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Mathematic v Conceptual Modeling Limitations

Words: 342 Length: 1 Pages Document Type: Thesis 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.


Aspinall, D. (2007). "Designing interaction." University of Edinburgh. Accessed 30 July 2009.

Kay, J. (2006). "Amaranth and the limits of mathematical modeling."…… [Read More]


Aspinall, D. (2007). "Designing interaction." University of Edinburgh. Accessed 30 July 2009. 

Kay, J. (2006). "Amaranth and the limits of mathematical modeling." Financial times, 10 October. Accessed 30 July 2009.
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strategies to improve mathematic performance for children

Words: 1361 Length: 4 Pages Document Type: Capstone Project Paper #: 56539671

Improve Mathematic Performance for Children With Learning Difficulties and Their Effectiveness

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


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.
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Three Mathematic Textbooks Review

Words: 1840 Length: 6 Pages Document Type: Term Paper Paper #: 99003285

Precalculus With Limits by on Larson

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

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


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.
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George Cantor

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


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]


Author not Available. "Georg Cantor." 2004. 13 April 2004.

Breen, Craig. "Georg Cantor Page." Personal Web Page. 2004. 13 April 2004.

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.
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Workshop Teacher

Words: 620 Length: 2 Pages Document Type: Term Paper 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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Techniques Correlation

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


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]