NCR Trail Marathon

This past Saturday I ran the NCR Trail Marathon. I'd definitely recommend it for anybody looking for a marathon in the Baltimore area in November. It's a primarily flat course (besides the first and last mileish) on some sort of paved path (but probably more forgiving than roads), and pretty, with lots of trees and water and farms. It'd probably be even nicer when there are leaves on the trees, but still. It's basically an out-and-back, for whatever that's worth. Before I get to talking about my run (sorry), I want to thank all of the volunteers, staff, supporters, etc. You all were fantastic, and deserve medals for standing out there in the cold all that time. The aid station volunteers were great about calling out where water was, versus gatorade. And all of the cheering was wonderful; I definitely got a good boost every time. Thanks, all.

My goal going in was to qualify for Boston, requiring a 3:10:59 clock time. I wasn't really sure I could do it, though I was pretty confident I could get a 3:20. I tried not to get my hopes up too much, but couldn't really help it. I've been feeling like I've been running pretty well recently, even if I've only averaged 33 mile weeks for the past 9, topping out with one 41 mile week. My longest training run was a 2:34 21.2 miles, 3 weeks ago.

I got up in the 5 o'clock hour, dawdled for about an hour, slowly getting ready, and stressing myself out. My sister, like a champ, got up early to head out to the course with me, and we got to the Sparks Elementary School, where the start/finish are, by about 8. It's a 9am start time, which is sorta nice and late. Of course, that meant another hour of sitting around, stressing myself out. And checking out all the other runners. Oh man, that guy looks serious. Are there supposed to be holes in that guy's shirt in those places? And look at all those ultra shirts. And Boston apparel. Etc.

I started off a few rows back, worried that the trail might not be too wide, and I'd get cut off (no worries there, it's a car's width throughout). Put in a sub-6:50 first mile, and joked with the guy next to me... "just a few more of those, huh?" It was sort of fun looking at the runners around me... that guy surely is gonna blow up... I wonder if I can keep up with that guy for a few minutes. Etc.

At the first water stop I threw water at my face. Some of it made it to my mouth. The rest reminded me that it was probably not yet 40 degrees, and windy. Somehow the wind honestly managed to be against us in both directions. I'm not the only one who says so, so it must be true.

By mile 2 or 3, the pack had thinned out pretty well, and I was basically running with another guy (who I recognized from the shuttle, also trying to qualify for Boston), putting in just-faster-than-7s. Before too long he got a little lead, and I was worried about blowing up, myself, so I let him go. About the same time another guy caught up to me, and we also ran together for several miles, still putting in 7s pretty consistently. At every mile marker we'd both check our watches. I'd do a quick calculation in my head to make sure we were still on track, and he'd check a pace chart on his arm. After the first one or two, I said something about "nice pace, huh?" and he didn't respond. Headphones. Alright, fine. We must have run about 7 or 8 miles together in silence, putting in basically 7 minute miles throughout. Occasionally I'd think he was getting ahead, and I'd think, "ok, just let him go, you gotta do your own thing." And then I'd think, "see what he's got, maybe you two can push each other the whole time". And, "should he be breathing that hard if he's hoping to keep this pace for 2 more hours? Am I breathing that hard?" Somewhere along the line he dropped off behind me. So I ran on alone.

Since the course is basically an out-and-back, you see lots of mile markers, in addition to the ones that are just part of the NCR trail. I definitely got in to looking for the backs of the second-half signs, then the yellow NCR signs, and then the first-half signs (and the other order after the turn around). At some point there's a "fitness walk" along the side of the trail. 10ish stations set up with "do so-and-so exercise here". I was a little amused.

Hit the half in the 1:31 minute, a pace just over 7:00s. Then the turn around. And over the second half, somehow managed to basically keep my pace, and pass several runners. According to the results, 8 of the 10 guys who came in just after me overall were ahead of me at the half. So that was sorta nice. I'd keep seeing people ahead and think, ok, you'll just tail this guy in. And then I'd catch up. And nobody passed me. It was kinda crazy.

Somewhere around mile 18 I started hurting. I was hoping that'd hold off until 20, but there it was. Just kept telling myself I only had so much time left. And wondering if I'd hit my 3:10. I knew I was doing ok with all of the 7s I'd put in, so thought about trying to drop off to 7:15s or 7:30s consistently. But I couldn't convince myself I knew what that pace felt like, so I just kept pushing. I couldn't tell what I was running, so it was always a pleasant surprise when another mile would drop off at somewhere in the 7s.

At mile 22 I was ahead of my 21 mile training run time, feeling pretty rough, but basically optimistic. With every mile I kept saying, "ok, you could run 9s and still make 3:10", and then it was 10s... Of course, each mile the calculations got more difficult, with my mind not really sure why we were still doing this. What time was I at at the last mile? What mile am I at? Am I still running 7s, or am I at 12s? (I know that my 23rd mile was still sub-7, which still surprises me) Why is that girl running toward me smiling? (It was my sister, who had headed out for a run of her own) Is it a bad sign that my hands hurt like that?

With about a mile to go I scooped up one more runner. And saw two ahead of me. I figured they'd keep their lead, but it kept getting shorter. Coming up the final hill, a little before the final turn, the three of us were together. I feel sorta bad passing people at the end like that, but I gave it a kick to see if I had anything left (gotta do my run, not anybody else's, after all), and if they'd answer. I sorta did, and they sorta didn't. Came in at 3:04:55 clock time, 20th overall, and 5th in my age division (2 ahead of me were in the top 5 overall, so I could have picked up my 3rd place award for my group). Pretty proud of myself, if the length of this post didn't give that away. Sorry.

The folks at the end grabbed my tear-off bib number, grabbed my chip, and gave me a metal blanket and medal. I took a few more steps and plopped down in a chair. Other runners walked on by, "good run". I rarely had energy to answer. It was still cold and windy out, so I walked a little bit further down the hill, trying to make it back in to the school, but had to sit down again. My legs hurt, and with the blanket, I could just about avoid the wind. At some point while I was sitting there, my sister made it back from her run, and sat with me. She must have been cold, but she stayed with me anyway. A few more small walks and stops, and I eventually made it back into the school (cursing the whole way). Stopped right inside the doorway huddled up against a wall. One lady walked by and saw me shivering and gave me her metal blanket. I kept shivering. My sister kept chuckling. People kept walking by telling me about the hot soup just inside. Eventually I made it back onto my feet, and to the soup table. I must have looked pretty ragged; the lady seemed a bit concerned. I was shaking quite a bit, so she gave me some coffee to warm me up, and some soup. Made it to a seat at a table, and didn't get up for probably half an hour. Sat there with my sister, talking about our runs, shivering. Feeling like the other runners didn't look nearly as rough as I felt. The soup really was quite good. And my sister was awesome.

I think it was probably about 45 minutes after I stopped running that I finally stopped shivering. Sorta makes me think probably I gave just about all I could to the run, which is a good feeling. I definitely don't think I could have done any better. And now I guess I start looking forward to Boston :) Of course, there's an ultra in March I've got my eyes on...

A Textbook Poll

In association with my class project of making our own book, one of my students has made a quick poll about textbooks. If you are a student, or wouldn't mind sharing this with any you know, we'll be happy to have your feedback. So, if you've got a minute,

Take The Poll!

Well, In My Defense...

I gave my Ph.D. thesis defense the other day. It's sort of an odd thing to call it a defense, for a math paper. You argue in the humanities (I think, I haven't spent much time there). In math, you're just presenting facts, it's (sorta) the nice thing about math. Well, that's the ideal, I guess. There were certainly some weak joints in my work, but, as expected, people didn't have enough time to really stress about them. Which is nice.

When the thesis committee told me they were allowed to torture me with questions after everybody left, I told them, "knock yourselves out." Got a little chuckle. One professor asked what the hardest part was. I had wondered if somebody would. The hardest part was convincing myself it was worth doing --- was more worth doing than the other things I wanted to be doing. Luckily, he extended his question a little before I got to it (besides a grin), and I ended up just telling him about what math took the longest to piece together. The same professor asked if I was going to do anything with this later, that it would require some re-writing. I told him I had no intent of doing much with it, but that it would be freely available online, and he could do with it as he liked. He also said they could send me some changes that I should make. I guess when I said "whatever flips your switch", he realized I didn't care much to do them, and he, appropriately, didn't care enough to send the suggested changes to me. I didn't make any comments about how they were still allowed to make me jump through hoops, which is a little too bad.

The talk itself was fun. I do enjoy giving math talks, especially when I understand what I'm talking about. Threw in a couple jokes, got a few chuckles, put at least one professor to sleep. All in a day. I've got some notes about the presentation itself on my other blog. Or you can poke around the thesis material at my homepage.

So that means I'm nearly done. Still some administrative nonsense to do. And still a few weeks of "teaching". But nearly there.

A Homework Experiment

At the beginning of the semester I decided to try something new with homework. Basically, students were supposed to do as many problems as they thought necessary to get the understanding of the material that they desired. If a student notices that there are essentially one or two types of problems in a section (as is frequently the case with our textbook), they probably don't need to do many problems. Other students might require more practice to feel comfortable with material. I gave them the responsibility of deciding for themselves how much to do.

Each week, students turned in a sheet saying which problems they did, how they would grade their own understanding, what major and minor issues they had, any questions they had, and a "well-written" solution to one problem. Grading has been pretty easy, and I've basically just graded on completion. It's been nice to get questions on homework (and respond with individual answers), and to see students evaluating their own mistakes. Quality of "well-written" solutions varied a bit, but I did see many good ones.

Our first exam really didn't go so great, even though I hadn't seen many students rate their own understanding on homeworks much below a B. I think this was partially due to this relaxed structure of homework. After the exam I asked the students to tell me (anonymous feedback was fine) if they wanted to see anything change to make the class better for them, and I never heard anything. Our second exam, last week, went a bit better, and I like to think perhaps study habits had improved.

Anyway, part of what I wanted to see, doing homework this way, was if there was a relationship between number of problems done for homework and exam scores. I've been keeping track of how many problems each student did each week (probably miscounting slightly occasionally), and so after this last exam I broke out gnumeric. In the name of privacy (thanks to those in my twitter/facebook network for their thoughts here), I varied each point by some random small perturbation, and have removed axes labels and scales, with the following result:

The x-axis is number of problems done, and the y-axis is the sum of the two exam grades divided by the sum of the two best possible exam grades. It's nice to see that the linear fit has a positive slope, at least. The correlation coefficient for the actual scores was about 0.23, so not so great. What I find slightly interesting is that it just about looks like (and does in the actual scores too) there are 3 clusters... a large collection on the left, another 8 there in the middle, and 3 more at the end who did lots of problems.

I know it wasn't particularly scientific, or rigorous, but that's what I've got. I never told the students I was collecting this data (I'll show this to them in class tomorrow), in hopes that they wouldn't be just making up how much they did, but it's still a possibility. I almost wish I'd kept track of the scores students gave themselves, but it's too late now.

Speaking of class tomorrow, I better go sort out what we're doing...