DR. CAROL JVF BURNS

Carol Jane Vreeland Fisher Burns
Statement of Teaching Philosophy
(pdf version)

College Teaching
2011–2012: full-time Instructor at Northern Arizona University, Flagstaff, Arizona

I got married in September 2011, had a long-distance marriage (Flagstaff/Tucson) for the academic year, and moved to Tucson in May 2012.
High School Teaching/Chair Experience
2008–2009: Chair of the Mathematics Department at Lenox Memorial Middle and High School, Lenox, MA

I left this job to pursue math-on-the-web fulltime. (I also did some consulting work and online tutoring.)

1999–2008: Miss Hall's School, Pittsfield, MA, Mathematics Department
MATH-ON-THE-WEB
My ‘portfolio’ is my web site, with about 400 dynamic, interactive math web exercises. Since about 1999, I have been creating web resources for my students (and the world) and spreading the word about Math Markup Language (MathML) and MathJax.
University Teaching Experience
I taught mathematics at the university level for most of the period from 1981–1999: first while a graduate student at the University of Oklahoma; thereafter at Idaho State University, where I completed my doctoral degree and held a position as an Adjunct Assistant Professor of Mathematics. I taught a wide variety of undergraduate courses (listed alphabetically):
- algebra (all levels)
- analytic geometry
- calculus I, II and III (for majors)
- developmental mathematics
- engineering mathematics (ordinary differential equations)
- essentials of calculus (for non-majors)
- foundations (introduction to the rigors of mathematical proof for math majors)
- language of mathematics
- linear algebra
- mathematics for elementary school teachers
- probability and statistics
- trigonometry
Engineering Technician
I left academia for one year, from June 1995 to July 1996, to work as an engineering technician at American Microsystems, Inc. (Pocatello, Idaho) and help them with some mathematical modeling problems. While there, I developed and implemented a genetic algorithm for multivariate function modeling. Also, I compiled, formatted, edited and typeset the first AMI Design Manual, a collection of application notes on a variety of aspects of circuit design.
Programming/Technology
Over the years, I've had experience with a wide variety of programming languages and math technology tools: MathJax, JSXGraph, MathML, JavaScript, HTML, XHTML, CSS, TeX, GeoGebra, both PC and MAC platforms, Moodle, AppleScript, SVG, PERL, PHP, algebraic and reverse-polish notation graphing calculators, MATLAB, Mathematica, Fortran, Basic, LISP, SAS, and more.

I'm an independent learner. To acquire a new skill, I find a good book and read it cover-to-cover. Along the way, I ‘give back’ to the publisher/author by submitting errata—I'm an excellent proof-reader, with keen attention to detail.

TeX Commands Available in MathJax
Compilations of my Web Lessons:
One Mathematical Cat, Please!, copyright 1998.
Many people have trouble with mathematics: not necessarily because the ideas are difficult, but because they are being presented in a foreign language. This book takes the time to teach the structure of the mathematical language, while exploring ideas that are central to all of mathematics—ideas that require no computational skill beyond arithmetic with numbers like 1, 2, and 3. The book is appropriate as a supplement to any math class, from junior high school through college-level. (165 pages) This book has been ‘filled out’ to a complete first course in algebra.
Identifying Hidden Periodicities in Discrete-Domain Data, doctoral dissertation, copyright 1994.
This book is written for the person who has a data set (a collection of ordered pairs), and who seeks to understand this data, for the primary purpose of predicting future behavior of the process that generated the data. The dissertation is written as the basis for a textbook, and assumes a mathematical background typical of an undergraduate degree in engineering. Implementation of all techniques are incorporated throughout the text, using the MATLAB software package. (321 pages)
Understanding Calculus, 1993
To fulfill a teaching internship requirement at Idaho State University, I wrote a calculus book (about 450 pages) that incorporates mathematical language issues, and taught from it. I also wrote a complete Solutions Manual and MATLAB supplement.
Survey of Undergraduate Mathematics, 1991
While preparing for an exam over all undergraduate mathematics, I compiled an extensive set of notes (about 300 pages) highlighting important ideas in all areas of undergraduate mathematics; these notes were still being using by DA students preparing for the written exam when I left ISU in 1999.