real" or normal reality) does not necessarily align with the normal paradigm. Constructivism does embrace this relativistic and existential approach to reality, but it also holds as a primary value the idea of constraint which enables the thinkers to participate in social interaction and mainstream reality. (Glasersfeld)

One interesting area of constructionist theory is…. [read more]

Education Factors Relating to the Development Term Paper

… Education

Factors Relating to the Development of Relationships between Teacher Leaders and Their Principals

America's teachers face an educational system that is increasingly complex. They must navigate between the needs of students, and the demands of administrators. In most instances, the principal represents the average teacher's first contact without the outside world of school boards and bureaucratic regulation. There are federally-mandated goals and tests, state benchmarks and funding requirements, and parental and media activists. Principals must respond to, or enforce, the demands of all these groups. Teachers must either find a way to comply, or else must defend their choice to follow an alternative path. The opinions of lone teachers or groups of teachers, count for little when stacked up against the weight of government…. [read more]

Music Education or Cross Platform Development Term Paper

… Music Education or Cross Platform Development

Pitch is commonly mistaken for being a term which is analogous to frequency; however, pitch is actually based on perception. Pitch is the human perception of the frequency of a musical note. (Heresiarch 2005) While pitch is related to the frequency, or physical rate of vibration in a sound wave, it is distinctly different.

The current standardized relationship between pitch and frequency is that the note a above middle C. sounds like a 440 Hz tone. In a musical context, the exact frequency of a note is far less important than its relationship to other notes. Numerous systems exist for defining the relationship between notes in a scale, usually involving a fixed frequency ratio between successive notes. The chromatic…. [read more]

Compare and Contrast the Differing Definitions of Critical Term Paper

… ¶ … integrating critical as well as thinking. But several earlier conceptualizations try to concentrate primarily on the process of thinking and avoid its important qualifier, i.e of critical. Hence they tend to give over importance to the process of thinking and reduce the importance of critical aspects. Encouraging and facilitating the process of critical thinking of students is now being considered as an increasingly significant objective for higher education. Analyzing the element of critical thinking of students is important for estimating its progress. (Cheung; Kwan; Yue, 2002) Those whose education have not trained them to deal critically with issues as well as conflicts are in fact not being enabled to interact efficiently with other people, whether be it be the same or varied from…. [read more]

Teacher Motivation Research Proposal

… Teaching is one of the professions that many and indeed probably even most people enter with a large measure of idealism. They seek out education as a profession not for the salary or the benefits (despite the belief of many non-teachers that teachers are primarily motivated by the long vacations) but because they feel that teaching is their vocation, their calling. And yet despite this initial strong motivation to teach, many teachers leave the profession after a short time, often after only a year in the classroom. For example, about twenty percent of new Vancouver teachers leave the profession after their first year (Richmond, 2005), which is about middling, with some regions losing up to fifty percent of their novice teachers after their first year…. [read more]

Managerial Impact on Small Businesses Context Term Paper

… Managerial Impact on Small Businesses

Context of the Problem

Today, all businesses are made up of two kinds of constituents: the physical and the non-physical (virtual). The physical constituents are objects such as machinery, building, along with people; the non-physical (virtual) constituents are objects such as information in relation to clients, intelligence in relation to how to get the optimum from a mechanized process and the privileges to make use of a specific development.

The information development offers, both large and small, corporations with an unmatched prospect to move constituents of their businesses from the physical sphere to the virtual sphere. The development of new products and services does not have to be carried out on paper, selling to customers does not have to take…. [read more]

Solving the 1D Bin Packing Thesis

… The NASA antenna was created using "evolutionary computation" programs, so named because they solve problems in a way that mimics biological evolution, natural selection, and "the survival of the fittest" (2009, p. 23). It is also important to point out, though, that the "automatic" aspects of the design process are based on carefully formulated requirements that software engineers must develop based on the specific requirements of the initiative. In the case of the NASA space antenna, the "fitness criteria" for the design specified that the antenna must be able to transmit and receive signals broadcast within certain frequency parameters as well as the antenna's overall size; however, these fitness criteria to not instruct the algorithm as to what types of materials should be used or…. [read more]

Classroom Behavior Management Policies Research Paper

… Classroom Behavior Management Policies

Title suggestions:

Bridging the Gap Between Systems Theory and Elementary Classroom Management

An Evolution: Systems Theory and Classroom Management


Systems Theory by the Three B's

Robert Freed Bales


Living systems theory

Social entropy theory

Entropy management in organizations


Ludwig von Bertalanffy

The concept of the whole

GST and integrative studies

Science and society

The importance of the individual

A Comparison of the Three B's




Theoretical similarities


Annotated Bibliography

Classroom management definition and challenges

Strategies and methods

Techniques and training

Self-efficacy and beliefs

Culturally responsive classrooms

Evidence-based strategies

Theory -- and model-based strategies

Comparison to Bertalaffny

Top recommended classroom management strategy





Sociology and the study of social systems has taken many…. [read more]

Attitudes and Values of High Term Paper

… They were participating in classroom discussions, going back over work they could not grasp, taking time to figure out schoolwork, and submitting homework on time. Moreover, most of these students are aware of entrance requirements for various colleges; they attended college presentations at their high schools. It was further learned that Hispanic immigrant students typically enrolled in lower level and basic math courses compared with European-American students who may be said to show greater discernment a propos the significance of mathematics.

As mentioned before, the results of studies sometimes throw skewed or contradictory light upon the topic in question. A survey prepared by Public Agenda, for instance, showed that higher education is seen as the means to the American dream by the American public; and…. [read more]

Why Angles Are Measured in Degrees Minutes and Seconds Term Paper

… ¶ … Angles Are Measured in Degrees Minutes and Seconds

An Analysis of Why Angles are Measured in Degrees, Minutes and Seconds

According to Richard Kittler and Stan Darula (2004), "In the era of computers and sophisticated technology many basic principles and concepts inherited from antiquity are sometimes forgotten" (141). Given its ancient origins, the reason angles are measured in degrees, minutes and seconds today has likewise been forgotten by many modern observers. In fact, the basis for this method was developed almost five thousand years ago in Sumeria based on their use of sundials to track time. In her book, Time's Pendulum: The Quest to Capture Time -- from Sundials to Atomic Clocks, Jo Ellen Barnett reports that the convention of the 24-hour period…. [read more]

Creative Powers it Is a Fact Term Paper

… Creative Powers

It is a fact that the society in which we live will never be truly free in all areas of life. Indeed, it has been suggested by some that total freedom would result in anarchy, and that rules are necessary in order to ensure a civilized society. On the other hand, too little freedom would hardly be conducive to creativity in any sense of the word. It would therefore be useful to what degree freedom within society, in terms of the law, culture, education, politics, and other influences, relates to individual and collective creativity in the same society.

Freedom in Society

Freedom is a very wide concept, and difficult to define. It means different things to different individuals and different societies. If Hayek's…. [read more]

Information Technology and Its Uses in the Nano Thesis

… Information Technology and Its Uses in Nano Technology


Information Technology and Nanotechnology

The future of modem society is often referred to in terms of technology and particularly new and innovative technological discoveries. While from one perspective science and technology has been blamed for many of the ills of modern society, such as the threat of climate change, on the other hand discoveries associated with new technologies have also increased optimism with regard to a better future for humanity. (Murphy & Pardeck, xv) One need only think of the controversy about the discoveries in genetics and cloning, which is seen as positive from a medical point-of-view and condemned from various ideological and mortal perspectives.

Thinkers and scientists have also explored the ways in which technology…. [read more]

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