Super Troopers

Super Troopers is one of my favorite movies. At some point recently I decided it was time to watch the Broken Lizard collection again. Then a friend pointed out their most recent just came out. So it's been a good time for movies recently.

As I was sitting down to watch Super Troopers, I thought up a fun project: try to pick a single frame "for" the movie. I haven't really been able to further describe what I mean... "advertising" the movie doesn't quite cut it, nor does "capturing", entirely. But something like that. So I pulled out a couple, and thought I'd share them. That's what the ends of semesters are for, right? Movies? I guess exam time was always Dr. Mario time when I was a student...

I've put a good line with most of the frames. It's not always the line going on in the frame, but it's nearby.

A friend who has seen the movie many times (perhaps not particularly recently) suggested the following from memory:

"Do we look like the two dumbest guys in the world to you?"

Another friend, who hasn't seen it quite so frequently, picked out the following scene (I grabbed what seemed a good frame to me):

"Good enough for me!"

There's a lot of magic in the first scene, but I'm not sure I found a particularly great frame. From it, I picked out:

"What'd you say man?"

Of course, one of the most-quoted lines, I expect comes at the burger joint:

"I don't want a large Farva."

But a good frame should probably be a little independent of the lines it suggests. There's a fair amount of humor tucked in this frame, but it might be a bit buried:

"Ten deep breaths, I got it 'cap."

This one's a little bit more obviously funny:

"Okee silly dilly dokey oh, I'm an idiot."

As is this one:

"Finish it up, rook."

I also like frames with the group, in uniform, but not looking particularly official, like:

"It's really funny 'cap. It's Afghanistanimation."

or

"Maybe we should take another look."

I think if somebody made me pick a single frame, it might just be this last one.

Apparently my point is you should probably just go watch it. And maybe let me know what frame(s) you'd pick.

Finishing Up

Still have one student that needs to take a make-up final, but I'm basically done for the semester. I all honesty, I probably checked out a few weeks ago. I've got something like a vaguely un-scheduled week ahead of me (besides a Flying Karamazov Brothers show!), until a math conference in Georgia in the second half of next week. People tell me it'll be good to go. That remains to be seen. And basically as soon as I get back, I start a summer programming internship at Rosetta Stone. Could be something. So with my loose week, I just gotta bang out a thesis so I don't have to come back in the fall...

Err, right. So this post was supposed to be about thoughts about my class this semester. Things that went well (it ended). Things that went poorly (the other parts). Things to do differently next time (next time‽). Something I can look back on in the fall for guidance.

So... reading assignments with homework due before we talked about it in class didn't go hugely well. I stand by the method. But I've also been reading about how homework itself, as a graded assignment, sucks (maybe start at joebower.org if you want to follow along at home), so I'm a little torn. Halfway through the semester I switched to the following setup: read the book for Tuesday, and submit a "discussion seed" based on the reading, as your homework assignment for Tuesday. I then used the those discussion seeds as what I brought up in class Tuesday, and then had written problems due Thursday. Seemed to go fairly ok, as a setup. Basing class time on questions students had actually submitted seemed like sort of a fun idea. Having the questions as a Google Docs presentation seemed to work ok.

My students really seemed intrigued when I showed actual housing cost data, so I should work to bring more actual data into my classroom. I was also thinking it might be cool to have guest speakers, maybe from banking or realty. Perhaps I'll look into that more for next semester. Probably the best thing about this class is that students can actually mostly see it as something useful. Putting money in an account, saving up... sorta easy to relate to, I think. There's some amount of intrinsic motivation there, if I can just capture it.

One important thing I didn't know going in to the semester was what sorts of students took the course. It's a 100-level course; I was expecting mostly freshman and sophomores. No dice. Probably half of my class was graduating seniors, many of whom already probably knew basically all of the material. I sorta have a hard time believing these students should actually be allowed to take this course... this is part of the stupid game I hate about education when I think about it these days. I had friends in undergrads who, as graduating actuarial science seniors, took 100-level "finite math" sorts of classes. This seems like what sorta happened with the class I taught this semester. The impression I get is that many of them were then upset with the class for being boring. What the hell do you want from me? Other students, in the last few days, have mentioned that they thought I did well trying to balance for these students along with those who actually didn't know much of the material coming in. I think it helps that mostly the students who didn't need to be there stopped showing up.

Another thing I didn't know coming in was the content of the course. I was reading the book along with the students. Turns out, there's very little material. In a few-minute wrapup I did on the last day, I told my students how essentially we did one thing all semester: move money around on a timeline. Compound interest is just iterated simple interest. Bank discount interest is just simple interest from a different perspective. Annuities formulas are just conveniences for dealing with many things moving around at compound interest. And that's all we did. I'm a little curious to see if I could teach all of the formulas in a week or two. Knowing this, I intend to go faster next semester and cover more material. I think this should help with some of the boredom issue.

I'm toying with the idea of using next semester, when I'll likely be teaching the course again, as a chance to have the students write their own textbook. There were enough errors and oddities in the textbook we did use, I have a hard time believing we couldn't do better. We'll do a big collaborative project, as the entire class, writing a book. I think a project like this could be good for having students involved and interested. I also think it should be a good way for students to learn the material - you learn best by teaching. And, finally, I think we could make a pretty decent book.

Each semester we math grad students are given a teaching request form, where we get to request what to teach the following semester. Basically it's one of the four calculus sections (two levels of calc 1 and calc 2), and then occasionally this financial math course, or a calc 3. On my form, I requested to teach this financial math class again. A friend thought I was joking when I told her. My advisor asked if I was a masochist. I think, having gone through it once, the next time can't help but go better, which will be nice. I know the material now, and might not be quite as caught off guard by my class being mostly seniors. Also, the class has no emphasis on algebra, my current frustration with calculus courses. I do need to try to design better assignments that have students explain their work more, but hopefully I can sort something out. Writing a book should be good for that.

Anyway, I'm off. Take 'er easy.

Teaching

I've started thinking that, perhaps, I don't actually enjoy teaching. Which is to say, there seems to be quite a bit about being a teacher that I really don't care for. Or I'm doing it wrong. Perhaps this is just how it all goes... nothing's perfect, right?

I love learning (my own, I'm not sure I can sense others'). I love reading. I think I enjoy meeting with individuals, or with small groups, who are truly motivated to learn something that I can help with. Not motivated in the sense of finishing an assignment, but in understanding material for understanding-sake. Perhaps it's content I already know, or something I can join them in learning. That might just be where my joy in teaching ends. Sadly, this doesn't seem like much of what school is (or, like I said, I'm doing it wrong).

I want to help individuals learn something that they are interesting in learning. I have no interest in talking to a classroom full of students about things few of them care about. I have no interest in trying to motivate them to care. I have a hard enough time with my own motivation to encourage others in that regard. And, looking back, I know that when I was a student, I didn't care about most of my classes, and don't expect I was interested in being told I should care. I didn't try to learn the material for its intrinsic value. This is especially true outside of math and computer science, but I expect even in some of those classes I was just getting through assignments (at least sometimes). Now that I'm about done with taking school, I'm finally ready to learn just about anything.

Probably I should just suck it up. There are always at least a few students who are paying attention, who are learning something, right? I should focus on them, right? I should figure out how to make things so exciting that people just can't help themselves but want to learn? I should continue giving homework and exams and playing the grading game, without it helping my students much at all. I should humor the notion, hinted at by award nominations, that I'm a "good teacher", despite knowing that I'm hardly doing anybody much good.

I should continue playing this game.

But I think I've realized about myself that I don't like other people's games. I like my own games. I think I might go find some of those...

A Smile

As my amused smile
turned full-face grin
staring at my plate
I hated her for making it so

I couldn't look up
I knew I'd see
Her smile.
Her eyes on mine.
His smile.

It's ok to smile
I told myself
and never came
her sass about it

The mistakes I've made.

=========
Sorry usual readers. Back to my usual confused rants with the next post, surely. I reckon this one at least fits the "confused" trend.

Textbooks

(begin rant)

Two days ago, an email went around the math department here indicating that the higher ups were thinking about changing calculus textbooks, and that there would be a meeting today to talk about it. The meeting was essentially a presentation from a salesman from the textbook company about how great the new textbook is. A few minutes of discussion before-hand, and a comment that those making the change (I'm pretty sure it's a foregone conclusion) would hear our thoughts on the matter. I sorta felt, leaving the meeting, that we'd get a somewhat formal (at least an email) request for comments. Now, a few hours later, I'm guessing we wont. In fact, they probably just signed a contract while the guy was here today.

Sorry, I'm a bit cynical.

Before I go on, I'm probably supposed to make some disclosures. I have at times made (and am currently making) money doing things associated with the Webwork online homework system (admin, library tending). I grew up on Stewart's textbook (used it as a student, and it's what UVA has been using since before I got here). The textbook we are thinking about switching to (like, apparently, everybody else considering switching textbooks) is Briggs and Cochran. At the meeting today, I got a free copy. They also gave us an access code to their online software, MyMathLab.

In all fairness, the new book looks fine. It looks like basically every other recently-released calculus textbook I've looked at (don't take that to mean I've looked at a lot, of for large amounts of time). There are lots of pretty pictures, and apparently the author(s) are big on geometric intuition, which is great. We were also told to be impressed that in the worked examples, each step was given a little explanation. And, gosh, isn't this something amazing, the authors organized the problems at the end of each section carefully. We were told several times that this was not a lower level book, clearly something the publishers are worried about people thinking. It is, as @MitchKeller opined about the projects it has, "a bit hand-holdy".

Oh, and there'll be a new edition along every 3 years.

Of course, the textbook by itself isn't, I expect, what people are all giddy about. The textbook is paired up with MyMathLab. You can make online homework assignments and quizzes. There are little tools for the students to use to get help, like looking at worked examples, looking at a digital copy of the textbook, and probably some others I forgot. Students can also see a little "Study Guide", a sort of summary of what sorts of problems they missed, so they would know what to go back and look at. Oh, and some large collection of those pretty pictures in the text are pretty animations (calculus being about change, we were reminded by the salesman) in the MyMathLab system.

Students have the option to not buy the physical book (at least, in theory, who knows what our goofy school will require), and instead spend somewhat less and just use the e-book in MyMathLab. I seem to recall the e-book being in the $70 range, the first year textbook in the $90s, and the 3 semester book in the $130s, +$6 for the MyMathLab software if you buy the textbook. These numbers might all be before bookstore markup (we were also told to be pleased that the UVA bookstore markup of ~25% is really low... go team!), and we were told that these prices are cheaper than Stewart. The presenter today did this cute thing where he pretended not to already know the price of the books, and looked them up online.

Digital rights management didn't really come up at the meeting today, and I'm ashamed that I didn't bring it up.

Quite honestly, it seems like a not entirely bad thing. Switching textbooks isn't the worst thing we could do. Like I said on twitter after the meeting, though, it feels like shuffling deck chairs on the Titanic.

If I were given freedom to set up the course however I wanted, I wouldn't require that my students purchase this, or any other, textbook. There are simply too many free resources online for me to justify requiring students to spend that money. If students want to buy the book, or the software (more accurately: access (likely temporary) to it), good for them. Go for it. But if a student would rather use their brother's old textbook, say, or the free ones they find online, that's fine too. If instructors are going to lecture (I generally do, more than I'd like), many students can likely get by on class notes (their own, or a friend's), maybe in combination with some office hours.

Sure, the pictures in the book were nice. And the animations. But there are plenty of calculus animations online (I'm not gonna google that for you). In fact, I could roll my own (and have, happily), and would be delighted to teach students to do so as well. It'd be awesome to talk to students about pictures during class, draw them on the board, and then have them make a digital version of the picture, or an animation (for the ambitious) (and release them all under a CC license, wouldn't that be a fun thing to talk about in class). Heck, why not have the calc students write a book, complete with pictures? Write about the things they got hung up on, and what got them over it. Make a wiki. The instructor likely has access to several textbooks. Use them to put together an outline for the semester. Lecture if you want, or tell them to go see what they can learn online or at the library (then use class time to synthesize what was found). Looking up resources online, you also get to talk about evaluating resources, and how to compare different sources. You can build up a big huge list, and have students rate each source (and share your result with... everybody!).

And as for step-by-step explanations, WolframAlpha jumps to mind, but there are certainly others (I'm not gonna google that for you either). Don't like W|A's solution to a problem (they can be a bit... pedantic)? Have students talk about improvements. This also points out that those problems are pointless anyway. A computer does them more quickly and more accurately, so let it. Let's work on understanding concepts, instead of continuing to test pointless algebra tricks. Use the time that we're not doing mechanical manipulations to come to the geometric understanding slowly, guiding students to discover it for themselves.

Webwork has, for me, done a perfectly adequate job as an online homework system. If UVA doesn't think the problem library is nice enough, of the interface good enough, perhaps they should invest some money in improving it (I know they (at least, Dr. Jeff Holt, through a grant) have to some extent, and also that there is money floating around). Then even more people benefit (webwork is open source), and UVA gets some nice credibility. Webwork can do most of the things the guy today tried to sell us on for online assignments, though it's interface might not be as gosh durn pretty. It will not show students which section from the book they missed problems on (it's not tied to any one book). But I don't really see the problem here. I think it would be a great exercise to teach students how to evaluate for themselves which sections they need to look at.

I know I'm not going on much but youthful optimism and naivety. It's not the first time, nor likely the last. I have no expectation at all that the powers that be will take my thoughts seriously. At least here I can pretend that my thoughts are worthwhile (thanks Blogger). I'm leaving after next year anyway, and have seen no evidence (I suppose I haven't asked) that the younger grad students think like I do. I should probably just let it go (until I'm at another school). [As I was writing this post, I decided to email the math grads, to see if they'd like more flexibility in their teaching.]

All I want is for the department to allow instructors to try something different. Let us not require our students to purchase the (any) textbook. Get out of the publisher's pointless "new edition" cycle

Think about dropping the heavy emphasis on algebra.

(end rant (for now))

Thoughts on "Dehumanized"

You should go read "Dehumanized: When math and science rule the school." Even if you've read it before, and even if it was recently, go read it again. Perhaps a few times.

In this essay, Mark Slouka expresses disappointment that education is being "retooled... into an adjunct of business" at the expense of the arts and humanities.

This is certainly a fair thing to be disappointed about.

I've never really been "in to" the humanities. I don't remember ever much caring about my history classes, or social studies. I don't think I took many literature classes, and can't say I feel like I got much out of any that I did take. I blame nobody but myself, of course. While reading "Dehumanized" I became convinced that I have seriously missed out. It's sad that now, age 26, supposedly 1 year away from a Ph.D., I'm finally ready to go to school.

I do not agree with everything in the article, though. Throughout, Slouka seems to wish that civics were the highest goal of education. I'm not sure I see why this should be. Of course, I'm pretty sure I don't even know "what" this would be, so I don't have much basis for argument. But I think many of the goals Slouka advocates, with the apparent intention of improving individuals as citizens, are goals I do agree with.

Slouka asks, "What do we teach, and why?" Clearly a fantastic question. He even provides some answers: "whatever contributes to the development of autonomous human beings", "in order to expand the census of knowledgeable, reasoning, independent-minded individuals." I like those answers, even if Slouka seems to want these things for the purpose of "the political life of the nation." I guess I feel like I want these things for the individual, and those around the individual. Perhaps that's what politics is/are. I don't know, I probably wasn't paying attention that day.

The humanities, it is claimed, are there to talk about "what it means to be fully human," to teach "not what to do but how to be". The output is "the reasoned search for truth." But then Slouka says these things are all, "inescapably, political." Perhaps the reasons why all point out why I don't know what "political" means: "they complicate our vision", "grow uncertainty", "expand the reach of our understanding" (and thus "compassion" and "tolerance"). One goal seems to be "an individual formed through questioning". The de-toothing of humanities education is summarized:

Worried about indoctrination, we've short-circuited argument. Fearful of propoganda, we've taken away the only tools that could detect and counter it.

The arts and humanities are there to "upset people", prompt "unscripted, unapproved questions", and, according to Don Randel, "force us into 'a rigorous cross-examination of our myths about ourselves'". Slouka quotes the teacher Marcus Eure who wants students to have "depth of experience and a willingness to be wrong", and notes that "every aspect of life... hinges in some way on the ability to understand and empathize with others, to challenge one's belief, to strive for reason and clarity."

These all sound like awesome things.

What confuses me about the article is that the author doesn't seem to think math and science help with these goals. I just don't see that at all. Uncertainty? Understanding? Questioning? Cross-examination? Reason and clarity? How are those not in the realm of math and science? Sure, the topics that are questioned and reasoned about are different for mathandscience than for the humanities, as it pointed out by the article. But how can the questioning nature of mathandscience, the logic and reasoning, not be helpful in the humanities? Is it because math and science education, in parallel to education in the humanities, isn't what it really could and should be? Of course, having also just re-read "A Mathematician's Lament", I worry that this is quite likely the case. But that's probably the topic for another day.

Project Wrapup

I want to share my thoughts on how my recent in-class project went. Basically I still think it's a reasonable project. It certainly needs some tweaking though. I'm kinda excited to try it again.

Recap

Class began and I started as close to on time as possible. I had already posted the assignment, and some students had seen it. I did a quick run-through of the setup, explaining the two parts (write your own problems, with solutions, and solve a different groups problems). As students divided themselves into groups I distributed printed copies of the assignment. Students got in and settled and started working pretty quickly, which was nice. Throughout, it seemed like students were doing a reasonable job staying focus on the task. I think the time pressure helps with that.

I let students work without any interruption for a few minutes. One student came to me and asked if the problem he had written was ok. It looked quite similar to textbook problems, which I told him, and he went away a bit disappointed. After a few minutes I started wandering around to each group, asking how things were going. Many of the groups were perfectly happy, and didn't have any questions for me. A few groups were having a hard time coming up with things. I tried to indicate how one might make up a new problem. For example, make up crazy rules a bank might use for some sort of account. Or: look at a textbook problem. They solve an equation for one of the 4 variables in our formula. Change the problem around so that a different variable is the one to be found. Sometimes this might not make a particularly new problem, but I think sometimes it could. The students I gave these suggestions to seemed to think they could make progress, and got back to work.

A few other students showed me problems that looked like textbook problems. One told me that it was different, and I challenged him to explain how. He noted that his problem tested the interpretation of the answers from some textbook questions. I can't really argue. He had 3 problems, 2 of which looked like textbook problems, and the third asked for the interpretation. Fair enough I guess.

At the half-hour mark, when students were supposed to be done writing problems, nobody was. I talked to them about it, and it was pointed out that probably solving problems that are already written would be quicker than writing your own. So the second half should go quicker. Makes sense. I told them all to take 15 more minutes on writing their own questions and solutions.

Just after the first group finished, it occurred to me that I should emphasize that they are all getting the same grade. So they should make sure to double check each other's work. I think many groups were divvying up work, so that each person wrote a solution to one problem. This is fine, but I think it is important that all of the group members double-check this work too. I made an announcement about this.

We were running out of time. With 25 minutes, groups were mostly starting to finish, and I re-distributed problems to groups that were done the first part. Since the time wasn't working out as I had anticipated, I told them to solve 2 of the 4 problems they were given.

With about 15 minutes to go, all but 2 groups had begun the second part of the assignment, solving another groups problems. One of the two remaining groups finished (group A), and the other was done 3 of 4 problems (group B). I took the 3 problems over to the group A to start the second part, but let group B continue working on their own problems. Group A eventually finished, about 5 minutes over time, and group B didn't have any time to work on group A's problems when they had finished writing their own. I'm still trying to decide what to do about that. [I assigned them some of the more challenging problems I had written]

While students were working on problems other groups had written, I decided it might be interesting to have them rate the creativity of the problems they were given. I told them to rate each problem they were given with either a 0 (this is a textbook problem), 1 (kinda new), or 2 (terribly interesting). I'm not sure how seriously they took this task, I have not yet (as I write this), looked at the work that was turned in. [Mostly I think this turned out ok, though some 2's were pretty questionable]

As students were finishing, I told them (a) I wanted feedback on the project, what they liked/disliked, how it could have been better, and (b) that I'd probably like to try this again, so to keep track of questions they think of outside of class.

After Class

I've been trying to write daily (we only meet twice a week) blog posts for my class, on whatever we talked about that day. I don't think any of the students are reading them, but I could be wrong. Today I posted questions I had dreamt up, to give students some sort of idea what I had in mind. Some of the questions I had though up before class, others were inspired by discussion in class.

As I was writing up my questions, it occurred to me that several of them weren't quite as original as I had originally (bam!) thought. I could see how to translate my problems into textbook problems. I do still feel like there would be a translation step though, and I guess that's part of the game. Or perhaps I'm fooling myself.

I emailed the class, specifically encouraging them to read my post, and also to provide feedback. Hopefully the reminder generates some feedback.

Initial Reaction

I mis-judged timing. I had originally given more time for doing other groups problems than writing one's own. Definitely backwards. Probably we could do 45 minutes writing problems, and 30 answering others'. Also, I think I need to be firm on the deadline if I try this again. At 45 minutes, you will have to give me your paper, and will lose points for not having written enough problems (well, you just don't earn the points you would have). Of course, that means the group that gets your paper isn't being graded out of as many problems, which must be accounted for. Hmmm.

I think trying this again, students may have a better sense about the project. Writing problems might come easier. Hopefully, then, timing would work out a little better. Perhaps showing students a list of questions before-hand would have been a good idea.

I didn't plan enough about organizing the work that got turned in. I'm sort of dreading looking at the pile. Here's how I think I'd organize it next time: Each group is assigned a number. There are then 4 things they turn in to me by the end of class:

1. The list of problems they wrote. This should have "Written by group N" on it. It should also have "Solved by group M", the group that gets these problems.
2. The list of solutions to their own problems. This should have "Written by group N" on it.
3. The list of solutions to the problems they were given. This should have "Solutions written by group N, for group M's problems" on it. These solutions should not be on the same paper with the questions, since it mucks up re-distributing papers (more on this below).
   
4. A paper with the group number and names of all of the group members. I suppose this information could just go on, say, the list of solutions a group writes for their own problems

I need to bring a stapler to class.

I sorta like the idea of getting students to rate the problems they are given for creativity. I can't quite decide what to do about giving points based on those ratings, as they'd be pretty easily gamed. One option I came up with: Have students rate the problems they were given on the 0-2 scale above. As I'm grading, type up all the problems that earned a 2. Distribute this list, without any identifying marks, back to the students, and have them pick their favorite n, say (outlawing voting for your own (more bookkeeping for me, but doable as long as I have them write their name on the paper)). Any problem that gets more than m "favorites" earns the authoring group p points (1, likely).

Grading

As I organized papers, and got to a point I could start grading, I realized that I could extend this project to have the students do the grading. Group A gives their answers to Group B, and when Group B is done, Group A grades the solutions. This could be a valuable exercise for the students, seeing how their questions were interpreted, perhaps seeing other ways to solve questions they had designed. Of course, it leads to problems about what grade gets written down in the grade book... suggestions?

As I was grading, I realized that students can game the grading system by writing easy questions. This guarantees 3 points for solutions to each problem the group writes, even if they lose a point or two for writing uninteresting problems (I was pretty relaxed about taking points off for this). Perhaps this can be corrected for by having other groups rate "originality" first, (maybe "difficulty" too) and then base the score solutions are worth out of that grade?

Maybe take interesting problems in to class, have everybody do them, and talk about answers. Also problems with difficult wording.

On re-distributing papers: Group A did Group B's problems. Giving A's solutions back to A, they probably won't be able to see B's questions, to look back at.

Student Feedback

At this point, I still haven't gotten much. One said they enjoyed the project, even if making up problems was difficult. Another suggested just writing up questions individually and exchanging papers with partners; that working in larger groups was hard. Also the timing issues were pointed out.

Current Thoughts for Next Time

Be more organized about what names I need to see on which papers. I found that the paper-shuffling aspect of grading was easier for groups where group A did group B's problems and vice-versa. I'm not sure that it matters too much though.

Perhaps break this project into two class period. In the first, groups will meet to try to create interesting problems that they could solve (though I won't ask for solutions just yet). The problems will be re-distributed around the room, and groups will rate the originality and difficulty of the problems they were given. I will then gather up all of the problems, and we'll end class. Before the next class, I'll go through all the problems, find all those that earned good originality/difficulty ratings, and compile them into a list. In class the next time, all of the students will work those problems, maybe just working with a neighbor. Then we can spend time in class discussing solutions to the problems, talking about different interpretations of questions, what makes questions well-written, etc. There's issues here about turning in solutions - if students just wait until we talk about solutions in class, they can just copy those.

Thoughts?

I'd really like to know what you think about any or all of this. I know it's rather a lot to read through, sorry.