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Growth of Mathematics Term Paper

… Growth of Mathematics

Mathematics Hard and Soft

Mathematical truth is time-dependent, although it does not depend on the consciousness of any particular live mathematician," (p. 415). In other words, mathematics grows as the body of human knowledge grows; each generation gleans new wisdom from the environment, experimentation, or personal experience and transmits that knowledge to contemporary and future generations either orally or in writing. Noted mathematicians may get their names printed in textbooks or permanently etched on the name of their theorems but the greater body of mathematics grows whether or not momentous discoveries warrant an individual mathematician's fame. One of the primary ways mathematics changes over time is through the transformation of soft sources of information such as common knowledge, intuition, or hunch, into…. [read more]


Mathematics Learning Essay

… " (p. 1) The teacher as an instructor has the intended outcome for students of "skills mastery with correct performance." (Ernest, 1991. p. 1) Whereas the role of the teacher as an explainer has the intended outcome of "conceptual understanding with unified knowledge." (Ernest,, p. 1) Finally, the teacher as a facilitator has the intended outcome of "confident problem posing and solving." (Ernest, 1991, p. 1) Swan (2006) speaks of the traditional method of teaching mathematics and states that when it is reversed it is "builds on the knowledge that students already have" and additionally "exposes and discusses common misconceptions" and "uses higher-order questions." (p. 169) Swan additionally reports that traditionally teaching utilizes small group work and encourages "reasoning rather than 'answer getting' and uses…. [read more]


Objective Map Essay

… Mathematics

Grade 9

H.S School Curriculum

Lynchburg, VA

Spiritual Principle

To everything there is a season, and a time to every purpose under heaven (KJV Ecclesiastics 3:1-8)

Standard 1: Students will be able to explain the principles of, graph, and solve step and piecewise functions.

They will be able to convert absolute into piecewise functions.

Standard 2: Students will be able to graph and solve exponential functions and use them to model and predict real life scenarios.

Standard 3: Students will be able to solve quadratic equations and inequalities in one variable. Students will be able to determine and graph the inverses of linear, quadratic and power functions, including restricted domains

Suggested Activities and Experiences

Standard

Students will list the types of real world experiences…. [read more]


Pre-Calc Trigonometry Journal

… Modeling Real-World Data with Sinusoidal Functions

The sinusoid which is sometimes referred to as the sine wave referrers to a function of mathematics describing a smooth oscillation that is also repetitive. It usually takes place in pure mathematics and also in physics, electrical engineering and signal processing besides numerous other fields. Its form as a function of time (t) is:

A, which is the amplitude. It is the peak deviation of the function from its center position.

, which is the angular frequency, specifies the number of oscillations occurring in a unit time interval, in radians per second, which is the phase, gives specifications where in its cycle the oscillation begins at t = 0.

The swinging of an undamped spring-mass organization round the equilibrium…. [read more]


Mathematics Curriculum Education Research Proposal

… Mathematics Curriculum Education

One aspect of math instruction and instruction in general that has been particularly important with high stakes testing reform is staff development and system support of staff and students to improve outcomes and/or balance information offered by high stakes testing and ultimately improve mathematics teaching practice. This emphasis has, as of yet gone relatively unexamined, beyond the actual high stakes test results themselves. For this reason the results of the findings section of this work are important and meaningful, especially as we embark on the future, with a new presidential administration along with a changed congress and changes in local officials, who may have significant amendments to make to the educational standards of the nation. In short the new administration, on all…. [read more]


Mathematics My Role as a Special Education Term Paper

… Mathematics

My role as a Special Education Teacher

Despite the fact that education is not referenced in the U.S. Constitution, nations that declared that they have "undertaken to provide" it ought to provide extended educational prospects fairly. Appropriate development securities are assured by the Fifth and Fourteenth Amendments that are:

No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws."

Initially intended as safety measures in opposition to any sort of undeserved custody and securities for real estate tenure, "liberty" and "property" agreements…. [read more]


Bayesian Methods for Data Analysis in Transcription Networks Term Paper

… ¶ … Bayesian method refers to methods on probability and statistics particularly those related to the degree of belief interpretation of probability as opposed to frequency interpretation. In Bayesian statistics, a probability is assigned to a statement, whereas under frequency conditions the hypothesis is tested without this probability. Bayesian method, or probability, may be seen as an extension of logic that involves dealing with uncertain situations and statements. To evaluate the probability of a hypothesis, the Bayesian statistician specifies some prior probability, updates the condition of the statement according to current data and then applies standard calculations and formulaes to assess probability of its occurrence and accuracy.

In general, Bayesian methods are characterized by the following concepts:

The use of hierarchical models (a topic in…. [read more]


Hart, B. And Risely, T ) Term Paper

… Hart, B. And Risely, T (2003). The early catastrophe: The 30 million word gap by age 3. American Educator, Spring

Fairly commenting on an investigator's research endeavor is a task that must be taken seriously. Although it is quite easy to have an opinion of another's research, it is something quite different to be able to evaluate the research activity in terms of topic specificity and soundness, intent or purpose, data analysis, and informational importance. The focus of this paper was on whether or not the research investigators of the above cited research publication were prudent in stating a research question and a testable hypothesis along with informing the reader of the chosen research design, statistical data analysis and reporting the results, limitations, limitations and…. [read more]


Middle School Mathematics Curriculum and Standards Research Paper

… Middle School Mathematics Curriculum and Standards

In a preface to a discussion about curriculum and standards for middle school, the National Council on Teachers of Mathematics (n.d.) notes

The middle grades represent a significant turning point in students' lives [and they] solidify conceptions about themselves as learners of mathematics. They arrive at conclusions about their competence in mathematics, their attitudes, their interest, and their motivation. These conceptions will influence how they approach the study of mathematics in later years, which in turn will affect their later career and personal opportunities.

The standards guide curriculum development in ten areas: numbers and operations, algebra, geometry, measurement, data analysis and probability, problem solving, reasoning and proof, communications, connections, and representation. For each area, the standards specify what students…. [read more]


Mathematics Summer Institute Statement Term Paper

… All curricula will meet the mandate of the Summer Institute, and be consistent with Maryland State Core Learning Goals and NCTM standards. As well, the unit of study will be fully inclusive, addressing issues of diversity applicable to students across the state of Maryland. Strategies (and suggestions for modifications to those strategies) will be developed to address varying cultures, language specifications, special needs, and multiple intelligence theory. In accounting for diversity, learning strategies will be varied and highly interactive. In keeping with my philosophy of education, students will have the opportunity to express any given concept in a variety of ways, ensuring that they are able to learn and succeed regardless of their preferred learning style. This will build a strong mathematics foundation in students…. [read more]


Math Problems and Concepts in Teaching Research Paper

… Mathematics of Mathematic Puzzles

Using mathematics puzzles is a frequently-used deployed pedagogical device to teach critical concepts to math students of all ages. "Understanding in mathematics is born not only from formulas, definitions and theorems but, and even more so, from those networks of related problems… Mathematicians seek knowledge. In search of knowledge, they enjoy themselves tremendously inventing and solving new problems" (Bogomolny 2015). The mathematics of puzzles is also designed to challenge the student's instinctive conceptions of how the world works. For example consider the question posed 1702 of how long would a rope encircling the earth have to be "for it to be one foot off the ground all the way around the equator -- this can be used to illustrate the geometric…. [read more]


PHI Golden Ratio Term Paper

… History Of Phi, Mathematical Connections, And Fibonacci Numbers: Nature's Golden Ratio

Throughout history, humans have been seeking to define beauty in quantifiable and meaningful ways. For many observers, the connection between beauty and the rhythmic patterns evinced in the Fibonacci series is clear. While the Fibonacci series is named for an early 13th century Italian mathematician, the so-called Golden Ratio known as phi is repeated throughout nature and a surprising number of human endeavors alike, including music, architecture, language and even stock market cycles. In some cases, the manifestation of the Golden Ratio in human endeavor in these ways may be unintentional, but in others it is clearly an integral part of the design process. Likewise, in nature, the ubiquity of the Fibonacci series may…. [read more]


Mathematical Knowledge for Teaching Article Review

… Mathematical Knowledge in Education

Differentiating Types of Mathematical Knowledge and Relevance to Education

Ball, D.L., Lubienski, S., and Mewborn, D. (2001). "Research on teaching mathematics:

The unsolved problem of teachers' mathematical knowledge." (In Handbook of Research on Teaching. New York: Macmillan).

Generally, mathematics proficiency among teachers corresponds to higher achievement in their students. While that conclusion has been supported by a substantial volume of empirical research, much less empirical research has been devoted to trying to understand how and why teacher achievement in mathematics benefits student outcomes, or what it is about mathematics, specifically, that generates this apparent relationship. Most importantly, there is a need to understand whether and to what extent teacher mathematics achievement in different aspects of mathematics matters with regard to the…. [read more]


Mathematics Education Research Proposal

… PERCEPTIONS of EDUCATORS in a Massachusetts URBAN SCHOOL DISTRICT of CHANGES in REFORM-RELATED PRACTICES in MATHEMATICS INSTRUCTION SINCE the IMPLEMENTATION of STATEWIDE TESTING

This study, which examined the effects of mathematics reform on teacher practices in Massachusetts, had two central purposes: (a) to identify reform-related practices in mathematics instruction that have increased, decreased, or not changed since the implementation of high-stakes testing according to educators' perceptions and (b) to determine educators' perceptions of the effects of reform-related practices on student achievement since the implementation of high-stakes testing. High-stakes testing is a dramatic change in education practice and has changed the face of mathematics instruction, yet there is only limited research on its effects. This study investigated the perceptions of educators, both generally and by demographic,…. [read more]


Math Curriculum Development Term Paper

… Math Curriculum

Science and its modes of studies are very much reliant on the mathematical techniques which have been heavily evaluated over the past few years. Numerous studies like the ones conducted by Mike Cass et al. (2003) and Lynn T. Goldsmith and June Mark (1999) have analyzed both the teaching techniques used for mathematics as well as the overall sections that are included in its course. In these studies the common conclusions that were made regarding fundamental knowledge of mathematic formulas and techniques is that these allow the students to develop essentially their primary aptitudes in the subject. Other studies also highlight that by solving the simpler questions through the use of fundamental formulas allows the students to find vague and difficult answer to…. [read more]


Mathematics Curricula Term Paper

… Concentration will aptly shift away from integrating mathematics and Internet to the demanding subjects of inquiry-based teaching, and learning (Cobb & Bauersfeld, 1995).

Conclusion

Public enthusiasm for getting mathematical classrooms on the Internet is at present based mainly on the idea that students ought to have access to the vast information resources on the World Wide Web. This insight of immense intellectual resources online has led to the conviction that the Internet ought to develop into a central constituent of modern education -- necessary to training students for the difficulties of the 21st century place of work and for keeping the nation aggressive and viable.

The experiential and hypothetical subjects have been raised in a lot of studies in the preceding decade that confront educators…. [read more]


History and Present Day Applications of Logarithms Essay

… Logarithm

History and Modern Applications of Logarithms

The first time a publication contained a mention of logarithms, their method of derivation, and a table of logarithms was in 1614 with the publication of Mirifici Logarithmorum Canonis Descriptio by the Scottish nobleman John Napier (ST 2005). Napeir's book did not describe or list logarithms as they are known today, but rather the logarithms contained in this work were meant to replace the trigonometric multiplication functions needed in astronomy and other branches of science with a simplified addition from other established figures (Capmbell-Kelly 2003). Henry Briggs, a professor of geometry at Oxford, was very inspired by Napier's work, developing his own ideas based on those in the Descriptio and meeting with Napier to discuss developments and recalibrations…. [read more]


Decision to Become a Math Research Paper

… Math majors seeking a career in this field will be rewarded by high salaries ($42.14 per hour median), faster than average job growth (27%), and a non-competitive job market ("Actuaries: Summary" 2012). In addition, a bachelor's degree is usually sufficient for obtaining an actuary position, although certification is generally required.

For math majors interested in research, but uncertain about pursuing a graduate degree, there are a few opportunities available. Biostatistics is a discipline barely more than a decade old, but the need is great for mathematicians interested in applying their talents and skills to problems in basic biology research, medicine, and public health (epidemiology). Biologists and biomedical researchers have advanced to the point where they have too much data and not enough knowledge about statistics…. [read more]


Dislocation Dynamics in an Anisotropic Stripe Pattern Research Paper

… Crystal Review

A review of "Dislocation Dynamics in an Anisotropic Stripe Pattern"

This paper reviews the findings of a specific published study regarding the patterns that emerge form dislocation occurring across domain walls in physical systems, and specifically anisotropic stripe patterns. Different electromagnetic and conductive patterns emerge due to the striped patterns that are created by distortion movement occurring parallel to domain walls, and the study reviewed examines the nature of these variances and the degrees of distortion and pace of change that occur. Analysis of the article published as a result of the study is also conducted form a quantitative and qualitative/critical perspective, for which other related studies and information are utilized.

Topological defects occur in almost all crystals, though they vary in their…. [read more]


Stigmatization and Therapy Counseling of Gay Men Research Paper

… Unnatural sexual orientation is not an independent, standalone issue for those professing inclination towards same sex individuals for their sexual needs. Such individuals invariably face difficulties, humiliation, and consternation in many other areas of their lives, thereby being isolated, stigmatized, and finding it difficult to lead normative, meaningful life. In recent times, there are concerted efforts to address their concerns through various empirical psychological theories, tools, and practices to give more meaning to their individuality. Assimilation of such persons into the mainstream is sought through a change in the perspective of both, the LGB individuals as well as the society (mainly those who are closest to them, often meaning family members, colleagues, and even friends). Various theories view the problems faced by LGB individuals from…. [read more]


Calculus and Definitions Assessment

… In simple terms the Riemann sum is used to define the definite integral of a function. We begin by considering a simple case, whereby the definition of the Riemann integral of a continuous function f over a rectangle R. In this case rather than having a one-variable case, we can overcome the tendency of connecting integration too strongly with anti-differentiation. (Buck 2003)

Formal definition

It is the definition of a function by use of graphs to define the limits; it uses Greek letters epsilon (?) and Delta (?). Epsilon always represents any distance on the limiting side and delta represents the distance on the x- axis. The limits of a given function clearly explain how that given function behaves when it nears the x value.…. [read more]


Nonlinear Aerostatics Stability Analysis of Suspension Bridges Literature Review

… Su, Luo & Yun (2010) performed an aerostatic reliability of bridges with long spans. According to their study, the response surface Monte Carlo method (RSMCM) is suggested to be suitable for the analysis of the reliability of both the aerostatic stability and the aerostatic response for various types of long-span bridge structures. In these bridges, the nonlinear effects that come about as a result of the geometric nonlinearity as well as loads that are dependent of deformation are taken into due consideration. In their study, the geometric parameters, aerostatic coefficients of the girders used on the bridge as well as the parameters of the materials used are treated as random variables. The response surface Monte Carlo method (RSMCM) is pointed out to possess a higher…. [read more]


Dispel Article Review

… 1045). If these considerations are not met then the proposed question may not be appropriate for research study.

Other considerations include statistical consideration such as the statistical power needed to find a significant result, the costs associated with the proposed project, and alternative ways to answer the question. Research questions are often quantitative in nature and many questions did not lend themselves to quantitative measurements (Beya & Nicoll, 1998, p. 1045-1046).

Discussion/Conclusions

There is no formal discussion section, but affect the entire paper is a discussion of the practicality of research in specific instances and when students should consider using research and type of questions/qualifications the need to be met in order to use research to answer particular questions. Beya and Nicoll (1998) state that…. [read more]


Null Hypothesis and an Alternate Essay

… Most importantly, the alternative hypothesis is that although it can be negative, it should not be assumed that the alternative hypothesis is a negation of the null hypothesis. Instead, the alternative hypothesis often establishes whether the H0 is true or false. In other words, the alternative hypothesis is a critical component of statistical hypothesis testing and works well in guiding the research process to arrive with the best results (Albright, Winston, & Zappe, 2010).

The significance of the null hypothesis and alternate hypothesis are key in making critical business decisions

The null hypothesis is used to predict the outcome of the decision or action to be undertaken at a given time is significant in making critical business decisions. This is by allowing business leaders to…. [read more]


Forecasting Methods Essay

… The answers are then collated and given to the participants. Participants are then asked to reassess their original opinion in the third and final round vis-a-vis opinions advanced by other participants. The Delphi method helps in narrowing opinions (Hanke & Reitsch, 1992). It is regarded as the most accurate method relative to group discussions.

Simulation methods use analogs to model complex systems. The analogs can take on several forms like mechanical analog, metaphorical analog, and game analogs. Mathematical analogs are integral in forecasting applications. The technique begins with initial set of assumptions. S-curve is the most common mathematical analog in societal growth. It is based on the concept of logistic or normally probability distribution (Brown, 1959). Multivariate statistical analysis, another mathematical analogue is used to…. [read more]


Probability Probabilities According to Becker Essay

… In a game spinner or wheel spinning competition, participants are required to spin a wheel with several colored sections. A winner is identified when a predetermined color aligns itself with a fixed pointer. In this particular case, my chances of winning would effectively be determined by the number of colors in the game spinner. For instance, four colors would give me a 25% chance of winning. The more the colors, the lesser my chances of winning would be. The reverse is true.

Determining the Most Important Measurement from a Business Perspective

Before deciding on the most important statistical measurement, it would be prudent to first offer a definition of each. The mode according to Black (2009) "is the most frequently occurring value in a set…. [read more]


Inferential Statistics? What Are the Differences? Essay

… ¶ … inferential statistics? What are the differences? When should descriptive and inferential statistics be used?

Descriptive and inferential statistics: Summary explains the similarities and differences between descriptive and inferential stations and when each method should be used. Descriptive statistics comprises the kind of analyses to describe a study population that is small enough to include every case. Descriptive statistics can also describe the actual sample under study, but allow a researcher to extend conclusions to a broader population.

With descriptive statistics, a researcher can describe how issues affect study groups and how variables are related in to other study groups. However, the research cannot describe how those issues affect the members of the study groups and how these variables are related in those groups.…. [read more]


Structure the Research Term Paper

… Individual researchers must monitor a vast number of research results and activities that have a bearing on their own particular specialties.

By definition, measurement must be objective, quantitative and statistically valid. Simply put, it's about numbers, objective hard data. A scientifically calculated sample of people from a population is asked a set of questions on a survey to determine the frequency and percentage of their responses. For example: 240 people, 79%, of a sample population, said they are more confident of their personal future today than they were a year ago. Because the sample size is statistically valid, the 79% finding can be projected to the entire population from which the sample was selected. Simply put, this is quantitative research. Qualitative research, is much more…. [read more]


Achievement of a Teaching Task Term Paper

… Both the traditional and contemporary style of teaching mathematics has concepts that profoundly allow the learners to use their intellectual abilities to solve problems. The difference however is in the manner of their approach in establishing the interest of the learners. The contemporary approach allows the learners to engage themselves more in activities such as the use of computer technology, while the traditional approach is more on engaging the learner on individual activity of problem solving. M. Klein states one consequence of how the contemporary positively affects the learner.

A as students engage themselves in those learning processes that educators recognize as powerful and productive, they are simultaneously subject to positioning within the familiar storylines and practices of the classroom.

This means that the classroom…. [read more]


Educational Assessment Methods and Standards Term Paper

… However, the transition to from traditional to alternative assessments can be tricky at times, particularly when students have become accustomed to conventional methods. Typically, students initially respond to alternative assessments with confusion and frustration, since they are not sure what is expected of them under this new method. Therefore, teachers that utilize alternative assessment methods are trained to explain the situation and the assignment very carefully before students begin their work on the problem, also known as modeling assessment tasks. This action provides students with a framework for completing the assignment using individual skills, and this model creates student confidence in the tasks being performed (Silbermann, 2003). However, it is somewhat of a challenge for teachers when performing alternative assessments, as they must be careful…. [read more]

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