Mathematics of Digital Photography

Words: 925 Length: 3 Pages Document Type: Essay Paper #: 49569363Mathematics 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…… [Read More]

References

Higham, N. (2007). The mathematics of digital photography. Retrieved from:

http://www.maths.manchester.ac.uk/~higham/talks/digphot.pdf .

Hoggar, S.G. (2006). Mathematics of digital images. Cambridge, UK: Cambridge

Image Compression: How Math Led to the JPEG2000 Standard. (2011). Society for Industrial

Higham, N. (2007). The mathematics of digital photography. Retrieved from:

http://www.maths.manchester.ac.uk/~higham/talks/digphot.pdf .

Hoggar, S.G. (2006). Mathematics of digital images. Cambridge, UK: Cambridge

Image Compression: How Math Led to the JPEG2000 Standard. (2011). Society for Industrial

Mathematics Education the Objective of

Words: 677 Length: 2 Pages Document Type: Essay Paper #: 56963059

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…… [Read More]

Bibliography

Jones, Tammy (2000) Instructional Approaches to Teaching Problem Solving in Mathematics: Integrating Theories of Learning and Technology. Online available at http://www.mindymac.com/educ6100projects/TjonesProblem6100.htm

Adding it Up: Helping Children Learn Mathematics (Free Executive Summary)

http://www.nap.edu/catalog/9822.html

Barr, Leslie (2003) it's Elementary: Introducing Algebraic Thinking Before High School. SEDL Newsletter - Mathematics & Science. Volume XV Number 1, December 2003.

Jones, Tammy (2000) Instructional Approaches to Teaching Problem Solving in Mathematics: Integrating Theories of Learning and Technology. Online available at http://www.mindymac.com/educ6100projects/TjonesProblem6100.htm

Adding it Up: Helping Children Learn Mathematics (Free Executive Summary)

http://www.nap.edu/catalog/9822.html

Barr, Leslie (2003) it's Elementary: Introducing Algebraic Thinking Before High School. SEDL Newsletter - Mathematics & Science. Volume XV Number 1, December 2003.

Mathematics From Conch Shells to

Words: 659 Length: 2 Pages Document Type: Essay Paper #: 23071973

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,…… [Read More]

References

Abas, S.J. And AS Salman: Symmetries of Islamic Geometrical Patterns. Symmetry in Ethnomathematics 12(1-2). Retrieved July 29, 2006 at http://www.ethnomath.org/resources/abas2001.pdf

Deck, K. Spirograph Math. Humanistic Mathematics Journal March 1999, Vol.19, p13-17. Retrieved July 29, 2006 at http://web.stcloudstate.edu/szkeith/index11.html

Patterns, Order, and Chaos."

Abas, S.J. And AS Salman: Symmetries of Islamic Geometrical Patterns. Symmetry in Ethnomathematics 12(1-2). Retrieved July 29, 2006 at http://www.ethnomath.org/resources/abas2001.pdf

Deck, K. Spirograph Math. Humanistic Mathematics Journal March 1999, Vol.19, p13-17. Retrieved July 29, 2006 at http://web.stcloudstate.edu/szkeith/index11.html

Patterns, Order, and Chaos."

Mathematics Concepts in Profession Mathematics Concepts in

Words: 767 Length: 2 Pages Document Type: Essay Paper #: 61139470Mathematics 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…… [Read More]

References

Ben-Zvi, D and Garfield, J. (2008). Introducing the Emerging Disciplines of Statistics Education. School Science & Mathematics. Vol 108, Issue 8. Pg 355-361.

Liu, C., Chang, J and Yang, A. (2011). Information Computing and Applications: Second International Conference, ICICA 2011, Qinhuangdao, China, October 28-31, 2011. Proceedings, Part 1. New York: Springer.

Ben-Zvi, D and Garfield, J. (2008). Introducing the Emerging Disciplines of Statistics Education. School Science & Mathematics. Vol 108, Issue 8. Pg 355-361.

Liu, C., Chang, J and Yang, A. (2011). Information Computing and Applications: Second International Conference, ICICA 2011, Qinhuangdao, China, October 28-31, 2011. Proceedings, Part 1. New York: Springer.

Mathematics A Spreadsheet Data Analysis B State

Words: 580 Length: 2 Pages Document Type: Essay Paper #: 82365815Mathematics

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,…… [Read More]

Mathematics Professional Mathematical Societies the

Words: 924 Length: 3 Pages Document Type: Essay Paper #: 12844500SIAM'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…… [Read More]

References

"About the AMS." (2009). Retrieved April 22, 2009, from American Mathematical Society Web

site: http://www.ams.org/ams/about.html

"About Siam." (2009). Retrieved April 22, 2009, from Society for Industrial and Applied

Mathematics Web site: http://www.siam.org/about/pdf/brochure09.pdf

"About the AMS." (2009). Retrieved April 22, 2009, from American Mathematical Society Web

site: http://www.ams.org/ams/about.html

"About Siam." (2009). Retrieved April 22, 2009, from Society for Industrial and Applied

Mathematics Web site: http://www.siam.org/about/pdf/brochure09.pdf

Words: 2026 Length: 6 Pages Document Type: Essay Paper #: 68478036

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…… [Read More]

REFERENCES

Allexsaht-Snider, M. And Marshall, M. (2008) Linking Community, Families and School: Opportunities for the Mathematics Education of Children from Excluded Communities. ALM International Journal Volume 3(2a), pp 8-9. Retrieved from: http://www.academia.edu/6750909/Adults_Learning_Mathematics_An_International_Journal

Askew M., Brown M., Rhodes V., Johnson D. And William D. (1997) Effective Teachers of Numeracy, Final Report London Kings College

Askew M., Brown., V., Johnson D. And William D. (1997) Effective teachers of numeracy, Final Report London Kings College.

Bandura, A. (nd) Social Learning Theory. University of Pennsylvania. Retrieved from: faculty.mwsu.edu/psychology/paul.guthrie/powerpoint/bandura2.ppt

Allexsaht-Snider, M. And Marshall, M. (2008) Linking Community, Families and School: Opportunities for the Mathematics Education of Children from Excluded Communities. ALM International Journal Volume 3(2a), pp 8-9. Retrieved from: http://www.academia.edu/6750909/Adults_Learning_Mathematics_An_International_Journal

Askew M., Brown M., Rhodes V., Johnson D. And William D. (1997) Effective Teachers of Numeracy, Final Report London Kings College

Askew M., Brown., V., Johnson D. And William D. (1997) Effective teachers of numeracy, Final Report London Kings College.

Bandura, A. (nd) Social Learning Theory. University of Pennsylvania. Retrieved from: faculty.mwsu.edu/psychology/paul.guthrie/powerpoint/bandura2.ppt

Mathematics in the Arts and Nature

Words: 558 Length: 2 Pages Document Type: Essay Paper #: 58318853Mathematics 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…… [Read More]

References:

Meersschaert, K. (2012). Does Math + Art = Teachable Data Visualization? Columbia University, Web, Available from: http://edlab.tc.columbia.edu/index.php?q=node/8057 . 2013 June 14.

Meersschaert, K. (2012). Does Math + Art = Teachable Data Visualization? Columbia University, Web, Available from: http://edlab.tc.columbia.edu/index.php?q=node/8057 . 2013 June 14.

Mathematics Textbooks Technology Used in Mathematics Textbooks

Words: 1127 Length: 4 Pages Document Type: Essay Paper #: 73992804Mathematics 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…… [Read More]

References

Math Archives (2010). Mathematics contests and competitions. Retrieved December 18, 2010 from http://archives.math.utk.edu/contests/

Rock, N.M. (2006). Seventh grade math is easy! So easy. Los Angeles: Team Rock Publishing.

Math Archives (2010). Mathematics contests and competitions. Retrieved December 18, 2010 from http://archives.math.utk.edu/contests/

Rock, N.M. (2006). Seventh grade math is easy! So easy. Los Angeles: Team Rock Publishing.

Mathematics Room 8th Grade Junior

Words: 664 Length: 2 Pages Document Type: Essay Paper #: 67240092Teachers 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…… [Read More]

References

Brophy, J.E. (1983, Mar). Classroom organization and management. The Elementary

School Journal, 83(4): 264-285.

Marsh, C.J. (2004). Key concepts for understanding curriculum. New York: Routledge

Umich. (n.d.) ED 422: Teaching Science in the Secondary School. Retrieved July 11, 2007:

Brophy, J.E. (1983, Mar). Classroom organization and management. The Elementary

School Journal, 83(4): 264-285.

Marsh, C.J. (2004). Key concepts for understanding curriculum. New York: Routledge

Umich. (n.d.) ED 422: Teaching Science in the Secondary School. Retrieved July 11, 2007:

Mathematics in Gambling Casino Games

Words: 1091 Length: 3 Pages Document Type: Essay Paper #: 6904774627% 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…… [Read More]

Works Cited

Barker, Thomas and Marjie Britz. Jokers Wild: Legalized Gambling in the Twenty-First Century. Westport, CT: Praeger, 2000.

Casinos. (2004). Encyclopedia Britannica.com [premium service].

Coyle, Cynthia a. And Chamont Wang. (1993). Wanna Bet?: On Gambling Strategies That May or May Not Work in a Casino. The American Statistician, 47(2):108.

The Vigorish. (2002). Craps Gambling Casinos. Available: http://www.craps-gambling-casinos.com/the-Vigorish.htm.

Barker, Thomas and Marjie Britz. Jokers Wild: Legalized Gambling in the Twenty-First Century. Westport, CT: Praeger, 2000.

Casinos. (2004). Encyclopedia Britannica.com [premium service].

Coyle, Cynthia a. And Chamont Wang. (1993). Wanna Bet?: On Gambling Strategies That May or May Not Work in a Casino. The American Statistician, 47(2):108.

The Vigorish. (2002). Craps Gambling Casinos. Available: http://www.craps-gambling-casinos.com/the-Vigorish.htm.

Mathematics Grade 9 H S School

Words: 629 Length: 2 Pages Document Type: Essay Paper #: 34990302Students 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…… [Read More]

Resources

Exponential function. (2010). Purple Math Forums. Retrieved July 26, 2010 at http://www.purplemath.com/modules/expofcns2.htm

Mathematics benchmarks. (2010). UT Dana Center. Retrieved July 26, 2010 at http://www.utdanacenter.org/k12mathbenchmarks/secondary/algebra.php

McClain, Liz & Steve Rieves (2010). Teaching techniques to tackle some sticky topics in Algebra 2. Retrieved July 26, 2010 at nctm.mrrives.com/NCTM%20Piecewise%20PP.ppt

Ormond, Kathy (et al. 2010). Atmospheric CO2 concentration. Retrieved July 28, 2010.

Exponential function. (2010). Purple Math Forums. Retrieved July 26, 2010 at http://www.purplemath.com/modules/expofcns2.htm

Mathematics benchmarks. (2010). UT Dana Center. Retrieved July 26, 2010 at http://www.utdanacenter.org/k12mathbenchmarks/secondary/algebra.php

McClain, Liz & Steve Rieves (2010). Teaching techniques to tackle some sticky topics in Algebra 2. Retrieved July 26, 2010 at nctm.mrrives.com/NCTM%20Piecewise%20PP.ppt

Ormond, Kathy (et al. 2010). Atmospheric CO2 concentration. Retrieved July 28, 2010.

Mathematics Curriculum Education One Aspect

Words: 2680 Length: 10 Pages Document Type: Essay Paper #: 79672220

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…… [Read More]

Parent involvement in instruction and classroom success must also be reiterated continually, during and after change implementation. Parents, just like teachers and students must be sold on the ideal of reform-based standards so they can ultimately assist students in achieving greater exam outcomes as well as real classroom outcomes. Continued assessment of parent involvement and improvement of such is essential to reform success.

Last but certainly not least student perception of assessment reform and instructional reform is also essential to success of assessment reform applications. Students must understand the stakes of assessments both for themselves and for their schools and districts and must give the assessments the proper credence in correlation with real instructional growth in the classroom. A whole perceptual study regarding students, at every level of proficiency, would constitute a completely different and informative assessment of how students perceive reform changes and how effective they believe them to have been for themselves or fellow students post high stakes testing reform.

Draft August 24, 2008

Last but certainly not least student perception of assessment reform and instructional reform is also essential to success of assessment reform applications. Students must understand the stakes of assessments both for themselves and for their schools and districts and must give the assessments the proper credence in correlation with real instructional growth in the classroom. A whole perceptual study regarding students, at every level of proficiency, would constitute a completely different and informative assessment of how students perceive reform changes and how effective they believe them to have been for themselves or fellow students post high stakes testing reform.

Draft August 24, 2008

Mathematics in Special Education

Words: 3320 Length: 10 Pages Document Type: Essay Paper #: 45667184

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…… [Read More]

References

Billingsley, B.S. (1993). Teacher retention and attrition in special and general education: A critical review of the literature. The Journal of Special Education, 27, 137-174.

Billingsley, B., Carlson, E., & Klein, S. (in press). The working conditions and induction support of early career special educators. Exceptional Children.

Billingsley, B.S., & Cross, L.H. (1992). Predictors of commitment, job satisfaction, and intent to stay in teaching: A comparison of general and special educators. The Journal of Special Education, 25, 453-471.

Billingsley, B., Pyecha, J., Smith-Davis, J., Murray, K., & Hendricks, M.B. (1995). Improving the retention of special education teachers: Final report (Prepared for Office of Special Education Programs, Office of Special Education and Rehabilitative Services, U.S. Department of Education, under Cooperative Agreement H023Q10001). (ERIC Document Reproduction Service No. ED379860)

Billingsley, B.S. (1993). Teacher retention and attrition in special and general education: A critical review of the literature. The Journal of Special Education, 27, 137-174.

Billingsley, B., Carlson, E., & Klein, S. (in press). The working conditions and induction support of early career special educators. Exceptional Children.

Billingsley, B.S., & Cross, L.H. (1992). Predictors of commitment, job satisfaction, and intent to stay in teaching: A comparison of general and special educators. The Journal of Special Education, 25, 453-471.

Billingsley, B., Pyecha, J., Smith-Davis, J., Murray, K., & Hendricks, M.B. (1995). Improving the retention of special education teachers: Final report (Prepared for Office of Special Education Programs, Office of Special Education and Rehabilitative Services, U.S. Department of Education, under Cooperative Agreement H023Q10001). (ERIC Document Reproduction Service No. ED379860)

Mathematics the Minnesota Multiphasic Personality

Words: 995 Length: 3 Pages Document Type: Essay Paper #: 7986433

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…… [Read More]

References

Karp, Cheryl L. And Karp, Leonard. (2009). MMPI: Questions to Ask. Retrieved June 29, 2009,

from Web site: http://www.falseallegations.com/mmpi-bw.htm

Minnesota Multiphasic Personality Inventory. (n.d.). Retrieved June 29, 2009, from Web site:

http://www.cps.nova.edu/~cpphelp/MMPI.html

Karp, Cheryl L. And Karp, Leonard. (2009). MMPI: Questions to Ask. Retrieved June 29, 2009,

from Web site: http://www.falseallegations.com/mmpi-bw.htm

Minnesota Multiphasic Personality Inventory. (n.d.). Retrieved June 29, 2009, from Web site:

http://www.cps.nova.edu/~cpphelp/MMPI.html

Mathematics Determine Whether the Lines Will Be

Words: 418 Length: 2 Pages Document Type: Essay Paper #: 47131533Mathematics

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…… [Read More]

Mathematics Puzzles and Their Relevance to Life

Words: 658 Length: 2 Pages Document Type: Essay Paper #: 63983172Mathematics 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…… [Read More]

References

Pickover, C. (2010). Ten of the greatest: Maths puzzles. The Daily Mail. Retrieved from:

http://www.dailymail.co.uk/home/moslive/article-1284909/Ten-greatest-Maths-puzzles.html

Pitici, M. (2008). Geometric Dissections. Cornell University. Retrieved from:

http://www.math.cornell.edu/~mec/GeometricDissections/0.%20Front%20page.html

Pickover, C. (2010). Ten of the greatest: Maths puzzles. The Daily Mail. Retrieved from:

http://www.dailymail.co.uk/home/moslive/article-1284909/Ten-greatest-Maths-puzzles.html

Pitici, M. (2008). Geometric Dissections. Cornell University. Retrieved from:

http://www.math.cornell.edu/~mec/GeometricDissections/0.%20Front%20page.html

Words: 1762 Length: 6 Pages Document Type: Essay Paper #: 48508713

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).…… [Read More]

References

Edu.gov.on.ca. (2005). The Ontario Curriculum: Mathematics. Retrieved from Edu.gov.on.ca: http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

Edugains.ca. (n.d.). Gap Closing. Retrieved from Edugains.ca: http://www.edugains.ca/newsite/math2/gapclosingmain.html

GCISD. (2007). Developmental Characteristics of Third Graders. Retrieved from Glendale.k12.wi.us: http://www.glendale.k12.wi.us/3_char.aspx

Jumpmath.org. (n.d.). Educational Approach. Retrieved from Jumpmath.org: http://jumpmath.org/cms/taxonomy/term/6

Edu.gov.on.ca. (2005). The Ontario Curriculum: Mathematics. Retrieved from Edu.gov.on.ca: http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

Edugains.ca. (n.d.). Gap Closing. Retrieved from Edugains.ca: http://www.edugains.ca/newsite/math2/gapclosingmain.html

GCISD. (2007). Developmental Characteristics of Third Graders. Retrieved from Glendale.k12.wi.us: http://www.glendale.k12.wi.us/3_char.aspx

Jumpmath.org. (n.d.). Educational Approach. Retrieved from Jumpmath.org: http://jumpmath.org/cms/taxonomy/term/6

Mathematics Relationship Between Learning Styles

Words: 2029 Length: 6 Pages Document Type: Essay Paper #: 1780399Leaning 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.…… [Read More]

references among undergraduate physiology students. Advances in Physiology

Education, 31153-157. doi:10.1152/advan.00060.2006

Education, 31153-157. doi:10.1152/advan.00060.2006

Words: 798 Length: 3 Pages Document Type: Essay Paper #: 31839369

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.…… [Read More]

Bibliography

Differentiating Mathematics Instruction. (2008, Sep). Capacity Building Series. Ontario, Ontario, Canada: The Literacy and Numeracy Secretariat.

Communications in the Mathematics Classroom. (2010, Sept). Capacity for Building Series. Ontario, Ontario, Canada: The Literacy and Numeracy Secretariat.

Asking Effective Questions. (2011, July). Capacity Building Series. Ontario, Ontario, Canada: Student Achievement Division.

Differentiating Mathematics Instruction. (2008, Sep). Capacity Building Series. Ontario, Ontario, Canada: The Literacy and Numeracy Secretariat.

Communications in the Mathematics Classroom. (2010, Sept). Capacity for Building Series. Ontario, Ontario, Canada: The Literacy and Numeracy Secretariat.

Asking Effective Questions. (2011, July). Capacity Building Series. Ontario, Ontario, Canada: Student Achievement Division.

Mathematics Teachers in the Classroom

Words: 724 Length: 3 Pages Document Type: Essay Paper #: 62520803nctm.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…… [Read More]

The University of Cornell (http://www.tc.cornell.edu/Services/Education/Gateways/Math_and_Science)providesa math and science gateway to link science and math educators K-12. Its aim is to facilitate information exchanges and enhance professional contacts, particularly the use of the Internet such as webquests and WebPages in the classroom.

The University of Chicago School Mathematics Project (UCSMP) (http://social-sciences.uchicago.edu/ucsmp/index.html) providesresources for student evaluation and professional development, and even includes the ability to access translations of international materials from nations such as Russia. It also provides information about professional associations and journals, and is dedicated to the cause of mathematical improvement.

The University of Central Florida provides a Math Guide, with a variety of links to hands-on materials about math, including crafts (like making a looped Moebius strip), lesson plans, and professional development website. (http://www.useekufind.com/learningquest/tmath.htm).

The University of Chicago School Mathematics Project (UCSMP) (http://social-sciences.uchicago.edu/ucsmp/index.html) providesresources for student evaluation and professional development, and even includes the ability to access translations of international materials from nations such as Russia. It also provides information about professional associations and journals, and is dedicated to the cause of mathematical improvement.

The University of Central Florida provides a Math Guide, with a variety of links to hands-on materials about math, including crafts (like making a looped Moebius strip), lesson plans, and professional development website. (http://www.useekufind.com/learningquest/tmath.htm).

Mathematics Major Mathematical Concepts One

Words: 806 Length: 3 Pages Document Type: Essay Paper #: 28187967To 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 of…… [Read More]

Works Cited:

Salend, S.J. (2005). Creating an environment that fosters acceptance and friendship. Creating Inclusive Classrooms. 5th edition. Pearson, Upper Saddle River, N.J.

Salend, S.J. (2005). Creating an environment that fosters acceptance and friendship. Creating Inclusive Classrooms. 5th edition. Pearson, Upper Saddle River, N.J.

Mathematics Instructions for Students With

Words: 1429 Length: 4 Pages Document Type: Essay Paper #: 9533933Unlike 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…… [Read More]

References

Daniel, Y. (2005). The Textual Construction of High Needs for Funding Special Education in Ontario. Canadian Journal of Education / Revue canadienne de l'education, 28,(4):763-

Janus, M., Lefort, J, Cameron, R., & Kopechanski, L. (2007). Starting kindergarten: Transition issues for children with special needs. Canadian Journal of Education / Revue

canadienne de l'education, 30(3), 628-648.

Marshall, M.N. (1996). Sampling for qualitative research. Family Practice 13 (6): 522-525.

Daniel, Y. (2005). The Textual Construction of High Needs for Funding Special Education in Ontario. Canadian Journal of Education / Revue canadienne de l'education, 28,(4):763-

Janus, M., Lefort, J, Cameron, R., & Kopechanski, L. (2007). Starting kindergarten: Transition issues for children with special needs. Canadian Journal of Education / Revue

canadienne de l'education, 30(3), 628-648.

Marshall, M.N. (1996). Sampling for qualitative research. Family Practice 13 (6): 522-525.

Mathematics Secondary School Experiences and

Words: 1445 Length: 4 Pages Document Type: Essay Paper #: 21821345

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…… [Read More]

References

Yu, J., Newman, L. & Wagner, M. (2009). Secondary School Experiences and Academic

Performance of Students With Mental Retardation U.S. Department of Education

Institute of Education Sciences National Center for Special Education Research

Kaplan a. (1963).The conduct of inquiry: Methodology for behavioral science. London: Harper

Yu, J., Newman, L. & Wagner, M. (2009). Secondary School Experiences and Academic

Performance of Students With Mental Retardation U.S. Department of Education

Institute of Education Sciences National Center for Special Education Research

Kaplan a. (1963).The conduct of inquiry: Methodology for behavioral science. London: Harper

Real Life Uses for Mathematics and Puzzles

Words: 627 Length: 2 Pages Document Type: Essay Paper #: 38571992Mathematics 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…… [Read More]

References

Gardner, M. (n.d.). Wheels, life, and other mathematical amusements. New York: W.H. Freeman.

Kramer, M. (2015). Math is a tool to understand our world. HuffPost. May 22, 2015. Retrieved online: http://www.huffingtonpost.com/matt-kramer/math-is-a-tool-to-underst_b_7355210.html

Gardner, M. (n.d.). Wheels, life, and other mathematical amusements. New York: W.H. Freeman.

Kramer, M. (2015). Math is a tool to understand our world. HuffPost. May 22, 2015. Retrieved online: http://www.huffingtonpost.com/matt-kramer/math-is-a-tool-to-underst_b_7355210.html

National Council of Teachers of Mathematics

Words: 1019 Length: 3 Pages Document Type: Essay Paper #: 25471320Mathematics 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…… [Read More]

References

Fennell, F. M., & National Council of Teachers of Mathematics. (2011). Achieving fluency: Special education and mathematics. Reston, VA: National Council of Teachers of Mathematics.

Fennell, F. M., & National Council of Teachers of Mathematics. (2011). Achieving fluency: Special education and mathematics. Reston, VA: National Council of Teachers of Mathematics.

Analyzing Mathematics for Special Needs Children

Words: 1337 Length: 4 Pages Document Type: Essay Paper #: 16085580Mathematics 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…… [Read More]

Bibliography

Golestaneh, S. M., Nejad, T. S., & Reishehri, A. P. (2014). The effect of schema based instruction on improving problem solving skill and visual memory of students with mathematics learning disabilities. International Journal of Review in Life Sciences, 18-23.

Jitendra, A. K. (2011). Meeting the Needs of Students with Learning Disabilities in Inclusive Mathematics Classrooms: The Role of Schema-Based Instruction on Mathematical Problem-Solving. Theory Into Practice, 12-19.

Lim, C. B. (2015). Implementing Schema-Based Instruction in the Elementary Classroom (Project). Honorable Mentions, 13.

Powell, S. R. (2011). Solving Word Problems using Schemas: A Review of the Literature. Learn Disabil Res Pract., 94-108. Retrieved from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3105905/

Golestaneh, S. M., Nejad, T. S., & Reishehri, A. P. (2014). The effect of schema based instruction on improving problem solving skill and visual memory of students with mathematics learning disabilities. International Journal of Review in Life Sciences, 18-23.

Jitendra, A. K. (2011). Meeting the Needs of Students with Learning Disabilities in Inclusive Mathematics Classrooms: The Role of Schema-Based Instruction on Mathematical Problem-Solving. Theory Into Practice, 12-19.

Lim, C. B. (2015). Implementing Schema-Based Instruction in the Elementary Classroom (Project). Honorable Mentions, 13.

Powell, S. R. (2011). Solving Word Problems using Schemas: A Review of the Literature. Learn Disabil Res Pract., 94-108. Retrieved from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3105905/

Analyzing Mathematics for Special Needs Children

Words: 1337 Length: 2 Pages Document Type: Essay Paper #: 69648272Mathematics 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…… [Read More]

Bibliography

Golestaneh, S. M., Nejad, T. S., & Reishehri, A. P. (2014). The effect of schema based instruction on improving problem solving skill and visual memory of students with mathematics learning disabilities. International Journal of Review in Life Sciences, 18-23.

Jitendra, A. K. (2011). Meeting the Needs of Students with Learning Disabilities in Inclusive Mathematics Classrooms: The Role of Schema-Based Instruction on Mathematical Problem-Solving. Theory Into Practice, 12-19.

Lim, C. B. (2015). Implementing Schema-Based Instruction in the Elementary Classroom (Project). Honorable Mentions, 13.

Powell, S. R. (2011). Solving Word Problems using Schemas: A Review of the Literature. Learn Disabil Res Pract., 94-108. Retrieved from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3105905/

Golestaneh, S. M., Nejad, T. S., & Reishehri, A. P. (2014). The effect of schema based instruction on improving problem solving skill and visual memory of students with mathematics learning disabilities. International Journal of Review in Life Sciences, 18-23.

Jitendra, A. K. (2011). Meeting the Needs of Students with Learning Disabilities in Inclusive Mathematics Classrooms: The Role of Schema-Based Instruction on Mathematical Problem-Solving. Theory Into Practice, 12-19.

Lim, C. B. (2015). Implementing Schema-Based Instruction in the Elementary Classroom (Project). Honorable Mentions, 13.

Powell, S. R. (2011). Solving Word Problems using Schemas: A Review of the Literature. Learn Disabil Res Pract., 94-108. Retrieved from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3105905/

Growth of Mathematics Hard and

Words: 615 Length: 2 Pages Document Type: Essay Paper #: 22544929For 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…… [Read More]

Learning Mathematics Acquisition of Numeracy Has Been

Words: 967 Length: 2 Pages Document Type: Essay Paper #: 91488451Learning 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…… [Read More]

References

Azar, B. (2010).Gender + culture=gender gap. Retrieved April 29, 2013 from http://www.apa.org/monitor/2010/07-08/gender-gap.aspx

Dimakos, G., Tyrlis, L., & Spyros, F. (2012). Factors that influence students to do mathematics. Retrieved April 29, 2013 from http://elib.mi.sanu.ac.rs/files/journals/tm/28/tm1514.pdf

Holmes, E.E. (2012).Gender and Mathematics learning. Retrieved April 29, 2013 from http://www.education.com/reference/article/gender-mathematics-learning/

Mohamed, Z.G & Lazim, A. (2012). The Factors Influence Students' Achievement in Mathematics: A Case for Libyan's Students. Retrieved April 29, 2013 from http://idosi.org/wasj/wasj17(9)12/21.pdf

Azar, B. (2010).Gender + culture=gender gap. Retrieved April 29, 2013 from http://www.apa.org/monitor/2010/07-08/gender-gap.aspx

Dimakos, G., Tyrlis, L., & Spyros, F. (2012). Factors that influence students to do mathematics. Retrieved April 29, 2013 from http://elib.mi.sanu.ac.rs/files/journals/tm/28/tm1514.pdf

Holmes, E.E. (2012).Gender and Mathematics learning. Retrieved April 29, 2013 from http://www.education.com/reference/article/gender-mathematics-learning/

Mohamed, Z.G & Lazim, A. (2012). The Factors Influence Students' Achievement in Mathematics: A Case for Libyan's Students. Retrieved April 29, 2013 from http://idosi.org/wasj/wasj17(9)12/21.pdf

Mathematics as Creative Art P K

Words: 340 Length: 1 Pages Document Type: Essay Paper #: 6319239if, 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…… [Read More]

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Mathematic v Conceptual Modeling Limitations

Words: 342 Length: 1 Pages Document Type: Essay Paper #: 11907322" 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."…… [Read More]

References

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 October. Accessed 30 July 2009. http://www.johnkay.com/decisions/464

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 October. Accessed 30 July 2009. http://www.johnkay.com/decisions/464

Mathematics on Economics Medieval Era

Words: 377 Length: 1 Pages Document Type: Essay Paper #: 47463138"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."…… [Read More]

Work Cited

Sachs, Stephen E. "New math: The 'countinghouse theory' and the medieval revival of arithmetic." History 90a. May 25, 2000. November 10, 2009.

http://www.stevesachs.com/papers/paper_90a.html

Dickson, Paul. "Mathematics through the Middle Ages (320-1660 AD).

History of Mathematics 07305. University of South Australia, 1996.

Sachs, Stephen E. "New math: The 'countinghouse theory' and the medieval revival of arithmetic." History 90a. May 25, 2000. November 10, 2009.

http://www.stevesachs.com/papers/paper_90a.html

Dickson, Paul. "Mathematics through the Middle Ages (320-1660 AD).

History of Mathematics 07305. University of South Australia, 1996.

Mathematics Teaching and Learning in

Words: 1718 Length: 6 Pages Document Type: Essay Paper #: 59311095

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…… [Read More]

References

Burrill, G., Allison, J., Breaux, G., Kastberg, S., Leatham, K., & Sanchez, W. (2002). Handheld graphing technology in secondary school mathematics: Research 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 Research in Mathematics Education. 34(5), 433-463.

Kaput, J. (2007). Technology becoming infrastructural in mathematics education. Models & Modeling as Foundations for the Future in Mathematics Education. Mahwah, NJ: Lawrence Erlbaum.

Burrill, G., Allison, J., Breaux, G., Kastberg, S., Leatham, K., & Sanchez, W. (2002). Handheld graphing technology in secondary school mathematics: Research 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 Research in Mathematics Education. 34(5), 433-463.

Kaput, J. (2007). Technology becoming infrastructural in mathematics education. Models & Modeling as Foundations for the Future in Mathematics Education. Mahwah, NJ: Lawrence Erlbaum.

Art and Mathematics Are Related

Words: 2688 Length: 10 Pages Document Type: Essay Paper #: 96643501Note 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…… [Read More]

Works Cited

Corbitt, Mary Kay. "Geometry." World Book Multimedia Encyclopedia. World Book, Inc., 2003.

Dunham, Douglas. "A Tale Both Shocking and Hyperbolic." Math Horizons Apr. 2003: 22-26.

Ernst, Bruno. The Magic Mirror of M.C. Escher. NY: Barnes and Noble Books, 1994.

Granger, Tim. "Math Is Art." Teaching Children Mathematics 7.1 (Sept. 2000): 10.

Corbitt, Mary Kay. "Geometry." World Book Multimedia Encyclopedia. World Book, Inc., 2003.

Dunham, Douglas. "A Tale Both Shocking and Hyperbolic." Math Horizons Apr. 2003: 22-26.

Ernst, Bruno. The Magic Mirror of M.C. Escher. NY: Barnes and Noble Books, 1994.

Granger, Tim. "Math Is Art." Teaching Children Mathematics 7.1 (Sept. 2000): 10.

History of Chinese Mathematics

Words: 1633 Length: 6 Pages Document Type: Essay Paper #: 88393683Chinese 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…… [Read More]

Works Cited

Martzloff, Jean-Claude. A History of Chinese Mathematics. New York: Springer Verlag, 1997.

Needham, Joseph. Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Cambridge: Cambridge University Press, 1959.

Spence, Jonathan D. To Change China: Western Advisers in China, 1620-1960. New York: Penguin Press, 200

Swetz, Frank. Was Pythagoras Chinese?: An Examination of Right Triangle Theory in Ancient China. Philadelphia: Pennsylvania State University Press, 1977.

Martzloff, Jean-Claude. A History of Chinese Mathematics. New York: Springer Verlag, 1997.

Needham, Joseph. Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Cambridge: Cambridge University Press, 1959.

Spence, Jonathan D. To Change China: Western Advisers in China, 1620-1960. New York: Penguin Press, 200

Swetz, Frank. Was Pythagoras Chinese?: An Examination of Right Triangle Theory in Ancient China. Philadelphia: Pennsylvania State University Press, 1977.

Araybhata's Contributions to Mathematics &

Words: 518 Length: 2 Pages Document Type: Essay Paper #: 28926339..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…… [Read More]

Bibliography

Selin, Helaine (2001) Mathematics Across Cultures: The History of Non-Western Mathematics. Vol. 3 Science Across Cultures. Ubiratan D'Ambrosio 2001.

Dutta, Amartya Kumar (2002) Mathematics in Ancient India. Resonance Journal Vol.7, NO. 5 April 2002.

Hooda, D.S. And Kapur, J.N. (2001) Aryabhata: Life and Contributions. New Age International 2001.

Indian Mathematics (2009) Aryabhata and His Commentators. History online available at: http://www-history.mcs.st-and.ac.uk/Projects/Pearce/Chapters/Ch8_2.html

Selin, Helaine (2001) Mathematics Across Cultures: The History of Non-Western Mathematics. Vol. 3 Science Across Cultures. Ubiratan D'Ambrosio 2001.

Dutta, Amartya Kumar (2002) Mathematics in Ancient India. Resonance Journal Vol.7, NO. 5 April 2002.

Hooda, D.S. And Kapur, J.N. (2001) Aryabhata: Life and Contributions. New Age International 2001.

Indian Mathematics (2009) Aryabhata and His Commentators. History online available at: http://www-history.mcs.st-and.ac.uk/Projects/Pearce/Chapters/Ch8_2.html

Career That Requires Mathematics and Uses it Often

Words: 741 Length: 2 Pages Document Type: Essay Paper #: 17013191Actuaries

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…… [Read More]

References

Braverman, B. & Jeffries, A. (2009, December 1). Top-paying jobs. CNNMoney.com. Retrieved from http://finance.yahoo.com/personal-finance/article/108264/top-paying-jobs.

Department of Mathematics. (n.d.). Actuarial studies. University of Texas at Austin.

Retrieved from: http://www.ma.utexas.edu/dev/actuarial.

Kouba, D. (n.d.). Why choose a mathematics-related profession? University of California.

Braverman, B. & Jeffries, A. (2009, December 1). Top-paying jobs. CNNMoney.com. Retrieved from http://finance.yahoo.com/personal-finance/article/108264/top-paying-jobs.

Department of Mathematics. (n.d.). Actuarial studies. University of Texas at Austin.

Retrieved from: http://www.ma.utexas.edu/dev/actuarial.

Kouba, D. (n.d.). Why choose a mathematics-related profession? University of California.

Mathematical Proofs Middle School Mathematics

Words: 386 Length: 1 Pages Document Type: Essay Paper #: 44875390As 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 rigorous…… [Read More]

Reference

Kleiner, Israel & Movo*****z-Hadar, Nitsa. "Proof: A Many-Splendored Thing." The Mathematical Intelligencer. 1997. 19(3).

Kleiner, Israel & Movo*****z-Hadar, Nitsa. "Proof: A Many-Splendored Thing." The Mathematical Intelligencer. 1997. 19(3).

Problem Solving in Mathematics GCSE or the

Words: 3517 Length: 11 Pages Document Type: Essay Paper #: 25602444Problem 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…… [Read More]

References

Anderson, J. (2009) Mathematics Curriculum Development and the Role of Problem Solving. [E-Book] The University Of Sydney. Available Through: ACSA Conference 2009 Http://Www.Acsa.Edu.Au/Pages/Images/Judy%20Anderson%20-%20Mathematics%20Curriculum%20Development.Pdf [Accessed: 11th February 2013].

Bloom, B. (1971) Handbook Of Formative And Summative Evaluation Of Student Learning. New York: Mcgraw-Hill.

Boaler, J. (2002). Experiencing School Mathematics: Traditional And Reform Approaches To Teaching And Their Impact On Student Learning. Mahwah, N.J., L. Erlbaum.

Davies, I. (1975) Writing General Objectives And Writing Specific Objectives. In: Golby, M. Et Al. Eds. (1975) In Curriculum Design . 1st Ed. Open University Books .

Anderson, J. (2009) Mathematics Curriculum Development and the Role of Problem Solving. [E-Book] The University Of Sydney. Available Through: ACSA Conference 2009 Http://Www.Acsa.Edu.Au/Pages/Images/Judy%20Anderson%20-%20Mathematics%20Curriculum%20Development.Pdf [Accessed: 11th February 2013].

Bloom, B. (1971) Handbook Of Formative And Summative Evaluation Of Student Learning. New York: Mcgraw-Hill.

Boaler, J. (2002). Experiencing School Mathematics: Traditional And Reform Approaches To Teaching And Their Impact On Student Learning. Mahwah, N.J., L. Erlbaum.

Davies, I. (1975) Writing General Objectives And Writing Specific Objectives. In: Golby, M. Et Al. Eds. (1975) In Curriculum Design . 1st Ed. Open University Books .

Curriculum Design Mathematics -- Trigonometry

Words: 580 Length: 2 Pages Document Type: Essay Paper #: 54278228

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…… [Read More]

Improving Mathematics in Middle School

Words: 1168 Length: 4 Pages Document Type: Essay Paper #: 37032386These 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…… [Read More]

References

Falco, L., Crethar, H. & Bauman, S. (Apr 2008). "Skill-builders: Improving middle school students' self-beliefs for learning mathematics." Professional School Counseling, 11(4). p. 229-235.

House, D. & Telese, J. (Feb 2008). "Relationships between student and instructional factors and algebra achievement of students in the United States and Japan: An analysis of TIMSS 2003 data." Educational Research & Evaluation, 14(1). p. 101-112.

Silver, E. (Mar 1998). Improving mathematics in middle school. Lessons from TIMSS and related research. Retrieved December 14, 2010, from http://www2.ed.gov/inits/Math/silver.html.

Falco, L., Crethar, H. & Bauman, S. (Apr 2008). "Skill-builders: Improving middle school students' self-beliefs for learning mathematics." Professional School Counseling, 11(4). p. 229-235.

House, D. & Telese, J. (Feb 2008). "Relationships between student and instructional factors and algebra achievement of students in the United States and Japan: An analysis of TIMSS 2003 data." Educational Research & Evaluation, 14(1). p. 101-112.

Silver, E. (Mar 1998). Improving mathematics in middle school. Lessons from TIMSS and related research. Retrieved December 14, 2010, from http://www2.ed.gov/inits/Math/silver.html.

New California Mathematics Framework

Words: 642 Length: 2 Pages Document Type: Essay Paper #: 99998553new 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…… [Read More]

References

Editors. "California Mathematics Framework." California Department of Education. 2008. 4 Nov. 2009.

.

Editors. "California Mathematics Framework." California Department of Education. 2008. 4 Nov. 2009.

Descartes Mathematics of the Billions

Words: 457 Length: 1 Pages Document Type: Essay Paper #: 74272633

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,…… [Read More]

Student Engagement Within Mathematics Create a Set

Words: 2690 Length: 10 Pages Document Type: Essay Paper #: 47792652student engagement within mathematics, create a set of dependent measures. Follow the rules for writing test items, and please include the correct answers, as well.

Dependent Measures

Student Engagement

Five Multiple Choice Items

What is the square root of 49?

Which number is not a prime number?

How many degrees is a right angle?

A diagonal line cutting through two parallel lines creates angles which are?

unequal

congruent

immeasurable

What is 3 to the third power?

A composite engagement score would have to be tallied in order to total the average score of all of these variables so that one could assess how all of these variables interacted with one another, giving the researchers a sense of the total and complete interest, enjoyment, capability, and confusion that all students experienced when engaging with these problems, and to determine which variables were most often experienced simultaneously.

Five True-false items

The infinity…… [Read More]

References

Igo, L., Riccomini, P., & Bruning, R. & . (2006). How should middle school students with LD approach online note-taking? Retrieved from Learning Disability Quarterly: https://resources.oncourse.iu.edu/access/content/user/mikuleck/Filemanager_Public_Files/L700/Potential_Readings/Igo%202006%20mixed.pdf

Quenneville, J. (2001). Tech Tools for Students with Learning Disabilities: Infusion into Inclusive Classrooms. Retrieved from colorincolorado.org: http://www.colorincolorado.org/article/6380/

Trochim, W. (2006). Scaling. Retrieved from socialresearchmethods.net: http://www.socialresearchmethods.net/kb/scaling.php

W-uh. (2013). Correlation vs. Causality. Retrieved from w-uh.com: http://w-uh.com/posts/030302a_correlation_vs_ca.html

Igo, L., Riccomini, P., & Bruning, R. & . (2006). How should middle school students with LD approach online note-taking? Retrieved from Learning Disability Quarterly: https://resources.oncourse.iu.edu/access/content/user/mikuleck/Filemanager_Public_Files/L700/Potential_Readings/Igo%202006%20mixed.pdf

Quenneville, J. (2001). Tech Tools for Students with Learning Disabilities: Infusion into Inclusive Classrooms. Retrieved from colorincolorado.org: http://www.colorincolorado.org/article/6380/

Trochim, W. (2006). Scaling. Retrieved from socialresearchmethods.net: http://www.socialresearchmethods.net/kb/scaling.php

W-uh. (2013). Correlation vs. Causality. Retrieved from w-uh.com: http://w-uh.com/posts/030302a_correlation_vs_ca.html

Effects of Mathematics Instruction in English on ELL Second Grade Students

Words: 3174 Length: 12 Pages Document Type: Essay Paper #: 74903495Mathematics 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,…… [Read More]

Students With Disabilities and Their Mathematics Instruction

Words: 2038 Length: 6 Pages Document Type: Essay Paper #: 35104826Individuals 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…… [Read More]

Gavigann, K., & Kurtts, S. (2010). Together We Can: Collaborating to Meet the Needs of At-Risk Students. Library Media Connection, 29(3), 10-12.

King, C. (2011, March). Adults Learning. Retrieved from http://content.yudu.com/A1rfni/ALmarch2011/resources/a29.htm

Sellman, E. (Ed.). (2011). Creative Teaching/Creative Schools Bundle: Creative Learning for Inclusion: Creative. Port Melbourne: Routledge.

King, C. (2011, March). Adults Learning. Retrieved from http://content.yudu.com/A1rfni/ALmarch2011/resources/a29.htm

Sellman, E. (Ed.). (2011). Creative Teaching/Creative Schools Bundle: Creative Learning for Inclusion: Creative. Port Melbourne: Routledge.

Teaching Mathematics at Secondary School Level

Words: 3099 Length: 12 Pages Document Type: Essay Paper #: 45392237achievement of a teaching task. Despite of the different approach that teachers and instructors used, there is a part in teaching that allows the learners to gain knowledge, or better, to gain skills.

The different methods of teaching, since the past years up to the present times, have shown and demonstrated their respective means of imparting knowledge. Each method provides ways of capturing the abilities of the learners, as well as communicating ideas and information. Wherever there is teaching, it is always essential that there must be learning since the essence of a teaching task is to be able to bestow knowledge.

One example where we can see the process of growth in a teaching task is in a mathematics class. efore, mathematics is taught in a more visual manner, "literally" speaking, where the process involves materials such as chalk and board, and paper and pencils. Now, in the days…… [Read More]

Bibliography

2003). From Our Readers.

Instructor, 113(2).

Boeir, G.B. (2000). Management Accounting Education: Yesterday, Today, and Tomorrow.

Issues in Accounting Education, 15(2).

2003). From Our Readers.

Instructor, 113(2).

Boeir, G.B. (2000). Management Accounting Education: Yesterday, Today, and Tomorrow.

Issues in Accounting Education, 15(2).

Culture Affects the Way Students Learn Mathematics

Words: 1825 Length: 6 Pages Document Type: Essay Paper #: 423849culture 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…… [Read More]

References

Bharucha, J. (2008). America can teach Asia a lot about science, technology, and math.

Chronicle of Higher Education; Vol. 54 Issue 20, pA33-A34.

Cotter, J. (2009). Right start mathematics. Retrieved 13 Nov. 2009 from the Abacus.com Web site: http://www.alabacus.com/Downloads/RightStart%20Mathematics.pdf. 1-5.

Editors. (2000). How Japanese students learn math. Christian Science Monitor; Vol. 92 Issue 127, p17.

Bharucha, J. (2008). America can teach Asia a lot about science, technology, and math.

Chronicle of Higher Education; Vol. 54 Issue 20, pA33-A34.

Cotter, J. (2009). Right start mathematics. Retrieved 13 Nov. 2009 from the Abacus.com Web site: http://www.alabacus.com/Downloads/RightStart%20Mathematics.pdf. 1-5.

Editors. (2000). How Japanese students learn math. Christian Science Monitor; Vol. 92 Issue 127, p17.

How New York State Presents Its Core Standards for Mathematics

Words: 998 Length: 3 Pages Document Type: Essay Paper #: 77644030Education

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…… [Read More]

Works Cited

Common Core Standards. "Grade 8 -- Introduction / Common Core State Standards Initiative."

Retrieved July 31 from http://www.corestandards.org/Math/Content/8/introduction. 2011.

IXL -- New York Eighth-Grade Math Standards. "New York: Skills available for New York

Eighth-Grade Math Standards." Retrieved July 31, 2014 from http://www.ixl.com/standards/new-york/math/grade-8.

Common Core Standards. "Grade 8 -- Introduction / Common Core State Standards Initiative."

Retrieved July 31 from http://www.corestandards.org/Math/Content/8/introduction. 2011.

IXL -- New York Eighth-Grade Math Standards. "New York: Skills available for New York

Eighth-Grade Math Standards." Retrieved July 31, 2014 from http://www.ixl.com/standards/new-york/math/grade-8.

Words: 1795 Length: 4 Pages Document Type: Essay Paper #: 38682236

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.…… [Read More]

Bibliography

ITS. (n.d.). Retrieved from www.itseducation.asia: http://www.itseducation.asia/overcoming-blocks.htm

(n.d.). Pastoral Care. Retrieved from: http://www.strath.ac.uk/media/ps/sees/equality/e-and-d-for-academics-factsheet-pastoral-care.pdf

Zeiger, S. (n.d.). Retrieved from work.chron.com: http://work.chron.com/5-important-characteristics-become-good-math-teacher-8926.html

ITS. (n.d.). Retrieved from www.itseducation.asia: http://www.itseducation.asia/overcoming-blocks.htm

(n.d.). Pastoral Care. Retrieved from: http://www.strath.ac.uk/media/ps/sees/equality/e-and-d-for-academics-factsheet-pastoral-care.pdf

Zeiger, S. (n.d.). Retrieved from work.chron.com: http://work.chron.com/5-important-characteristics-become-good-math-teacher-8926.html

View Full Essay

strategies to improve mathematic performance for children

Words: 1361 Length: 4 Pages Document Type: Essay Paper #: 56539671Improve 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…… [Read More]

References

de Boer, H., Donker-Bergstra, A. S., & Konstons, D. D. N. M. (2012). Effective strategies for self-regulated learning: A meta-analysis. Gronings Instituut voor Onderzoek van Onderwijs, Rijksuniversiteit Groningen, Groningen.

Hott, B. L., Isbell, L., & Oettinger, T. (2014). Strategies and Interventions to Support Students with Mathematics Disabilities. Council for Learning Disabilities.

Maag, J. W., Reid, R., & DiGangi, S. A. (1993). DIFFERENTIAL EFFECTS OF SELF-MONITORING ATTENTION, ACCURACY, AND PRODUCTIVITY. Journal of Applied Behavior Analysis, 26(3), 329-344.

Mercer, C. D., Mercer, A. R., & Pullen, P. C. (2011). Teaching students with learning problems (8th ed.). Upper Saddle River, NJ: Pearson Education.

de Boer, H., Donker-Bergstra, A. S., & Konstons, D. D. N. M. (2012). Effective strategies for self-regulated learning: A meta-analysis. Gronings Instituut voor Onderzoek van Onderwijs, Rijksuniversiteit Groningen, Groningen.

Hott, B. L., Isbell, L., & Oettinger, T. (2014). Strategies and Interventions to Support Students with Mathematics Disabilities. Council for Learning Disabilities.

Maag, J. W., Reid, R., & DiGangi, S. A. (1993). DIFFERENTIAL EFFECTS OF SELF-MONITORING ATTENTION, ACCURACY, AND PRODUCTIVITY. Journal of Applied Behavior Analysis, 26(3), 329-344.

Mercer, C. D., Mercer, A. R., & Pullen, P. C. (2011). Teaching students with learning problems (8th ed.). Upper Saddle River, NJ: Pearson Education.

Application of the Discrete Mathematics

Words: 949 Length: 3 Pages Document Type: Essay Paper #: 99406245Coding 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…… [Read More]

Reference

Key, J.D. (2000). Some error-correcting codes and their applications. College of Engineering and Science Clemson University.

Moon, T.K. (2005). Error Correction Coding. New Jersey: John Wiley & Sons.

Pless, V. (1998), Introduction to the Theory of Error-Correcting Codes (3rd ed.), Wiley Interscience.

Rosen, K.H.(2012). Discrete Mathematics and Its Applications. (Seventh Edition).New York. McGraw-Hill Companies, Inc.

Key, J.D. (2000). Some error-correcting codes and their applications. College of Engineering and Science Clemson University.

Moon, T.K. (2005). Error Correction Coding. New Jersey: John Wiley & Sons.

Pless, V. (1998), Introduction to the Theory of Error-Correcting Codes (3rd ed.), Wiley Interscience.

Rosen, K.H.(2012). Discrete Mathematics and Its Applications. (Seventh Edition).New York. McGraw-Hill Companies, Inc.

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Three Mathematic Textbooks Review

Words: 1840 Length: 6 Pages Document Type: Essay Paper #: 99003285Precalculus 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…… [Read More]

References

Larson, R., Hostetler, R., & Edwards, B. (2011). Calculus I, with precalculus (3rd ed.). Boston: Houghton Mifflin.

Larson, R., Hostetler, R., Edwards, B., & Heyd, D. (2013). Precalculus with limits (3rd ed.). Boston: Houghton Mifflin.

Mirsky, L. (2012). Introduction to Linear Algebra. Dover Publications.

Larson, R., Hostetler, R., & Edwards, B. (2011). Calculus I, with precalculus (3rd ed.). Boston: Houghton Mifflin.

Larson, R., Hostetler, R., Edwards, B., & Heyd, D. (2013). Precalculus with limits (3rd ed.). Boston: Houghton Mifflin.

Mirsky, L. (2012). Introduction to Linear Algebra. Dover Publications.

Financial Terms Using Consumer Mathematics

Words: 1199 Length: 3 Pages Document Type: Essay Paper #: 69588424The 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…… [Read More]

Works Cited

Orman, Suze, "The True Cost of Home Ownership." Yahoo.com. January, 2007. http://biz.yahoo.com/pfg/e10buyrent/art011.html.

Infoplease. "Installment Buying and Selling." Infoplease.com. Website: http://www.infoplease.com/ce6/bus/A0825286.html.

Orman, Suze, "The True Cost of Home Ownership." Yahoo.com. January, 2007. http://biz.yahoo.com/pfg/e10buyrent/art011.html.

Infoplease. "Installment Buying and Selling." Infoplease.com. Website: http://www.infoplease.com/ce6/bus/A0825286.html.

Differential Learning in Mathematics

Words: 913 Length: 3 Pages Document Type: Essay Paper #: 81429044conveyed 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…… [Read More]

Chapter 6: Algebra

Algebra is often taught relatively early in a student's middle school or high school career but many students, particularly students with learning disabilities, struggle to grasp its basic concepts (Lannin & Van Garderen, 2013, p.141). Weak abstract reasoning skills, combined with computational and memory deficits as well as low self-esteem all conspire to make learning algebra especially difficult for LD students. The most basic concepts of algebra can be fostered as early as grade school, when children learn the intrinsic properties of numbers such as even and odd and zero. Even elementary school children should understand that adding and subtracting the same thing does not change the property's intrinsic value (Lannin & Van Garderen, 2013, p.146). By grade 6 or so they should be able to write their own equations to understand simple word problems; by grade 8 they should understand linear functions (Lannin & Van Garderen, 2013, p.148). But always, the emphasis must be on real understanding. Tables, graphs, and other methods can be useful although it is important for the instructor to be focused on conveying the meaning of the equation to the student, above all else. Linking the equation to a physical representation is key, not simply using a graphic without an expressed pedagogical purpose (Lannin & Van Garderen, 2013, p.152).

For LD students in particular, developing a step-by-step method to approach algebraic equations is critical. Pictorial representations can also be useful. Finally, self-monitoring is important, given that LD often have a weak skill set in this area. All of these approaches can be useful for all students but a teacher must be especially mindful of using this approach with LD students. Both authentic tasks and cognitive understanding is essential for true mastery (Lannin & Van Garderen, 2013, p.157). Peer-based learning can be helpful to enhance motivation.

Algebra is often taught relatively early in a student's middle school or high school career but many students, particularly students with learning disabilities, struggle to grasp its basic concepts (Lannin & Van Garderen, 2013, p.141). Weak abstract reasoning skills, combined with computational and memory deficits as well as low self-esteem all conspire to make learning algebra especially difficult for LD students. The most basic concepts of algebra can be fostered as early as grade school, when children learn the intrinsic properties of numbers such as even and odd and zero. Even elementary school children should understand that adding and subtracting the same thing does not change the property's intrinsic value (Lannin & Van Garderen, 2013, p.146). By grade 6 or so they should be able to write their own equations to understand simple word problems; by grade 8 they should understand linear functions (Lannin & Van Garderen, 2013, p.148). But always, the emphasis must be on real understanding. Tables, graphs, and other methods can be useful although it is important for the instructor to be focused on conveying the meaning of the equation to the student, above all else. Linking the equation to a physical representation is key, not simply using a graphic without an expressed pedagogical purpose (Lannin & Van Garderen, 2013, p.152).

For LD students in particular, developing a step-by-step method to approach algebraic equations is critical. Pictorial representations can also be useful. Finally, self-monitoring is important, given that LD often have a weak skill set in this area. All of these approaches can be useful for all students but a teacher must be especially mindful of using this approach with LD students. Both authentic tasks and cognitive understanding is essential for true mastery (Lannin & Van Garderen, 2013, p.157). Peer-based learning can be helpful to enhance motivation.

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Words: 673 Length: 2 Pages Document Type: Essay Paper #: 15623545

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…… [Read More]

References

Author not Available. "Georg Cantor." Fact-Index.com. 2004. 13 April 2004. http://www.fact-index.com/g/ge/georg_cantor.html

Breen, Craig. "Georg Cantor Page." Personal Web Page. 2004. 13 April 2004. http://www.geocities.com/CollegePark/Union/3461/cantor.htm

Everdell, William R. The First Moderns: Profiles in the Origins of Twentieth-Century Thought. Chicago: University of Chicago Press, 1997.

O'Connor, J.J. And Robertson, E.F. "Georg Cantor." University of St. Andrews. 1998. 13 April 2004. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Cantor.html

Author not Available. "Georg Cantor." Fact-Index.com. 2004. 13 April 2004. http://www.fact-index.com/g/ge/georg_cantor.html

Breen, Craig. "Georg Cantor Page." Personal Web Page. 2004. 13 April 2004. http://www.geocities.com/CollegePark/Union/3461/cantor.htm

Everdell, William R. The First Moderns: Profiles in the Origins of Twentieth-Century Thought. Chicago: University of Chicago Press, 1997.

O'Connor, J.J. And Robertson, E.F. "Georg Cantor." University of St. Andrews. 1998. 13 April 2004. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Cantor.html

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Words: 620 Length: 2 Pages Document Type: Essay Paper #: 26655832

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…… [Read More]

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Words: 484 Length: 2 Pages Document Type: Essay Paper #: 26083929

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…… [Read More]

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Capturing Astronomical Geometry the Greek Way

Words: 580 Length: 2 Pages Document Type: Essay Paper #: 90109615Mathematics -- to the Moon & Back

Once upon a time, Alexander, a young man from Athens fell in love with a local girl, Adrianna, whose beauty was far greater than any other young woman he had ever seen. Alexander was so smitten with Adrianna that he promised her the moon. Being an astute girl, Adrianna told Alexander that she wasn't at all sure that he could deliver the moon, but he could begin to convince her that he was intelligent and clever by measuring the distance from the earth to the moon. Alexander had long heard the stories about his Greek ancestors who were experts in mathematics and astronomy, so he sought out some wise elders to learn more.

Alexander spent some time with two elders, one of whom told him he knew how to measure the size of the earth (which, Alexander mused, was bound to impress, Adrianna),…… [Read More]

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Globalization and the Structures of

Words: 1054 Length: 3 Pages Document Type: Essay Paper #: 28982792Use 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…… [Read More]

REFERENCES

Askey, R. (1999). "Knowing and Teaching Elementary Mathematics." American

Educator. Fall 1999, Cited in:

http://www.aft.org/pubs-reports/american_educator/fall99/amed1.pdf

Blanton, M. (2008). Algebra and the Elementary Classroom. Heinemann.

Askey, R. (1999). "Knowing and Teaching Elementary Mathematics." American

Educator. Fall 1999, Cited in:

http://www.aft.org/pubs-reports/american_educator/fall99/amed1.pdf

Blanton, M. (2008). Algebra and the Elementary Classroom. Heinemann.

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Personal Statement University Waterloo I'm Applying

Words: 929 Length: 3 Pages Document Type: Essay Paper #: 73007798personal statement University Waterloo . I'm applying Mathematics (Co-op Regular ) . Please write essay stating reasons choosing program waterloo 1. Education Goals 2. Interest chosen programs

My life experiences have come to define who I am today and the choices that I am currently making reflect my background. From a very young age I realized that I enjoy studying and applying formal sciences and this practically influenced me to achieve better results in these fields, as I enjoy doing what I like and this felt natural. Whenever someone questioned me about my degree or about how I saw my future I always responded by saying a joke involving mathematics hoping that the respective individual would immediately understand that this particular domain is very important for me.

Many people in the contemporary society tend to ignore the importance of mathematics because of its "cooler" counterparts. With technology experiencing significant advancement…… [Read More]

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Aristotle and His Contribution to

Words: 685 Length: 2 Pages Document Type: Essay Paper #: 13309586Aristotle used mathematics in many of his other studies, as well. Another writer notes, "Aristotle used mathematics to try to 'see' the invisible patterns of sound that we recognize as music. Aristotle also used mathematics to try to describe the invisible structure of a dramatic performance" (Devlin 75-76). Aristotle used mathematics as a tool to enhance his other studies, and saw the value of creating and understanding theories of mathematics in everyday life and philosophy.

During his life, Aristotle also worked with theories developed by Eudoxus and others, and helped develop the theories of physics and some geometric theories, as well. Two authors quote Aristotle on mathematics. He writes, "These are in a way the converse of geometry. While geometry investigates physical lines but not qua physical, optics investigates mathematical lines, but qua physical, not qua mathematical" (O'Conner and obinson). He also commented on infinity, and did not believe that…… [Read More]

References

Devlin, Keith E. The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are like Gossip. 1st ed. New York: Basic Books, 2000.

Lane, David. "Plato and Aristotle." The University of Virginia's College at Wise. 2007. 18 June 2007. http://www.mcs.uvawise.edu/dbl5h/history/plato.php

O'Connor, John J. And Edmund F. Robertson. "Aristotle on Physics and Mathematics." Saint Andrews University. 2006. 18 June 2007. http://www-history.mcs.st-andrews.ac.uk/Extras/Aristotle_physics_maths.html

Robinson, Timothy a. Aristotle in Outline. Indianapolis: Hackett, 1995.

Devlin, Keith E. The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are like Gossip. 1st ed. New York: Basic Books, 2000.

Lane, David. "Plato and Aristotle." The University of Virginia's College at Wise. 2007. 18 June 2007. http://www.mcs.uvawise.edu/dbl5h/history/plato.php

O'Connor, John J. And Edmund F. Robertson. "Aristotle on Physics and Mathematics." Saint Andrews University. 2006. 18 June 2007. http://www-history.mcs.st-andrews.ac.uk/Extras/Aristotle_physics_maths.html

Robinson, Timothy a. Aristotle in Outline. Indianapolis: Hackett, 1995.

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Words: 1382 Length: 4 Pages Document Type: Essay Paper #: 7447267

Division by Zero

Mathematics is unique in that it is an objective subject. hen answering a question, something is either empirically true or it is completely false; there is little if any subjectivity about it in most situations. One of the most interesting aspects about math is that there are certain laws which are irrefutable and must be accepted in order for the correct answer to be discovered. A particularly intriguing and potentially frustrating aspect of math has to do with the division of zero. According to the laws of math, division by zero is impossible. hen someone solves a problem and finds themselves with a fraction where zero is in the denominator, the answer is always undefined because in mathematics, there is no such number. Mathematically, it is not possible to divide a numerator by zero and have either a real or imaginary number for an answer.

There are…… [Read More]

Works Cited:

Czajko, J. (2004). On Cantorian spacetime over number systems with division by zero. Chaos,

Solitons and Fractals. (21:2). 261-71.

Fosnot & Dolk (2001). Young Mathematics at Work: Constructing Multiplication and Division.

Heinemann: Portsmouth, NH.

Czajko, J. (2004). On Cantorian spacetime over number systems with division by zero. Chaos,

Solitons and Fractals. (21:2). 261-71.

Fosnot & Dolk (2001). Young Mathematics at Work: Constructing Multiplication and Division.

Heinemann: Portsmouth, NH.

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Words: 749 Length: 2 Pages Document Type: Essay Paper #: 56141920

Thus, in 1 Kings 7:23, the word "line" is written Kuf Vov Heh, but the Heh does not need to be there, and is not pronounced. With the extra letter, the word has a value of 111, but without it, the value is 106. (Kuf=100, Vov=6, Heh=5). The ratio of pi to 3 is very close to the ratio of 111 to 106. In other words, pi/3 = 111/106 approximately; solving for pi, is pi = 3.1415094... (Tsaban, 78). This figure is much more accurate than any other value that had been calculated up to that point, and would hold the record for the greatest number of correct digits for several hundred years afterwards. Unfortunately, very few people know this fact.

Archimedes of Greece was the first person to make serious use of the pi calculation. In 287 to 212 BC, he focused on the polygons' perimeters as opposed to…… [Read More]

References

Archimedes. "Measurement of a Circle" in Pi: A Source Book. Heidelberg: Springer

Verlag, 1997.

Baumgart, J.K.J.K.)." The history of algebra: An overview." In Historical topics for the mathematics classroom. 31st National Council of Teachers of Mathematics Yearbook. Washington, DC: NCTM, 1969

Blatner, David. The Joy of Pi. Walker Publishing Company, Inc. New York, 1997.

Archimedes. "Measurement of a Circle" in Pi: A Source Book. Heidelberg: Springer

Verlag, 1997.

Baumgart, J.K.J.K.)." The history of algebra: An overview." In Historical topics for the mathematics classroom. 31st National Council of Teachers of Mathematics Yearbook. Washington, DC: NCTM, 1969

Blatner, David. The Joy of Pi. Walker Publishing Company, Inc. New York, 1997.

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Low Math Scores of American Elementary Students

Words: 2870 Length: 8 Pages Document Type: Essay Paper #: 59310843Low math scores of American elementary students has been a major issue in education for some time. The Third International Mathematics and Science Study (TIMMS) conducted in 1995 showed the extent of the problem. The TIMMS study compared students in 42 countries, allowing American students to be compared with international students. The study rated the math ability of American students as adequate in fourth grade and poor in twelfth grade compared to other countries. This study was not the first time that concerns had been raised about American students achieving poorly in science and math. It was however, the largest and most comprehensive look at the real extent of the problem. The study made people realize the significance of the issue and resulted in the awareness of the public, the government and education and mathematics researchers. The major question that needs answering is why the low math scores occur, and…… [Read More]

Works Cited

Ma, L. Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, 1999.

Mokros, J., Russell, S.J., and Economopoulos, K. Beyond Arithmetic: Changing Mathematics in the Elementary Classroom. Palo Alto, CA: Dale Seymour Publications, 1995.

Ma, L. Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, 1999.

Mokros, J., Russell, S.J., and Economopoulos, K. Beyond Arithmetic: Changing Mathematics in the Elementary Classroom. Palo Alto, CA: Dale Seymour Publications, 1995.

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NCTM Process Standards Problem-Solving in

Words: 649 Length: 2 Pages Document Type: Essay Paper #: 27216512This engaged the whole class, regardless of their previous comfort level with mathematics. Graphing was also helpful for students to visualize what things really 'meant' in terms of the numbers they were studying.

Communication

Solving word problems as a class in a hands-on fashion forced all students to communicate with one another about mathematics. This increased student comfort levels and generated a collective interest in the mathematical solving process.

Students were given stories that illustrated mathematical concepts to read and asked to tell their own 'stories' to show they could understand mathematical concepts in a qualitative fashion. They were often asked to interpret graphs using verbal descriptions.

One of the most popular activities was the use of online research. Students were asked to research concepts on the web, such as examples of fractions, proportional rectangles, or the use of certain calculation techniques, and report back on their independent research the…… [Read More]

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Standards Five Process Standards Describe

Words: 1149 Length: 3 Pages Document Type: Essay Paper #: 45737537If the captain knows the position of the lighthouses from a map, can the captain determine the position of the ship?"

Analysis of the five processes in the context of problem solving

Problem solving

Using problem solving to solve a mathematical problem, the student does not know which method they will use when they start tackling the problem to reach the solution. The student will arrive at the correct solution by employing a couple of other ideas instead of just using mathematical calculations.

easoning and proof

Thinking on their feet students will learn how to be analytical of every situation they are encountered with. They will not only apply this analytical thinking in mathematics but will also apply it to other situations that they encounter. For the problem given in the, the first thing a student will need to analyses is how many legs chickens have and how many legs…… [Read More]

References

Mathematics, N.C. o. T. o. (2000). Principles and standards for school mathematics. 1906 Association Drive, Reston, VA 20191-1502: National Council of Teachers of Mathematics.

Mathematics, N.C. o. T. o. (2000). Principles and standards for school mathematics. 1906 Association Drive, Reston, VA 20191-1502: National Council of Teachers of Mathematics.

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Organizational Health Educational Institutions Generally Approach Organizational

Words: 2709 Length: 8 Pages Document Type: Essay Paper #: 11719523Organizational Health

Educational institutions generally approach organizational improvement by addressing the performance standards to which students, educators, and administrators are held. The standards movement has been a dominant theme in educational policy arenas and in the public eye. With roots in the 1950s Cold War mentality, the thrust of educational improvement has been prodded by perceptions of international industrial and scientific competition. If the rigor of educational standards in the nation -- according to the logic of this argument -- falls below that of other countries, our economy will falter and the balance of trade will be compromised, perhaps beyond the point of recovery.

Fears for the future of the country and our citizens run deep; these fears propel a course of action that is not particularly based on rational thinking and lacks a base of evidence. The course of action adopted by educational policy makers and educational leaders in…… [Read More]

References

Barth, P. (1997, November 26). Want to keep American jobs and avert class division? Try high school trig. Education Week, 30,33.

Bosch, G. (2000). The Dual System of Vocational Training in Germany. In Tremblay, D.-G. And Doray, P. (2000). Vers de nouveaux modes de formation professionnelle? Le role des acteurs et des collaborations. Quebec: Presses de l'Universite du Quebec.

____. (1998). Business Coalition for Education Reform. The Formula for Success: A Business Leader's Guide to Supporting Math and Science Achievement. Washington, DC: U.S. Department of Education.

Hacker, A. (2012, July 20). Is algebra necessary? The New York Times [national ed.], SR1, SR6.

Barth, P. (1997, November 26). Want to keep American jobs and avert class division? Try high school trig. Education Week, 30,33.

Bosch, G. (2000). The Dual System of Vocational Training in Germany. In Tremblay, D.-G. And Doray, P. (2000). Vers de nouveaux modes de formation professionnelle? Le role des acteurs et des collaborations. Quebec: Presses de l'Universite du Quebec.

____. (1998). Business Coalition for Education Reform. The Formula for Success: A Business Leader's Guide to Supporting Math and Science Achievement. Washington, DC: U.S. Department of Education.

Hacker, A. (2012, July 20). Is algebra necessary? The New York Times [national ed.], SR1, SR6.

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Mathematician Maria Gaetana Agnesi

Words: 587 Length: 2 Pages Document Type: Essay Paper #: 34412770Mathematician - Maria Gaetana Agnesi

JAFLOR

Maria Gaetana Agnesi

Since the olden days, mathematics has been an area of study that has contributed much to diverse discoveries, inventions, and innovations of science and technology. Without mathematics, we will not experience the remarkable events of science, as well as the convenience that high technology brings to us. The academic mastery of mathematics is dominated by men, even up to these days. There are very few mathematician women who made a name in the field of mathematics. More especially in the past, social prejudices became a hindrance for women to master mathematics. At present, only three women captured success in the field of mathematics. They are Sonia Kovalevsky of Russia, Emmy Noether of Germany and U.S., and Maria Gaetana Agnesi of Italy (from Maria Agnesi and Her "Witch"). The following discussions in this paper is about Maria Gaetana Agnesi and her mathematics.…… [Read More]

Bibliography

Crowley, Paul. Maria Gaetana Agnesi.

New Advent. 08 Dec 2003. http://www.newadvent.org/cathen/01214b.htm

Unlu, Elif. Maria Gaetana Agnesi.

1995. Agnes Scott College. 08 Dec 2003. http://www.agnesscott.edu/lriddle/women/agnesi.htm

Crowley, Paul. Maria Gaetana Agnesi.

New Advent. 08 Dec 2003. http://www.newadvent.org/cathen/01214b.htm

Unlu, Elif. Maria Gaetana Agnesi.

1995. Agnes Scott College. 08 Dec 2003. http://www.agnesscott.edu/lriddle/women/agnesi.htm

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George Polya the Hungarian Mathematician

Words: 1317 Length: 4 Pages Document Type: Essay Paper #: 96083587He however refused. Because of this, Polya could only return to his home country many years after the end of the war. Having taken wiss citizenship, Polya then married a wiss girl, tella Vera Weber, the daughter of a physics professor. He returned to Hungary only in 1967.

George Polya's professional life was as interesting as his personal pursuits. Before accepting an offer for an appointment in Frankfurt, Polya took time to travel to Paris in 1914, where he once again came into contact with a wide range of mathematicians.

Hurwitz influenced him greatly, and also held the chair of mathematics at the Eidgenssische Technische Hochschule Zurich. This mathematician arranged an appointment as Privatdozent for Polya at this institution, which the latter then accepted in favor of the Frankfurt appointment.

In addition to his teaching duties, Polya further pursued his passion for mathematics via his research efforts. He collaborated with…… [Read More]

Sources

Motter, a. "George Polya, 1887-1985. http://www.math.wichita.edu/history/men/polya.html

O'Connor, J.J. And Robertson, E.F. "George Polya." 2002. http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Polya.html

Polya Math Center. "George Polya, a Short Biography." University of Idaho, 2005. http://www.sci.uidaho.edu/polya/biography.htm

Motter, a. "George Polya, 1887-1985. http://www.math.wichita.edu/history/men/polya.html

O'Connor, J.J. And Robertson, E.F. "George Polya." 2002. http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Polya.html

Polya Math Center. "George Polya, a Short Biography." University of Idaho, 2005. http://www.sci.uidaho.edu/polya/biography.htm

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Guess and Check Is a Strategy That

Words: 615 Length: 2 Pages Document Type: Essay Paper #: 94667810Guess and check is a strategy that can be used with middle school math students to help them develop skills in mathematical thinking and problem-solving. As Guerrero (2010) points out, the guess and check lets students focus on the quantitative relationships between numbers rather than their mathematical value. Many students find word problems difficult because they have trouble seeing these relationships. Using the guess and check method, students choose a reasonable number to "plug in" to an equation to see if it makes mathematical sense and satisfies the conditions posed by the problem.

With increased emphasis on algebra in the K-8 curriculum, teachers are encouraged to foster discussions about mathematical relationships as part of their lessons and to help their students focus on "sense making rather than merely applying rote computational strategies" (Guerrero). When students are able to develop this deeper understanding of mathematics, Guerrero asserts, teachers can "potentially influence…… [Read More]

References

Guerrero, S.M. (2010). The value of guess and check. Mathematics Teaching in the Middle

School 15(7), pp. 392-398.

Guerrero, S.M. (2010). The value of guess and check. Mathematics Teaching in the Middle

School 15(7), pp. 392-398.

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Words: 1680 Length: 5 Pages Document Type: Essay Paper #: 9888180

The student then places it on the playing field. The system allows a chosen playing card to be dragged by means of a mouse to the playing field and, if properly placed, to "stick" in place on the playing field. (Improperly placed cards "snap" back to their original file position.) After each card has been correctly placed, a line between properly placed cards is generated connecting proper statements and reasons to each other and the GIVEN or CONCLUSION displays the completed proof (Herbst, 2002).

In working with geometric proofs, it is important for the student and teacher alike to approach this new and intimidating subject with an open mind. Even though students may have never experienced any type of logic or reasoning prior to the introduction of proofs, if presented correctly, this new way of approaching math can be both fun and enlightening. Teachers should keep this in mind when…… [Read More]

References

Discovering Geometry: A Guide for Parents. 2008, Key Curriculum Press. Retrieved October 19, 2009 at http://www.keymath.com/documents/dg4/GP/DG4_GP_02.pdf

Herbst, Patricio G. Establishing a Custom of Proving in American School Geometry: Evolution of the Two-Column Proof in the Early Twentieth Century, Educational Studies in Mathematics, Vol. 49, No. 3 (2002), pp. 283-312,

Discovering Geometry: A Guide for Parents. 2008, Key Curriculum Press. Retrieved October 19, 2009 at http://www.keymath.com/documents/dg4/GP/DG4_GP_02.pdf

Herbst, Patricio G. Establishing a Custom of Proving in American School Geometry: Evolution of the Two-Column Proof in the Early Twentieth Century, Educational Studies in Mathematics, Vol. 49, No. 3 (2002), pp. 283-312,

Words: 741 Length: 2 Pages Document Type: Essay Paper #: 61146665

Ethnomathematics views mathematics as a way of managing reality "specifically by ciphering, counting, measuring, classifying, ordering, inferring and modeling patterns arising in the environment," and the learner's environment and culture must be integrated into the lesson plan to make learning math meaningful (Patterson, 2005). "The suffix 'tics' means art or technique" specifically referring to the practical, lived application of mathematics (Patterson, 2005).

Ethnomathematics has the power to make mathematics accessible to groups that may have felt excluded from mathematical education in the past. For example, in one ethnomathematics unit called "One Grain of Rice," a girl called Rami must budget her rice consumption, illustrating the necessity of mathematics in the daily life of the poor as well as the wealthy. Including ethnically appropriate names and situations in word problems is not just politically correct. It provides 'role models' for children -- if the child in the word problem needs math,…… [Read More]

Works Cited

Demi. (1995) "One Grain of Rice." Retrieved 5 Aug 2007 at http://iml.math.wvu.edu/portals/0/NtForums_Attach/Ethnomathematics%20revised.ppt

Eglash, Ron. (2003). "Culturally Situated Design Tools." The Rensselaer Polytechnic

Institute. Retrieved 5 Aug 2007 at http://www.rpi.edu/~eglash/csdt.html

Fugit, Jamie & Smith, Nicolyn. (Dec 1995). "Ethnomathematics." ISGEm Newsletter.

Demi. (1995) "One Grain of Rice." Retrieved 5 Aug 2007 at http://iml.math.wvu.edu/portals/0/NtForums_Attach/Ethnomathematics%20revised.ppt

Eglash, Ron. (2003). "Culturally Situated Design Tools." The Rensselaer Polytechnic

Institute. Retrieved 5 Aug 2007 at http://www.rpi.edu/~eglash/csdt.html

Fugit, Jamie & Smith, Nicolyn. (Dec 1995). "Ethnomathematics." ISGEm Newsletter.

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Words: 1088 Length: 3 Pages Document Type: Essay Paper #: 50106405

Proof, a NOVA episode aired on PS [...] review the video, with a focus on what the video tells us about how people learn to do mathematics. Compare and contrast this with your own experiences with mathematics, particularly your approach toward learning about new mathematical problems and trying to solve them. "The Proof" is more than just a video about solving a complex mathematical problem. It is a story of determination, setting goals, and finding out that solutions come from many different places and ideas. You have to be open to new ideas when you try to solve anything, whether it is a complex mathematical problem, or a personal problem. The proof is really about keeping an open mind, and looking at all the angles of a problem.

The Proof

The Proof" is an interesting look at one man's obsession with proving (or disproving) a theory (Fermat's Last Theorem), written…… [Read More]

Bibliography

The Proof." Dir. Simon Singh. Perf. By Andrew Wiles, Stacey Keach. NOVA. 28 Oct. 1997.

The Proof." Dir. Simon Singh. Perf. By Andrew Wiles, Stacey Keach. NOVA. 28 Oct. 1997.

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Chaos Theory Has Filtered Down

Words: 1570 Length: 6 Pages Document Type: Essay Paper #: 68288574

Gleick's explanation is more conversational and has a popular appeal, as noted, while Stewart's explanation, while not impenetrable by any means, is more mathematical in nature, more technical, and more extensive in many ways. He is not telling the story of chaos as much as he is showing how it was derived and how it is applied in different scientific fields of investigation. He even follows poets in considering the nature of such chaotic systems as water flowing in a brook, something that has long fascinated poets and physicists alike and something that is not easy to analyze or predict. Different tools have been developed for measuring different physical properties, such as oscillators and various sound equipment. Stewart looks at these for what they show about both order and chaos at the same time. Stewart also raises the Hyperion issue and how it illuminates chaos theory and is in turn…… [Read More]

Works Cited

Gleick, James. Chaos: Making a New Science. New York: Penguin, 1988.

Stewart, Ian. Does God Play Dice?: The Mathematics of Chaos. New York: Basil Blackwell, 1987.

Gleick, James. Chaos: Making a New Science. New York: Penguin, 1988.

Stewart, Ian. Does God Play Dice?: The Mathematics of Chaos. New York: Basil Blackwell, 1987.

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Geometry Manipulative Elementary Geometry Manipulative

Words: 586 Length: 2 Pages Document Type: Essay Paper #: 16427374This will not only introduce elementary students to geometry, but also begin the complicated thinking associated with algebraic concepts. Using the formula to plug in the known degrees and then find the x is the beginning of much more abstract algebraic thinking.

Handout

Circles rule our lives and have rules of their own! Each circle measures to 350 degrees, and with this knowledge we can begin to find unknown angles!

If a circle measures 360, that means that a half circle measures half -- 180 degrees. In a half circle, there are many different angle combinations. But, we know that they all equal out to 180 degrees.

Knowing this, we can find the great unknown!

Well, we know that the total of the two angles equals 180 degrees. Therefore, angle 1 = angle 2 = 180 degrees.

Let's just plug the numbers into the equation.

63 + x = 180.…… [Read More]

References

National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

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National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

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45

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Words: 403 Length: 1 Pages Document Type: Essay Paper #: 66385489

The formula is found in Mathematics in Our World on page 273.

Sn = the sum of n terms of the sequence (currently unknown)

a1 = the first term of the sequence an = the nth term of the sequence a1= 100

an= 300

Sn= n (a1+an)

Sn= 9(100 + 300)

Sn = 9(400)

Sn = 4.5(400) = 1800

It will cost $1,800 to build a 90-foot tower.

Question 37: A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account?

Each year, 5% is added to the balance (B) in the savings account. This problem represents a Geometric sequence because each year is multiplied by the same number. In this case it is 1.05. It is 1 plus an additional 5% each year.

B + B (.05)

B…… [Read More]

References:

Bluman, a.G. (2005). Mathematics in our world (Ashford University Custom Edition). United States: McGraw-Hill.

Bluman, a.G. (2005). Mathematics in our world (Ashford University Custom Edition). United States: McGraw-Hill.

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Words: 944 Length: 3 Pages Document Type: Essay Paper #: 14093439

They must also solve polynomial, exponential and logarithmic equations both analytically and graphically.

tandard 4: tudents must be able to understand and use matrices to perform basic operations. This includes addition, subtraction, multiplication and inversion of matrices. They must also be able to identify the appropriate methods and technology to accomplish this. In addition, students must demonstrate the ability to find the inverses of two-by-two matrices without only with the use of pencil and paper, without additional technology.

tandards for Grade Level 11

tandard 1: At the end of this grade level, students must be able to explore rational functions in terms of investigating and explaining the characteristics of rational functions. Elements such as domain, range, zeros, points of discontinuation, and intervals of increase and decrease must be included in this ability. They must also find the inverses of rational functions with discussions of domain and range, symmetry, and function…… [Read More]

Sources

Cox, K. (2006). Georgia Performance Standards: Mathematics 2. Georgia Dept of Education. Retrieved from https://www.georgiastandards.org/standards/Georgia%20Performance%20Standards/Math-II-Stds-rev-0409.pdf

Cox, K. (2006). Georgia Performance Standards: Mathematics 3. Georgia Dept of Education. Retrieved from https://www.georgiastandards.org/standards/Georgia%20Performance%20Standards/Math-III-Stds-rev-0409.pdf

Cox, K. (2006). Georgia Performance Standards: Mathematics 4. Georgia Dept of Education. Retrieved from https://www.georgiastandards.org/standards/Georgia%20Performance%20Standards/Math-IV-Stds.pdf

Dillon, S. (2010, Mar 10). Panel Proposes Single Standard for All Schools. The New York Times. Retrieved from http://www.nytimes.com/2010/03/11/education/11educ.html

Cox, K. (2006). Georgia Performance Standards: Mathematics 2. Georgia Dept of Education. Retrieved from https://www.georgiastandards.org/standards/Georgia%20Performance%20Standards/Math-II-Stds-rev-0409.pdf

Cox, K. (2006). Georgia Performance Standards: Mathematics 3. Georgia Dept of Education. Retrieved from https://www.georgiastandards.org/standards/Georgia%20Performance%20Standards/Math-III-Stds-rev-0409.pdf

Cox, K. (2006). Georgia Performance Standards: Mathematics 4. Georgia Dept of Education. Retrieved from https://www.georgiastandards.org/standards/Georgia%20Performance%20Standards/Math-IV-Stds.pdf

Dillon, S. (2010, Mar 10). Panel Proposes Single Standard for All Schools. The New York Times. Retrieved from http://www.nytimes.com/2010/03/11/education/11educ.html

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Words: 598 Length: 2 Pages Document Type: Essay Paper #: 84120603

He made three main contributions to the theory of numbers: congruence theory, studies on the separation of the circle into equal parts, and theory of quadratic forms.

Algebra and Analysis

Up to Gauss's time, no one had been able to prove that every algebraic equation has at least one root. Gauss offered three proofs. And he modified the definition of a prime number.

Astronomical Calculations

We discussed briefly his assistance to astronomers in relocating Ceres. His success in this effort spurred him to develop the mathematical methods he used further. In 1809 his Theoria motus corporum coelestium used the method of least squares to determine the orbits of celestial bodies from observational data. In arguing his method, Gauss invented the Gaussian law of error, or, as we know it today, the normal distribution.

Non-Euclidean Geometry

Mathematicians, for centuries, had been attempting to prove Euclid's postulate concerning parallels (the sum of…… [Read More]

Bibliography

Bell, E. (1986). Men of mathematics. New York: Simon Schuster.

Dunnington, G., Gray, J., & Dohse, F. (2004). Carl Frederich Gauss: titan of science.

Washington D.C.: MAA.

Encyclopedia of World Biography. (2005). Karl Friedrich Gauss biography. Retrieved September 29, 2009, from bookrags.com (Encyclopedia of World Biography): http://www.bookrags.com/biography/karl-friedrich-gauss/

Bell, E. (1986). Men of mathematics. New York: Simon Schuster.

Dunnington, G., Gray, J., & Dohse, F. (2004). Carl Frederich Gauss: titan of science.

Washington D.C.: MAA.

Encyclopedia of World Biography. (2005). Karl Friedrich Gauss biography. Retrieved September 29, 2009, from bookrags.com (Encyclopedia of World Biography): http://www.bookrags.com/biography/karl-friedrich-gauss/