My new, explicit, Mathematical Collaboration Expectations

So I was flipping through my feeds as a way of procrastinating finishing my calculus syllabus when I came across this post from cheesemonkeysf, where she shares a rubric for group work for her middle school math students.

For years I’ve been telling myself that I needed to make my expectations for groupwork more explicit. I’ve told them what not to do: groupwork is not four people working silently side by side, it’s not dividing up the problems and sharing answers, it’s not one person doing everything and not taking input from their teammates. But that’s not the same as saying what it actually is.

But that sort of thing takes a lot of time to develop well, and being pulled in a hundred different directions, I just never took the time to sit down and do it. But when Cheesemonkey gave me such a great starting point, all it took was a little editing to get this:

Mathematical Collaboration Expectations

Active Inclusion

You helped the group to develop its shared mathematical thinking by:

  • allowing others adequate time to express their own thinking
  • demonstrating patience when other group members have difficulty putting their ideas into words
  • making sure that everyone understands why or how a piece of shared thinking or reasoning is so

Individual Participation

You made your own personal contributions to developing the group’s shared mathematical thinking by:

  • developing your own unique insights
  • sharing your thinking and ideas respectfully with the group
  • encouraging and supporting others as they speak their ideas,
    confusion, or questions
  • managing your desire to do more than your fair share of the talking

Deep Listening

You developed your openness as a collaborator by:

  • listening attentively to your teammates
  • asking clarifying questions
  • building on others’ ideas

Exploratory Talk

You developed your voice as a math learner and as a member of a learning group by:

  • noticing and wondering about a problem
  • extracting information and forming questions
  • trying a variety of approaches

Reflective Talk

You developed a sense of self-awareness as a math learner by:

  • noticing out loud other learners’ insights, strategies, or contributions that helped to move the group’s learning forward
  • noticing what you personally did well as a member of the group
  • noticing what you personally need to keep working on to become a more effective member of a mathematical learning group.

I didn’t want a rubric, so I stripped off all the points, and just made it a set of expectations.  If you’re interested in the latex version, you can find it on my sharing handouts page (it’s at the bottom).

And this is my absolute last blog post until I get that stupid syllabus done.

My new favorite latex package

As I was reworking materials for the beginning of the semester (specifically, my Review of Prerequisite Material) and I thought to myself that there had to be a better way to arrange these problems on the page the way I wanted. So I asked on tex.stackexchange (which is full of very pleasant, very helpful people), and got an answer, which I was able to improve on a little to get the new template that I will be using any time I need to create a handout that consists of a bunch of questions/exercises.

\setlength{\spacing}{1in plus 1fil}
counter-format = tsk. ,
item-indent = 2em ,
label-width = 2 em,
resume = true,
after-item-skip = \spacing,
after-skip = \spacing
\setlength{\spacing}{#1 plus 1fil}
\settasks{after-item-skip = \spacing,after-skip=\spacing}

This is going to make it a lot easier for me to get things to look like I wanted them to.  Tables never really lined up right if the cells had text of different heights.  And plus, using tables is just a pain.  If you’re interested, here’s how my Pre-Cal Review of Prerequisite Knowledge looks now.  (ShareLaTeX doesn’t have the exsheets package yet, so if you really want to see it, you’ll have to download it and compile it yourself.  I put in a request, though!)

The blog project is on again!

Last year, I had a (mostly) optional project where I asked my applied calculus students to blog.  It had some very interesting results, and some students wrote some really interesting posts, but it was too unstructured for it to be beneficial the majority of students.  When I went to the Technology Integration Workshop a couple weeks ago, they helped me figure out how to add structure to the project.

At the time, I didn’t have a schedule yet, but all of the sections of the course I was designing it for were assigned to other faculty members.  At first (before the workshop), I was really disappointed about having to wait to do the project I was re-designing, but during the workshop I realized I had a lot of work to do, and maybe having a few months to do things slowly was not a bad idea.   I planned on asking if I could teach one section of Calculus I for Life Sciences in the Spring semester.  (Spring is usually significantly less crazy than Fall, and they will grant a request like that if they can.)  But then the schedule got rearranged, and I ended up with two sections of the course.

I decided very definitively last time around that there was no way that I could assess the writing of 90 students, do everything else that is required to teach mathematics well, and maintain my sanity, so only one section will be doing the blog project. Which is the perfect opportunity to evaluate whether writing about math really does help their conceptual understanding.  I’m still looking for the best way to do that.

Last time, I told students they had to post twice a week, and they could post anything related to math or learning math, although I wanted them to focus on the material we are learning in class.  That will still be the case,  but I am defining several types of posts that they can write, and I may require that at least one of certain kinds is required.  So many students had trouble just getting started last time.  The type of post that I got help with in the workshop is one I’m calling an “exercise report”.  This is basically making up a problem similar to a homework exercise and writing about the strategy (and why that particular strategy was chosen) and showing how to solve the problem.   I am still more interested in seeing students reflections on the concepts of calculus then their exercise reports, but I think that having a nice well-defined type of post with examples and a rubric will give students with less confidence an entry point.  And writing mathematically is definitely one of the standards I want to assess my students on.

I’m planning on writing up rubrics and examples for “application reports” as well, but that probably won’t happen before the semester begins.  The other types of posts will just get descriptions for now.

Background thoughts

I teach math at Texas State University.  My official title is “Lecturer” which is an adjunct position.  I do have to say that the math department at least pays its adjuncts fairly livable salaries (although it’s not great by any stretch of the imagination), and we are all guaranteed a full load, which is more than my colleagues in most other departments can say.

I got my MS in Math from Texas State in 2007.   I also got married right at the same time.  I was offered the lecturer job, and originally planned to teach for one year while I figured out which PhD program (in math ed) I wanted to apply to.  At that time, my husband was getting several calls from headhunters every week, so we felt confident in our ability to move anywhere in the country.  But then 2008 came, and the economy broke, and we couldn’t really justify moving and leaving his really excellent job just then.  And now it’s 2013, and we have a baby (a delightful one!) and I’m starting to think about my career in a wistful kind of way.

I have some serious frustrations with my current working situation.  Class sizes and lack of advance notice of what classes I’ll be teaching are the main problems.  Of course, since I only have a master’s degree, I’m very limited as to where I can teach in higher ed, and those problems will probably exist anyplace that would hire me without a doctorate.  And so I’m seriously considering several questions:

  1. Do I want to continue teaching in higher ed?
  2. Do I want to put in the time and energy for a PhD?  The money?
  3. Do I want to to do research? What kind and how much?
  4. What is my ideal working environment?  What would it take to get that?

I’m gearing up for the semester now, but these thoughts have been bouncing around my head all summer.  For most of the summer (and previously in the spring), I’ve been shifting around on the pessimistic end of the scale on how I feel about the future of higher education in this county (de-funding, hyper-focus on job preparation, framing education as simply the acquisition of facts), but the technology integration workshop I attended really put me in a more optimistic place.

More on that later…

So far this summer…

This summer has not been what I had planned.  Well, part of it has– I’ve been spending lots of time with my baby, which has been wonderful, but that has really been the only thing that has happened the way I expected.

First, I had to have my gallbladder out, so I had a planned surgery.  Then, it turned out that I should have had it out earlier, because I had a gallstone in my bile duct, so I had a second surgery on the next day.  I took it easy for a week or so, and then was planning on starting work on the materials for my online classes in the fall, when I realized that they never actually made it onto the schedule for students to register for.  I may have spent some time just being frustrated and angry about that.  I have no idea if the math department intends to support freshman-level online courses in the future.  Oh well.

Then I spent a little bit of time just being a mommy, which was fun but I realized quickly that I am a better mom if I get to spend some part of my week doing some kind of intellectual work.  So I decided to pick up an old programming project again.  There’s an open-source python library called sympy that is basically a computer algebra system.  It’s fabulous, and I use it as the basis for a practice problem/test generator that I wrote, among other things, but it does have one hinky bit.  It automatically distributes constants.  You can see what I mean if you go to SymPy Live and see the difference when you enter x*(x+y) versus 3*(x+y).  This frankly is annoying.  There are  workarounds: you can enter Mul(3,x+y,evaluate=False), but I find that really tedious, and if you enter Mul(3,x+y,evaluate=False) + x, you get 4x + 3y.  When you’re creating learning materials, you just need 3(x+y)+x to show up as 3(x+y)+x.  The team that works on it acknowledges that it’s a problem, but it was a decision that was made back at the beginning of the project, and everything depends on it.  It’s actually easy to change this behavior– you can just delete a couple dozen lines of code.  But changing this behavior breaks lots of other stuff.  Like, LOTS of stuff.  315 tests break.  And so I have taken on the project of actually fixing this.  There are a bunch of different modules, including ones for combinatorics, geometry, matrices, and quantum physics.  So this is kind of a big project, that requires me to refresh my skills in a wide variety of topics.  The sad thing is that I worked on this two years ago, and got it down to less than 50 tests failing.  But even though it was partly broken, it worked for everything that I would ever use it for, so I just used my crippled version.  Part of the reason I didn’t go back and ask the main devs for help was that the master branch was under rapid development, so by the time I got to this point, master had changed significantly, and I really didn’t have the energy at that point in the semester for rebasing.

But this software has been so incredibly useful (even in its broken state) that I would really like to contribute back to it.  So this time, when I reach the limits of what I can do, I’m going to ask for help.

Next week, I’m starting that workshop on effective technology integration for teaching.  That should be interesting.  Yeah, I really shouldn’t leave things as drafts for so long.  The two-week workshop is halfway over, but probably deserves its own post.  Or posts.  Let’s see how much time I have to write.