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).

Friday, December 31, 2010
Updated Basic Models You Must Know
(including three GeoGebra files).
Happy New Year, everyone!

Wednesday, December 29, 2010
I've now completed 164 sequencing updates in Algebra I,
which finishes the job! Woo hoo!
No matter what Algebra I page someone lands on,
they'll know where there are in the entire sequence,
and they'll have easy links to related exercises.
Now, I can really get to work on Algebra II.

Monday, December 27, 2010
I've now completed 120 sequencing updates in Algebra I.

Sunday, December 26, 2010
I've now completed 90 sequencing updates in Algebra I.
Going thru my entire Algebra I course helps me to appreciate ‘big’ numbers.
Even though each sequencing update only takes about ten minutes, $\,10\cdot 164 = 1640\text{ minutes} \approx 27\text{ hours}\,$ is a lot of time.
I'm dying to finish this up so I can make some real progress in Algebra II!

The last few days have been busy with holiday celebrations, getting in four truckloads of wood,
and renters coming/going (so lots of house-cleaning).
Not very many people are doing math on my site these last few days,
so I hope you're all having joyous times with your families and loved ones.

Friday, December 24, 2010
I've now completed 74 sequencing updates in Algebra I.
(I don't like having mixed styles in the Algebra I course,
so I'm working hard to finish this up.)
Merry Christmas Eve, everyone!

Thursday, December 23, 2010
Updated Graphs of Functions
(including two GeoGebra files).
This was a long one.

I've now completed 45 sequencing updates in Algebra I.

Wednesday, December 22, 2010
Yesterday I visited a colleague in Connecticut.
Updated Compound Interest Formula.

I've now completed 40 sequencing updates in Algebra I.

Monday, December 20, 2010
Greg's memorial service yesterday was an incredible tribute to his life.
The place was packed—not even any standing room, with a line outside the building.
Likely in excess of $\,350\,$ people.
At the end of the ceremony, all the fire/EMT people's pagers went off,
and the broadcaster said “this is Greg Finger's last call”.
It was a powerful and moving moment.
There was a procession of fire trucks, EMT vehicles, family, friends to the reception,
with police at every intersection stopping the traffic.

I've now completed 30 sequencing updates in Algebra I.

Sunday, December 19, 2010
Greg's funeral is today.
It will be a celebration of his life.

Did two more sequencing updates in Algebra I.

Saturday, December 18, 2010
I created a background for my concept discussion section
that has exactly the same texture as the page background,
and has the color (#EFEFEF) of my exercise divs.
So, I've finally made the leap to a ‘white’ background for the concept discussions!
This will be incorporated as I put in the sequencing info.

Have now completed twenty sequencing updates in Algebra I.

Updated Loans and Investments.
Did a major expansion of the concept section.

Friday, December 17, 2010
Sunday is the funeral service for my husbandnot's brother, Gregory H. Finger.
Here is the New York Times obituary submitted by the Center for Constitutional Rights.
(Also see Monday, December 13, below.)

I'm going to try and put in 5–10 sequencing updates in Algebra I each day,
and do one Algebra II update each day.
I'm switching to a new auxiliary file and CSS styling file as I update.

In Basic Addition Practice, the concept exercise box was waaayyy too big,
just to account for one problem type that had a big table.
So, I made that table appear to the right, using relative positioning, on demand. Much better!!

Updated Arithmetic and Geometric Sequences.

Thursday, December 16, 2010
Once again, Robert Fant has made me aware of a cool thing out there on the web:   JeopardyLabs
(Robert is amazing at locating high-quality, fun, math stuff.)
He's figuring out how to incorporate MathJax in the questions.
You can create your own Jeopardy game. Give it a try!

I may just remove my StatCounter from my pages, altogether.
I think it's slowing the page loads, and it isn't worth it,
since I can see some daily stats at my server's AwStats.
And, the stats I post each month come from AwStats, not StatCounter.
And, I spend way too much time looking at my StatCounter stats!

I tweaked my top header to look a bit nicer, based on the work with my daughter (thank you Julia!).
As I do the final updates (incorporating sequencing information) on Algebra I,
and as I now begin my Algebra II updates, I'm switching to this style:
Expressions versus Sentences
This moves the ads to the very top, gets my logo in, and moves my non-math personal links to the bottom.
It also has fixed width (about 1000 pixels) so I'm guaranteed that everyone will see the same arrangement.
On very small screen resolutions, they'll have to scroll to get to the right-most search box.

Plus, I learned about JQuery today (since the Jeopardy game uses it).
I'm definitely going to be checking it out!!

Also did my first update in Algebra II:   Introduction to Recursion and Sequences.
Productive day!

Wednesday, December 15, 2010
My selectric typewriter is fixed!
This is very sentimental to me—when I was a student, I typed loads of math papers and dissertations.
I've even got custom math elements.
And I learned something—it won't even turn on if its too cold!
(I had to get it upstairs, wrap it in a blanket, and let it warm up before it would work.)

What is in the air?
Yesterday, Firefox was broken.
Today, my StatCounter is down; since it wouldn't load, the math wouldn't either.
I removed my counter until I can tell if StatCounter is back up.

My daughter Julia is helping me re-design the format of my pages.
We're trying to clean up the top, and make the main content easier to find.
This is a good time to do it, since I need to go through every file again to incorporate the sequencing information.
Take a look at the new concept: (revised) Expressions versus Sentences

Tuesday, December 14, 2010
Discovered a problem today with the math fonts in Firefox.
I uploaded the new font folder, as they required, but initially the problem was not resolved.
It ended up that Firefox was using my old (cached) fonts,
and I had to clear the cache to force it to get the new ones from the server:
Tools—Clear Recent History—(make sure that ‘Cache’ is checked)
Some of my regular users may have to do the same thing.

Updated Domain and Range of a Function.
Last web exercise in the Algebra I course! Woo hoo!
This one took a long time, with 28 very MathML-intensive cases.
Now, I need to go back and put in indicators about where each exercise is in the entire sequenced course,
together with ‘forward’ links—from each exercise to the next one.
Then, on to Algebra II updates!

Monday, December 13, 2010
My husbandnot's brother, Greg Finger, died today.
He had been battling pancreatic cancer for about two years.
Greg gave in a way that people knew was not about him, but about them.
He didn't give to get anything in return.
He leaves many people with a hole in their heart.

Sunday, December 12, 2010
Updated More Practice with Function Notation.

Have been playing with a concept for showing people where they are in the Algebra I course,
and offering forward/back movements: Look at the bottom of the page.
It's still too busy. I do, however, want to make people aware that they are in the midst of an entire sequenced course.
Maybe I can just say something like: “this is exercise #2 of 170 in this online Algebra I course”.

Saturday, December 11, 2010
My first day (yesterday) of standing (instead of sitting) to work was successful.
Already, my legs are feeling better—less of the ‘pinched nerve’ sensation.
Must admit that I woke this morning thinking “oh boy—I need to stand to work all day”,
but I immediately caught this negative self-talk.
(I'm a big believer in the benefits of positive self-talk, and the detriments of negative self-talk.)
So, I replaced it with things like:
  • I get to stand while working today!
  • No negative leg-circulation issues for me today!
  • I'll burn a lot of calories today while standing!
  • I get to reinforce a new habit today, that will make me healthier for my lifetime!
(Such things, said with enthusiasm, really do help me.)

Updated Introduction to Functions.
I'm two exercises away from finishing the update of my Algebra I course!

My online survey told me that my users want Algebra II updated next, instead of Geometry.

I also finished sewing the names ‘Don Paquito’ and ‘Kitsa’ on two kitty stockings. This took a looonnnggg time.
Now, I'm just about ready to get my daughter's Christmas care package in the mail!

Friday, December 10, 2010
While teaching, I used to stand a lot.
I'd be actively teaching anywhere from three to five hours in a typical day.
And, I wasn't a passive teacher. I'd move. I'd bend. I'd talk with my hands and arms.

So, the biggest change since I left teaching at the end of the 2008–2009 school year
to pursue math-on-the-web fulltime has been that now—I sit a lot.
I typically sit and work on my web site from six to ten hours a day, six to seven days a week.
I'm noticing things that I don't like, and I suspect that all this sitting may be the culprit.

The main thing is that my legs are often feeling like the circulation isn't great—like nerves are slightly pinched.
Also, I'm beginning to have some minor back issues again, after decades without any problems at all.

I'm a big believer in catching things early, before they escalate to a big problem.
So today I'm embarking on a new journey—standing instead of sitting while I work.
Over the next few weeks, I'll let you know how this is going for me, via this blog.

Since leaving teaching, I've walked a lot more, since I now have time—about $\,3\,$ to $\,4\,$ miles each day.
(This may be why it took so long for all the extra sitting to catch up with me.)
Now that winter has hit, though, that's going to die way down, since frigid walks are nowhere near as enjoyable for me.
Now, I do shorter jaunts with Jesse (our dog)—up to Karl's house, down thru the woods, repeat if not chilled-to-the-bone.

So, I'm now standing downstairs, in the living room, instead of sitting in my upstairs office.
I took about fifteen minutes trying to figure out a good height for my laptop.
The height that's most comfortable for me to type is a bit too low for me to see the screen well.
The height that's most comfortable for me to see the screen well is a bit too high for me to type easily.
(Ah hah. If this standing-while-working thing catches on, I see a new market for screens separate from keyboards.)
I seem to have a good compromise now. I'm making good use of a few dictionaries and atlases as props.

So, in the first hour I've taken to write this entry, I'm feeling great.
It's easy to wiggle my hips from side to side. I can walk in place.
I actually feel energized to go out into the cold and walk.
So, I think I'll take an early break, upload this, do a loop with Jesse, stack fifty pieces of wood,
and then come back and get to work on my daily web exercise update.

11:00AM update:
Another advantage is readily becoming apparent.
Jesse (our golden retriever) has a habit of coming over, putting her head under my typing arm, and lifting my arm off the keyboard.
She wants attention. She can't just talk to me.
But, it drives me crazy (particularly when I'm coding).
While I'm standing, she can't do it. My typing arm is too high.
She can come and stand by me, and I rigorously rub her head and tell her what a good kid she is. Yeh!

Updated Parallel and Perpendicular Lines.
Did a minor expansion of the concept section;
decided this was a good opportunity to review some mathematical words.

I also improved my ‘toggle’ function, so it can more easily be used for several divs on the same page.

Thursday, December 9, 2010
Updated Horizontal and Vertical Lines.
Did a minor expansion of the concept section.

Also, updated the code for my Google Search Engine yesterday, to Google Custom Search.
Evidently I was still using an old version.

Wednesday, December 8, 2010
Updated Point-Slope Form.
Again did a major expansion of the concept section.

I also began a brand-new web exercise, prompted by a user's question: More on Multiples.
Haven't yet coded the exercise part, but thought I'd at least get the concept part up and being “spidered” by search engines.

Monday, December 6, 2010
Updated Finding Equations of Lines.

Sunday, December 5, 2010
Updated Graphing Lines.
Again, I did a major expansion of the concept section.
Eventully, I need to return and add a lot more variability to the web exercise.

Saturday, December 4, 2010
Finished updating Practice with Slope.
After many rewrites, I'm finally pleased with it, except that it's pretty long.
However, I've put in a link so people can avoid the conceptual discussion,
and jump right to the slope formula and how to use it.

The rest of today will be shopping, dump trip,
visiting an art exhibit of a friend, and starting my Christmas baking!

Friday, December 3, 2010
The ‘Practice With Slope’ update is going very slowly.
I'm really struggling with the expansion of the concept section.
Again, this section is going to end up being too long—eventually, I'll need to break it into two pieces.
I should have it done by the end of tomorrow.

Thursday, December 2, 2010
Updated Introduction to the Slope of a Line.
Did a major expansion of the concept discussion.

I also went through many of my “Fun Stuff” links in the right column of my Algebra I curriculum,
since I haven't checked them in a long time.
Got rid of some dead links, and some that didn't work in Safari.
In particular, I updated Chocolate math and How Does Chocolate Math Work?,
so that I'll never need to update them again to adjust for the year!

Wednesday, December 1, 2010
Put up my new monthly statistics for November 2010.

Updated Introduction to Equations and Inequalities in Two Variables.
Did a major expansion of the concept discussion.
I think the section is a bit too long now—may break into two smaller pieces at some future point.

Tuesday, November 30, 2010
Updated the Midpoint Formula.
The overline command (for putting a bar over a line segment) (still) isn't working properly in Internet Explorer,
but it is now working in Firefox. Progress!

Monday, November 29, 2010
Updated the Distance Formula.

Sunday, November 28, 2010
Updated Practice with Points.
Did a major expansion of the concept discussion,
including talking about reflecting points about lines;
it took a long time.

Also, finished updating my SAT math prep.

Friday, November 26, 2010
Updated Locating Points in Quadrants and on Axes.

Thursday, November 25, 2010
Happy Thanksgiving, everyone!

(We had ours early, so this is just a normal work day for me.
But, from my hits thus far, looks like I'm just about the only one doing any math today!)

Updated More Problems Involving Percent Increase and Decrease.
Expanded the concept discussion considerably, and put in more explanation when reporting solutions.
In the middle, I put a tiny “Need a break?” link.
I'm continuing my efforts to get people to my Fun Facts/Amazon page!
I actually think they'll have fun learning about me!

I also finished updating the web exercise for SAT #1.
Forty-nine cases! Took a while!

Wednesday, November 24, 2010
Hits are down this week, with the Thanksgiving holiday.

Updated Problems Involving Percent Increase and Decrease.
Expanded the concept discussion considerably, and put in more explanation when reporting solutions.
Just passed the $\,150\,$ mark on my MathJax updates!
I'm on schedule to finish Algebra I in early December.

I also updated a bunch of my SAT and MTEL (Massachusetts Teacher's Educator License) pages;
these are all available from my Main Table of Contents.
(I'm not yet finished updating the SAT stuff.)

Tuesday, November 23, 2010
Updated Writing Expressions Involving Percent Increase and Decrease.
Added a timing feature, which it didn't have.
Added variability to the exercise: instead of always using the variable $\,x\,,$ now a letter is randomly chosen.

After three very low AdSense days, I've moved my Fun Fact to the bottom of the page.
This makes the top a lot less cluttered.

Changed from MathML to TeX syntax in Two Special Triangles.
I think that now, all my exercises are coded with TeX syntax.
(This way, if I decide to load some math via my auxiliary file, it will be translated correctly in all my files.)

Monday, November 22, 2010
Changed from MathML to TeX syntax in Probability Tree Diagrams.

Aaarrrgggh. Someone is using the “math cat fisher” phrase
for one of those incredibly annoying “sell” sites where they won't let you close the window;
I had to close my entire browser.
I wish I knew a place to report unethical web behavior like this.
People must have the ability to find commonly-typed search phrases,
and then somehow hack their way into getting high on Google's list with these phrases.
I guess, as my site gets more popular, this is one of the consequences;
people want to try and steal traffic.

Updated Adding and Subtracting Fractions with Variables.

I can't figure out AdSense.
Since I put my random Fun Fact on each page, I've had my lowest AdSense income yet.
(For example, a whopping ten cents yesterday.)
There's no Amazon code there, so that shouldn't be a conflict.

Sunday, November 21, 2010
Yesterday was my family's “early Thanksgiving” (so no web work done).

Started off today by changing my above-main-title div to show a random Fun Fact about me.
(The words “FUN FACT” have randomly-generated colors on each page load.)
I want my users to get to know me a bit, even if they never make it to my Amazon/Fun Facts page.

I put in dynamic graphs that show puncture points
and horizontal/vertical asymptotes for Multiplying and Dividing Fractions with Variables.
This was very slow and tedious; spent about ten hours working on it today.
I had to do tests to make sure the puncture point is visible in the graphing window.
(I've decided that I don't want the horizontal and vertical axis scales changing from problem to problem.)
I also switched from MathML to TeX syntax.

Friday, November 19, 2010
Updated Solving More Complicated Quadratic Equations by Factoring.

Thursday, November 18, 2010
Updated Factoring Trinomials of the form $\,ax^2 + bx + c\,$.
Did a major expansion of the concept discussion and examples;
added both dynamic graphics and a timing feature.

I also wrote up a proof of the “factor by grouping” method, for more advanced readers.

Wednesday, November 17, 2010
Updated Solving Simple Quadratic Equations by Factoring.
Expanded the concept discussion and examples, and added dynamic graphics to the web exercise.

Also, it was a very exciting day for me—I got a web donation!!
It was soooo exciting to see the “Notification of Donation Received” in my email inbox!!

Tuesday, November 16, 2010
Updated Identifying Quadratic Equations.
Expanded the concept discussion and discussion of examples.
Also, added the timing feature (which it didn't have).

Went back and changed from MathML to TeX syntax in the Geometry “Perimeters and Areas of Similar Polygons” exercise.
I also expanded the concept discussion considerably.

Monday, November 15, 2010
Had jury duty, so didn't have a full work day.
Put up my “formula” link to the Amazon stuff.
(I thought it was working a bit better than just the text, but not really. Sigh.)
Since it's coded in TeX syntax, it didn't work in the handful of exercises
(all in Geometry and Algebra II) that I had left coded with MathML.
So, I'm going back and re-coding these few exercises in TeX syntax:
Quadrilaterals, Area Formulas, more tomorrow...

Sunday, November 14, 2010
Updated Factoring Trinomials, All Mixed Up.
Expanded the concept discussion and discussion of examples.

Saturday, November 13, 2010
Updated Factoring Trinomials of the form $\,x^2 + bx + c\,,$ where $\,c\lt 0$.
Expanded the concept discussion and discussion of examples.

I moved my “Get to Know the Teacher” stuff onto a separate page;
it's the ONLY page that has Amazon affiliate advertising on it.
There's a link from each of my content pages to this new page.
The content pages are back to a cleaner look, without the stuff at the bottom.

Friday, November 12, 2010
Adjusted my code—when someone clicks the “Get To Know the Teacher” link at the top of the page,
the “Get to know the teacher” button will automatically get the focus (be highlighted),
which will hopefully draw attention to it.

Updated Factoring Trinomials of the form $\,x^2 + bx + c\,,$ where $\,c\gt 0$.
Expanded the concept discussion and discussion of examples.

Thursday, November 11, 2010
Firefox seems to have fixed its “stretchy” problems! YEHH!!!!!
Now, fractions under radicals look right.
My overbraces and overtexts look right.

Updated Basic Concepts involved in Factoring Trinomials.
Expanded the concept discussion considerably, putting in number line interpretations of the key facts.

Wednesday, November 10, 2010
Yesterday, I installed a button to cycle through all the Amazon.com affiliate products (independent of the “get to know me” blurbs).

In honor of K's birthday (his number is the second Google number),
I got the reporting of my very first Amazon.com income today!
78¢, on three small purchases. It's a start!
Learned that we only get “advertising fees” credited after items have shipped.

Updated Word Problems involving Perfect Squares.
This one took a long time.
Only had a partial day yesterday, with Nielsen Lane cleaning, visit to Dad, and also a visit to my sister.

Monday, November 8, 2010
Switched all my bottom-of-the-page offerings over to the Amazon.com affiliate program.
I like the uniformity of the Amazon “link” style in the right column.
Have put in a bunch of my favorite kid's books, some music, movies, more.
Updated Solving More Complicated Equations involving Perfect Squares.

Sunday, November 7, 2010
Discovered the Amazon affiliate program yesterday, and joined.
I created a little button to let users browse thru some of our favorite kid's books (and buy them at Amazon).

Updated Solving Simple Equations involving Perfect Squares.

Saturday, November 6, 2010
Updated Factoring a Difference of Squares.
Expanded the concept discussion considerably, and added more variety to the web exercise.

Friday, November 5, 2010
Updated Writing Expressions in the Form $\,A^2\,$.

And, I re-did all my affiliate ads in text versions again (after trying out the banner concept yesterday).
I think the text looks more professional, and is better suited to my site.

Thursday, November 4, 2010
Put up my monthly stats for October 2010.
Really unusual flip-flop of stats this month—it's not a typo.
I kept checking and re-checking to see that I was looking at the correct figures.
Into November now, I've checked back, and things are normal again. Weird.

Updated Identifying Perfect Squares.

Wednesday, November 3, 2010
Changed the button name to “Get to Know The Teacher” at the bottom of each of my pages;
added a bunch more pieces of info about me.
Also, moved the link to this button to the top left, instead of the top right.

Updated Solving Absolute Value Sentences, All Types.

Tuesday, November 2, 2010
I put a “Get to Know Me” button at the bottom of each of my pages;
incorporated the affiliate advertising merchants into this same structure.
I think that people learn better if they have some connection with the teacher.
Also, I'm hoping that people might be more inclined to support my work
if they “know me” on some human level.

Updated Solving Absolute Value Inequalities Involving “Greater Than”.
Expanded the concept discussion considerably; added dynamic graphs.

Sunday, October 31, 2010
Updated Solving Absolute Value Inequalities Involving “Less Than”.
Expanded the concept discussion considerably; added dynamic graphs.

I'll be glad when I'm finished with this absolute value bunch of exercises.
They're tedious and they take a long time to update because there are many cases.

Saturday, October 30, 2010
Updated Solving Absolute Value Sentences.
Expanded the concept discussion considerably; added dynamic graphs.

I had to be really careful with my parameters with the JSXGraph graphs.
It ends up that if the $y$-intercept of an absolute value graph isn't in the viewing window, then the graph doesn't display at all.
(It took me a long time to figure out what was going on here!)

Friday, October 29, 2010
Updated Solving Sentences Involving “Plus or Minus”.
Expanded the concept discussion considerably; added dynamic graphs.

Also created a button so that users can “cycle through” my affiliate ads.
Right now, I've located them at the bottom of my pages, below the web exercise:
I suspect that many people won't ever see them there, though.

Thursday, October 28, 2010
I'm always wanting to paste the (say) next-to-last thing I had on my clipboard, which is of course no longer there.
Just discovered JumpCut. It keeps a stack of recent clips available to be pasted. Easy-to-use, simple interface, wonderful!

First day with my new StatCounter has gone well.
Customer support responded quickly, letting me know how I can get hold of some hourly data—you have to dig down a bit into the menus, but it's available.
It will take me a while to get comfortable with the new interface, but there's a lot more functionality than SiteMeter had, so I think it will work well for me.

Also checked out an affiliate program called ShareASale.
(I've been looking for such a thing for months, but didn't have the right word—affiliate—to google!)
This allows me to have more control over the advertisers on my site—to choose products that I believe in, and to be able to share with my users why I believe in them.
I've been accepted for their program, and I put my first merchant advertisement (WyzAnt) online!

Updated Solving Simple Absolute Value Sentences.
Added dynamic graphs to help users visualize the solution sets.
Put in a feature that I should use a lot more: on the worksheet, you're guaranteed to get different types of problems if you want less than or equal to the number of different cases.

Wednesday, October 27, 2010
Updated Simplifying Basic Absolute Value Expressions.

MOST IMPORTANTLY, I've switched my counter to StatCounter.com.
I was having a lot of trouble with sluggish-loading pages, and I kept noticing this dg.specificclick.net showing up.
A bit of web searching showed me that this was a serious problem with the SiteMeter site.
So, after all these years, I've switched to a counter that appears to be highly recommended.
Already, I'm seeing that my pages are loading much faster. Yeh!

I was able to keep settings similar to my previous counter:
if thirty minutes or more has elapsed since a visitor last visited a page on my website,
then that visitor is considered unique and my counter is incremented.
So, my counter isn't increasing for each page view, it's only increasing for each unique visitor (as defined here).
I started my unique visitors at 311,735 (the count when I installed the code).
(Set the page views to the same figure.)

Also updated Determining the Sign (positive or negative) of Absolute Value Expressions.
Added more variability to the questions.

Tuesday, October 26, 2010
Updated Solving Linear Inequalities with Integer Coefficients and
Solving Linear Inequalities Involving Fractions.
Added dynamic JSXGraph graphs.
Also went back to all the “solving linear equation” exercises and put in a dashed line
that follows the intersection point back to the $\,x\,$-axis, to make it easier to visualize the solution.

I also created a new web exercise:   Solving Linear Inequalities, All Mixed Up.

Monday, October 25, 2010
Used JSXGraph to put dynamic graphs into the updated exercise Solving Simple Linear Inequalities with Integer Coefficients.
Also, put a dashed line that follows the intersection point back to the $\,x\,$-axis, to make it easier to visualize the solution set.

Sunday, October 24, 2010
Updated Simple Word Problems resulting in Linear Equations and
Solving Simple Linear Inequalities with Integer Coefficients.
The first one took a long time.
I found it quickest to search for all the MathML entities, like <m:math>, and replace them with empty space.
Then, I went back in and inserted the correct MathJax delimiters and adjusted the code to TeX syntax.

Went back through all my web exercises, and replaced the “is equivalent to” symbol with \text{&#8660;} inside math mode.
It's really too short, but at least it looks reasonably okay in all major browsers.
This is my biggest compatibility problem so far.

Saturday, October 23, 2010
Wrote a brand-new exercise:
Don't Mix Up $\,3x\,$ Versus $\,x^3\,$!

Also, took out all the “Multi-Section Quizzes” from the Algebra I Table of Contents (since they're not updated to MathJax).

Friday, October 22, 2010
Updated Solving Linear Equations involving Fractions
and Solving Linear Equations, all mixed up.
I changed from MathML to TeX syntax, and added the key-in answer and timing features.

Thursday, October 21, 2010
Found a free, 2-dimensional, floor plan designer that is better for my needs than Google SketchUp: floorplanner.com.
Nice video tutorials to get you started; very user-friendly and easy to use.

Updated Solving Simple Linear Equations with Integer Coefficients and
Solving More Complicated Linear Equations with Integer Coefficients.
Used JSXGraph to get an (optional) graph of the left and right sides of the equation.
I love JSXGraph!! This is so cool, and it was so easy!!

IE behaved differently than everyone else; it was displaying the graphs even when I turned them off.
I fixed it (on an earlier web exercise, also) by using an “if” statement to avoid any JSXGraph call when the graph window is toggled off.

Wednesday, October 20, 2010
Updated Finding the Greatest Common Factor of Variable Expressions and Factoring out the Greatest Common Factor.

I'm already getting used to the advertising banner at the top; it's not as bad as I thought it would be.
We'll see if any of my users write to me to complain.

Tuesday, October 19, 2010
Updated Finding the Greatest Common Factor of $\,2\,$ or $\,3\,$ Numbers.
Improved the exposition considerably, and added in a section on why the efficient algorithm works.

I've put some ads on my math pages.
I hate to do this, but I really need to get some income from this site.
People just don't donate—it seems to be the web mentality.
I'm going to give it at least a week and see if it brings in any money.

At first, I tried a floating-right vertical banner.
But, after (way too many) hours of trying to get it to work in Internet Explorer,
I gave up and put a horizontal rectangular top banner.

I also re-updated Multi-Step Exponent Law Practice to change from MathML to TeX syntax,
for consistency with the other web exercises.
(Also, I noticed that this exercise wasn't displaying properly in Chrome.)
I expanded the examples at the same time.

Monday, October 18, 2010
Updated Identifying Common Factors and Listing all the Factors of a Whole Number.
Also, it's my daughter's birthday today! Happy Birthday Julia! I love you!

Learned something important.
If a computer already has MathPlayer installed, but an older version (pre-MathJax),
then the MathJax pages don't work—you get an error, and the page won't display.
I realized this when I pulled out my old Dell computer and tried to look at my pages.
After I installed the newest version of MathPlayer, then everything worked perfectly.
I've notified MathJax of this behavior; asked if it might be possible to have MathJax automatically detect old MathPlayer versions and alert the reader that they must update.

Sunday, October 17, 2010
Just found out about Twiddla.
It's a totally free interactive whiteboard, similar to Scriblink.
It has a really nice feature that Scriblink doesn't: you can “bring in” a web page and write on it together—it's really cool!
You can go into “Browse” mode and use the links to go to different web pages, too.
The MathJax and interactive web exercises don't work from within Twiddla, though.
Also, it doesn't seem to function well with the Safari browser; it's much better behaved with other browsers.
Try it out!
Twiddle this page!

Also passed the 300,000 mark on my Sitemeter sometime last night.
I hit 200,000 on May 31, 2010, so it took just under 5 months for this most recent 100,000.
I hit 100,000 on November 22, 2009, so it took just over 6 months for that 100,000.
Getting quicker! Woo hoo!

Updated Recognizing Products and Sums; Identifying Factors and Terms.
This one took a looonnnnggg time to update.

Saturday, October 16, 2010
Updated Practice with the Mathematical Words “and”, “or”, “is equivalent to”.
Rewrote createprob() so there are guaranteed to be no duplicates in the worksheet.

The \iff command is not recognized on a PC with Internet Explorer, but it is recognized in Firefox. Evidently, the MathML representations are interpreted differently in both browsers. An earlier “fix” didn't work well (kerning together left and right arrows); things must have been tweaked in the meantime. Ended up locating these unicode charts; but even using the character code “&#x27FA” didn't work on a PC with IE. Arrghh!! How to get the “if and only if” symbol with cross-browser support?

Friday, October 15, 2010
Updated Basic FOIL.
Changed from MathML to TeX syntax, and expanded the concept discussion considerably.
Also updated More Complicated FOIL, Simplifying $\,(a+b)^2\,$ and $\,(a-b)^2\,$,
and Simplifying Expressions like $\,(a-b)(c+d-e)$.
Four updates today—my best day ever!
(These were all very similar coding, which is what made this possible.)

Thursday, October 14, 2010
Updated Simplifying Expressions like -a(3b-2c-d).

Wednesday, October 13, 2010
Updated Combining Like Terms.
I also went “out of order” and updated Introduction to the Two-Column Proof.
This exercise has a link to it from Wikipedia, and so it gets quite a few hits.

Tuesday, October 12, 2010
Updated Identifying Variable Parts and Coefficients of Terms
Also, got my Math Tutoring page up.

Monday, October 11, 2010
Updated Writing Quite Complicated Expressions in the Form $\,kx^n$.
Expanded the “three-step” process considerably.
Tweaked my donation button verbiage a bit.

Sunday, October 10, 2010
Perfect tens—at a bit past 10:00 this morning, the date and time was:
10/10/10 10:10:10

Updated Writing More Complicated Expressions in the Form $\,kx^n$.
Expanded the examples considerably.

We just got notified of the winners of the Tech Awards education laureates.
One of the winners is beautifully aligned with my own mission: CK-12 FlexBooks
Here's their summary:
CK–12 is changing the textbook paradigm with its free, open-content, Web-based collaborative model called “FlexBooks.”

Textbooks represent a system of knowledge transfer that is centuries old and out of step with modern technologies and learning. Traditional textbooks can be expensive, difficult to update, and incompatible with multimedia educational resources. Given their cost, many students are learning from outdated materials.

The power of the FlexBooks system is that it is useable under any condition and enhances collaboration across district, county, and state lines as well as internationally. As more schools adopt these next-generation textbooks, the global implications for customized and high-quality digital learning are unprecedented.
I've contacted them about possibly making my materials available through their FlexBooks system,
and also possibly working for them to put math on the web.

I also posted the first Jing Math Video!

I also added a donation button to the bottom of each of my MathJax pages.
I estimate that I've conservatively put in about 1500 hours of work on this site,
just since I left teaching to pursue math-on-the-web fulltime.
I've just got to figure out how to make some money from this, so I can keep doing it.

Saturday, October 9, 2010
Updated Writing Expressions in the Form $\,kx^n$.
Expanded the examples considerably.

Friday, October 8, 2010
Updated Recognizing the patterns $\,x^n\,$ and $\,(-x)^n\,$.

Wednesday, October 6, 2010
Updated Mental Math: Addition and Equal or Opposites?
On “Equal or Opposites?” I improved/expanded the concept discussion, and added more variability in the problems.

Tuesday, October 5, 2010
FINALLY got up to Maine to see my sister's new home there.
Only took close to two years (sigh).
Took about five hours to get there; rained until I hit Maine.
And, what's with all this traffic in the middle of a Tuesday?
(I'm so spoiled with Monterey, Massachusetts traffic—or, should I say, non-traffic...)

Monday, October 4, 2010
Got the new jsxgraph.css and jsxgraphcore.js files from the JSXGraph site,
so I could use their new way to put MathJax inside JSXGraph constructions.
Went through every one of my existing JSXGraph files, to see if there was any difference in behavior;
the only thing that seems to have changed is the line-spacing between lines of text.
I did some adjustments, and uploaded my revised files.

Updated Practice with Products of Signed Variables and Practice with the Distributive Law.

Also worked on a tutoring flyer, and started some research into using Skype for online tutoring.
(The sound quality is the biggest drawback with all the online tutoring interfaces I've tried; why not just use Skype and screen sharing?)

Sunday, October 3, 2010
Updated Practice with $\,x\,$ and $\,-x\,$.

I was able to get my own voice on my Voki avatar by using their call-in option.
So, it's now my own voice, but the sound quality is nowhere near as good.
I have no idea why it isn't detecting my internal microphone.

Saturday, October 2, 2010
Put up my new monthly statistics for September 2010.
Created a new exercise: Mixed Basic Add/Subtract Multiply/Divide Practice.
Updated Practice with Rational Exponents.

I also decided to try and get some of my users to send me some Jing movies of them working on my web exercises!
We'll see if I get any takers! (I'm having a ball with Jing.)

Finally, I had great fun creating a free avatar at voki.com.
(I've put it on my blog, and on my homepage.)
It couldn't detect my microphone, so I wasn't able to record my own voice.
So, I now have a real “mathematical cat”!

Friday, October 1, 2010
(Yep, this is my second October 1 entry!)
I'm “killing two birds with one stone here”:
  • trying out Jing (instant screenshots and screencasts);
  • trying to see if someone can help me with MathType!
Any MathType user out there who can help me?
I'm a newbie to MathType, so perhaps I'm just doing something wrong.
I'm trying to grab this math (which was created with MathJax, using TeX syntax): $$ x = \frac{-b\pm\sqrt{b^2-4ac}}{2a} $$ and insert it into my document.
It's supposed to be possible, but I can't get it to work.
(By the way, I'm personally using Pages on a MAC.)
Here's my first Jing screencast to show what I'm trying: Grabbing some MathJax math into MathType
Can anyone out there help me?
(fishcaro at hotmail dot com)
Many thanks!

Friday, October 1, 2010
Rabbit, rabbit everyone!
(Does anyone else do this? You'll know what it is, if you do it!)

Updated Writing Rational Exponents as Radicals.
Changed from MathML to TeX notation, and added quite a bit more variability.

By the way, I saw a mother black bear and three cubs cross the road in front of my car
on the way through Tyringham, Massachusetts a couple days ago.
It was so exciting! (And, I was glad that I was in the car.)

Robert Fant is introducing me to LOTS of great technology tools that I haven't run across,
which should make my site better and better.
Thank you so much, Robert!

Thursday, September 30, 2010
Updated Writing Radicals in Rational Exponent Form.
Changed from MathML to TeX notation, and added more variability.

Wednesday, September 29, 2010
Updated Approximating Radicals.
Changed from MathML to TeX notation.

Tuesday, September 28, 2010
Updated Practice with Radicals.
Changed from MathML to TeX notation.
Removed the “non-MathPlayer” version from my Table of Contents.
Firefox doesn't have the radical cover the entire fraction; it looks like just (say) the square root of the numerator.
I put a warning at the top saying NOT to use Firefox for this particular web exercise.

Fixed Two Special Triangles.
The named entities &ThinSpace; (&8201;) and &approx; (&8773) were causing MathML errors,
so I replaced them with the numerical entities.
Again, I'm confused—I'm sure I would have caught this when I was testing the page in June. Has MathML suddenly gotten stricter?
(I knew I should be using the numerical entities; this was an oversight.)

I came across while searching for a free architecture program.
It's FANTASTIC!!!!!! I can't believe I haven't stumbled upon it before.
It's a 3-D modeling tool, and there are great video tutorials to get you started.
I highly recommend that you check it out!

Monday, September 27, 2010
Updated One-Step Exponent Law Practice.

Oh no! Not Apple, too!
I purchased an AppleCare service plan for my MacBook Pro when I bought it,
and have absolutely LOVED that I can call and quickly get a real human being to talk to.

Well, I haven't called in a long time; and today, when I called, I was extremely disappointed to discover that they've gone the “automated route” like everybody else. Sigh. I did manage (after about ten minutes) to get a case number and then used their new Express Lane, so I was called back quickly—and then put back on hold for about 10 minutes (to a first person) and another 10 minutes to get the correct person. So, it was a bit over half an hour (and the correct person very quickly answered my question). They didn't offer me a SILENT hold—so I had to listen to their music the entire time. Sigh.

(I still absolutely love my MAC. But, it saddens me to see part of what I love eroding.)

I've been credited as one of the first people to explore dynamic MathJax inside JSXGraph constructions!
Woo hoo! This made my day!!

Sunday, September 26, 2010
Updated Practice with $\,x^m/x^n = x^{m-n}\,$ and Practice with $\,x^{-p} = 1/x^p\,$.

Saturday, September 25, 2010
Updated Practice with $\,x^mx^n = x^{m+n}\,$ and Practice with $\,{(x^m)}^n = x^{mn}\,$.
Again, the overbrace doesn't display properly in Firefox.

Also updated this page and my Algebra I Table of Contents to XHTML;
MathJax inside links doesn't display properly in HTML documents.

Friday, September 24, 2010
Updated Basic Exponent Practice with Fractions.

Prior renters left a day early, so I thought I'd get a more leisurely renter transition.
But, the timing dial on the dishwasher broke, so lots of time has been spent dealing with that. Ah well!

Robert Fant got me working on something—check it out!
Dynamic graphics merged with my web exercise!
In Internet Explorer, the graph doesn't stay hidden; every time you press the ‘new problem’ button, it re-appears.
But, it works perfectly in Safari, Chrome, Firefox.

Thursday, September 23, 2010
In preparation for doing MCAS tutoring,
I've updated my Map of MCAS Objectives to Fisher Web Site, Grades 9–10
and MCAS Objective 10.N.2 Practice.

Also updated Practice with Order of Operations.

Wednesday, September 22, 2010
Updated Rate Problems and Practice with Exponents.
Again, the MathML was messed up on the Practice with Exponents exercise, which is very discouraging.

Tuesday, September 21, 2010
Updated Multi-Step Conversions.
I corrected some conversion factors—for a few, I was using 360 instead of 365 for the number of days in a year—sigh!
Also, made the singular/plural usage consistent with the One-Step Conversions exercise.

Also sent an email to the Common Core State Standards Initiative to make sure they know about MathJax, and saying that I'd be a good person to help them put standards-focused student/teacher preparation on the web.

Monday, September 20, 2010
Updated One-Step Conversions.
Improved the content and exposition; fixed some singular/plural issues on the web exercise.
When there is no commonly-accepted abbreviation for a unit, I decided to use the normal singular/plural forms:
for example, I say   ‘1 day’   versus   ‘2 days’ .

Sunday, September 19, 2010
Put my work on the K12 Math Taxonomy online.
This is a BIG file (even though it's only through the beginning of Grade 4), so it may take a while for the math to fully process.

Took my Dad (who is in advanced stages of Parkinson's) from the nursing home to his home for my sister Jean's birthday party (since I have now completed “car transfer” training). It went well!

Saturday, September 18, 2010
Updated Practice with Unit Conversion Information.
No MathJax here; just updated to XHTML/CSS.

Tweaked the look of my homepage (yet again). I've never liked the dark grey in the left column, and can't seem to find the right color. So, I just went with the same parchment background as the rest of the page, for now.
Also, put a link to my Grant Essays on my homepage.

Friday, September 17, 2010
Updated Practice with Unit Names.
No MathJax here; just updated to XHTML/CSS.

Also, I finished getting the Grant Essays online.

Created a cute little toggle button to show/hide information on my vita.

Thursday, September 16, 2010
Updated Practice with Unit Abbreviations.
No MathJax here; just updated to XHTML/CSS.

Also got my third Tech Grant essay online, and an entry point for these essays.

I've just got to mention this incredible tree-house-building site I discovered: http://www.treetopbuilders.net. If my Tech Grant had been funded, I'd be building one right now (so I'd have a tiny, affordable place-of-my-own to live, so I could do math-on-the-web without financial worries for the rest of my life). Their web site is beautiful, and you get highly-qualified, personal service when you contact them. Their prices seem really reasonable. I'm not giving up on my dream—at some future time, I want to be able to offer math tutoring in a tree house—which will also be my home!

Wednesday, September 15, 2010
Updated Classifying Units as Time, Length, Volume, Weight/Mass.
No MathJax here; just updated to XHTML/CSS.
But, I've decided to put the “MathJax” symbol in the Table of Contents anyway, just to keep track of the ones that have been updated.

Tuesday, September 14, 2010
Expanded one of my most popular web exercises, Calculating Percent Increase and Decrease,
to include the version of the formula with   100%   at the end.

Also did some minor adjustments on another of my most popular exercises, Introduction to Function Notation:
changed quotes (" ") to curly quotes (“ ”), and adjusted the amount of space for work on the worksheet (which was excessive).

Here's my second Tech Grant essay: Description of Technology Application. It addresses:
  • Fully describe the technology application.
  • What technology is being used? How is it being used?
  • Who is responsible? Who is benefiting?
  • What processes or systems are in place to deliver this technology application?
Following my work with Robert Fant, I've been thinking about the idea of creating stripped-down versions of my web exercises, that teachers could grab and insert into their own Google Sites page. (Google Sites looked easier than MediaWiki for non-techies.) However, after doing a prototype, I learned that Google Sites doesn't allow any Javascript code in their pages.

Productive day. Also updated Tables of Unit Conversion Information.
No MathJax here; just updated to XHTML/CSS.

Monday, September 13, 2010
Updated Rounding Decimals to a Specified Number of Places.
Improved the exposition and content presentation considerably.

I've been working with a teacher, Robert Fant, who'd like to offer his students dynamic exercises similar to what I do.
We've had great fun working together!
I was reminded that we need to have some MathJax in the body, before using Javascript-called math, or else you get a “Math processing error” on the first click. It can be as simple as an invisible thinspace:   $\,$

Robert has been successful in getting stripped-down versions of some of my web exercises embedded in his wiki (which uses MediaWiki).
In the process, he has introduced me to some cool things that I had never run across:

ThatQuiz is a totally free service that allows teachers to administer online quizzes, create custom quizzes, email them to students, look at the grades, and more. It's user-friendly; there are many high-quality quizzes already in place; there's a huge database of quizzes that teachers have contributed. Check it out! I'm going to incorporate some of these quizzes in appropriate places in my own exercises, under “Fun Stuff”.

WiziQ (pronounced whiz-IQ) is a new online teaching environment. To conduct paid classes costs about $50 per year. It's interesting to see the sorts of products that are emerging for teaching/learning on the WWW. I may get my “Math WIC” (Math Web Instructional Classroom) eventually!

Edoboard is a tutor's online toolbox. It is particularly well-suited to math tutoring; you can easily input TeX or LATeX syntax and very easily graph things.

Sunday, September 12, 2010
Updated Deciding if Numbers are Equal or Approximately Equal.

Decided to put my Tech Grant application (which wasn't funded) online.
I put many hours into it, and it gives a good, thorough introduction to what I'm all about,
so perhaps it will be useful to people.
Here's the first (of ten) essays: Problem Identification. It addresses:
  • What serious problem or challenge with broad significance does your use of technology address?
  • Explain your context and the existing conditions that you are trying to improve or rectify.

Saturday, September 11, 2010
Updated Deciding if a Fraction is a Finite or Infinite Repeating Decimal.

Visit in Safari/Chrome versus Firefox/IE. There's an inconsistency in browsers for the overline over the repeating decimal. I suspect it's a MathML issue (and not a MathJax issue), but I did fill out a comment form on it in MathJax. (At the same time, I noticed a very interesting new job they've posted!)

Came very, very close to buying a Jayco Jay Feather Sport 165 travel trailer.
Did many hours of online research on RVs; I knew I wanted the smallest thing I could get that has an inside toilet.
Near me, I found that Albany RV has the best prices,
and they have a great video that walks you through all the RV features (click on “streaming video”).
Their new prices were as good as lots of the used prices I was finding online.
Tony worked with me—he was wonderful: knowledgeable, friendly, professional.
Although my plans ended up changing and I didn't buy it, if I find myself in the market again in the future, I'll go there.

Thursday, September 9, 2010
Updated Recognizing Zero and One.
Near “renter transition” days, things get very busy, and I'm not likely to be able to update two exercises.
(I'm a cleaning fiend.)

When I took a look at this exercise (pre-update), some of the MathML was not displaying correctly, even in the correct viewing environment.
This is very strange—I guarantee that I made sure everything worked perfectly when I uploaded it.
My suspicion is that perhaps there were some errors in my MathML coding (perhaps, a missing end tag), and prior versions of MathPlayer were more “forgiving” about this—but new versions cracked down.
This is just my best guess of what's going on.
It's irrelevant now, because I'm completely getting rid of the verbose MathML code, and replacing it with the much more compact TeX code.
But, it's discouraging to know that some of my exercises were/are out there with errors. Drat.

Wednesday, September 8, 2010
Updated Identifying Inequalities with Variables as True or False and Solving Equations of the form xy = 0.
I'm going to try very hard to finish two exercises per day, to speed the updating process.

Undesirable Firefox behavior: math inside titles gets capitalized, so (say) x turns into X.
Take a look at the “Solving Equations...” exercise above in (say) Firefox versus Chrome, to see see what I'm talking about.

Tuesday, September 7, 2010
Updated Practice with the phrases “at least” and “at most”.

Monday, September 6, 2010
Updated Identifying Inequalities as True or False and Bigger, Smaller, Greater, Lesser.
(Finally, I managed to get TWO done in the same day! Yeh!)
School starts for lots of people tomorrow, so we'll see what happens with my hits!

Sunday, September 5, 2010
Updated Divisibility Equivalences.

Decided to advertise for a math-on-the-web job in my header. Let's see!

Saturday, September 4, 2010
Updated Adding and Subtracting Simple Fractions with Variables.
Changed from MathML to TeX syntax.

Just found out that I didn't win the Tech Award. Well... it was a nice rejection letter!

Friday, September 3, 2010
Updated Adding and Subtracting Fractions.
Expanded/improved the concept discussion a bit.
Added links to supporting web exercises.

I'm noticing that sometimes my pages are loading slowly, and I'm worried that people are leaving without seeing what the site offers.
It appears that my sitemeter may often be the weak link, so I've contacted them to see if upgrading to a paid version would improve the load time.
Perhaps my number of hits (1000+ per day) has reached the point where the free version is no longer appropriate.

Thursday, September 2, 2010
Updated Practice with Factors.
Expanded/improved the concept discussion a bit.
Added a bit more variety to the web exercise.
Changed to radio buttons for recording the yes/no answer, instead of typing it in.

Wednesday, September 1, 2010
Happy September, everyone!
Updated Renaming Fractions with a Specified Denominator.
Expanded/improved the concept discussion.
With the school year starting, hits are really picking up!
Had one of my highest days ever yesterday, with 1338 visits.
Actually went to check my site meter this morning, and got a message that “usage exceeds capacity”—this could be a problem.
A good problem, though!

We're getting vacation rental requests for next summer, which is superb.
This “income solution” may actually allow me to do math-on-the-web as my career! Woo hoo!
(Of course, the only minor problem is that I don't get to live/work in my own home;
but my living needs are pretty simple... a tiny little space that's all my own is enough...)
I'll finish updating everything; then complete the high school curriculum;
then go back and incorporate loads of JSXGraph stuff in the high school curriculum;
then on to early college-level—oh, the plans I have!

Also updated my Monthly Statistics for August.

Tuesday, August 31, 2010
Updated Finding Least Common Multiples.

Monday, August 30, 2010
Updated Practice with Multiples.

Sunday, August 29, 2010
Updated Renaming Fractional Expressions.
Changed from MathML to TeX syntax.

Saturday, August 28, 2010
Updated More Practice with the form a(b/c).
Changed from MathML to TeX syntax.

Now, heading out for a long walk to celebrate my birthday.
I'm just going to stroll and think about how wonderful my life is, as I turn 52 years young!

Friday, August 27, 2010
Spent the morning working on the Hill Cottage Notebook,
both to help our renters, and to give prospective renters a better idea of everything we offer.

Updated Practice with the form a(b/c).
Changed from MathML to TeX syntax.
This one took a while, because the coding was a bit different;
I had to figure out what I had done!

Thursday, August 26, 2010
Tried Google Ads again for about 4 hours, but (as usual) just can't stand the look of it.
(And, the ads "pop out" of the table structure in Internet Explorer, so it looks really awful.)
I wouldn't mind having some advertising if it was something I believe in:
math toys, logic puzzles, Design Science, WolframAlpha, things like that.
If only I could contract individually with appropriate advertiser(s) to get some steady income, that would be great.
Maybe once my hits (optimism!) are in the many thousands per day, then I'll have some leverage to do this!

Wednesday, August 25, 2010
Updated Multiplying and Dividing Fractions.
Changed from MathML to TeX syntax. Added a bit more variety to the exercise.
There are ten different problem types:
coded a worksheet feature so that users can request more than ten problems, and get “even” practice with all types.
For example, if 24 problems are requested, you'll get two sets of all 10 problems (each in random order),
plus an additional 4 problems chosen from the 10 available types.

Had a typo—an “m” where I was supposed to have an “n”—which took me forever to find. Sigh.

Tuesday, August 24, 2010
Updated Determining if a Product is Positive or Negative.

Monday, August 23, 2010
Updated Finding Reciprocals.
Added more variety to the web exercise; changed to horizontal fractions for the worksheet, instead of diagonal fractions.

Sunday, August 22, 2010
Updated Fractions Involving Zero.
Added a bit more variety to the web exercise; changed to horizontal fractions, instead of diagonal fractions.

Saturday, August 21, 2010
Updated Locating Fractions on a Number Line.
Changed from MathML to TeX syntax.

Friday, August 20, 2010
Updated Rewriting Fractions as a Whole Number plus a Fraction.
Changed from MathML to TeX syntax.

Thursday, August 19, 2010
Updated Significant Figures and Related Concepts.
Changed from MathML to TeX syntax.
Improved the exposition and coding, and inserted appropriate commas in large numbers.
I also created a JSXGraph exploration of precision versus accuracy (which I'm very pleased with).
Haven't done any JSXGraph stuff for a while now, so it took me a bit to get back into it.

Tuesday, August 17, 2010
Updated Scientific Notation.
Changed from MathML to TeX syntax.
Improved the exposition and coding, and inserted appropriate commas in large numbers.
My “life project” has settled, so I should now be back to (about) one update per day (except possibly on renter transition days, when I clean, clean, clean).

Monday, August 16, 2010
Updated Getting Bigger? Getting Smaller? (Direct and Inverse Variation).
Changed from MathML to TeX syntax.
This one took a while, just because of the sheer number of cases (64).

Saturday, August 14, 2010
Well, I didn't test all my updated files, but I checked enough so that I'm confident there won't be any major problems updating to MathJax 1.0.
(I did need to delete my "InvisibleTimes" elements in MathML; version 1.0 doesn't seem to recognize these.)
So, as of 1:00 PM EST, MathJax 1.0 is live on my server!
Be sure to let me know if you experience any problems.

Updated Solving for a Particular Variable.
Changed from MathML to TeX syntax.

Friday, August 13, 2010
Spent the morning playing with my new Hoover WindTunnel Bagless Upright vacuum cleaner. I love it! It's powerful. I really like not having to buy bags. Very easy to empty the dirt bin and clean the filters. It's very heavy, so you wouldn't want to be lugging it upstairs and down often—but I like an appliance that “feels solid”—and this definitely does. I'll primarily use it on the main level of our home—our old vacuum can be kept upstairs. I fell in love with this vacuum while visiting in Boulder, Colorado, and decided it would be my next vacuum. I've used canisters my whole life (and I vacuum a lot—it's how I keep my life in order!) so this is a radical departure for me. It will take some time to see, long-term, how it works for me. All indications thus far are that we'll get along just fine!

The new version of MathJax (1.0) is released! Boy, am I behind the ball—it was released on August 4th, and it's now the 13th. (My life project has me a bit distracted.) I've downloaded it, but I want to test it on all my updated files, before I actually upload the newest version to my server. Woo hoo! Go MathJax!

Wednesday, August 11, 2010
Updated Undoing a Sequence of Operations.
Changed from MathML to TeX syntax, and improved the appearance of the mapping diagram.

I've had several tutoring sessions now with kids who are vacationing at the Hill Cottage—ages 5 and 8—great fun!
(Each vacation rental comes with one free hour of tutoring or "fun with math" each day!)

Sunday, August 8, 2010
Updated Using Mathematical Conventions.
Changed from MathML to TeX syntax.

Thursday, August 5, 2010
Updated Solving Simple Sentences By Inspection.
Changed from MathML to TeX syntax.
(My “life project” is going well enough that I hope to update a web exercise at least every 3 days.)

Tuesday, August 3, 2010
Updated my new monthly web site statistics.
Definitely on (the normal) “summer mode”—hits are down.

Saturday, July 24, 2010
I have a major “life project” that will pretty much consume me for at least the next three weeks (and perhaps beyond),
so my progress on the web exercise updates is going to be slowed pretty significantly.
I'll try really hard to keep chipping away at them, though.

Friday, July 23, 2010
Updated Going from an Expression to a Sequence of Operations.
Changed from MathML to TeX syntax.

Thursday, July 22, 2010
Updated Going from a Sequence of Operations to an Expression.
Changed from MathML to TeX syntax.

Wednesday, July 21, 2010
Updated Reading Set Notation.
Changed from MathML to TeX syntax.

Tuesday, July 20, 2010
Updated Introduction to Variables.
Changed from MathML to TeX syntax.

Monday, July 19, 2010
Updated Interval and List Notation.
Changed from MathML to TeX syntax.

Sunday, July 18, 2010
Updated Introduction to Sets.
Ended up changing from MathML to TeX syntax.
Also, added questions on subsets to this web exercise.

Friday, July 16, 2010
Updated Changing Percents to Decimals.
Added quite a bit of variety to this web exercise.

Thursday, July 15, 2010
Updated Changing Decimals to Percents.
Got a cord of word delivered—I'll get my upper-body exercise stacking it!

Wednesday, July 14, 2010
Updated Multiplying and Dividing Decimals by Powers of Ten.
Improved the web exercise: more variety in notation, inserting commas (where appropriate) in worksheet answers.

Tuesday, July 13, 2010
Updated Changing Decimals to Fractions.
Added a lot more variety to this web exercise.

Evidently, the spacing problems below are browser-related problems in rendering the MathML, not MathJax problems. The recommendation was that I could "work-around" by putting this code in my config file:
TeX: {
  Macros: {
    times: '\\;\\unicode{xd7}\\;' }
but it didn't work; perhaps I need the newest version of MathJax to recognize this "Macros" section.
(I'm waiting for the 1.0 release before I re-download.)
I've left the code in place, though, so when I update MathJax, perhaps it will then work.
Also, I've decided that I'm going to "live with" the less-than-perfect spacing around the commas in IE.

Monday, July 12, 2010
Updated Multiplying By Powers of Ten.
Part of the reason that these updates are taking so long
is that I'm not merely switching to MathJax and changing the code to XHTML/CSS.
I'm also re-reading with “fresh” eyes, improving exposition, and sometimes improving the exercises.
For example, in this newest update, I wrote a little macro to insert proper commas (in appropriate groups of three) in the worksheet answers.

There is an inconsistency with how space around the \times symbol is treated:
in Firefox (using MathML), no extra space is inserted around the symbol, which is not desirable.
There is also inconsistency with how the TeX code $1{,}324$ is treated:
in IE with MathPlayer, extra space is inserted after the comma, which is not desirable.
I have reported these inconsistencies on the MathJax form.

Sunday, July 11, 2010
Updated Identifying Place Values.
Did my normal Sunday cleaning at Nielsen Lane (to help out my Mom and sister).
Also visited my Dad (which I do every Sunday and Wednesday) at Fairview Commons;
we finished the Sudoku we've been working on for a while!

Saturday, July 10, 2010
Updated Average of Three Signed Numbers.
Went blueberry picking yesterday, and picked 13 pounds of berries.
Made a gigantic batch of jam (about 4 pounds of berries makes about 9 cups of jam);
also froze two gallon bags for putting on cereal throughout the year. Yum!!

Thursday, July 8, 2010
Updated Average of Two Signed Numbers.

Tuesday, July 6, 2010
Updated Mixed Addition and Subtraction of Signed Numbers and Writing Fractions With a Denominator of 2 in Decimal Form.

Monday, July 5, 2010
Updated Deciding if a Number is a Whole Number, Integer, etc..
I've spent many hours clearing the path to the lake—it looks lovely!
First, spent hours pulling up weeds; then, raked the entire path, trimmed back branches, cut down the "pricker-bushes".

Saturday, July 3, 2010
Updated Divisibility.
These "early" web exercises seem to take me much longer to update than I think they should; and I think I've figured out why.
I didn't have a good "template" in place for the early exercises, so all the coding is a bit different.
I have to look carefully at my code to figure out what I did!

I've also got raspberries picked, crushed, and frozen for two more batches of homemade jam.
This will make four batches—hopefully enough for an entire year of renters!

Friday, July 2, 2010
Put in my June monthly statistics.
Have made two batches of raspberry jam—the raspberries are early this year!
I want to give each renter a homemade loaf of bread and a small jar of homemade raspberry jam.
Also cleared the entire path down to the lake; it was very overgrown.

Wednesday, June 30, 2010
Updated Multiplication.
Also getting close to having the house and lawn ready for July renters—I've been a cleaning and weeding fiend!
It's amazing how a yard and gardens can "go to seed" (both figuratively and literally) in two months!

Monday, June 28, 2010
Updated Basic Addition Practice.
Since I've already updated most of the "popular" web exercises,
I'll now just go in order through Algebra I, then Geometry, then Algebra II.

The summer "lull" has definitely begun, as most public schools are now out for the year.
Hits are down considerably (which is normal).
This actually makes summer the perfect time to do my updates, so I (hopefully) won't change the user experience mid-stream for anyone.

Sunday, June 27, 2010
I arrived home yesterday, after 500 miles. YEH!!!! I'm home!!!
2812 miles, total, from Tucson, Arizona to Monterey, MA.
I was welcomed home with a traffic jam off the turnpike in Lee; must have been Tanglewood traffic heading into Lenox.

I know that, eventually, I'll forget all the pain and discomfort of this trip, and just remember it as a glorious, worthwhile thing to have done.
Julia is settled into her new graduate school life.
I now "know" her place, and Antonio's place, so I have a mental image when I talk to her.
All good things. Two months well spent. (And, I got a FANTASTIC start on my website update while I was alone there.)

Lots of work to do here to get ready for renters; it's really important to me that I present my home to each new renter in PERFECT condition.
I'm also getting back on my at-least-one-web-update-a-day schedule; this is each day's #1 priority.
It's SO GREAT to be back home!

Friday, June 25, 2010
On Thursday, I got off late (about 8AM), so I was only able to do about 575 miles, from Brinkley, Arkansas to Bristol, Virginia (I40 again, then onto 81N).
Today (Friday) was only about 350 miles: from Bristol, VA to Harrisonburg, VA...
but about 200 of it was along the Blue Ridge Parkway, which was spectacular!
I stopped and hiked to the top of Sharp Top Mountain (about 3 miles total);
at the beginning of the hike, my right shin was incredibly tight (surprise, surprise... I've been doing a bit of driving, and I don't have cruise control).
After the hike, though, I felt WONDERFUL. Just what I needed after over 2000 miles of driving in 3 days.
I drove to the north end of the parkway, then took 64W and got back onto 81N.

Wednesday, June 22, 2010
Well, the air conditioner in Julia's apartment wasn't working well, so I took it as a sign—I'm heading back East (back home).
Did 699 miles on Tuesday (Tucson, AZ to Vega, TX: I10E, I25N, I40E).
Did 688 miles today (Vega, TX to Brinkley, Arkansas: I40E).
My Honda Civic just hit 175,000 miles, so the time has long since past that she deserves a name—Hermione, it is!
I'm averaging between 35 and 40 miles per gallon, so go Hermione!!!

My car air conditioning isn't working (this seems to be a theme).
I feel like I've been in a sauna for two days now.
With the window open, it's like a hot hair dryer blowing on you.
With my barely-functioning "air conditioner," it's like a warm hair dryer blowing on you.
With nothing on, I just can't breathe—so I'm going for the warm hair dryer.
About 1400 miles more to go; I'll do part of it on the Blue Ridge Parkway, which will be slow, but beautiful.
This is serious business, driving cross-country.
Needless to say, I'm not going to get many updates done this week!

Before I left, though, I did finish updating Expressions versus Sentences.
This one (both a timed AND a concept exercise) also took a long time.

Sunday, June 20, 2010
Updated The Addition Property of Equality a couple days ago.
Then, a couple busy "life" days: picked up Julia and Antonio at the airport—they were so happy to see the kitties! They look great! We spent a day together walking around Boulder. Julia and I got a new kid's book for our collection: "the Seeing Stick" by Jane Yolen. What a lovely book—the color and texture in the pages slowly emerge as the young princess gets closer to her "new sight". (By the way, I got a 10+ mile day!)

Then, flew back to Tucson, Arizona yesterday (Saturday). This morning, I'm groggy, sore, a bit disoriented... and consequently my crosswords score was HORRIBLE! (Sigh... Karl will clobber me today.) That's okay—there will be days like this. I'll get to work on another update, and feel better!

Thursday, June 17, 2010
Finally finished the update of Addition of Signed Numbers.
The good news: after that (looonnng) one, the update of Subtraction of Signed Numbers went really fast!

Wednesday, June 16, 2010
Aargh. Fought all day with the update to "Addition of Signed Numbers" and still haven't finished. This is the first updated exercise with BOTH a timed exercise AND a concept exercise, so I had to adjust the CSS information to allow for two forms on the same page. It's taking a long time.

Tuesday, June 15, 2010
Updated Writing Quadratic Equations in Standard Form and Perimeters and Areas of Similar Polygons.

Monday, June 14, 2010
I am keeping Davide Cervone (lead developer of MathJax) apprised of browser-specific incompatibilities in representations. His knowledge of typographic issues, ability to locate bug references, and suggestions for work-arounds are fantastic. Here are two recent issues:

Firefox in Mac has trouble with stretchy overbars, like for line segment representations. This is not a MathJax issue, but instead a MathML issue: I'm committed to using MathML capability where it is available, so I'll live with it. I have, however, switched to numeric entries as per this email correspondence:
[email correspondence with Davide Cervone, June 2010] This seems to be a Mac-specific bug in Firefox's native MathML renderer. See here for details.
< more details > If you use &#x00AF; rather than &OverBar; you should be able to get stretchy overbar in Windows versions of Firefox (but not Mac versions). Note that the MathML specification suggests that you NOT use the entity names, but rather use the numeric references, since the entities cause problems in a number of situations.
Furthermore, MathPlayer was unable to render the "equivalence" symbol (\Longleftrightarrow) in PC-mode on Mac, with IE, via VMWare Fusion; I ended up coding it as "\Leftarrow\kern-.15em\Rightarrow" (again following Professor Cervone's lead), which gives excellent representation in all situations.

Also, updated Translating Simple Mathematical Phrases.

Finally, I've decided to offer one free hour of tutoring per day, for people who rent my home.
This won't start until August, since I won't be back there until then.

Sunday, June 13, 2010
Updated Quadrilaterals.
I've worked for many hours on a "random quadrilateral generator"; it's tricky.
Once you have three randomly-generated non-collinear points, there's only a certain region in which the fourth point can lie, for the computer "polygon" method to correctly draw the resulting quadrilateral. (The order that the points are connected matters!)

Along the way, I wrote a function that "fills" an angle (there doesn't appear to be such a feature built-in to JSXGraph). I needed this to help me indicate to the user an acceptable region for a fourth point. I abandoned this approach due to slow performance—but it was another great JSXGraph learning experience.

I've settled on a less-random (but MUCH easier) quadrilateral-generating algorithm. I still don't want any three points that are even close to collinear; if the random generation isn't quickly coming up with a good set of points, then I present the user with a special case of a randomly-generated square, rectangle, trapezoid, parallelogram, or rhombus. I definitely don't want my users to experience a freeze-up (on a MAC, the "spinning wheel of doom").

Saturday, June 12, 2010
Updated Basic Properties of Zero and One.
Ended up switching this to TeX format, because there was relatively little MathML.

I'm really enjoying yoga; there was a Rodney Yee DVD in the apartment here, so I decided I'd give it a try.
I've been doing it daily for a little over a week now, and I'm benefiting physically, mentally, and spiritually.
In particular, I get my BEST crossword scores when I do them immediately after yoga!
And, my back has never felt this good, even though I'm working at the computer (with a non-ideal chair) for 10–12 hours per day.

Friday, June 11, 2010
Updated Two Special Triangles.
When using my "MathJaxText()" function for JSXGraph, I MUST remember to put the "preview" in front of any math, or else the math is not processed in Internet Explorer.

With this exercise, I learned how to use arcs to create the little "angle" symbol for labeling degree measures in triangles.
Eventually, I'll create a set of useful functions to automate these kinds of things for me.
(Of course, JSXGraph may also evolve to include some of these time-saving features.)

Thursday, June 10, 2010
I haven't updated my blog in a few days, because I've been so busy!
I've updated:
Area Formulas: Triangle, Parallelogram, Trapezoid (Check out the JSXGraph base/height explorer!)
the Multiplication Property of Equality
Factoring Simple Expressions
Writing Fractions in Simplest Form
Put notices on my "video" pages about updating the site.
Added in a "JSXGraph" column in my summary of Updates to MathJax,
so it's easy to see, at-a-glance, how many files incorporate dynamic graphics.
I was not successful in having more than one JSXGraph drawing board in Probability Tree Diagrams,
so I kept only one board, and used SnapZ Pro X to take pictures of the other desired configurations.
Take a look at the beautiful graphics!
Play with the random probability-tree generator!
This is my first real use of MathJax inside JSXGraph!

Monday, June 7, 2010
Another VERY VERY important and exciting day!
I got MathJax working INSIDE JSXGraph!
Indeed, when you click on "Do this!" in this file, these are divs created on-the-fly,
which contain randomly-generated text and MathJax!
The math educational world is going to have to bow down to MathJax + JSXGraph!

(By the way, the math is meaningless.
I was actually working on a function to create probability tree diagrams,
and I decided that I wanted the probabilities correctly displayed on the branches...
and it led me to this discovery.)

Times-they-are-a-changing, for math-on-the-web. Woo hoo!

Saturday, June 5, 2010
VERY important day!
Put my first JSXGraph graphics in a web exercise: check it out!
And, I had WAY too much fun with dyamically-generated right triangles here;
it was a great first learning experience for JSXGraph!

Friday, June 4, 2010
Updated Multiplying and Dividing Fractions with Variables.
Also updated my worksheet style, so that it looks good with less individual-file tweaking in a wide variety of situations.
Went back to all the "already-updated" files and put in the new worksheet information.

I'm not happy with the look of the minus (opposite) sign before a horizontal fraction.
I ended up coding it as "<mtext> - </mtext>", which seems to give the best appearance across browsers.
If I use "<mo> - </mo>", then the symbol is WAY too long.

Also, I'm not happy with the division symbol between horizontal fractions in Firefox; it's way too close.
It looks beautiful in all other browsers, though, so if I "tweak" it for Firefox, then it will be too far apart in the others.

Thursday, June 3, 2010
Implemented a button for practicing a particular problem type.
Updated both the Pythagorean Theorem and Introduction to Function Notation to include this button.

Also updated Probability Tree Diagrams.
This one took a lllooonnnggg time, but I'm pleased with the result.
I did some revisions of the concept discussion, and also did quite a bit of reformatting of the MathML.

Wednesday, June 2, 2010
Two more files updated:
Calculating Percent Increase and Decrease (yet one more time–I keep adding in new stuff!)
and Introduction to Function Notation.
Also updated the GeoGebra worksheet on this latter exercise.

Monday, May 31, 2010
Davide Cervone, the lead developer of MathJax, was able to solve the problems with Internet Explorer; the dynamic math in the div, and the dynamic worksheets. He's fantastic!! I've adjusted the code on the files that I've updated so far. Now, my code doesn't have ANY browser-specific hacks. Yeh! Good day!

Also passed the 200,000 mark on my Sitemeter today. I hit 100,000 on November 22, 2009. So, this second 100,000 didn't take very long!

Sunday, May 30, 2010
Another 6 hour snafu. Things weren't working, and I spent hours trying to debug.
Wasn't sure if I had inadvertently inserted a character somewhere in my JavaScript code, or what.
Ends up that I had "merely" failed to upload my auxiliary JavaScript file after adding one new variable; and that single undefined variable wreaked havoc.
The problem, at this very-early-MathJax-stage, is that I don't have sufficient confidence about what is correct code and what isn't, so it's harder for me to locate the problems. New things take time.

Thursday, May 27, 2010
Spent half of yesterday and half of today trying to get the dynamic worksheet to work in IE; no success. I did, however, discover lots of ways that DON'T work!

Except for the dynamic worksheet, everything else works fine. So (for now) I'm going to put a note on the worksheet button saying "To create and print a worksheet, use any browser EXCEPT Internet Explorer". This way, I'll only have to maintain one page for each web exercise; I'll re-name the new MathJax page with the original file name.

I'm deciding on all my CSS style tags—while I'm updating to MathJax, I'm also updating to XHTML/CSS.
Also, I'll make sure that all my links are relative, so I can potentially (when I'm done) create a CD of my entire math offerings to be used offline.

I also updated my common header to gain an extra "link" slot. In the process, I ended up messing up my entire site for about an hour... it was a stupid mistake on my part. Sorry about that!

Wednesday, May 26, 2010
Finally added in the Work Problems exercise to the Algebra I curriculum.
This was an experiment with a totally new look-and-feel, and was the first major MathJax test. Check it out!
I also updated Calculating Percent Increase and Decrease;
now, you can specify how many worksheet problems you want, and whether you want extra space for each.

Tuesday, May 25, 2010
Argh. There are days like this.
Spent all day (yet again) fighting with moving the focus in forms.
Theoretically, it should be extremely easy; but different browsers act differently when "tab" is pressed (which is common), often ignoring what I'm telling them to do, and doing what they want instead.
You won't believe the somersaults I've tried.
I finally came up with an interface that gives consistent performance and provides a reasonably good user experience for Safari, Firefox, and Chrome.
Check it out: Multi-step Exponent Law Practice
(I also had to fix the MathML on this exercise; it was gorgeous in Safari, but deficient in Firefox and Chrome.)

Monday, May 24, 2010
Updated the Pythagorean Theorem to MathJax.

It took a LONG time (hours) to upload the new MathJax version to my server (about 6 hours).
I can upload a compressed folder MUCH faster, but there doesn't seem to be any way to unzip it at the server level. Sigh.

Also updated Percent Increase and Decrease so that it works in Safari, Firefox, Chrome, Opera (no MathJax needed on this one).

I've made the following decision: when someone comes to one of my original pages, I check to see if they have IE.
If not, then they're automatically re-routed to the MathJax page (it should be seamless).
If they have IE, they stay on the same page. If they don't have MathPlayer, then they get an alert box to download MathPlayer.
I can't seem to get stuff working properly with MathJax in IE, so I'll probably have to keep my original pages intact.

Sunday, May 23, 2010
Almost done transforming my "Pythagorean Theorem" exercise to MathJax.
I've been away from this for a few weeks, so it has taken me a while to get back into things.
I've decided that if there isn't too much MathML in an exercise, then I'll just convert to TeX; makes it a lot easier to understand the source code.
I'm also creating a "flowchart" to help me to efficiently transform my exercises, so hopefully I'll speed up pretty soon!

Sunday, May 16, 2010
We're in Tucson, Arizona; 2635 miles of driving. Not trivial. Parts of I25 in New Mexico are gorgeous. I'm anxious to get settled, and get to work.

Wednesday, May 5, 2010
Spent the last couple weeks doing a THOROUGH cleaning/organizing/packing-up of the house, to ready it for rental. Take a look! I impressed myself with packing the two cars to head out to Arizona with Julia—she has a LOT of stuff!!

I'm hoping that house rental will be a sustainable income solution, even in the off-season. My home is lovely, I keep it meticulously clean, and I'm happy to share it with others in order to sustain my ability to work on my web site. After I return from Arizona, then I can move up to Karl's house while my own home is rented. I'll take care of all the cleaning, mowing, garden-tending, answering renter's questions, and so on. I'm even thinking of eventually offering homemade meals—instead of a "bed-and-breakfast" this could be a "home-and-harvest"!

I'm DYING To get back to work on my web site. MathJax isn't even out of the beta stage yet, though—it's due for its "1.0" release in June. So, it probably makes sense that I wait for the first "real" version for the major transitioning of my site. So—be patient, Carol! Very soon, you'll be hunkered down in Arizona with nothing to do but work on your web site for 12 hours each day! Woo hoo!

Saturday, April 24, 2010
Finally finished my application for the Tech Grant. Yeh!

Busy week; big life changes for my parents, and all the children have been helping. So, I've gotten virtually nothing done on my web site for the week. Also, I need to pack up the house to rent it for the summer—heading out west with my daughter to help her get set up for graduate school. I haven't had a long-distance car ride in a long time, so it should be fun. I'll bring my computer, of course!

Tuesday, April 13, 2010
Got my first MathJax revision up! If you go to my Multi-step Exponent Laws page in any browser other than Internet Explorer, then you're automatically redirected to the MathJax page! And, if you happen to come to the MathJax page in Internet Explorer, then you are redirected back to the original page (which requires MathPlayer), since the worksheet doesn't work in IE.

Friday, April 9, 2010
I've been really busy, so haven't updated this blog in a bit. Lots to report.

I've had several VERY fruitful emails with Davide Cervone, the creator of jsMath. I had coded my newest web exercise, Work Problems, in jsMath, and it works beautifully in Safari, Firefox, Chrome, Opera. (Unfortunately, the poorest user experience is in Internet Explorer; the math is very slow to load, and continually "rewrites" as you scroll the page, making it almost non-functional.) Work Problems was designed as a full-scale test of jsMath, and also presents a new "look-and-feel" for the page design; it's written in XHTML, and properly separates content and presentation, using CSS. The ability to use TeX-like syntax for the source code makes my work MUCH easier than using the extremely-low-level MathML syntax.

Well, it ends up that Professor Cervone is the lead developer for MathJax, which is an open source, Ajax-based math display solution designed with a goal of consolidating advances in many web technologies in a single definitive math-on-the-web platform supporting all major browsers. Professor Cervone also led me to JSXGraph, which is a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser. So, after learning about MathJaX, I created a version of Work Problems in MathJax, which also implements dynamic graphing capabilites with JSXGraph. Ends up that MathJax is even EASIER to use than jsMath, because I'm able to use the "dollar sign" syntax with the dynamic math (Javascript-generated), whereas in jsMath I seemed to have to write out spans/divs with class='math'.

So—WOO HOO!!!!!—it seems that I now have ALL THE TOOLS I need to get back to serious work on expanding my offerings! Lots of the stuff that's missing is missing for a reason—I couldn't do it correctly without dynamic graphics. Of course, MathJaX isn't "officially" released yet—it's in beta—but the beta versions seem to work amazingly well. (Ends up that Robert Miner of Design Science is also involved in this MathJaX project, so I'm not surprised that it's so wonderful; it has fantastic people working on it.) By using MathJaX, I can now reach the wider audience that I've been wanting for a decade, in a way that makes the best use of MathML NOW, and allows for the future use of MathML when browsers are ready (so I don't have to feel like I'm "giving up" on MathML). These last couple months have been incredibly exciting for the future of my site.

On a different note, I've started working on a K-12 Math Taxonomy (for my OpenVES work). Hours of web searching produced almost nothing, and I now understand why—it's hard. After several "false starts" I've decided to take a "language-based" approach in my classification scheme, using the "nouns" (expressions) of math and the "sentences" (equations, inequalities, theorems) as the over-arching themes. Things seem to be falling nicely into place, so I'm encouraged that I may have hit on the "right" organizational scheme.

Finally, I'm working on the essays for my Tech Awards 2010 application. This takes a lot of time. You can't say everything, and you can't say everything first. I've finished the first two essays: Problem Identification and Description of Technology Application. Writing these has been a good opportunity to try to give a "snapshot" of what my site is all about in 10,000 words or less. You have to view efforts such as this with a broader purpose, because there's only a pie-in-the-sky chance of actually winning. (But, if I *do* win... and if I *do* win the one-in-five monetary award—oh dear, that's a lot of "ifs"—then I can actually keep working on my site AND eat, stay warm, and pay the bills at the same time!)

Saturday, March 27, 2010
Spending a week doing a thorough look at the release of the National Common Core Mathematics Standards, and comparing them to the Massachusetts Math Standards (and supplement).

Sunday, March 20, 2010
Whoa. It's harder to try and design for both PC and MAC, Firefox, IE, Safari, and Chrome. I'm running into LOADS of issues with stuff handled slightly differently in different platform/browser environments. It's important that users can navigate the online exercises easily—pressing tab and enter, moving the focus in appropriate ways; this seems to be one area where there are the most browser differences. Also, I'm having issues with how the CSS is interpreted. My code validates in XHTML, so it's not a problem with not having the "correct" code.

Sunday, March 7, 2010
I've been working really hard on a new web exercise, "Work Problems".
It's a totally new design; a bit more mainstream.
It has unlimited guided practice, "talking" you through the solution steps.
It uses jsMath, so it should be available to all mainstream browsers and platforms.
I should have it up soon.
I'll advertise it on all my pages (top banner), and hopefully get some good feedback on this new format.

Monday, February 22, 2010
Finished the cataloguing of my utility functions—a collection of 71 JavaScript functions
that I've written over the past decade to use in my web exercises.
I divided them into two parts: Randomization functions (26) and Expression Generators (45).
For each function, I did the following:
  • gave it a "short title"
  • gave a longer description of the what the function does, including information about inputs, and what is returned
  • gave one or more examples illustrating its use
  • re-formatted my code, according to normal JavaScript conventions
  • made sure that all local variables are properly declared
  • indicated other functions that are required for usage
  • checked that the code works properly
  • indicated which of my web exercises use the function
    (I wrote an AppleScript to do this—ran the script while I was editing each function.)
Big job done. This will make the collection much more useful to myself, and to others.

Thursday, February 18, 2010
Finished the big job of updating my Map of MCAS Objectives to Fisher Web Site;
next—filling in the identified gaps!
I'll very likely be using jsMath for my new web exercises.
Also, freerice.com has expanded their offerings to now include basic math and multiplication tables,
so I've added these two links to my "Fun Stuff".

Thursday, February 11, 2010
One of my users brought to my attention that some of my exercises did not include links to the text exercise solutions.
(These links were only available from the right-hand column of the Table of Contents.)
I've corrected this situation. Thanks!

Sunday, February 7, 2010
I am filling out and improving my Map of MCAS Objectives to Fisher Web Site;
since I initially created this document, I've written a lots of new exercises that needed to be incorporated.

Wednesday, February 3, 2010
In doing some OpenVES work, I discovered that the entire first parts of my "Introduction to Exponential Functions", "Introduction to Logarithmic Functions", "Equations of Simple Parabolas", "Basic Arithmetic with Matrices", "Arithmetic with Complex Numbers", "Introduction to Logarithms", and "Properties of Logarithms" (all in the Algebra II curriculum) had been inadvertently deleted...
have no idea how long ago this happened. Sigh.
I must have had a period of time that I was really out of it!
Went to a back-up disk and restored them.
Sorry to everyone who may have been affected by this mistake on my part.

Saturday, January 30, 2010
Have been checking out jsMath as a way to expand my browser audience.
It works well for static content in web pages,
but I haven't yet gotten the dynamic part (writing exercises into floating frames) to work.
Using it would mean "giving up on" MathML, so I'm definitely torn.
But, I feel that it's worth some serious consideration.

Just got notice that my online Algebra I was reviewed by Curriki.org
and received the highest possible rating of 3–Exemplary.
Yeh! You can read the review here.

I'm also currently reading A Taxonomy for Learning, Teaching, and Assessing
(a Revision of Bloom's Taxonomy of Educational Objectives)
to better enable me to construct good math assessments.

And, I'm reading through a PISA study (Programme for International Student Assessment).
It affords a view of 15-year-old student capabilities, across nations,
as seen through the lens of mathematical literacy
as defined by the PISA 2003 mathematics framework and the resulting assessment.
I hope, again, to use this information to help me to write high-quality math assessments.

Wednesday, January 20, 2010
Have been sick for a couple days with chills, fever, nausea, diarrhea. Yuck.
Now, I'm going through each of my web exercises and summarizing each type of question (each "case")
in a commented section before the JavaScript begins.
I'm also locating (and marking with a named anchor) each part of the text that relates to a given case.

Monday, January 18, 2010
Submitted my self-nomination for the 2010 Tech Awards.
It's unfortunate that this nomination coincides with the sudden decrease in my daily hits;
wish I could figure out what has happened!

Wednesday, January 13, 2010
REALLY weird. My hits are WAAAAYYYY down.
They were low over the Christmas break (as usual), but they bounced back at the beginning of January to near-normal levels.
But now, this week, I'm only getting a few hundred visitors per day.
Has Google completely changed where it sends people for math?
Have I done something that got the search engines upset??
Is something not working on my site, that I'm not aware of?
It's a mystery to me!

Friday, January 8, 2010
Updated multiplication.htm to include content and questions on the Associative Property of Multiplication.

Thursday, January 7, 2010
Paid Bravenet the $39.95 to upgrade my Guestbook page to PRO so that I could get rid of the branding and annoying advertising.
I've had more comments in the last month than I've had in years,
so this forum does indeed seem to be working to get some feedback on my site. Yeh!
Also, I got a free "talking avatar" (limited to 150 audio streams per month) with the upgrade;
I had a fun time designing it and recording my welcoming message.
Check it out!

Monday, January 4, 2010
A new year! A new decade! And, this year started with a blue moon, which is quite rare.

I've now archived 2009 (see bottom of page), so this page is short again (for a while)!

Spent the day researching OpenVES.org (an open virtual educational space)
and jsMath (a method of including mathematics in HTML pages that works across multiple browsers and platforms).
Along the way, I learned about IMS GLC (Instructional Management Systems Global Learning Consortium);
they're working on standards that enable the development and adoption of innovative technologies to improve and transform education worldwide.

I will submit a self-nomination for the Tech Awards 2010;
since I'm now trying to make a living at math-on-the-web, the recognition and/or monetary award would be really, really helpful.

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