[Dr. Green]    [Introduction]    [Portfolio]    [Courses]    [Teaching Resources]   [Contact]    [Other/Links]

Already Published Research

The article "Promoting Mathematical Discussion and Community via Blackboard" appeared in PRIMUS Volume 17 Issue 4, October 2007.. The version available here is an earlier, author version of the submission and is posted by permission of Taylor & Francis publications. Full bibliographic information and a link to the final, published version are below.
Author Posting. (c) Taylor & Francis, 2007.
This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution.
The definitive version was published in PRIMUS, Volume 17 Issue 4, October 2007.
doi:10.1080/10511970601131563 (http://dx.doi.org/10.1080/10511970601131563)

My Ph.D. has yielded a paper on Tachyons (those theoretical particles in Star Trek that travel faster than the speed of light!) The paper has been published in Astrophysics and Space Science 286(2), pp. 327-346, January 2003. As soon as a link is available, you will be able to preview the article.

"Creating Effective Writing Assignments in Calculus" was published in PRIMUS XII(2), June 2002, a journal dedicated to Problems, Resources and Issues in Mathematics Undergraduate Studies. This paper is available online through many of the academic journal sources, such as ProQuest Education Complete.

Research in Progress

Currently, I am working on three physics-related papers. The first is in collaboration with Dr. Munawar Karim of the SJFC Physics Department regarding some asymptotic solutions to a particular form of the Matthieu equation. This equation arose from Dr. Karim's research on gravitational waves. The paper deals with how the study of such an equation connects to all areas of mathematics (numerical analysis, real analysis, differential equations, just to name a few areas) and how this could form the basis of a senior undergraduate capstone experience in mathematics. The second paper deals with an inexpensive (and highly engaging) way to have students experience and measure the Doppler effect in the classroom. The Doppler effect (encountered daily in the weather reports with Doppler radar and hopefully less frequently with police speed traps and radar guns) is the well-understood phenomenon in which the observed frequency of a wave depends on the relative velocities of the source and observer. The third paper deals with the design and physics of paper helicopters, which are fascinating little devices exhibiting any number of basic physical concepts. For example, the straightforward motion of these objects is related to Bernoulli's principle for fluid flow, simple vector addition for forces, conservation of angular momentum, and the lever principle.

Along with Dr. Allen Emerson, I am currently involved in developing a new mathematics course for business/management majors. This new course, MSTA 130, has replaced MATH 117 as the required math course for these students. It involves the use of Excel speadsheets, deep mathematical understanding, critical thinking, and writing (a lot of writing). Related to this project, we are writing a textbook (which includes lots of interactive spreadsheet tools and a heavy emphasis on writing and thinking) and are currently working on:

  1. A new method of assessment for courses that focuses the instructor's efforts on evaluating student work during the semester, then grading at the end of the semester, rather than doing both simultaneously. They anticipate writing a paper on this method this summer, after they have piloted the method in Spring 2002.
  2. A paper on the process of developing a new course
  3. A paper on "How to create realistic data" for such a course
  4. A paper on how a particular assignment for this course has evolved into a series of assignments
  5. A paper on the use of technology (BlackBoard, Excel, StatPro) to develop mathematical understanding
  6. A paper on the use of regression analysis and the difference quotient to justify the formulas for the "derivative shortcuts"

Finally, I am occasionally putting time into writing a paper relating the famous Matrix movie trilogy to the mathematical idea of a matrix, Markov chains, probability, finite state machines and how mathematics can help us "know the future" as the main character, Neo, seems able to do.

General Research Interests

Dr. Green is currently interested in all aspects of math and science education, especially the use of technology in the classroom. He is currently working on a paper relating his experiences and advice in using discussion boards in math and science classrooms in ways that enhance the class and extend the learning outside of the classroom.

Dr. Green is also working (slowly) with Dr. Edward Alexander at the University of Arizona, on a paper about the ways in which students respond to prompts in third semester calculus. This grew out of the reform movement in mathematics, which promotes the use of multiple representations - verbal, algebraic, data tables and graphs - to study mathematical topics.

This website will never be in a "permanent" state. At any time, the information may change or be supplemented.
Last change: December, 2003.