Mathematics Essays (Examples)

Mathematics in Digital Photography
The advances in both digital photography and computing have allowed more detailed and complex images to be shown on more realistic media than was ever previously possible. Through the use of more specialized equipment and digital imaging techniques the resulting photos of even the most novice user today can rival those of professionals from years before. This level of photographic precision could never have been achieved were it not for the tremendous advantages made in computing that allow both the hardware and software involved in digital photography to function at extremely high levels. Both hardware and software made today are capable of performing the necessary calculations in a fraction of a second, making focusing and editing pictures easier than ever before. The incorporation of mathematics directly into the digital photography process has been the primary impetus for the explosion of high-quality digital images available almost anywhere we…

alacheff (1987) described four levels of justification, which are those as follows: (1) Native empiricism;

2) Crucial experiment;

3) Generic example; and 4) Thought experiment. (Taflin, nd)

Naive empiricism is stated to be "an assertion based on a small number of cases." (Taflin, nd) Crucial experiment is stated to be "an assertion based on a particular case, but the case was used as an example of a class of objects." (Taflin, nd) the generic example is stated to be "...an assertion based on a particular case, but the case was used as an example of a class of objects." (Taflin, nd) Thought experiment is "an assertion detached from particular examples and begins to move toward conceptual proofs." (Taflin, nd)

The work entitled: "Adding it Up: Helping Children Learn Mathematics" states that proficiency in instruction of mathematics is "related to effectiveness: consistently helping students learn worthwhile mathematical content. It also entails versability: being able to…

Islamic art not only demonstrates the symbolic significance of geometric forms and their psychological, social, religious, and aesthetic functions. In addition to these purposes, Islamic art also demonstrates symmetry. Symmetry's appeal is well-known: babies tend to favor faces with symmetrical features over those with lop-sided noses or askew eyes. Although absolute symmetry is by no means a prerequisite for beauty, symmetry is usually perceived with pleasure. The Spirograph forms, explicated by Karin Deck, are sublimely symmetrical.

Spirograph hypotrochoids and epitrocoids illustrate the value of symmetry in aesthetics and they also demonstrate the prevalence of mathematics in visual art. While Spirograph patterns may not normally be considered fine art, they are nevertheless pleasing to the eye as well as the mind. Their symmetry no doubt contributes to their aesthetic appeal but Spirograph trochoids, like Islamic friezes, draw order out of chaos and reveal the prevalence of patterns throughout the universe. Moreover, Spirograph…

Mathematics Concepts in Profession
Mathematics Concepts in the Teaching Profession

Mathematical concepts in professions

My Profession and Applicable Math Concepts

Mathematics is a branch of knowledge dealing with scientific notions of logical qualitative and quantitative arrangements. It extensively covers different aspects as well as having several subdivisions. It is a tool specially designed to handle and implement relative concepts, regardless of the kind of situational problem presented. Alongside the concepts, mathematics uses invented formulas to help in solving the computations systematically. These concepts keep up a correspondence to the quantitative association to the computations they carry out.

Many career opportunities in life apply knowledge of mathematics and the subsequent concepts of the subject. All fields are dependable of conceptual facts and formulas taught in the math course. From critical analysis of career opportunities globally, and through applicable knowledge, I have settled my professional interests in becoming a mathematics instructor. Through this choice, I believe I…

Mathematics
a) Spreadsheet Data Analysis

b) State hypotheses:

Ho: Type of soft drink and resident are independent. (null hypothesis)

Ha: Type of soft drink and resident are not independent. (alternate hypothesis)

c) Conduct chi-square test of independence at 0.05 significance level: = 0.05

d) Calculate degrees of freedom: Number of rows = 2, Number of columns = 2

Degrees of freedom (df) = (Number of rows - 1) x (Number of columns - 1) = (2-1)(2-1) = 1

e) Calculate the expected frequencies from actual data:

f) Calculate the chi-square statistic using both actual and expected frequency tables:

In excel, the cursor was placed in cell M17 and the formula of chi test typed as:

=CHITEST (actual frequency range, expected frequency range)

=CHITEST (L4:M5, L13:M14), as shown in the formula bar above

The result gives, the calculated chi-square probability, p = 1.2203 x 10-10

g) Look up the Chi-Square value, ?2 from chi-square distribution tables for df = 1 and ? = 0.05

2…

SIAM's mission is to build cooperation between mathematics and the worlds of science and technology through its publications, research, and community. Over the last 50 years SIAM's goals have remained constant:
• They want to advance the application of mathematics and computational science to engineering, industry, science, and society.

• To was to promote research that will lead to effective new mathematical and computational methods and techniques for science, engineering, industry, and society.

• They want to provide media for the exchange of information and ideas among mathematicians, engineers, and scientists.

The applied mathematics and computational sciences have become essential tools in the development of advancements in science and technology. Ground-breaking mathematical and computational techniques have become prevalent in areas such as the biological sciences, information technology, climatology, combustion and emission control, and finance and investment. It is through its publications, conferences, and community, that Society of Industrial Applied Mathematics continues to foster…

Mathematics Teaching
Learners Studying Basic Mathematics To Enable Helping Their Children With Their Education

The work of Jackson and Ginsburg (2008) reports on a series of algebra classes involving a group of African-American mother and elementary-aged children, who are low income and who "had limited and negative formal experiences with algebra." (p. 10) The women in the study who arrived to the algebra classes are reported to have had "well-informed view of what algebra was -- a disconnected body of knowledge that they did not understand -- and corresponding views of who could 'do' algebra." (Jackson and Ginsburg, 2008, p. 11) The study resulted in the women's views of who could 'do' algebra being changed "through genuine, intellectual inquiry into the mathematics of algebra." (Jackson and Ginsburg, 2008, p. 11) It is reported that questioning "is recognized as a critical instructional tool in the teaching of mathematics for understanding." (Jackson and Ginsburg,…

Mathematics and Art
Mathematics

The application that I researched and found of mathematics and art is Data Visualization, which is closely related to Infographics. On a very simple level, data visualizations are artistic, aesthetic representations of data. The ways in which the data visualization can be "drawn" or created involves different kinds of mathematics, including vectors, fractals, algorithms, and statistics. Data visualization is a fairly new field, indigenous to the 21st century. There have been other ways to represent data graphically, but not with the detail, precision, and beauty offered by data visualization.

Presentation and aesthetics are very important in the consideration of data visualization. I found this application of mathematics and art particularly compelling because its existence seems to fly in the face of the long held stereotype that there are strict boundaries between science and art. Data visualization seems to be the artistic version or expression of science (and mathematics) and…

Mathematics Textbooks
Technology used in Mathematics Textbooks

Mathematics probably frustrates more students than any other subject in their course load. It seems that a logical, left brain is something that must be inborn and many students are not gifted with that natural ability. This means that there need to be some simple methods by which every student can be made to understand mathematical concepts. While many different teaching methods have been attempted with varying levels of success, none have been completely successful. However, with the advent of technology, this task is made simpler for the math teacher. Technology allows the student to work the problem successfully while helping the individual understand the application of the problems. Technology can be used via a text itself, or a teacher can utilize a text which offers parallel instruction via a companion web site. The following report will discuss how technology is used by the text…

Teachers and students alike must have the ability and the opportunity to move freely about, especially in high traffic areas, so congestion does not build to a level that causes distraction or frustration, whether from students or from teachers.
When teachers group desks in functional ways, according to activity, for example desks for high-activity or high traffic desks grouped separately from desks for test-taking, students are more likely to demonstrate superior behavior because their teachers (Brophy, 1983) can easily meet their instructional requirements (Marsh, 2004). The classroom arranged in a manner that reduces congestion produces an environment with more discipline, safety and respect, which is important especially among students at the 8th grade level and above, when students are more likely to demonstrate behaviors akin to their personality and interests. A mathematics classroom organized around function creates an environment that stimulates students to participate in learning, and concentrate on subject…

27% payoff. "He would begin with the $100 and get back $93.27 (theoretically) the first time he ran his money through the machine. If he continued to play until his $100 bankroll was gone, he would have put his money through the machine 71 times for a total of 1,967 plays on the machine" (7). The gambler's total wager (handle) would then be $1,475; however, the win (gambling revenue) for the casino would be $100, the amount of the player's original bankroll (Barker & Britz 2000). According to the International Gaming and agering Business (IGB, 1998, 5), a player could statistically generate a handle of $10,000 at a table game with a casino advantage of 1% before losing a bankroll of $100 (in Barker & Britz 7). This casino advantage is known as the "vigorish," which is discussed further below.
Vigorish. John inn is credited with inventing the book, the quarter…

Students will present their findings to the class.
2. In groups, students will graph population growth and predict future trends using exponential functions (Ormond 2010). A data set is available at: http://serc.carleton.edu/files/quantskills/events/NAGT02/quantskillsworldpop.pdf. Students will discuss the political and environmental implications of their findings.

3. Students will perform an exercise using exponential functions graphing increases in atmospheric CO2 concentrations (Ormond 2010). A data set is available at: http://serc.carleton.edu/files/quantskills/events/NAGT02/co2moe2edit.pdf

Students will discuss the political and environmental implications of their findings.

Standard 3:

4. Students will be divided into groups, given problems of quadratic inequalities and 'race' to see what group can come up with the correct solutions the fastest.

5. Students will be asked to periodically write and graph homework problems on the board to 'teach' graphing to the rest of the class.

6. Students will be given examples of graphs or tables of values of functions and asked to identify what type of function they are, based…

The foundations of high stakes testing indicate that their intention is to formulate change that is traceable and transparent. Accountability is essential to outcomes but instruction must be aligned to the needs of students and educators and most importantly must be inclusive of the perceptions and perceived needs of real life classroom teachers. Tracing the effectiveness of high stakes reforms and reforms that would be considered the fall out of such is essential to the development of alignment between curriculum and test results. (Bolt 2003) These changes cannot under any circumstances be judged solely on the perceptions of administers, as has been shown by this work administrators give a great deal more positive assessment of reform, prior to the acceptance of such reform as positive by real world classroom teachers. This is especially true with regard to those students who are clearly already at a disadvantage in the system, a…

In an open-ended study of 42 teachers decided to leave with the peer assistance being a contributing factor while in another research carried out with 99 teachers, only 4 said that the peer assistance was one of the decisive factors (Billingsley et al., 1993 & 1995). Some of the factors for the variation in these studies could be the way the teachers were asked these questions (like, open-ended polls vs. questionnaires), purpose to leave or the leaving conduct was calculated, as well as the huge trial dimension distinction of the two studies.

Therefore, in light of the mentioned study conclusions, the educational institutions should treat peer assistance as a determining factor to augment preservation of the teachers as well as the school system.

Support through Induction and Mentoring

Special attention needs to be given to the upcoming teachers in this particular field, to give them confidence and a sense of contribution to the…

The nature of the instrument, with true and false answers and patterns that are readily identifiable, has prompted the development of books to supply interpretations of the results. The interpretations are given in the form of descriptive statements that tend to be true of clients whose scores yield certain profiles. When used by a skilled and experienced psychologist, the MMPI is a powerful instrument. The psychologist administering and interpreting the MMPI must pay attention to all relevant factors, including age, sex, education, social class, religious background, place of residence, and other historical data (Karp and Karp, 2009). The criterion groups for this test were selected from patients at the University of Minnesota hospitals (Minnesota Multiphasic Personality Inventory, n.d.).

The MMPI has ten clinical scales and three validity scales in addition to many supplementary scales. It has been found to be difficult to consistently bias the MMPI because of the complexity and…

Mathematics
Determine whether the lines will be perpendicular when graphed.

For two lines to be perpendicular, the slope of one line must be the negative reciprocal of the slope of the other line. The slope can be determined by transforming the equation to its standard form of y = mx + b, where m = slope. Thus,

2y = 6 2y = 3x - 6 3/2x - 3, where m = 3/2

For the other line to be perpendicular, the slope of the equation for 2x + 3y = 6 MUST be m = -2/3. To check this, the equation can be transformed to its standard form:

3y = 6 3y = 6-2x y = 2-2/3x y = -2/3x + 2, where m = -2/3

Therefore, the lines of both equations will be perpendicular to each other when graphed.

Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73…

Mathematics puzzles provide indispensable tools for learning. Since the ancients started to ponder the mysteries of the universe, mathematics has been the underpinning of philosophical, scientific, and creative thought. Moreover, a historical analysis of the evolution of mathematical thought shows that puzzles, riddles, and complex problems have consistently been the means by which successive generations have pondered mathematics principles and advanced understanding of numerical equations, patterns, and proofs. Mathematics puzzles remain relevant throughout time, which is why it could take hundreds of years to solve one puzzle. Puzzles also transcend language and culture, providing the only true universal human language other than perhaps art and music. For example, Archimedes' riddle about dividing the square was not solved until thousands of years later, just like the riddle of crossing the bridges of Konigsberg (Pitici, 2008). ). Mathematical puzzles have inspired people throughout time and space to think deeply about conundrums and…

gov.on.ca). These are the goals for learning that students need to master, according to Ontario; Gap Closing focuses specifically on them. However, there's very little room for innovation.
Product and How Children Learn

The product reflects the way that only certain children can learn mathematics. Some children truly can understand mathematical concepts by having them presented on a page and through repetition. Other children can readily learn and master mathematical concepts through the pictures and diagrams that Gap Closing relies so heavily on. However, certain children will not be able to thrive off of Gap Closing. They will still find the concepts confusing and unclear, and that the work involved is exactly that -- work. It's not fun and it's not enjoyable and it does nothing to increase their appreciation of math or decrease their fear of math. These children might need more collaborative or tactile learning.

eferences

Edu.gov.on.ca. (2005). The Ontario Curriculum: Mathematics.…

Leaning style pefeences ae the method in which, and the cicumstances unde which, leanes most competently and successfully ecognize, pocess, stoe, and ecall what they ae tying to lean. Knowing the students' leaning style pefeences can aide in the development of the most effective teaching appoaches.
The gende-elated diffeences in math achievement have been attibuted to a numbe of vaiables, most notably, diffeential couse taking pattens and exposue to math, diffeent leaning styles, teache behavio and leaning envionment, paental attitudes and expectations, and socioeconomic status as well as othe backgound chaacteistics of students. One poblem that is not addessed in this eseach is the inability to isolate the effects of gende socialization fom obseved biological sex when obsevational data is used. One method by which the effects of envionment and socialization may be contolled fo involves the use of a popensity scoe, as developed by Rosenbaum and Rubin, fo gende.…

Communicating Mathematics
It is important for teachers and students to be engaged in communicating mathematics for higher understanding and the building of problem solving skills. Understanding mathematics means to define the measures of quality and quantity that connections have with new ideas and existing ideas. The greater understanding comes from the greater connections of network ideas. The goals of elementary teaching is to teach mathematics in meaningful and understanding ways to enhance problem solving skills and reasoning strategies based on real life. In doing so, students learn to visualize and communicate abstract ideas that creates opportunity for enrichment in reflective thinking.

A problem solving approach to mathematics engages students in inquiry that helps them build and improve current knowledge (Asking Effective Questions, 2011). A teacher who questions effectively can help students to identify thinking processes, see connections between ideas, and build new understanding in solutions that make sense to them. Reasoning skills…

nctm.org/publications/jrme.aspx?ekmensel=c580fa7b_116_412_btnlink)isa peer-reviewed journal of current research on what concepts work for students in the classroom and also allows for the submission of teacher manuscripts on relevant topics.
he Journal of Online Mathematics and its Applications (http://mathdl.maa.org/mathDL/4/)includesdiscussion of how to teach math to students, such as the use of 'spinners' when teaching probability, to cite one example, and webcasts about 'best practices' in math education. Because the journal is web-based and makes use of wiki technology, it is both easy to access as well as engaging.

Education Next, published by the Hoover Institution, provides a continuing overview of how American education, including math, measures up against America's international counterparts as well as compares different approaches to education throughout the nation (http://www.hoover.org/publications/ednext/).Itprovides examples of how math is taught in other countries, sobering assessment of America's state of math education, and a fairly blunt and opinionated view of what works and what does not in…

To my observation, a math teacher now has the ability to put a personal stamp on his approach to curricular material, with evolving technologies such as a class website serving as a reflection of his own ideas regarding math instruction and his own emphases on relevant principles. By enabling teachers to bring creative ingenuity into the process, the internet is helping instructors and students to make closer connections, which in turn may motivate them to assimilate material and ideas more effectively. Most districts with the means and understanding of these benefits have not only actively promoted the incorporation of the internet into everyday instructional activities but have endowed school websites with the networked capacity to enable every teacher to utilize the infinite virtual space to the advantage of their students. I will personally make an effort to explore the innovative instructional possibilities and ways of accessing the personal interests…

Unlike quantitative studies which engage the use of statistics qualitative work places greater emphasis on the narrative and in this case on answering the research question. The researchers found that the majority of experts demonstrate that LD affects the understanding of concepts, and this impedes the comprehension of mathematics. They were also able to identify four approaches that produce better results in students with LD. The four approaches, systematic and explicit instruction, Self-instruction, peer tutoring and visual representation have been demonstrated to produce significant results in persons with LD (Steedly et al. 2008, p.3). This finding has multiple implications for the teaching community.
If the teaching community engages these approaches in a systematic and comprehensive manner, it is very possible that more students will learn mathematics easier. To do this may require some retooling in many instances as the associated pedagogy may not be completely understood by present teachers. The…

When the different levels of functionality were compared highly functioning individuals took 55% of the academic courses the difference between the groups was significant (p< .01). Moderate functioning individuals took 46% of their classes as academic classes and for low-functioning persons only 40% of their classes were academic. When consideration was given to the setting in which the courses was taken it was found that 92% of the sample took at least one class in a special education setting and 69% in a general education setting.

The finding demonstrated that the students took a number of diverse courses within the semester. The courses were taken within the two settings of general and special education. Students with mental retardation however were more likely to do courses in the special education arena rather than the general arena, this finding was significant. Moderate functioning students and students with low functioning were more likely than…

Mathematics underpins every area of human life. From the simplest counting procedures to advanced physics, mathematics becomes the means by which people understand, communicate with, and interact with the world. As Kramer (2015) puts it, "math can be found everywhere," (p. 1). Mathematics puzzles are learning exercises that help people prepare their cognitive abilities for solving real-life mathematics issues. Puzzles can be fun and enjoyable means by which to understand mathematical theorems in ways that reveal real-world applications. There are also many different types of mathematics puzzles, including those that are strictly numerical in nature, those that are logical in nature, and those that involve calculus or the use of formulas. Mathematics puzzles can prepare a person to think creatively and critically about any number of fields, such as architecture and music.
One real world application of mathematics puzzles is in the field of games and gaming. Both traditional board and…

Mathematics Instruction for Students With Disabilities, Grades 7-12
Fennell & National Council of Teachers of Mathematics, (2011, p. 164), quote Freudenthal that 'geometry with respect to children's education plays a role in how children grasp the space in which they operate'. It provides useful and practical knowledge that enables children to not only know and conquer this space, but also conquer and make it better to live in. More importantly, there is enhanced revelation and development of unsuspected strengths, such as drawing and manipulating forms in children with special needs when they learn geometric and special tasks (Fennell & National Council of Teachers of Mathematics, 2011, p. 164). It thus offers alternatives in which learners capitalize on, especially those with language and communication difficulties (Fennell & National Council of Teachers of Mathematics, 2011, p. 178).

With respect to geometry, the pre-k-12 instructional programs enable learners to achieve various tasks.

They should learn the…

Mathematics for Special Needs Children
Solving Math Word Problems (For Ex: Teaching Students with Learning Disabilities Using Schema- ased Instruction)

One of the most challenging things to learn for children with LD (Learning Disabilities) is basic math concepts and problem solving skills. This challenge can negatively affect their ability to solve new problems. However, improving a child's ability to solve problems is not an easy exercise. And this might be due to several reasons, such as problems with visual-spatial processing, strategy knowledge and use, language processes, vocabulary, background knowledge, memory and attention. Thus, it is important for policymakers to focus on addressing these problems when designing interventions. Several studies indicate that interventions / practices such as peer-assisted learning opportunities, visual representations, student thinkalouds, and systematic/explicit instruction can help improve learning outcomes for students with disabilities. SI (Schema- ased Instruction), an alternative to conventional instruction, incorporates many of the above-mentioned practices to improve…

Mathematics for Special Needs Children
Solving Math Word Problems (For Ex: Teaching Students with Learning Disabilities Using Schema- ased Instruction)

One of the most challenging things to learn for children with LD (Learning Disabilities) is basic math concepts and problem solving skills. This challenge can negatively affect their ability to solve new problems. However, improving a child's ability to solve problems is not an easy exercise. And this might be due to several reasons, such as problems with visual-spatial processing, strategy knowledge and use, language processes, vocabulary, background knowledge, memory and attention. Thus, it is important for policymakers to focus on addressing these problems when designing interventions. Several studies indicate that interventions / practices such as peer-assisted learning opportunities, visual representations, student thinkalouds, and systematic/explicit instruction can help improve learning outcomes for students with disabilities. SI (Schema- ased Instruction), an alternative to conventional instruction, incorporates many of the above-mentioned practices to improve…

Learning Mathematics
Acquisition of numeracy has been an issue that has attracted a lot or research .The research is mostly aimed at finding out the personal and social factors that affect the acquisition of numeracy as well as the impact the public or popular perceptions of mathematics on a learner. The paper will look at some of the social and personal factors that might have an impact of the acquisition of numeracy. It will also look at the popular perceptions that influence a learner when it comes to studying mathematics.

Personal factors

There are several personal factors that might affect an individual's acquisition of numeracy one of them is a parent's education level. Parents are role models when it comes to the academic achievement of a person. Acquisition of numeracy is particularly influenced by the beliefs that are held by an individual's parents regarding mathematics. If parents have negative attitude towards mathematics then…

For instance, classical mathematicians by definition rely on Plato's theory of forms as the underlying basis of their mathematical worldview. The Platonist assumes the existence of true, immutable, and universal forms and structures that the mathematician approaches through the language of numbers and equations. For instance, the classical mathematician holds to the Platonic belief in the expansion of pi; to approach the expansion of pi from any other perspective "would require a restructuring of all of mathematical analysis," (p. 414). The paradigm would have to change; a most likely candidate for the restructured mathematical analysis would be constructivism, which relies more exclusively on the number system. The very existence of varied paradigms in mathematics points to the essentially "soft" core underlying all mathematical pursuits.
Finally, the growth of mathematics depends partly on the evolution of technology as well as the evolution of thinking. Paper and pencil has largely given way…

if, as Halmos suggests, math is a creative art then math must also be the handmaid of science.
Describing mathematics as a creative art helps students of math better understand the true roles of the mathematician. Numbers, while in many ways central to the art of math, do not comprise the whole lexicon of mathology. Mathematics does stem from "sheer pure intellectual curiosity," enabling students to perceive the world through new eyes (p. 379). Teaching mathematics can therefore be like teaching art. Some pupils will exhibit innate, almost supernatural talents and abilities and others struggle with the language and media unique to each subject.

Because mathematics integrates seamlessly with daily life, however, teachers can easily point out the ways mathematics underlies reality. Teaching mathematics from a multifaceted and creative perspective can enhance student learning, retention, and interest in one of the most…

Mathematics is closely connected to economics, commerce and business modelling, as well as systems for military weapons. Due to the widespread of its use, it was noted that students in the U.S. were beginning to perform a little worse in mathematics than children from other countries worldwide. Mathematical knowledge among citizens was considered a very important factor for a country to be a leading world power. Assessment activities have been a continuing focus of academic research for more than twenty-five years. In that period, there have been new tools developed. In addition, the curriculum has shifted its focus to the results of learning. The shift of focus in the theory of learning to constructivism from behaviourism has greatly influenced the learning and teaching of mathematics. Conventional tests are only centred on the mathematical procedures and skills of students. Thus, application of authentic tools for assessment to measure the learning of…

" This reflects the gap that exists between the complexities of the real world and the abilities of abstract models. Models are by definition simplified ways of understanding complex phenomenon; they are necessarily incomplete in their estimations and valuations of real world figures and occurrences. This is why "all models are wrong." "Some models are useful," however, because they are able to approximate to a high degree the outcomes of real world events despite the incomplete nature of the information processed by the model. To make a model useful, bias must be removed. This is not an issue with the certainty of mathematical models, but conceptual models are necessarily subjective, built on the modeler's understanding of an issue. educing bias is key to the model's performance.
eferences

Aspinall, D. (2007). "Designing interaction." University of Edinburgh. Accessed 30 July 2009. http://www.inf.ed.ac.uk/teaching/courses/hci/0708/lecs/intdesign-6up.pdf

Kay, J. (2006). "Amaranth and the limits of mathematical modeling." Financial times, 10…

"Theorists of capitalism" such as erner Sombart state unequivocally that the "beginning and end" of capitalist activities is "a sum of money," which must be calculated and trace the renewed interest in higher mathematics to mercantile capitalism and the need for an easily convertible medium of exchange (Sachs 2000).
However, exposure to the Arab world through the Crusades was also a factor in a renewed interest in mathematics independent of capitalism -- interest in rationalism as a concept also spawned theorizing later useful to economists. Fibonacci (1175-1250 AD) "wrote Liber Abaci, a free rendition of Greek and Arabic works in Latin which taught the Hindu methods of calculation with integers and fractions, square roots and cube roots, this book made available the masses the number systems heretofore sequestered in monasteries throughout Europe" (Dickinson 1996).

ork Cited

Sachs, Stephen E. "New math: The 'countinghouse theory' and the medieval revival of arithmetic." History 90a.…

Implications and Conclusions

Suffice is to say the amalgamation of technology in primary school is a two sided-sword saying that one cannot ignore the empirical benefits achieved. It is the responsibility of the education department to set workshops and indulge the teacher in incorporating technology in teaching mathematics to students in primary level. In addition, mathematical competitions should be organized to attract students to take interest in mathematics.

eferences

Burrill, G., Allison, J., Breaux, G., Kastberg, S., Leatham, K., & Sanchez, W. (2002). Handheld graphing technology in secondary school mathematics: esearch findings and implications for classroom practice. Dallas, TX: Texas Instruments. Available at http://education.ti.com/sites/U.S./downloads/pdf/CL2872.pdf.

DiSessa, A.A. (2001). Changing minds: computer, learning, and literacy. Cambridge (Mass.): The MIT Press.

Ellington, A.J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in pre-college mathematics classes. Journal for esearch in Mathematics Education. 34(5), 433-463.

Kaput, J. (2007). Technology becoming infrastructural in mathematics education. Models…

Note the distinct similarities.
An examination of Escher's Circle Limit III can thus tell us much about distance in hyperbolic geometry. In both Escher's woodcut and the Poincare disk, the images showcased appear smaller as one's eye moves toward the edge of the circle. However, this is an illusion created by our traditional, Euclidean perceptions. Because of the way that distance is measured in a hyperbolic space, all of the objects shown in the circle are actually the same size. As we follow the backbones of the fish in Escher's representation, we can see, then, that the lines separating one fish from the next are actually all the same distance even though they appear to grow shorter. This is because, as already noted, the hyperbolic space stretches to infinity at its edges. There is no end. Therefore, the perception that the lines are getting smaller toward the edges is, in…

Chinese Mathematics
In ancient China, the science of mathematics was subsumed under the larger practice of suan chu, or the "art of calculation." The Chinese are believed to be one of the first civilizations to develop and use the decimal numeral system. Their early mathematical studies have influenced science among neighboring Asian countries and beyond.

This paper examines the history of mathematical knowledge in China. It looks at the early Chinese achievements in the field of mathematics, including the decimal system, calculation of pi, the use of counting aids and the application of mathematical principles to everyday life. It also examines the influence of Indian and later, European mathematical knowledge into Chinese mathematics.

Early China

Unlike the ancient Greeks who prized knowledge for its own sake, much of the scientific studies conducted in ancient China were spurred by practical everyday needs. Because of its geographic location, China was prone to devastating floods, particularly along…

..an approximation for ?, which is surprisingly accurate. The value given is: = 3.1416. With little doubt this is the most accurate approximation that had been given up to this point in the history of mathematics. Aryabhata found it from the circle with circumference 62832 and diameter 20000. Critics have tried to suggest that this approximation is of Greek origin. However with confidence it can be argued that the Greeks only used ? = 10 and ? = 22/7 and that no other values can be found in Greek texts." (Indian Mathematics, 2009)
There is stated by Selin (2001) in the work entitled: "Mathematics Across Cultures: The History of Non-Western Mathematics" to be "...no evidence of the method for extracting cube roots having been known earlier than Aryabhata I." (Selin, 2001)

Conclusion

Aryabhata made great contributions to mathematics and algebra and his greatest contribution to Algebra was that of his approximation for?

stated…

Actuaries
The Jobs ated Almanac has printed five editions from 1998 to 2001 (Society of Actuaries, n.d.). In two of these editions, "actuary" was rated as the best career in terms of environment, income, employment, outlook, physical demands, security, and stress. In two other editions, "actuary" was rated as the second best career. In only one other edition was it rated fourth. The data used to calculate these findings came from trade association and industry group studies, as well as government sources such as the U.S. Census Bureau and the U.S. Bureau of Labour and Statistics. In addition, Actuaries were rated number six by PayScale.com in terms of highest salary (Braverman & Jeffries, 2009). The average actuary makes around $129,000 a year and a top actuary make around $257,000. This paper will further explore the role and purpose of an actuary, the use of mathematics within this career, and how it…

As Kleiner & Movo*****z-Hadar show, the burden of proof lies with the mathematician eager to uncover some unknown universal law or theorem. His or her colleagues will, as the authors point out, be harangued and criticized because of a general resistance to new ways of thinking or profound revelations. Because of the difficulty in obtaining proof and subsequently communicating those proofs to the academic community, math remains one of the last bastions of reason in our society. Mathematics stimulates analysis and critical thinking, essential components of a good life. Philosophers use proofs too, such as to illustrate the existence or non-existence of God. Perhaps the most salient issue brought out by Kleiner & Movo*****z-Hadar in their article and the one most relevant to modern classrooms is their celebration of diversity of thought. While mathematics may occasionally manifest as speculation or even intuition, ultimately mathematicians demand proof: evidence, firmness, and…

Problem Solving in Mathematics
GCSE or the General Certificate of Secondary Education is basically a system that is present in England, Northern Ireland and in Wales. In this system, a student is awarded an academic qualification based on the grades that they attain. The qualification that a person attains is equivalent to either a level 2 or Level 1 key skills qualification. Normally, a student can uptake as many subjects as he or she wants. However, different systems set a requirement for how many subjects or GCSEs a student must take. There is present an international system of IGCSE as well and these subjects can be up taken anywhere in the world. This was just a precise history of what exactly the GCSE system is all about. Interestingly enough, the GCSE system was not the first one of its kind. Prior to this, GCE and the English Baccalaureate System were…

Activity -- Work through the rock face problem as a class using an overhead or projector. Ask for input on alternatives to this set of functions? Ask for, and brainstorm other measurements in which we can try our new method (e.g. measurement without a measurement tool).

2. Working on the concept of ratios. Using the measurement skills from Activity 1, students will calculate measurement and ratios to find patterns of sides of a triangle. This will develop the concepts of sine, cosine, and tangent ratios of angles. Students should have a basic concept of ratio, be able to convert fractions to decimals up to three places and be able to measure the length of sides of a triangle.

Divide class into 4 groups, each group will have a set of triangles copied on colored paper. The triangles should be cut and set aside. Class will also need three large charts (one for…

These include: question/answer, lecture, demonstration, discussion, individual student projects, laboratory, technological activities, and supervised practice. Previous research has demonstrated that the use of informal knowledge, real world settings and opportunities to apply mathematical thinking are effective instruction methods for introductory algebra. For this reason, instructional factors are related to achievement in algebra (p. 102).
When comparing the test scores from Japan and the United States, House and Telese (2008) found a correlations between positive beliefs in the student's mathematical ability and their test scores. Those who believed they could do well in math performed better than those who expressed a negative opinion about their skills, when compared to their peers. In addition, students who worked problems on their own had higher test scores. This supports Silver's (1998) analysis that much of the reason why American students have poorer test scores than their international peers is due to the classroom instructional…

new California Mathematics Framework. Specifically it will discuss how these changes affect teaching math in grades 6-12. The new California Mathematics Framework (CMF) provides teachers with techniques to teach mathematics in the classroom, and it has been changed significantly from previous frameworks. The framework's changes will certainly alter how many teachers teach in the classroom, and some of the changes may be difficult to implement.
To begin with, the framework provides some goals for teachers to meet in the classroom. For example, it is the goal of the teacher to "Provide the learning in each instructional year that lays the necessary groundwork for success in subsequent grades or subsequent mathematics courses" (Editors 2). This is extremely important in grades 6-12, where students will be layering new types of math learning on top of each other, such as algebra followed by geometry followed by calculus. To build a good foundation can…

Before "cogito ergo sum" was ever conceived, Descartes introduced a number of enthymemic principles. The first was that he, as an individual, had the right to assert his wishes. The concept that the mere state of being a living, breathing human implies right and privileges is fundamental to most present-day beliefs, but at the time it was worse than disgusting; it was blasphemous.

Another example was his unshakeable self-confidence. Despite signs of anti-sociality, such as moving from house to house yearly without notice and keeping strange hours, Descartes was not intimidated by his separation from society, but rather insistent on it. It allowed him to work in peace and, perhaps most importantly to avoid contaminating sources of thought.

It is worth noting that the key to this vital constancy was rooted in the fact that his beliefs confirmed his individuality and personal powers of thought. At the age of twenty-three, he related…

Mathematics Instruction in English on ELL Second Grade Students
J. Elizabeth Estevez

Educ2205I-Content Research Seminar

Mathematics is a powerful tool for interpreting the world. Research has shown that for children to learn how to use mathematics to organize, understand, compare, and interpret their experiences, mathematics must be connected to their lives. Such connections help students to make sense of mathematics and view it as relevant. There has, however, been controversy with regard to children from non-English backgrounds and the best ways to get them to make those connections. Questions are raised regarding how to instruct these children who are referred to as English language learners (ELL's). Should they initially be taught in their native language with gradual exposure to English in language classes, or should they be immersed in English as early as possible. Based upon ideas presented in research studies and my own ideas as a former bilingual teacher, I decided…

Individuals with Disabilities Education Act (IDEA) governs how the U.S. states offer special education services to children with disabilities. It addresses the educational needs of the children with disabilities from birth to age 21, and involves more than a dozen specific categories of disability. Congress has reauthorized and amended IDEA several times, most recently in December 2004. Although historically, students with disabilities have not had the same access to the general education curriculum as their peers, IDEA has changed the access and accountability requirements for special education students immeasurably (NCTM, 2011).
The challenges for meeting the needs of students with disabilities and ensuring their mathematical proficiency, confront teachers of mathematics every day. Teachers must use the results of all assessments, formative and summative, to identify the students whose learning problems have gone unrecognized, and monitor the progress of all students. Regardless of the level or method of assessment used, teachers…

culture affects the way students learn mathematics, and how different cultures learn differently. Students in Korea and Japan learn differently than students in the United States for a number of reasons. Statistically, Asian students seem to do better at mathematics than American children do, and they way they learn their mathematics at an early age may be on reason this is so.
Identification and Investigation

US students often show lower test scores in understanding mathematics, while Asian students consistently score higher. There are many reasons for this, from different cultures to different methods of instruction. For example, one researcher found that Japanese children think of numbers differently, and see their relationships in depth. She writes, "She discovered part of the reason was the way they named their numbers. Following ten, they say, "ten 1, ten 2, ten 3" for 11, 12, 13, and say "2-ten, 2-ten 1, 2-ten 2" for 20,…

Education
hat are the differences between the Common Core Standards for grade eight and the New York State standards of mathematics?

Common Core Standards

For one thing, the Common Core Standards offer narrative (rather than bullet points) and go into more specific and in depth instructions through narrative. The Common Core Standards expressly mentions three critical areas out in front: a) formulating and reasoning about "expressions and equations," which includes "modeling an association in bivariate data with a linear equation" -- and that includes being able to solve "linear equations and systems of linear equations"; b) students are asked to "grasp the concept of a function" and to use functions in order to understand "quantitative relationships"; and c) students must be able to apply the Pythagorean Theorem when it comes to being able to analyze two and three dimensional space and figures using "distance, angle, similarity, and congruence" (www.corestandards.org). These directions are provided…

Personal specification for GCSE Mathematics position
Appropriate knowledge and skills related to the area of teaching required and a willingness to keep up-to-date.

In order to be a successful GCSE mathematics teacher, it is important that I must know appropriate knowledge about the course that I am delivering to the students and have good skills of communication so that the students understand my way of teaching as well. I have taken different courses of calculus, statistics, geometry and algebra in college as well as during the graduation level. Taking the courses has strengthened my command in mathematics and I can easily and confidently transfer the processes and concepts over to the students. Answer key in mathematics is one of the short-cuts that should be avoided so I do not allow my students to have the key with them at all as this would lower their confidence as well as mine. If the…

Improve Mathematic Performance for Children With Learning Difficulties and Their Effectiveness
Students with learning disabilities face several problems. More often than not, these students advanced approximately one academic year for every two academic years they attended school. Strategies employed by teachers can have a major impact on enhancing this particular performance in all levels of schooling. The lack of comprehensive strategies and interventions students with mathematics disabilities end up considerably lagging behind compared to their peers. Statistics indicated that approximately 25% to 35% of students experience difficulty with math knowledge and application skills. Moreover, 5 to 8% of all students in school have such considerable deficits that influence their capability to solve computation problems (Sayeski and Paulsen, 2010). In accordance to Hott et al. (2014), strategy training has been beneficial to students with learning disability when learning math conceptions and practices. As presented in the article one of the strategies…

Coding Theory for Discrete Mathematics
In the contemporary IT (information technology) environment, increasing number of organizations are using large computer to transmit data over a long distance and some of these data are transmitted across billions of kilometers. During data transmission, some data can be degraded; the coding theory is an effective strategy to recover degraded data in order to guarantee reliable data transmission. Coding theory also assists in recovering and detecting errors, which assists in enhancing efficient data storage and data communications.

Objective of this paper is to discuss the coding theory and its real world application. The paper discusses the errors detecting codes and its application in the next section.

Error Detecting Codes

A simple strategy to detect errors is to add parity in order to check bit. To detect errors, a bit strong will be transmitted in order to add a parity bit. Typically, when a bit string has an…

Precalculus With Limits by on Larson
This book as well as the other two books are for college freshman level or college introductory level mathematics courses. The strengths of the book are mainly focused on its layout. For example, the book has a great way to demonstrate a varied and large amount of information easily and simply. This means that people reading the text just have to look for certain visual cues like colors or pictures that will point the information they seek. For example, the diagrams have a different background color than the text. All of this removes time spent looking for things. The use of bold also further differentiates the text, highlighting key words, phrases and things to memorize.

The weaknesses are in lack of context surrounding the topics and footnotes. Another book reviewed has footnotes and yet another provides adequate background for each topic. This book sacrifices breadth for…

The amount of interest that we would pay each month is the rate (say 6%) divided by twelve (multiplied by the principal). Therefore, the yearly compounded rate is higher, actually, than the disclosed rate. In Canada, mortgages use semi-annual compounded rates, while payments are still monthly. Mortgages in the U.S., however, are mostly payable and compounding monthly, which means that U.S. homeowners are paying more in interest on their homes than Canadians, as the yearly compounded rate is higher than the disclosed rate.
Buying a home, we found, is a lot like buying smaller things, as we have been doing, on credit, with credit cards, which is called "installment buying." Installment buying stipulates that, although one may "purchase" something with a credit card and use it, it legally still belongs to the seller until the last payment is made. If the buyer defaults, the goods revert to the seller and…

conveyed in an effective manner to meet the needs of students. It is an important aspect of differentiating instruction. Students with diagnosed learning disabilities will receive an IEP designed to address their specific learning issues and deficits. Presentation, response, timing (scheduling) and setting can all be addressed in differentiation. Memory; auditory, visual, and even motor processing; attention deficits; abstract reasoning issues; and organizational problems can all cause issues for students that can be improved with differentiated instruction (Ginsberg & Dolan, 2003, p. 87).
In-class assessment can take place in both in traditional formative and performance-based ways. Formative assessment is used during the learning process so the teacher can check in to see what the student has retained. This can be observational or in the form of quizzes or other graded formats. But while performance-based assessment can take the form of conventional tests there are other methods besides exams, including flexible…

Whole-Number Computation
Equal-groups math problems can be delineated as word problems where an individual is given a number of equal groups, and then the task is to find the missing number within the problem. In other words, equal-groups are groups that comprise of the similar number of equivalent items.

To simplify the understanding of these questions, a full equal-groups math problem comprises of three different parts including the number of groups, the number of items contained in every group, and the total number in all of the groups. The following formula makes it possible to comprehend how to comprehend these three parts using multiplication:
The number of groups × the number of items in every group = total

The number of groups is one factor, and the “in each” number is the other factor. The total number in all groups is the product. It is imperative to note that in equal-group math problems, one…

Mathematics
George Cantor

The purpose of the paper is to develop a concept of the connection between mathematics and society from a historical perspective. Specifically, it will discuss the subject, what George Cantor accomplished for mathematics and what that did for society. George Cantor's set theory changed the way mathematicians of the time looked at their science, and he revolutionized the way the world looks at numbers.

George Cantor was a brilliant mathematician and philosopher who developed the modern mathematical idea of infinity, along with the idea of an infinite set of real numbers, called transfinite sets, or the "set theory." In addition, Cantor found that real numbers were not countable, while algebraic numbers were countable (Breen). Cantor's views were quite controversial when he first developed them in the late 1800s, and some mathematicians today question some of his hypothesis ("Transfinite Number"), however, his work is recognized as some of the most important…

Mathematics Summer Institute Statement of Goals
Attending the 2002 Summer Institute for Elementary School Teachers represents and exciting opportunity for me to further explore my interest in teaching mathematics, as well as an opportunity for me to apply and share my knowledge and experience with like-minded educators.

I am a strongly committed to and enthusiastic about mathematics education at the elementary school level. I believe that ensuring that children are engaged and interested in mathematics in early elementary school is essential to building strong numeracy in our youth. When young children develop an interest in math and strong skills as youngsters, they are more likely to continue studying mathematics as they grow older. In addition to these academic benefits, understanding and being able to apply math principles and concepts helps children grow into effective critical thinkers with a broader skill set.

I hope to achieve several personal learning goals by participating in the…

Mathematics
Analysis Techniques: Correlation

A positive correlation between annual income and amount spent on car would be expected. This means that there is a relationship between the two and that, in general, higher annual income would show an increase in the amount spent on car, while lower annual income would show a decrease in the amount spent on car.

However, it would not be expected that this would be a strong relationship because other factors would influence the amount spent on car. For example, some individuals with an income in the middle range may consider an expensive car a key priority, while others would have other priorities. In addition, annual income level is not a true measure of wealth because it does not take into account a person's expenses. For example, a young single person without a family and without a mortgage would have more disposable income than a married person with four…

Use the appropriate representations to model problems in the physical and social sciences (Ibid.)
Numeration Systems and Number Theory -- Number theory is a basis for all areas of mathematics. Number theory and sense are precludes to computation, to estimate, and to have an understanding of the ways numbers are represented and interrelated. Fluency of also understanding the way positive and negative numbers can be visually represented on a line, or how numerical values interrelate, are essential prior to moving toward higher level concepts (Kane, 2002).

Algebraic Thinking and Problem Solving -- ather than viewing the subject of algebra as certain sets of problems, the appropriate way to introduce it into elementary levels is as the relationship among quantities, the use of symbols, the modeling of phenomena, and the study of change. Students should be able to understand patterns, relations, and functions and how numbers may be represented in different ways.…