Maybe I shouldn’t, but here goes…

So, in spite of everything else I’m doing (you know, like teaching Business Calculus, finishing up the online College Algebra, taking on the Math Alumni Connections project, and — oh yeah — having a baby in about three weeks, give or take) I’ve decided to sign up as a (free) MOOC participant in Athabasca University’s course Openness in Education.

I actually signed up towards the end of the first week, so I’ve got some catching up to do.  Fortunately, I’ve read two of week 1’s readings before (although I really should re-read one of them) and so there’s just a chapter in an OECD report (which so far seems eerily familiar) and a video that I still need to watch.

The fact that I’m not being faced with a ton of new information (at least in the first week) makes me feel better about joining this party a little late.  And even if none of the information in this course is exactly new to me, I think it’s a good opportunity to process what I know/feel about OER as part of the course conversation.  And hopefully I’ll be able to be a valuable part of that conversation, in spite of the fact that my attention will obviously be shifting after the baby comes.

On a somewhat related note, I’ve meant to make a lot of my course materials public for a long time, but figuring out the best way to do that is time-consuming.  So it may not be the best way, but right now I’m sharing several things with ShareLaTeX.  It’s not perfect (if I wait for perfect, nothing will ever get done) but it’s got potential.  I’m planning on making some feature requests, but I am aware that using ShareLaTeX to share OER is not the intended use-case.

I may make a page on the blog here linking to my projects over there (which are mostly class handouts), but in the meantime you can find them in the Public Projects list.  Mine are all read-only, and are named according to the course I designed them for.  So far, I’ve got about ten documents up, and they’re all Pre-Cal or Applied Calculus.

Class-Size Envy

So all summer I took a break from reading blogs. (Instead I did a lot of reading about cognitive development in infancy and early childhood, which is absolutely fascinating.) And so, with these last couple of weeks, I’ve been catching up on the huge backlog in my Reader account.

In addition to that, it’s the beginning of the school year, so people are posting about their new classes and mentioning class sizes.  Like a “giant class of 19” or an “enormous class of 26”.   I want to be absolutely clear that I’m not picking on anyone here– circumstances and expectations vary, and if your largest class last year was 14, then I know that 19 must seem huge, but my god, I am so jealous.

I have 47 students in my class. (Although one of them said that he was planning on dropping, since he didn’t feel like he understood the prerequisite material at all– I may get down to 46.  Yup.)  I should also mention that the furniture in this classroom (and in almost all of the rooms “owned” by the math department) is meant for no more than 40.  So they shove a bunch of those little onesie desks at the back of the rooms, many of which are broken.

Do you know how awesome it would be to have reasonable class sizes?  What I could do with a class of 24?  Or 30?  19 students would  be a dream come true.

Last fall, I taught 5 classes of 48 (which is the fire marshal limit for the classrooms my classes were held in).  Only one of the classes dropped significantly in size during the course of the semester, which I think had more to do with the time of day than anything I did.  And yes, if I could figure out how to get students to drop my class, I probably would.  I’ll be able to care about student retention again when they start giving me reasonably-sized classes again.

There’s no real point to this post.  Last year, I was actively looking for strategies to deal with larger classes.  Now I think I’ve resigned myself to the idea that classes this size mean that I can’t teach the way that I want to.  So I do my best, and muddle through.

Can’t help being jealous though.

TikZ is the Bestest Thing Ever (or, A Personal History of Creating Math Documents)

I resisted learning LaTeX for awhile.  It wasn’t that I felt like it was too complicated (heck, I’m someone who taught myself Python mostly so I could make my media center do exactly what I wanted it to), but in my Master’s program it was almost discouraged by faculty (bizarre I know, I still don’t understand that).  Also, after years of administrative work, I was familiar enough with the advanced features of Word that I could layout my handouts exactly how I wanted without thinking to hard about it, which was a very good thing, because it allowed me to focus on the content of what I was creating.  I also used Adobe Illustrator, combined with the Mac graphing calculator program Grapher to make whatever graphics I needed.  I actually got really good at creating graphics I was happy with, but it was incredibly time-consuming.  I also wrote a test generator for multiple choice tests, which swapped around the order of the multiple choice answers (for those of you that teach classes of reasonable size, that may seem unnecessary, but trust me when you’re teaching five classes of fifty in extraordinarily crowded rooms it matters a lot).

Of course, since I was using Word, I used MathType (the professional version of equation editor) to typeset the math.  But then the mac version of Office 2008 eliminated VBA. It was fine at first– I just stuck with 2004.  For a long time.  Eventually it seemed annoying and sluggish, especially once I upgraded the OS, but I needed VBA for the MathType and for the test generator (not to mention a bunch of other macros I wrote to make my life easier).  And eventually the compatibility issues were fixed, and at the end of 2010, Office 2011 came out.

But then there were problems.  The most serious one was that equations that showed up fine on screen printed as white space.  During final exams for the Fall of 2010, I had a pretty serious respiratory infection (not uncommon for me) but I was pushing through it (also not uncommon), and I did not proofread the printed version of the test very carefully.  On a test with forty questions, six or seven equations were missing.  Missing!  On a final exam!  I managed to figure out what needed to be there for the most part, and had students make corrections to their exams.  It came out alright in the end, but it still was a disaster.  I felt betrayed by MathType.

And so I started thinking more about latex.  It had occurred to me in the past that I would be able to write a test generator in Python using latex (and that I could really do a lot more with Python and latex than with VBA and MathType).  And, as with most major lifestyle changes (yes, I called changing how I make documents for my classes a major lifestyle change), it bubbled around in the back of my mind for a long time before I did anything about it.

It was daunting at first, especially since I am very particular (much more so than I need to be, I admit) about the way my documents look.  Obsessive even.  And TexShop… well, it worked just fine.  But when my workflow would spiral into tweak/typeset/judge/tweak/typeset/judge/tweak/etc/etc/etc…  it got to be annoying.  It doesn’t take that long to compile the sorts of documents I was working on, but it was long enough to be irritating when you add it all up.  I tried a few other applications, including TextMate, which is what I use for almost everything else that’s text-based.  But still you have the tweak/recompile/tweak/recompile/tweak/recompile cycle.

Enter Latexian.

This was a total game-changer for me.  Latexian is a latex editor with many features that I would except in any IDE: it’s got basic syntax coloring (TextMate’s was more customizable, but that’s not a major thing for me), a spell-checker that ignores latex commands (very necessary), decent code completion, and the ability to assign shortcuts to paste in frequently used code.  But all that has nothing to do with why I love this application.  I’m all about the Live Preview panel.

I make my changes, and they’re reflected in the panel to the right.  Bam!  This may not be as big a deal to anyone else (I’m honestly a little disappointed that none of my real-life mathy friends find this as wonderful as I do– although one of them said he would switch if it were free, but he doesn’t believe in paying for software) but it brings joy to my heart.  Lots and lots of joy from a $10 application.  Totally worth it.

So I switched wholeheartedly to creating documents in latex.

There have been a few challenges (especially with formatting tables) but I used Python to write a function that would take whatever strings I had, and build them into a table.  This came in very handy, since I was constantly creating handouts of problem sets for my Pre-Cal class, and I needed a quick way to write problems, switch the order around until I was happy, and then arrange them in a table for the document.

The other major challenge was creating and editing graphics until I was happy with them.  At first, I was using the same process to create graphics as before (Illustrator and Grapher), but that’s a very time-consuming way to do things.  I looked into other more TeX-y ways to create graphics, including Asymptote, which is what my colleagues use, but I found that unsatisfying.  It wasn’t really faster (although that’s mostly because I was used to my earlier method, and I had a learning curve with Asymptote) and I couldn’t get things to look exactly like I wanted them to.  And of course then you’ve got the revise and recompile issue again.  You can embed asymptote code into a latex document, but I couldn’t get that to work with Latexian (and no way was I going to give up my new favorite toy!) and then I discovered TikZ.

I can create graphics embedded in my latex document (which makes the documents MUCH easier to share, by the way) that show up perfectly and immediately in my preview panel.  Woo!  It’s a dream come true (at least for those who dream geeky math-graphics dreams like me).  And I’ve got my graphics looking exactly like I want them to.

So I’m posting some examples.  Each example below requires
\usepackage{tikz}
in the preamble. Some of the examples also require other preamble code, which I’ve noted below.

\begin{tikzpicture} [domain=-5:5, scale=0.65, baseline=0, >=stealth]
\draw[step=1cm,very thin] (-5,-5) grid (5,5);
    \draw [thick] (-5,0) -- (5,0);
    \draw [thick] (0,-5) -- (0,5);
    \draw[ultra thick, smooth] plot ( \x , {4.0/(1.0*(\x)^2 + 1.0)});
    \draw [ultra thick, dashed] (-5,0) -- (5,0);
    \filldraw [fill=white,draw=black,thick] (0.500,3.200) circle (1.7mm);
    \filldraw [fill=white,draw=black,thick] (1.500,1.231) circle (1.7mm);
    \filldraw [fill=white,draw=black,thick] (2.500,0.552) circle (1.7mm);
    \filldraw [fill=white,draw=black,thick] (3.500,0.302) circle (1.7mm);
    \draw [ultra thick, ->] (-5,0.154) -- (-5.1,0.148);
    \draw [ultra thick, ->] (5,0.154) -- (5.1,0.148);
    \draw (0,-5) node[below] {$f_2(x) = \frac{4 \left(x -\frac{1}{2}\right) \left(x -\frac{3}{2}\right) \left(x -\frac{5}{2}\right) \left(x -\frac{7}{2}\right)} {\left(x -\frac{1}{2}\right) \left(x -\frac{3}{2}\right) \left(x -\frac{5}{2}\right) \left(x -\frac{7}{2}\right)\left(x^2+1\right)} $};
\end{tikzpicture}

In the preamble:
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.3}
\usepgfplotslibrary{polar}

In the body:
\begin{tikzpicture} [baseline=4cm]
\begin{polaraxis}[ytick={0,1,...,20}, yticklabels={,,,3,,,6,,}, xticklabels={,, $\frac{\pi}{6}$, $\frac{\pi}{3}$, $\frac{\pi}{2}$, $\frac{2\pi}{3}$, $\frac{5\pi}{6}$, $\pi$, $\frac{7\pi}{6}$, $\frac{4\pi}{3}$, $\frac{3\pi}{2}$, $\frac{5\pi}{3}$,$\frac{11\pi}{6}$,}]
\addplot+[black, very thick, mark=none, domain=0:720, samples=600 ] {2-5*cos(x)};
\end{polaraxis}
\draw (3.43cm,-.7cm) node [below] {$r=2-5\cos\theta $};
\end{tikzpicture}

\newlength{\chartscale}
\setlength{\chartscale}{0.208in}
\begin{tikzpicture}[>=stealth, baseline=-0.05in]
\draw [<->, thick] (-1.25in,0) -- (1.25in,0);
\draw (-1.5in,0) node {$\displaystyle f'(x)$};
\foreach \x/\xtext in {2/nd, -1/0, -4/0, 5/0}
{    \draw [thick] (\x*\chartscale,-0.05in) -- (\x*\chartscale,0.05in);
\draw (\x * \chartscale,0) [above=.05in] node {\scriptsize{\xtext}};
\draw (\x * \chartscale,0) [below=.05in] node {\footnotesize{$\x$}};
}
\draw (-4.99*\chartscale, 0) [above=0.05in] node {\footnotesize{${}+++{}$}};
\draw (-2.49*\chartscale, 0) [above=0.05in] node {\footnotesize{${}++++{}$}};
\draw (0.4*\chartscale, 0) [above=0.05in] node {\footnotesize{${}----{}$}};
\draw (3.50*\chartscale, 0) [above=0.05in] node {\footnotesize{${}----{}$}};
\draw (5.50*\chartscale, 0) [above=0.05in] node {\footnotesize{${}+{}$}};
\end{tikzpicture}

\begin{tikzpicture} [>=stealth, baseline=0]
\draw [thick,fill=white] (0,0) circle (3cm);
\draw [thick, <->] (-3.5,0) -- (3.5,0);
\draw [thick, <->] (0,-3.5) -- (0,3.5);
\draw (0,0) --  node [fill=white] {$\frac{\pi}{4}$} (45:3);
\draw (0,0) --  node [fill=white] {$\frac{\pi}{2}$} (90:3);
\draw (0,0) --  node [fill=white] {$\frac{3\pi}{4}$} (135:3);
\draw (0,0) --  node [fill=white] {\footnotesize{$\pi$}} (180:3);
\draw (0,0) --  node [fill=white] {$\frac{5\pi}{4}$} (225:3);
\draw (0,0) --  node [fill=white] {$\frac{3\pi}{2}$} (270:3);
\draw (0,0) --  node [fill=white] {$\frac{7\pi}{4}$} (315:3);
\draw (0,0) --  node [near end, fill=white] {$\frac{\pi}{6}$} (30:3);
\draw (0,0) --  node [near end, fill=white] {$\frac{\pi}{3}$} (60:3);
\draw (0,0) --  node [near end, fill=white] {$\frac{2\pi}{3}$} (120:3);
\draw (0,0) --  node [near end, fill=white] {$\frac{5\pi}{6}$} (150:3);
\draw (0,0) --  node [near end, fill=white] {$\frac{7\pi}{6}$} (210:3);
\draw (0,0) --  node [near end, fill=white] {$\frac{4\pi}{3}$} (240:3);
\draw (0,0) --  node [near end, fill=white] {$\frac{5\pi}{3}$} (300:3);
\draw (0,0) --  node [near end, fill=white] {$\frac{11\pi}{6}$} (330:3);
\end{tikzpicture}

In the preamble:
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}

In the body:
\begin{tikzpicture} [baseline=1.2in]
\draw [thick] (1,1) -- (1,0) -- (5,0) -- (5,1) -- (6,1) -- (6,5) -- (5,5) -- (5,6) -- (1,6) -- (1,5) -- (0,5) -- (0,1) -- (1,1) ;
\draw [semithick,dashed] (1,1) -- (1,5) -- (5,5) -- (5,1) -- (1,1);
\draw [thick, decorate,decoration={brace,amplitude=10pt},xshift=0pt,yshift=2pt] (0.05,6) -- (5.95,6) node [black,midway,yshift=16pt] {\footnotesize $5$ cm};
\draw [thick, decorate,decoration={brace,amplitude=10pt},xshift=2pt] (6,5.95) -- (6,0.05) node [black,midway,xshift=26pt] {\footnotesize $5$ cm};
\end{tikzpicture}

In the preamble:
\usepackage{tikz}
\newcommand{\opendot}[2]{\filldraw [fill=white,draw=black, thick] ({#1},{#2}) circle (.13) ;}
\newcommand{\closeddot}[2]{\filldraw [fill=black,draw=black, thick] ({#1},{#2}) circle (.13) ;}

In the body:
\newlength{\graphscale}
\setlength{\graphscale}{.35cm}
\begin{tikzpicture} [domain=-10:10, scale=1, >=stealth,x=\graphscale,y=\graphscale]
\draw[step=\graphscale,very thin] (-10,-5) grid (10,8);
\draw [very thick] (-10,0) -- (10,0);
\draw [very thick] (0,-5) -- (0,8);
\draw [ultra thick] (-10,-4) -- (-6,4);
\draw [ultra thick] (0,0) arc (0:180:3 and 1);
\draw [ultra thick] (0,0) parabola (2,4) -- (5,3);
\draw [ultra thick] (5,2) -- (10,7);
\opendot{-9}{-2}
\opendot{-6}{4}
\opendot{-3}{1}
\opendot{5}{3}
\opendot{8}{5}
\closeddot{-6}{0}
\closeddot{-3}{6}
\closeddot{5}{2}
\closeddot{8}{-1}
\end{tikzpicture}

As I said, having the graphics code embedded in the document does make sharing easier.  I was planning on posting a bunch of stuff up here, just in case someone might find it useful, but apparently WordPress doesn’t trust a .tex extension.  So I’ll look around for another way to share latex documents.  Anyone know of any?