Abstract This paper begins by providing a history of the evolution of zero and discusses the origin of the symbol. It then discusses the origins of the concept of "zero" and how this was perceived differently by various ancient cultures such as the Egyptians, the Mayans and the Babylonians. It then focuses specifically on the "Babylonian zero" and how this differed in concept from other figures at the time. The paper includes several diagrams and pictures.
From the Paper "The symbol zero evolved into its present form after quite a number of transformations. The idea of how the symbol was devised also harbors a few contradictory ideas. Opinions range from it being a dot originally, replaced by a circle with a dot in the center and then maturing to the current form, an oval shape that we all are familiar with. (Pearce, I., 2002). The Egyptian zero that evolved has also been equated with the hieroglyph for beauty, and that of the human windpipe, heart and lungs. (Williams, S. W., 2002)"
Abstract Details the current teaching and testing methodologies in high school mathematics classes. Also discusses some alternative strategies for teaching math that have been employed at the secondary school level.
Outline
Current Teaching and Testing Methodologies in High School Mathematics
Classes
Alternative Strategies for Teaching Math Employed at the Secondary
School Level
Learning Concepts and Mathematics Education
The High School Environment: Putting it all Together
Conclusion
From the Paper "As I have stated, the perceived general needs of the high school can be seen as duo-fold: to provide an education that encourages excellence to exceptional students, and to provide an education that encourages competency to average students. Based on the size, location and level of heterogeneity at any particular school, these needs attract varying degrees of attention."
Abstract This paper considers the problem of low math scores for American elementary students and looks at how there are considerable differences between Chinese and American teachers and how these differences account for the poor performance of American students. It also analyzes how the problem goes beyond the teachers themselves, with the base cause being the American approach to mathematics.
Outline
Possible Explanations for Low Math Scores
Comparing Elementary Mathematics Teachers
The Problem with American Mathematics
Conclusion
From the Paper "Ma argues that the American approach to teaching mathematics is based on teaching procedurally, not conceptually. According to Ma mathematics is approached as a collection of facts and rules where mathematics means following set procedures step-by-step to arrive at answers. This American approach appears to be a correct definition of how mathematics is seen. Unlike subjects like English and geography, the emphasis is not on understanding, but on remembering. Students do not have to know why a certain number is the area of a shape. Instead, all they have to do is remember the formula for calculating the area."
Abstract This paper describes Eratosthenes' calculation of the Earth's diameter, based on one assumption and two measurements, that the Earth was a sphere and that the two measurements made are the degree of the Earth's shadow at noon at two points and the distance between those points. It outlines how this experiment can be repeated by measuring the degree of the shadows cast at two locations either directly north or south of each other at noon on the same day and details the equipment required, the measurements to be taken and the mathematical equations involved.
From the Paper "Eratosthanes used the city of Syene in Egypt as the first point. This point was selected because it was known that on noon on the first day of summer the sun was directly overhead. This was known because people observed that at this time, the buildings cast no shadows (York University). Therefore, the degree of the shadow at Syene was 0o.
Eratosthanes then needed to know the degree of the shadow at another point either directly north or directly south, at the same time of day. Eratosthanes selected Alexandria as the second city. The degree of the sun's shadow was measured and found to be 7.2o (HEASARC)."
Abstract This paper 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
Indian Influence
Tenth Century to Ming Period
Influence
From the Paper "Suan chu was thus developed, which covered a wide array of practical and spiritual concerns. Subjects as diverse as religion and astronomy were tapped to devise ways to control the floods (Martzloff 21-22). The science of mathematics was an integral aspect to the of suan chu, particularly in the construction of dams strong enough to shore up the river banks and in the development of the Chinese calendar to record and predict the monsoon season."
Abstract In this essay, I will discuss the question of mathematical truth and attempt to decide whether there can be such a thing as an "absolute fact."
Abstract R. Rucker helps us better understand Godel's "Theorem on Incompleteness" by discussing infinity and whether it can be seen as a real entity. In his view, infinity can be seen as a tangible reality. He argues that it is quite possible that time may actually continue forever - and that is precisely what infinity is. Rucker also sees the possibility of the potential infinite divisibility of space into smaller and smaller pieces.
Abstract This essay discusses Alfred North Whitehead's view of math and science in philosophy. His basic theme is that concrete entities are not enduring substances but events that are connected to each other by their space-time relations and qualitative and mathematical patterns. In Whitehead's view, time is differentiated from space by the acts of inheriting patterns from the past.
Abstract This essay discusses whether infinity can be seen as a real entity. R. Rucker argues that it is quite possible that time may continue forever. Lakoff and Nunez argue that mathematics is the result of the human mind creating metaphors for phenomena it encounters.
Abstract This essay talks about the similarity between mathematical statements and language structures. What is essential to both is that there are fixed rules which determine what mathematical symbols have meaning and what do not. Language also functions in a similar way. As Keith Devlin states, all languages are variations on a single theme (Devlin 7). Thus, Both mathematics and language are governed by particular rules that are syntactically or structurally similar.
Abstract This paper gives the reader a short biographical overview of ancient Greek mathematics. The author of this paper takes the reader on a tour of how mathematics was developed and the important role that Greece played in that development.
Abstract A paper on the link between the lack of proper education of elementary school math teachers and the education system's poor mathematics results.
Abstract This is on the topic of gender differences in boys and girls. Specifically, the paper looks at the different levels of understanding in mathematics as wekk as how girls often suffer from depression during the adolescence years.
Abstract This paper discusses the similarity between mathematics and language. Human languages have certain structures that facilitate the expression of ideas. These structures operate by the same rules as mathematics.
Abstract This paper examines the mathematical event known as the Copernican Revolution. This revolution was the introduction of natural laws into the world of science and religion.
