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.
