I grew up in Edmonton, Alberta, Canada and got my teaching degree at the University of Alberta in Edmonton. After completing my bachelor's degree my wife, Nola, and I moved to Richmond, British Columbia, Canada to teach. I taught in the Richmond School District (High Boyd High School) for five years and then left to do a Masters Degree at the University of Georgia. While in Georgia, I worked under Dr. Jim Wilson, who re-ignited my passon for teaching and technology. Under his tutiledge I gained both a greater understanding of mathematics, teaching and technology. He was the perfect advisor for me - He was involved in so many cool grants and projects!!
In the summer of 1998, I got ambitious and began designing a website for my high school geometry classes. I put the usual things on the site (the syllabus, the course expectations, the basic instructor information, and a list of our upcoming assignments and tests) but I also wanted to provide my students with more resources. This desire prompted me to summarize the entire textbook so that they would have additional notes to reference while at home or during class if they had printed them out. The support resources continued: I linked to my textbook's online quizzes, I provided a few quicktime videos, and I also made a few java applets for interactive discoveries but the most popular item that was created was the PoW, the Problem of the Week. Each week students would be given an online weekly geometry challenge problem that would push their understanding and ability. The site was a great resource for my classroom. Over the year the resources of the site grew and so did its impact. I found many of my students finding greater success in geometry because of this support mechanism. The site was called e-zgeometry.com. This site still exists but now it holds less relevance because of the implementation of the common core and much of the material created there will be moved over to this site.
It was this huge success that led to a very special award that I received. In 2003, I was named by RadioShack, as one of their National Teachers of the Year. This was a great honor but even more rewarding was that this little site was making such a huge impact on classrooms and students.
Geometry Independent Study Team Patton Creek
See the surprise of me being awarded the Milken Award.
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David Hyder's The Determinate World is ambitious and challenging. It is an exciting and tough read, and it covers a great deal of ground. Hyder constructs a careful and stimulating narrative, to make a number of significant and well-constructed arguments concerning Helmholtz's epistemology, his relationship to Kant, and his empirical geometry. The Determinate World is an excellent contribution to the history of philosophy of 19th century science -- those who work in the field will need to engage with this book.
Bevilacqua (1993) identifies the relevance of Kant's Metaphysical Foundations of Natural Science to Helmholtz's argument in On the Conservation of Force. Turner (1996) and Kremer (1993) examine Helmholtz's work in colorimetry and his dialogues with Graβmann and Maxwell. Hyder builds on and analyzes these contexts to show in detail how Helmholtz's relationship to Kant and his research in colorimetry and metric spaces illuminate his arguments in his papers on geometry and in On the Conservation of Force.
The subtitle of the work, 'Kant and Helmholtz on the Physical Meaning of Geometry,' describes its two main parts. 'Physical meaning' here has two senses. In one sense, Hyder is referring to Kant's use of geometrical construction, in the Metaphysical Foundations, to attempt to isolate the a priori relations of necessity within Newton's Principia. In another sense, Hyder is referring to Helmholtz's empirical theory of geometry.
Within this framework, Hyder constructs two historical narratives. First, he gives an account of Helmholtz's relation to Kant, from the famous Raumproblem, which preoccupied philosophers, geometers, and scientists in the mid-19th century, to Helmholtz's arguments in his four papers on geometry from 1868 to 1878 that geometry is, in some sense, an empirical science (chapters 5 and 6). Here, Hyder responds to the reading of Moritz Schlick, according to whom the 'chief epistemological result' of Helmholtz's work is his argument that 'Euclidean space is not an inescapable form of our faculty of intuition, but a product of experience' (Schlick's note in Helmholtz 1977 [1921], 35). Schlick's story papers over Helmholtz's deep relationship to Kant, especially in Helmholtz's early work. Hyder's work here puts this relationship at center stage, and contributes a much richer picture of the reasons for Helmholtz's later decision to turn away from the Kantian perspective.
The second theme is the argument for the necessity of central forces to a determinate scientific description of physical reality, an abiding concern of Helmholtz's, and one that, as Hyder shows, has Kantian roots. Helmholtz's commitment to the necessity of central forces was key to his responses to rival views on electromagnetism, and is a deep and often underappreciated element of his epistemology of science.
In general, a central force is a force that is directed along the line between two bodies or particles. A tensor force between two nucleons is not a central force, but the gravity pulling an object to the earth's center of mass is. Over the 19th century, work on various problems of central forces became the object of renewed study, especially in Lagrangian mechanics, with the problem of two bodies free to move. It was found that the problem of two interacting particles free to move can be reduced to the problem of a single free particle acted on by a central force from a fixed point (Whittaker 1999 [1904], 77ff). Even as advances were made in the problems of central forces, Maxwell's and Weber's theories of electromagnetism proposed new interactions that were not central.
Hyder focuses on a very intriguing strand in this history. In the Introduction to Helmholtz's On the Conservation of Force, (self) published in 1847, Helmholtz cites Kant's Metaphysical Foundations of Natural Science. Bevilacqua (1993), whom Hyder cites here, pointed out that Helmholtz traces his methods in On the Conservation of Force to the Metaphysical Foundations. Hyder mines this relationship further, and in careful detail.