I have taught at ERCLC since 2003. Previously I taught Physics, Math, Computer Programming, and Astronomy ranging from Jr. High through Jr. College, in public and private schools, here and in South India since 1972, except for a year working as a full-time computer programmer. I have a BS in Physics from Harvey Mudd College in Claremont, an MA in Education from Claremont Graduate School, and an MS in Mathematics from Cal Poly Pomona.

I am very interested in astronomy. In the mid 1970's I figured out how to make a rotating star dial (called a planisphere) with less distortion than the kind I had when I learned the constellations in the Boy Scouts. I started a business called David Chandler Company to sell my improved planispheres. Besides the planispheres I have written astronomy software, an astronomy book, and a sky atlas.

When I first came to ERCLC I started working on a companion to one of the best high school geometry texts (Geometry: A Guided Inquiry by Chakerian, Crabill, and Stein) to make it more homeschool friendly. It makes heavy use of demonstrations created with The Geometer's Sketchpad to make the concepts easier to understand intuitively. Geometry students at ERCLC are using this text and software. I also recently finished a series of video lessons for the Algebra I course: one video lesson for each section of our Algebra text. (I also have a shorter collection of Algebra videos of content that is tested on the California High School Exit Exam, or CAHSEE). This is also available in the school library. I am currently working on a similar series covering our Algebra II textbook. I plan to eventually cover the entire high school math curriculum with this kind of supplementary materials, through Pre-Calculus. Samples of the Geometry demonstrations, CAHSEE Algebra, and the Algebra I and Algebra II videos are posted on Google Video. See the links at MathWithoutBorders.com..

Besides my math-science interests I write essays and articles about issues that matter to me. Some of these articles have been published in newspapers and magazines. I have collected my writings from the past thirty years, or so, and have posted them on a website. Some of these articles (and web sites) apply mathematical insights to social issues. (There is an amazing amount of overlap between mathematical/scientific issues and social issues.) For instance, my most viewed web site (~10,000 hits per month) is a graph of the US income distribution called L-Curve.org. Understanding the information in that graph is a key to understanding much of the sociology of this country. A few years ago I organized a group of writers called the Progressive Writers Bloc to jointly write a column in several local papers. As you would expect of any thinking person, I have opinions. I don't expect my students to have the same opinions I do, but I do expect them to become critical thinkers. If you follow the links in the web sites listed above you will come to know my perspectives on a numbr of current issues.

Some of my recent projects:

Driving in the Fog

The year before I started here at ERCLC I taught at Corcoran High School, which was a 50 minute commute out into the middle of the San Joaquin Valley. The fog can get very bad along that route in the winter, so I did what any physics/math oriented person would do: as I drove I wondered how to figure out a safe driving speed, and followed through by working on the problem until I came out with a pretty good method that can be applied by anyone in actual driving conditions. Other questions came to mind: Is it "safe" to drive at the "safe" speed when the car behind you might be driving too fast? (The answer, surprisingly, is that the driver behind you is less of a threat than what may lie on the road ahead.)

I wrote up my results and submitted them to a few Valley newspapers. Here is a version of the article and an Excel spreadsheet you can use to try out different scenarios for yourself. This might be helpful in coping with this very real problem in the San Joaquin Valley, and it is an example of using the math you know to answer questions for yourself. (If you don't have Excel, you might download Open Office -- a free, open source "office suite" that supports Word document, Excel spreadsheet, and Powerpoint presentation formats, and more.)

Comet Trails

Back in the mid 1990's I observed what I believed was reflected sunlight from debris scattered along the orbital paths of comets. The major astronomy magazines were unwilling to publish this because no one had been able to photograph what I was seeing. They assumed I couldn't possibly be seeing something that couldn't be photographed. Over the last few years professional astronomers started being able to photograph these trails, and recently an amateur was able to do the same. Therefore I am resubmitting my article. Here is a draft of what I am sending to Sky and Telescope and/or Astronomy Magazine. Here is a recent picture of a comet trail imaged by Mike Holloway, an amateur astronomer living in Arkansas, on Feb. 22, 2007. The comet is the small bump in the middle of the picture. The faint streak from the top left to the bottom right of the image is the debris trail.

Expanding Universe Demo

One demonstration I designed some years ago has been published in physics and astronomy journals, incorporated into astronomy textbooks, and was even presented by someone at an astronomy conference in the former Soviet Union! It is a simple demonstration of the expansion of the universe.

The key idea is this: the whole universe is expanding. There is no center to the expansion. Every point is expanding away from every other point. As seen from earth, the universe is expanding outward from us. As seen by people in a distant galaxy, the universe is expanding outward from them. The demo consists of two "pictures" of the universe (lots of random dots): one representing the universe today, and the other representing the universe one billion years ago. All the dots are in the same relative position, except the scale is slightly expanded in one vier relative to the other. If the two pictures are printed on transparencies and overlaid (or if one is printed on paper and the other is printed on a transparency), a dramatic radial pattern is produced. If the top transparency is shifted relative to the bottom printout, the center of the patterns shifts. Whatever dot is matched up with the corresponding dot on the other sheet becomes the center of the radial expansion pattern.

The rate of expansion can be used to determine the age of the (artificial) universe represented by the two pictures. Compare the distance any galaxy (dot) has moved in one billion years to the distance it is from the center of expansion. If the distance to the center is, for instance, 15 times the distance it has moved in one billion years, the implication is the universe is 15 billion years old. Try it!

Math Explorations

Math Explorations are "off the wall" activities related to math that may or may not look like math to most people. These have all just been out of my head so far, but if I ever run dry there are lots of resources on topics like these. Here is the collection of topics I have dreamed up so far. We have done most of these over the last two years, but some are still in the hopper for coming weeks. [During a lower grade class working on mazes, I discovered an interesting way to solve mazes quickly and easily with a computer. Check it out! A good class is where the techer learns at least as much as the students do!]

Math Teaching Workshop for Parents

We will be using the National Council for Teachers of Mathematics (NCTM) "Standards" as a text for this workshop. It is available online at http://standards.nctm.org/document/index.htm.

Instructions and practice problems for the Chinese abacus (pdf file).

 

I also recommend looking at the results of Project 2061's Middle Grades Mathematics Textbooks: A Benchmarks-Based Evaluation, especially as it applies to the Saxon textbooks. (Project 2061 is the American Association for the Advancement of Science's project to improve science and mathematics education in America. For more information on how the textbook study was conducted, start HERE.)

[We have two copies of a book in our library called, Unfolding Mathematics with Unit Origami. It is an interesting book, and one I recommend for using with your children, but in playing around with its construction of a regular pentagon I discovered their method is not really "correct". It produces a very good approximation which would be fine, if the goal were to produce 5-pointed stars for art projects, but it is not fine if the point is to teach mathematics. This discovery motivated me to stay up late one night and derive a rigorous (i.e. a really correct) method. The challenge of documenting the method led me to try doing origami with the program Geometer's Sketchpad (a tool I also recommend) and to create a Javascript slide show. All-in-all, it was a marvelous learning experience on several levels. See the final results here: Origami Construction of a Regular Pentagon.]

Science

I highly recommend that parents look at the web site http://www.project2061.org. This is a project of the American Association for the Advancement of Science (AAAS) to raise the level of science and mathematics teaching nationwide. One of their most useful and interesting publications, available both as a printed book and online on the Project 2061 site, is Benchmarks for Science Literacy. This book does for science education what the NCTM standards do for mathematics. Browse the web site for reviews of science and mathematics textbooks, research on teaching and learning, and much more.