New Homework

I'm thinking about trying something new with homework this semester. The goal is to have students evaluate their own understanding, and have each individual decide how much they need to do in order to attain the understanding they desire. So each week I will tell them to work on particular sections. What they will turn in to me will be something like the following

• I attempted problems: (list of problems)
• Overall (or perhaps per section), I would rate my understanding at: (letter)
• I had the following minor issues: (list of problem with issue, things like... algebra/computational mistake, counting mistake,...)
• I had larger issues with: (list of problems, with work, and a description of the issue - couldn't start, got so far but didn't know what to do next, finished but got the wrong answer and don't understand why)
• Here's a well-written (sentences, little algebra) solution to problem X: (well-written solution).

As far as grading goes, I will probably do something like check for completion - is the student showing me evidence that they are thinking about the problems outside of class? Perhaps I'll use a 0 (didn't turn anything in), 1 (didn't spend more than 5 minutes on what they turned in), 2 (gave it an honest attempt).

There's certainly lots of potential for students to not take this seriously. To some extent, I'm willing to let them, basically. If they choose to not think about the course material, they can see what happens when an exam comes. If they do fine on the exam, so be it. I'm not here to do much for the students who don't need me for help (ok, whatever, I should try to challenge everybody?). I could also use quizzes to see if students claimed understanding is accurate.

So we'll see how that goes, I guess.

Netflix History

I'm in my 6th straight year of my Netflix subscription. I decided to see my complete history, and found that I've gotten approximately 600 movies through Netflix. A quick average tells me that's 100 movies each year, or about 1 movie every 3.5 days. That's nearly turn-around time for mailing movies. Since I'm currently on the 1-at-a-time, 2-per-month plan, I was kinda surprised. But I guess that's how averages go. In my most prolific month, I returned 20 movies. I was probably on the 5-at-a-time plan then.

Not that it's particularly useful, but I made a chart with the google chart api, showing (to first approximation) the number of movies I got each month. Basically I love coming up with excuses to play with the chart api. Anyway, here it is (even if some of the alignment isn't exactly right):
 

Colorado Hiking

Just got back from a great hiking trip in Colorado. I got to go with my best friend, Peter, whose parents live near Boulder and were great to us (Thanks you two!). It even sounds like they might not mind if I go back next year! Sweet!

We arrived in Denver in the late evening on Friday, and I don't remember doing much before bedtime. All of the evenings were pretty relaxed, sitting around eating and drinking, wandering around whichever town we were in at the time. Combined with hiking and running, there probably aren't many better ways to spend your time (though, of course, some dawdling around online doesn't hurt).

Saturday we woke up and Peter took me for a run of a few miles, to start getting used to altitude. Peter always kicks my ass running, and makes it look easy. I'm just happy he'll humor me with a run occasionally. It was a fairly flat route (east of the "Front Range", everything is pretty flat), but I certainly remember one hill (which might not even qualify as such in Charlottesville) in particular, and trying to catch my breath for a while. After we got back, we (me, Peter, and his dad, Gary - the same combo for all the hikes) headed out to NCAR (National Center for Atmospheric Research) for a hike up Bear's Peak. Actually, we were going to do South Boulder Peak, but there was maybe some map mis-reading, and it was on the other side of what we were anticipating, I guess. Still, it was a fun hike. Scrambling up rocks, lots of nice views, and more getting used to altitude. It was a... 6ish, let's say, mile hike with something like 2000' elevation gain, ending up in the 9000s. Good times. This was also our only hike without rain.

Sunday we got up and headed out past Rollinsville along a 7 mile or so dirt road to the trailhead for a hike up to Heart Lake. I think this hike came in closer to 8 miles, started around 9k, and finished up around 11k ft or so. I could be mistaken. It was a much easier, technically, hike than Bear's Peak, and gorgeous. Maybe someday I'll be in shape and go back to run the road and also the trail. Someday. Around the time we got the top, it started to drizzle, and it just kept raining harder the whole way down. By the end it was pouring, and lightning was getting pretty close (2 one-thousand ish). I regretted not bringing more of a change of clothes (or leaving clothes in the car - my pack wasn't exactly waterproof), but once Peter sorted out the heat in the car, things were looking better. We stopped in Rollinsville looking for a cup of coffee, but didn't have much luck. We did, however, catch guys with pistols and shotguns standing around the parking lot (we're talking right outside the store) shooting at birds. I don't think I'd last long in Rollinsville on my own. We drove to Nederlands for coffee, and it seemed like a cool little place.

Monday we took it pretty easy. Another half hour run with Peter, and his dad this time, to start the day, then we headed out to Golden (where Coors is made, or so), Red Rocks, and some nearby dinosaur tracks. I think it was this day that I started noticing more how brown everything was. Not that there's anything wrong with that, it's just a change from Virginia (I guess that's sorta part of the point of travel, huh? the change?). Apparently at Red Rocks people like to exercise, among all the stairs. You can run back and forth along the rows of seats; apparently getting 4 miles in without hardly changing your geographical coordinates. Watching everybody, I got pretty tempted to just try bounding up the rows of the stadium. Eventually I decided on a 'next time' approach. After all, we were resting up for our big hike the next day, Long's Peak.

Monday night we went to bed early. It's what you gotta do when you're going to wake up at 1 in the morning. Out the door at 1:30, then a bit of a drive, and on the trail by 3am. This out and back hike is something like 15 miles with 5000' of elevation change, ending above 14000'. Long's Peak, I hear, is the only "14er" in the Rocky Mountain National Park. I also hear it's one of, if not the most, hiked 14er (at least, the Keyhole route that we took), but that only 3 in 10 who try it successfully summit.

So anyway, starting at 3am, there's not much to see for a while. Just hiking along with headlamps on, seeing the first 20 feet, or whatever, of trees on either side of the trail. When we popped out above the tree line, it was still dark. However, the moon was half-full (half-empty?), and I found that it provided plenty of light to see by. We had a gorgeous view of the stars, and even saw a few shooting stars. I was feeling a little dizzy, and couldn't decide if it was the altitude or possibly just something strange with walking with your main light source being a headlamp. I felt a little better when I turned of my headlamp, but the dizzy didn't entirely go away. Probably I just started focusing even more on walking and staying upright, and didn't have as much time to notice the dizzy.

The keyhole route has a handful of landmarks. After you get above the tree line (a bit further than that, even), you come to a Boulder Field, where people camp, and there's some toilets. There are also marmots - always handy to have around for a Lebowski reference. From here you can see the summit basically (though not the route you'll take to get there), and the Keyhole. After the Keyhole comes, if I remember correctly, the Ledge (across, scary), the Trough (up, scary), the Narrows (across, scary), and the Homestretch (up, scary). You'll notice a theme here. At several points I considered telling Peter and his dad I was just going to sit tight and wait for them on their way back down. I kept plodding along though, happy to tell anybody who asked that I was terrified. Peter was worried I was getting mad at him for "making" me do this, but I was far to scared for that. And also too scared to notice much trouble with the elevation. Sure, I got out of breath, but not too bad.

You're welcome to call me a wuss, I don't care. I was scared. Death was quite honestly a possibility (indeed, it has happened to many on this mountain). All it would have taken was one wrong step. I wondered if there was any way I'd be able to catch Peter's (or his dad's) arm if he fell. Lacking anything like upper-body strength, I knew it wouldn't go well. We're all glad it didn't come to that.

We made it to the top around 8:30am. I sat around telling Peter and his dad that there was no way off this rock besides a helicopter. And I wasn't sure they'd be able to make it that high. Eventually (9ish) they decided it was time to head down. "Just take it easy, slide down on your butt", I was told. Of course, everything I know (nothing) says that sliding is exactly what you don't want to do. Despite all of my fears, down was, quite honestly, easier. I'm not here to ponder why (and why would you listen to me anyway?), but it was. Still scary, of course, but manageable.

We were back in the Boulder Field around noon, but decided (mostly) to not stop for lunch because the clouds were clearly starting to form. We wondered a little how the rest of the hike would go for the lady who happily professed that she was "Too f*ing old for this s*" when we passed her on our way down and her way up. Or the couple with their infant (seriously). I hardly wanted to be up there when the clouds weren't there. Perhaps lacking the panoramic view of everything (the cliff a step away) makes it easier, but I doubt it.

As we descended, I was looking forward to getting pictures of the "Alpine fields" we had walked through in the dark, and the forest further down. But right behind us was a rapidly growing, and darkening, storm cloud. Our pace quickened. And paused so we could take pictures, or just gaze around, check our packs for... whatever. And then quickened some more as the lightning and thunder built up. We were still above the tree line (and 2.5ish miles from the parking lot). While I appreciated being tall and lanky during other parts of the hike (scrambling over boulders and trying to make my way up the mountain), I no longer appreciated being the tallest thing around. Peter was behind me on the trail, so slightly higher still, but that wasn't much help. As we were about getting to the tree line, the hail started. I wondered about tornadoes, but couldn't quite believe they'd occur "at elevation". The lightning was more worrying. Eventually I pulled off the trail underneath a tree and next to a rock. Even after Peter said that's not what you're supposed to do, we stayed for a few moments. People passed us, just ambling down the trail, so we decided to go as well.

Eventually the storm calmed down, and I could start feeling the tired in my legs and feet again. The white of the hail all over the ground made everything fairly pretty, even if it was a little hard to appreciate, being a bit cold and wet. We made it back to the parking area, and changed into dry clothes, by about 3pm - 12 hours, 15 miles, and 5000' of elevation gain after our start. Good times.

When we got back and settled and fed and warm, we all started looking around for articles or trip reports about hikes from the day. Apparently the day we hiked was the 50th anniversary of the first successful summit attempt along a particular route (and by a math Ph.D. no less!). I didn't see many other articles. Now, a few days later, Peter and his dad have found some articles about another hiker who's trip didn't go as well as ours. I hope he recovers quickly. And I hope that everybody else on the mountain that day (and others, of course), made it home safely.

Wednesday was another relaxed day, and the day of my flight home. It didn't seem like the end of my trip, though. The flight was scheduled for 6:10pm departure, with arrival in BWI around midnight. We left at least an hour and a half late, due to weather, and got to Baltimore around 1:30am. Then the drive to Peter's place, and I was probably in bed by around 3am. Back up at 5 for work today. I can't say today was my most productive day of programming :) But I did stay awake the whole time, so I consider it a success. And I made it home, and my cats even seem basically happy to see me. So I guess now my trip is done, even if I'm not unpacked.

My pictures are posted (Warmup Hikes and Long's Peak). My memories are written. And my last dose of caffeine is wearing off. So it's bed time.

Some trail wisdom, straight from Sir:

It's always raining somewhere.

Take it easy.

Update 20100807: Peter posted his pictures.
Update 20100808: Gary's pictures and trip report.

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.

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