homepage: Dr. Carol JVF Burns


Blog is short for weblog (weBLOG).
Check here to see the latest information about my site (and, occasionally, about my life in general).

Saturday, December 22, 2012
I've been back East for my Dad's funeral, and stayed a while to be with my Mom so my sister could get a much-deserved vacation.
I haven't gotten any web work done recently, but should be back to it shortly after Christmas.
I wish you all peace, love, and wonderful times with friends and family during this joyous season.

Tuesday, December 11, 2012
My Dad, Jim Vreeland, died today, very early in the morning. He had Parkinson's disease for over a decade.
Since I live far away, I've said ‘good-bye’ to him many times, often wondering if it would be the last time.
When he stopped eating and drinking a few days ago, I was thinking of many wonderful times in my life with him.
I wrote him the letter below, for my family to read to him—even though he was unresponsive, I hoped he might be able to hear it.
However, he died before it could be read, so now I know that he'll hear it in heaven.
I love you, Dad.

Monday, December 10, 2012

Dear Dad,

I've been thinking back through my life about all the wonderful memories I have because of you! I want you to know how precious these are to me (and many more):
  • the ice-skating rinks you made in the backyard for us
  • the tight-rope walking rope you hung between two trees
  • the fantastic family camping trips at Tolland, where you and Mom set up the amazing kitchen; and we had to show you that we could safely capsize and ‘right again’ the canoe; visiting the ‘Frog’ rock; the ‘bump’ we went over in the car on the way in/out
  • the ‘beauty walks’ that I joined you on
  • the tree swings you made for all of us out back
  • I've never known anyone else with swings in their cellar
  • playing ping-pong with you in the cellar
  • shoveling the driveway with you
  • the incredible magic shows you put on; I remember you and Rick running around the backyard ‘catching a rabbit’ to pull out of the hat
  • our family meals together, with you sitting at the head of the table
  • digging up potatoes in your potato patch
  • jumping in the massive pile of leaves at your Mom and Dad's home in Middlefield
  • I always knew you could fix anything, and solve any problem I had—that you would listen carefully, and think deeply, and were always logical and kind and gentle in your response
  • all the cool lights and patterning and creeping/crawling stuff you created for Jean in the cellar (that I got to play with, too)
  • when you'd be asked something like ‘Would you like apple pie or pumpkin pie?’ and you'd answer, with a smile, ‘Yes!’
  • I knew you loved me when you had me wear the steel-toed shoes for mowing the lawn
  • I felt so grown-up when you and Mom trusted me and Rick to take charge when you had to go somewhere for Jean or Mary Ann
I love you so very, very, very much. I cannot imagine there being a better Dad on the entire Earth. Thank you for the lifetime of love and support that I will always hold in my head and in my heart.

your middle child,

Monday, December 10, 2012
I've just about finished the graph of an inverse function.
On to the study of polynomials!

Monday, December 3, 2012
I've finished finding inverse functions (switch input/output names method).
It includes some practice checking that $\,f(f^{-1}(x)) = x\,$ and $\,f^{-1}(f(x)) = x\,$ for a function and its inverse.

Saturday, December 1, 2012
I updated my monthly stats and website income for November.

Friday, November 30, 2012
I've finished the concept discussion for finding inverse functions (switch input/output names method).
I've also updated multiplication so people can practice individual multiplication tables.

Wednesday, November 28, 2012
I've finished finding inverse functions (when there's only one $x$ in the formula).
There are only four different problem types, but there's considerable variability within each of these.

Saturday, November 24, 2012
I've just about finished finding inverse functions (when there's only one $x$ in the formula).

Monday, November 19, 2012
I've just about finished Properties of Inverse Functions.
I'm pleased with my graphics in these last few exercises.

Thursday, November 15, 2012
I've finished ‘Undoing’ a One-to-One Function; Inverse Functions.

Saturday, November 10, 2012
I've almost finished One-to-one Functions.
In the search for Christmas gifts I can make, I found these instructions for crocheted snowflakes, which are beautiful.

Thursday, November 8, 2012
I finished Using a Function Box ‘Backwards’.

Wednesday, November 7, 2012
I finished Writing a Function as a Composition.
Ray helped me with the exercise—he's absolutely amazing!!

Monday, November 5, 2012
I finished Composition of Functions.
The exercise was a bit tricky to randomize—I had to keep my wits about me!

Friday, November 2, 2012
I finished Combining Functions to get New Functions.
I like my graphic for explaining the sum function!

Thursday, November 1, 2012
I updated my monthly stats and website income for October.

Tuesday, October 30, 2012
I finished four different word problems for the exercises in Max/Min Problems Resulting in Quadratic Functions;
it's all I'm going to do for now. I'm considering this a ‘stub’ due to the limited exercises.

Monday, October 29, 2012
I've got the concept discussion done for Max/Min Problems Resulting in Quadratic Functions.
I still need to write the exercises.

Friday, October 26, 2012
I've finished Review of Quadratic Functions: Vertex Form, Max/Min, Intercepts, More.
Most people in PreCalculus are very comfortable with quadratic functions.
This is just a convenient summary of results, with links to earlier sections for people who need more serious review.

Tuesday, October 23, 2012
I've finally finished all the exercises in Extreme Values of Functions (Max/Min).
Took me over a week for this single section.
I learned how to include JSXGraph content directly in ‘newProbDiv
(instead of loading it in a separate window to the side).

My donation button was going to my old email, and a user informed me of this problem. It's fixed!

Thursday, October 18, 2012
(Great day! It's my daughter's birthday!)
What a painful section for me— Extreme Values of Functions (Max/Min).
To talk precisely about extreme values (and locating them) really requires the language of Calculus.
I want to be honest, but illuminating. I really didn't want to talk about the Calculus concepts here.
So, I kept writing, throwing away, rewriting. I'm finally pleased with what I have.

Friday, October 12, 2012
I finished Even and Odd Functions. Enjoy!

Wednesday, October 10, 2012
I ended up putting a lot more graphics in the graphical transformations exercises, which took a long time.
Also, I'm very pleased with my Multi-Step Practice with all the Graphical Transformations.

Thursday, October 4, 2012
All the graphical transformation lessons went very quickly, because the concepts were thoroughly covered in the Algebra II curriculum.
I did get a nice, color-coded-with-the-text graphic in place to illustrate why the counter-intuitive transformations (involving $x$) work the way they do;
take a look at (say) Shifting Graphs Up/Down/Left/Right.

Tuesday, October 2, 2012
I'm on a roll—another quick one! In just one day, I completed a stub for Proportionality Problems.
I also updated my monthly stats and website income for September. My very best month ever! Hooray!
And, I'm experimenting with rotating several Amazon products for my ‘short break’ section.

Monday, October 1, 2012
Finally, a reasonably quick one!
I got a stub up for Direct and Inverse Variation.
The concepts are reasonably complete, but there are limited exercises.

Thursday, September 27, 2012
I seem to be incapable of doing true ‘stubs’.
I keep saying ‘I need to include this...’ and ‘I need to include this...’ and pretty soon the stub isn't so stubby.
This has definitely happened in my newest web exercise, piecewise-defined functions.
After days, I'm finally done with the concept section, and now will put up some very limited exercises.

Sunday, September 23, 2012
Today is my first wedding anniversary, for my marriage to Ray Burns!
It seems I blink, and a year goes by.
My experience has been that time passes more quickly, the older I get.
(I have a theory about this—as you age, each day is a smaller part of your entire life.)

To celebrate, we took a 2-day backpacking trip to the top of Mount Pinal (Arizona).
I love to hike (and have done lots of it), but have always done day hikes.
This time, I carried a 40-pound pack (Ray's was heavier!) and we spent the night camped out near the peak.
This trail hasn't been traveled much recently; there were many sections where we truly had to whack through the bushes.
I really miss big trees (although I am growing quite fond of the Arizona desert vegetation);
Ray chose this hike so that I could be in the trees for a few days.
It was an incredible trip!!

Tuesday, September 18, 2012
I've almost finished Basic Function Models You Must Know;
even though I'm considering this a ‘stub’ since it has very few web exercises, it actually is quite complete in concept discussion.
This one is taking me days to code!

Saturday, September 15, 2012
I've almost finished four stubs in the Precalculus course;
I can do about one stub per day, which is a lot quicker than one complete web exercise per week.
Finding the Domain and Range of a Function
Working with Linear Functions
Reading Information From the Graph of a Function (I love my worksheet in this section!)
Increasing and Decreasing Functions
At this rate, I should have stubs up for the entire Precalculus course in several months, and will then work on filling in common core concepts. The stubs provide an essential concept and limited exercises—they should be useful, even though they are nowhere as complete as my normal web exercises.

Wednesday, September 12, 2012
I finished mapping the Common Core Math Standards to my web exercises.

I've decided to put ‘stubs’ in place for the entire Precalulus course, and for missing Common Core standard content.
The stubs will essentially be my ‘index cards’ from when I've taught the material (where available), with limited graphics, and with very few or no exercises.
Then, I can gradually go back and fill out these stubs to complete web exercises.

Saturday, September 6, 2012
I'm taking a break from Precalculus and creating a document that maps the Common Core Math Standards to my web exercises.
When you Google something like ‘N-RN.1’ there are very few relevant sites that emerge, so there should be good potential here!

Saturday, September 1, 2012
I updated my monthly stats and website income for August.
I now have three problem types (two reciprocal functions, square root function) for the guided practice for More on Difference Quotients, and am leaving it there for now.
I figured out what is often causing the misalignment of sentence words and math in the worksheets—vertical-align:top;.
It seems to happen when there is a horizontal fraction in the sentence.
By changing it to   vertical-align:middle;   the problem is solved.

Thursday, August 30, 2012
I've created some step-by-step guided practice for More on Difference Quotients; this takes a lot of time to code.
Only two problem types so far, but there's more to come.
We've been remodeling a guest house and doing lots of yard work, so web work time has been modest for the past few days.

Thursday, August 24, 2012
I've finished the concept section for More on Difference Quotients.
I included a WolframAlpha widget to show a specified tangent line, and I also went back and put a graphing widget in my Testing Equations for Symmetry exercise. These widgets are easy to make, easy to use, easy to embed in a web page, and incredibly powerful!

Monday, August 21, 2012
Finally finished Testing Equations for Symmetry. Finally!
Hits have started to increase again, as schools are beginning again after summer vacations.

Monday, August 20, 2012
Only one more problem type to go in Testing Equations for Symmetry.
This web exercise has taken me a LONG time to write, because I wanted a lot of variability in the types of equations that could be generated to check for various symmetries.

Tuesday, August 14, 2012
I figured out how to get repeated JSXGraphs in the worksheets in Testing Equations for Symmetry.
In prior exercises, I limited the number of problems on the worksheet so that we were guaranteed to have no repeated problems, since the JSXGraph questions only worked once. Now, I use a global variable to keep track of how many boxes have been created to hold a JSXGraph, and create the box name dynamically. I also figured out how to get functions to work in the worksheets—I write in a ‘JSXGraphFunctions’ string just after ‘headerstring’ So, good progress today, which will be useful in future exercises.

Friday, August 10, 2012
I've finished the concept discussion for Testing Equations for Symmetry.
The JSXGraph spline feature is useful for creating graphs with various symmetries.

Wednesday, August 8, 2012
I finished Sketching Regions in the Coordinate Plane, and am pleased with the JSXGraph problems in the randomly-generated worksheets. It seems to be taking me almost a week for a start-from-scratch exercise that includes a reasonable amount of graphics and JSXGraph; at that rate, it will take me close to three years to finish the Precalculus curriculum. So, I certainly hope I get more time to work and/or get faster!

Tuesday, August 7, 2012
I'm almost finished with Sketching Regions in the Coordinate Plane; I just need to incorporate the JSXGraph exercises into the worksheet.

After almost two weeks, I haven't gotten even one purchase for the song I highlighted on the tops of my pages and the ‘need a short break’ section. Maybe a math item will work better! So, I'm now trying the QED book.

Friday, August 3, 2012
I've finished the concept discussion for Sketching Regions in the Coordinate Plane.
I've written three little Javascripts functions to use for easily constructing regions, which will be useful in the web exercises.

Wednesday, August 1, 2012
I finished another quick web exercise, Distance Between Points; the Midpoint Formula.
I also updated my monthly stats and website income for July.

Thursday, July 26, 2012
I've just about finished Review of Lines and Slopes of Lines.
I just need to finish the exercises.

I spent the morning figuring out how to put a little Amazon ad at the TOP of my pages, with a link to things I love.
This gives a bit of color at the top of the pages.
I'm thinking that many visitors never get to the bottom of the concept section, where I typically put my ‘need a short break’ plug for support.
Ah, the never-ending-battle to improve my income from this site!

Wednesday, July 25, 2012
I've finished Circles and the ‘Completing the Square’ Technique.
I took a lot of exercises from two existing web exercises, tweaked them and combined cases to make them more level-appropriate.
I also wrote a new case, which shows the graph of a circle and asks for its equation, using JSXGraph. I like it!

On a web exercise like this, I could merely refer to existing exercises, and move on. This would go MUCH quicker, and allow me to get to new content faster.
I think I'll continue to have a mix—sometimes I just refer to earlier exercises, sometimes I provide a summary.

Monday, July 23, 2012
Oh, I had forgotten how tricky it is to get the JSXGraph stuff working in the dynamically-created worksheets.
The javascript has to be written AFTER the div that will hold it, which means it must be part of the string that is written to the window.
Then, because I've got a string within a string, backslashes get complicated: for example, \strut must actually be encoded as \\\\strut.
And there's other tricky stuff, too. I just spent hours trying to get a segment to appear, and scratching my head about why things just weren't working!

Saturday, July 21, 2012
I've now got 22 different problem types for Absolute Value as Distance Between Two Numbers.
Haven't yet implemented the worksheet—this is going to be tricky, since I'll have to figure out how to get the JSXGraph functions working when I dynamically write a new page.

So far, I've highlighted ‘the Dot and the Line’ and ‘Veggie Tales’ on the bottoms of my pages, but haven't had even one purchase for a highlighted item. I was so hopeful! Of course, the only people who will see these ads are those who make it through the entire lesson—but I really don't want to clutter up the top of the page with ad stuff.

Tuesday, July 17, 2012
I'm working on Absolute Value as Distance Between Two Numbers.
Notice, at the bottom, that I've changed my "Need A Short Break?" function, to include an advertisement for one of my favorite books, from Amazon, with a picture.
This same ad will appear at the bottom of every one of my web exercise pages.
It adds a splash of color to each page, and maybe some of my users will buy some of my favorite books!

I also put a new email for me on the web—for now, my verizon email (in image form, to prevent email spidering).

Thursday, July 12, 2012
I finished the exercises on my last Test Point web exercise. Hooray!

Lost my hotmail account—there was fraudulent use—someone used my account to send out a bunch of spam.
Unfortunately, I was totally negligent and had an obsolete email as my alternate contact—and there's no way to change it so that I can get the code from Google that's needed to unblock my account.
Sigh. Sigh. Sigh.
So, I'll likely need to get a new email, and then spend days correcting the multitude of places on the web (and in my life) which have the old address.
Sigh sigh sigh.

I've also changed my ‘Need a short break?’ code at the bottom of each page to include a link to my Web Site Earnings page.
I'm just hopeful that if people see how much time I've put into this site, and how little I'm making from it, then maybe they'll feel charitable and support my work. (I'm such a dreamer...)

And, I've finished another web exercise, Absolute Value as Distance From Zero.
This one was really fast, because it referred to and drew on content that I already had.

Tuesday, July 10, 2012
I decided to write one more Test Point web exercise, which summarizes and gives more practice.
I've finished the concept discussion, but still need to write the exercises.

I seem to be getting a smidgeon more Amazon orders, since I now have a few links to my Web Site Earnings page.
So, I've now added this link in, just to the right of the online exercises, on about a half dozen of my most popular pages.
We'll see if this translates into any more income!

Wednesday, July 4, 2012
I finished all the exercises for my second Test Point web exercise.
Now, I can go on to absolute value (which should be much quicker)—hooray!

Tuesday, July 3, 2012
Finished the first Test Point web exercise—finally!
Not quite the variety of exercises I eventually want, but I need to keep progressing.
This is good enough for now.

I also got the concept discussion done for the second Test Point web exercise—this went incredibly fast, after all the work I did on the first one!

Saturday, June 30, 2012
I decided to add in dynamic JSXGraph graphs for the exercises, and create more problem types, for the first Test Point web exercise. I had a lot of trouble getting the dynamic graphs to work—still not exactly sure what was going wrong (I think it was a global versus local variable issue). So, lots of time wasted this morning—sigh. But, at least I've now got some dynamic graphs in place!

Wednesday, June 27, 2012
I've finally finished my first Test Point web exercise.
I spent a long time writing a general function for creating arbitrary expressions involving polynomials, trigonometric functions, logarithmic functions, roots, and absolute values.
I've now put this into my ‘javascript utility function’ collection, and it will likely be used a lot in the future!
There isn't as much variety as I'd like for test point problems, but these take a long time to code, and I want to keep making progress.

Saturday, June 23, 2012
I've finished Solving Nonlinear Inequalities in One Variable (Introduction).
I'll be glad to be done with these ‘test point’ exercises!

Friday, June 22, 2012
I had a two-week visit to Massachusetts; a couple of my new children got a chance to meet some of their relatives!
I didn't get any web-work done during this visit.
I've almost finished with Solving Nonlinear Inequalities in One Variable (Introduction).
It's taking me a long time to decide how best to talk about the test point method(s).

Tuesday, June 5, 2012
I've finished the third section in my new online Precalculus course: Solving Linear Inequalities in One Variable.
I also created an outline for the entire Precalculus course. There will likely be about 150 web exercises, when it's all done!

I also updated my monthly stats for May.

Thursday, May 31, 2012
I've finished the first couple sections in my new online Precalculus course:
Prerequisites: Language of Mathematics Essentials and Prerequisities: Function Review; Difference Quotients.
I'm spending mornings at my daughter's place working on my website, and afternoons and evenings with my family. It's working out great!

Monday, May 28, 2012
I'm now down living in Tucson full-time, with my new family!
I've begun an online Precalculus course, based on the course I taught for many years at Miss Hall's School (Pittsfield, Massachusetts).

Tuesday, May 1, 2012
I updated my monthly stats for April.
I'm working on a new Mixed Integration Practice web exercise. My students are having a series of short quizzes on mixed integration problems this week.
Things are very busy with the end-of-term!

Tuesday, April 24, 2012
Hooray! I've finally finished my Differentiation Formula Practice web exercise.
I've spent about 25 hours on this web exercise—it has 48 different problem types, with lots of variability within each type.
Took a long time, but I'm pleased with the result!

I've tried putting a link to my 15-second Amazon video in the blank space to the right of the form where students click-click-click to do online exercises.
I'm hoping it might be a bit more visible there.
The topic of ‘if I make money on this web site’ came up during office hours the other day,
and I was informed that those students never even remember seeing my Amazon link—so it clearly isn't working where it is!
I've tried to not bombard my users with ads and requests for support.
But, there needs to be a happy compromise—something that works for my users, and something that works for me.
Since I'm again leaving a full-time (paying) job, I need to come up with a way that my web site can generate some meaningful income.

Wednesday, April 19, 2012
I finished some more problem types for Differentiation Formula Practice.
I've probably spent about 12 hours so far on this web exercise, and I'm still only through the Simple Power Rule for differentiation!

Wednesday, April 18, 2012
I got more problem types done for Differentiation Formula Practice.
Still lots to go, though.
On my daily walk, I also ran into a former student from Miss Hall's School, who is living here in Flagstaff!!

Tuesday, April 17, 2012
I got a lot more problem types done for Differentiation Formula Practice.
I want to finish this, before coding an exercise on mixed integration practice.

Tuesday, April 10, 2012
I have finally finished Mixed Differentiation Practice (strict parentheses version). Took way too long!

Thursday, March 29, 2012
I removed the header line about my pages ‘working best in Safari and Chrome’—my hits have been down this month, and I'm wondering if people with other browsers are being scared away. Also, my pages have been very slow loading for weeks now—I've had to resort to ‘the old method’ of writing hand-written notes on the board during class several times. I've contacted my server to see if they have any insights on what is causing this poor performance. I'm averaging about 4000 unique visitors per day these days—has the load on the server gotten large enough that it is no longer handled well?

Wednesday, March 7, 2012
I saw this black soloist, Alex Boye, perform live, with the Mormon Tabernacle Choir. He was amazing!!!
Here, he is becoming an American citizen, and was asked—impromptu—to sing the national anthem. Very moving!

And, this is a fun riddle I got from one of my students today:
Why do computer science majors mix up Halloween and Christmas?
Answer: Because OCT 31 (octal 31) is the same as DEC 25 (decimal 25)

Thursday, March 1, 2012
I've added some Bolero videos to my Beginner Dance Links.
I updated my monthly stats for February.

Tuesday, February 28, 2012
Ray sent me this link that he came across: Finite Simple Group (of Order Two), the Klein Four Group.
It's wonderful!! (I like to put things like this on my blog, so I don't lose track of them.)

Friday, February 24, 2012
Just updated my testimonials page; I've gotten some beautiful emails recently, but my life has been so crazy that I didn't have the presence to ask if I could use them online. So, I feel good about getting this new one up.

I'm making good progress on this Mixed Differentiation Practice exercise.

Thursday, February 23, 2012
I've just got to share this link of Jackie Evancho singing ‘To Believe’.
So beautiful! I don't want to lose track of this link. It's hard for me to believe that this sound can come out of such a young girl.
Anyways, it's a beautiful song, a beautiful message, and it's very powerful delivered by this little girl.

Thursday, February 16, 2012
I finished my third calculus web exercise, Basic Differentiation Shortcuts.
I'm wondering if I should put a notice on each page, saying something like
‘these pages are best viewed in Chrome or Safari’.
There are just a lot of bugs in Firefox; and, without MathPlayer, things are painfully slow in IE.

Tuesday, February 7, 2012
I finished my second calculus web exercise, Introduction to Limits.
This is now the first exercise where I have randomly-generated JSXGraph graphics in the randomly-generated worksheets.
This is a LOT of work; I can't use functions that generate JSXGraph code from the main page when creating the worksheet, which is a real pain.

Thursday, February 2, 2012
I got a good start to my second calculus web exercise, Introduction to Limits.
It's still really slow going; I love JSXGraph, but it takes me a long time to get the graphics right.
I need to write lots more problems for this exercise!

Wednesday, February 1, 2012
Rabbit, rabbit, everyone!
No one in any of my three classes here at NAU knew about the ‘rabbit, rabbit’ tradition—perhaps it's more of an east coast thing?
I updated my monthly stats for January, and also did my archiving for 2011. January was a record month, both for hits and for income. Woo hoo!

Thursday, January 19, 2012
A belated Happy New Year to everyone!
Well, I've finally begun my Calculus curriculum!
I have a fantastic schedule this term, so I hope to be able to write one to two web exercises per week.
The first one, Average Rate of Change, took me forever (and it's still far from complete)—I haven't worked on web exercises in many months, and have forgotten lots of stuff.
Hopefully, future ones will go more quickly now.
Also, I put up the first “video’ of me talking about an index card, to see how this works for my students.

Blog Archive, 2011
Blog Archive, 2010
Blog Archive, 2009
Blog Archive, 2008
Blog Archive, 2007
Blog Archive, 2006
Blog Archive, 2005