DR. CAROL JVF BURNS
Carol Jane Vreeland Fisher BurnsStatement of Teaching Philosophy
(pdf version)

Doctor of Arts in Mathematics, May 1994, Idaho State University, Pocatello
Dissertation title: Detecting Hidden Periodicities in DiscreteDomain Data
GPA: 4.0/4.0 on all work at Idaho State University 
Featured Speaker at CAMT 2015 (Conference for the Advancement of Mathematics Teaching).
My three talks are online:  Recipient of the MathWest 2007 Teacher of the Year Award for grades 7–12, April 2007. This award recognizes a teacher in Western Massachusetts for outstanding contributions to the advancement of mathematics education and training.
 Recipient of the Leonhardt Teaching Chair, June 2002, Miss Hall's School, Pittsfield, MA
 Recipient of the first DA Student of the Year Award for the School of Graduate Studies and Research, April 1994

Master of Arts in Mathematics, May 1984, University of Oklahoma, Norman
GPA: 4.0/4.0 on all work at the University of Oklahoma  Bachelor of Science Magna Cum Laude in Civil Engineering, February 1981, University of Massachusetts, Amherst
 Summer Research Scholarship, Summer 1980, Princeton University, Princeton, New Jersey
 Valedictorian, June 1976, Monument Mountain Regional High School, Great Barrington, Massachusetts

College Teaching
2011–2012: fulltime Instructor at Northern Arizona University, Flagstaff, Arizona
I got married in September 2011, had a longdistance 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 mathontheweb fulltime. (I also did some consulting work and online tutoring.)
1999–2008: Miss Hall's School, Pittsfield, MA, Mathematics Department

MATHONTHEWEB
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 nonmajors)
 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 reversepolish 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 covertocover. Along the way, I ‘give back’ to the publisher/author by submitting errata—I'm an excellent proofreader, 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 collegelevel. (165 pages) This book has been ‘filled out’ to a complete first course in algebra. 
Identifying Hidden Periodicities in DiscreteDomain 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.
I married Ray Burns on September 23, 2011.
We live in a tiny house (Pebble) way out in the country in Sahuarita, Arizona.
I have one biological daughter, Julia, who graduated in June 2007 with a Bachelor of Arts in Mathematics from Carleton College (summa cum laude, Phi Beta Kappa, with distinction in mathematics). She taught high school mathematics for two years in the Rio Grande Valley for the Teach For America program. Julia spent her junior year in high school on a Rotary Exchange Program in Taiwan, and graduated in 2003 from Miss Hall's School. She has earned both a Master's degree in Statistics (2015) and a PhD in Linguistics (2017) from the University of Arizona in Tucson.
For more fun facts about me, click here.
I have one biological daughter, Julia, who graduated in June 2007 with a Bachelor of Arts in Mathematics from Carleton College (summa cum laude, Phi Beta Kappa, with distinction in mathematics). She taught high school mathematics for two years in the Rio Grande Valley for the Teach For America program. Julia spent her junior year in high school on a Rotary Exchange Program in Taiwan, and graduated in 2003 from Miss Hall's School. She has earned both a Master's degree in Statistics (2015) and a PhD in Linguistics (2017) from the University of Arizona in Tucson.
For more fun facts about me, click here.