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He looks at three methods: history (melding information about the diverse geographical origins of algebra with the problems themselves), multiple representations (using notation, narrative, geometric, graphical, and other representations together to build understanding), and the object concept of function (teaching functions without generalizing about how traits of an individual relate to traits of a group). The article serves to offer some inventive solutions to a common problem in math education: How to make material relevant and compelling to a breadth of students.
Martinez, a.A. (2010). Triangle sacrifice to the gods. 1-11.
The article looks at Pythagoras, particularly the mythology surrounding his life and his most famous discovery, the Pythagorean theorem. It calls into question the historical evidence on which mathematics teachers base their teaching of this theory. The author points out how very little is known about Pythagoras and how he has been canonized by the math discipline because his theory is so useful. He outlines evidence that exists about Pythagoras, taking a critical eye to where and from whom the histories were derived. The tone of the article is playful but also makes an important point. It is critical that teachers take a close look at what information they are passing along as historical fact....
It is not enough to simply believe that Pythagoras was a mathematician who gave the world one key principle. It is more advisable to do one's own research and avoid misleading students.
Westfall, R.S. (2001). Newton. In W.H. Newton-Smith (Author), a companion to the philosophy of science (pp. 320-323). Malden, MA: Blackwell Pub.
This excerpt from a reference source is a biographical sketch of Isaac Newton,
17th century mathematician, scientist, and philosopher. It begins by discussing his relative unimportance as a lecturer and the focus he gave to his research in several fields, including math. The piece contextualizes Newton's research on gravity by giving historical background on the theories of Copernicus, Galileo, and Descartes. Newton blended these philosophies to create a whole picture of gravity. In addition, the article references the impact that Newton's work had on mechanical applications. Lastly, the piece points out how Newton used the thought patterns associated with calculus in what appears to the modern reader as a work of geometry (with respect to his book "The Principia"). In this way, the article functions as a reminder of how scientific discoveries are created, which is by building upon the theories of others and by giving weight to the importance to mathematical principles.
references the impact that Newton's work had on mechanical applications. Lastly, the piece points out how Newton used the thought patterns associated with calculus in what appears to the modern reader as a work of geometry (with respect to his book "The Principia"). In this way, the article functions as a reminder of how scientific discoveries are created, which is by building upon the theories of others and by giving weight to the importance to mathematical principles.
scientific notation, its uses and rules for calculations. One example from everyday life: a computer hard disk holds 4 gigabytes of information, that is 4,000,000,000 bytes of information. Written in scientific notation, that is 4 X 109 bytes. Scientific notation is used to write very large and very small numbers. While ordinary numbers are useful for everyday measurements, for large measurements like astronomical distances, scientific notations offers a way of
Those studying physics and astronomy, and perhaps other scientific disciplines as well, are accustomed to the use of scientific shorthand and in some fields it is essential -- the example above of distance between energy waves from supernovae is a good example. There is a high level of variation in these distances, so a shorthand like the one on financial statements would be apply, but the numbers are very
The new universe made room for God because the collective mind was opened to the notion of a divine entity controlling all aspects of the universe not just one corner of it. The Industrial Revolution can call Britain "home" (Craig 627) because at the time, Britain was the "single largest free-trade area in Europe" (627). Mechanical inventions spark the beginning of this revolution. In 1769, the spinning jenny was patented,
Metric System -- One of the reasons measurement can be complicated is that there is more than one system in use. Based on the Ancient Roman system, the metric system is based on powers of 10; which is called decimalization. The metric system has been the preferred European and scientific method of measuring sine the 18th century, but is not part of the International System of Units, which is also
Students should be able to reflect on the process of problem solving. Reasoning and Proof Students should recognize that proofs are a fundamental aspect of mathematics. Within that understanding, they should develop the ability to select and use various types of mathematical reasoning. Communication The standard calls for students to communicate their mathematical thinking in a coherent and clear way to teachers, peers, and others. Students should be able to express their ideas
It helped lead to more accurate readings of inanimate objects like rocks, too, which helped scientists narrow down the age of the Earth and how it has evolved through time. Macdougall uses many differing sources for his book, as his "notes and further reading" section indicates. He uses books, journal articles, essays, and scientific data, and offers some of that data up in Appendixes in the back of the book.