Monday, November 30, 2009


Well that's it. This marks the end of National Blog Posting Month (which I mentioned earlier), or at least my participation. So what have the results been?
  • It turns out that over the course of November I wrote about 10,000 words for my blog. That's fully 1/5th of the goal for NaNoWriMo (National Novel Writing Month), so who knows, maybe someday I'll try that too. I can finally write my novel about the smart, hip, jet-setting, handsome mathematician who has men fawning all over him. (Hey, this is my Mary Sue, right?)
  • I started this blog August 2005, which is about 4 years and 4 months ago, or 52 months. At the start of November, I had 162 public posts. That means I was averaging around 3 posts a month, until this month when I produced ten times as many. Or, over the course of this month, I've increased by almost 1/5th my total postings.
  • Sometimes I faced some writer's block of course, but usually once I picked a topic, I found I had things to say.
  • I've written about an enormous variety of things. I've talked about students and teaching (including the good, the bad, and the ugly), holidays, dreams, visiting a conference, and random musings of my own mind. Some days I wish I had a more interesting life, but often I like it fine.
  • Not everything I've written has been a gem. But I've definitely written things I've liked, and some of them seem to have inspired other people to chime in. It does definitely convince me that I should write more often. Having an explicit (and public) goal definitely spurs some creative work. I'm not sure if I'll participate again in the project or not in any sort of semi-official way. (As I noted, I wasn't doing anything official this time; I just thought I'd try it.) For the moment, 'though, I may take a pause before I write again.
Well, a good night to all, and a happy upcoming December. Be seeing you!

Sunday, November 29, 2009


I don't care for the cold. (I don't know what I think I'm doing up here. Who am I, Nanook?) But I do like burying myself under a heavy pile of blankets to go to sleep at night when it's cold. Flannel sheets, a big artificial down comforter, maybe a quilt, 'til I'm nice and toasty, and trying not to let any part of me poke outside my nest. It's wonderful. The only problem is that it's still cold in the morning when I wake up and have to get out of bed. I think bears are onto something. If I could just sleep through the winter and wake up again when it's spring, I'd be all set.

Or I just need to live someplace warmer.

Saturday, November 28, 2009

What students hear

I sometimes think about what students hear when we (their teachers) talk. I don't think undergraduate students (even good ones) manage to grasp the essentials of mathematics. I don't think they see what we are doing as logical reasoning based around some fundamental principles. They hear the specific words and explanations for a particular problem, but don't grasp that what we say comes from some coherent system. This is not necessarily because we don't say that this is so. It just seems that this concept doesn't completely register in the time we have them. It might later, or it might not.

When, for example, we want to find all solutions to x2 = x, I might suggest dividing both sides by x, getting x = 1, which is one solution. I then note that we can only divide by x if we assume x is not zero, and in fact x = 0 is the other solution. We then have all solutions to the equation. To me, at this point in my life, I see division of both sides of an equation as a legal operation with very specific restrictions (namely, that we cannot divide by zero). I also recognize that since we can view both sides originally as multiplied by x, that x = 0 is certainly a solution. But I remember when things were not quite so coherent, and then the step back to note that we cannot divide by zero seemed like a trick just to justify a zero solution. It seemed that a lot of algebra (and some other mathematics) was made up of a bunch of special rules and exceptions, and it seemed like teachers had a never ending supply of these to pull out to justify whatever they said the answer was. It seemed a bit like playing pretend with a small child, where there is an exception to everything, to be made up on the spot: "Oh yeah? Well I had my invisible anti-force field magic belt on, so I could escape from your force field!"

How do people learn to see mathematics (or any field) as a unified whole? Perhaps part of it comes from time and experience. It may just take a certain amount of time working with the concepts before they become solidified and can be deftly manipulated. It may be similar to the feeling I can still remember in college, when I became sufficiently comfortable with algebraic manipulations that I could use them to do faster mental arithmetic, by disassembling and reassembling the numbers in convenient ways, making the numbers dance as needed. It's not that no one had ever suggested the idea before; it's popular to present these ideas to students, but until those concepts are internalized, it doesn't make mental arithmetic any easier. It just seems like a trick--and a somewhat painfully difficult one, at times.

Or maybe we need to give students more opportunity to see mathematics as a unified whole from the beginning. That would be one reason I've for years pushed for depth over breadth. Whenever a curriculum issue comes up, my first thought is usually, "What can we cut out?" Skimming quickly over dozens of topics and techniques encourages that sense of mathematics as a big collection of tricks, rather than something that has meaning and can be reasoned about. We need time to think about ideas, process them, wrestle with them, and make them our own. If students can understand a few concepts deeply, they'll have a better chance of figuring out something new on their own.

For the same reasons, I also feel drawn to inquiry based learning or Moore method teaching, where students are asked to figure things out with minimal guidance. We start with a few ideas--say, some definitions and a few axioms--and students are asked to build on that framework. Each new step has to be justified, and students need to figure out what works and what doesn't, without being told specifically what to do or what's right and wrong. They should rather be led by careful questioning to notice for themselves what works and what doesn't. If instead of just saying, "No, that's wrong," the teacher can simply present another problem and let the students figure out that their previous approach is flawed, they may internalize the structures much better. After all, structures you yourself have built are already essentially internalized. And it's hard to view a subject as filled with arbitrary tricks when you yourself have built up those "tricks" because they were needed.

In any case, what I would most like is for the students to come away with a sense of my subject (and others) as a unified whole, as something they can investigate and reason about, rather than just a collection of tricks and techniques. The techniques are useful, and the tricks are powerful, but without a strong foundation, it all falls apart.

Friday, November 27, 2009

Random thoughts

Random thoughts for today:
  • I ended up with leftovers of everything but turkey yesterday, since I supplemented the contents of a frozen dinner for my Thanksgiving feast. So I may have been the only person in the world to go out and buy frozen turkey dinners today, so I can use up the rest of the stuff.
  • From the "Things I wish my Students Knew" file: You cannot tell which of x or -x is negative without knowing something about x. (Of course, if x = 0, neither is. But I'm not looking to completely blow their minds.)
  • Two more weeks of classes to go. The end is in sight. But the spring semester is too near. There is a monster at the end of the semester!
  • The weather is finally turning cold. My fingers are getting cold while I'm at home. I've noticed I have more of a problem with my "mousing" hand while I'm at the computer, I think because it's the one I can never put in a pocket for a while.
  • There are occasional television shows that I keep up with a little because I think I'm hopeful the show will get better. The premise is interesting, and there's cool stuff going on, but the writing is pretty mediocre. Often the writing never improves. I find myself wishing some particular episode had a better writer, because I often walk away disappointed.

Thursday, November 26, 2009

Another Thanksgiving

I'm doing it again. I was originally going down to see my partner, but everyone down there is still sick with flu, so I had to give up and just fake Thanksgiving here. Pretty much just like last year, when we were having snow. Frozen turkey dinner again this year, although I actually purchased both a can of yams and cranberry sauce for the occasion. I also decided last night while shopping in the Medium City (I can't seriously call it the Big City, but it's decent and only half an hour away) that I would go ahead and make a pumpkin mousse pie, which was fairly traditional when I was growing up. I decided to wait until I got home and looked up the recipe, so I could go to the local grocery store to get needed ingredients. I also thought I might already have most of the necessities for my green bean casserole at home.

Back at home I made my list, and discovered I did indeed have the green beans, french fried onions, and cream of mushroom soup, so one less set of stuff I needed. But I found last night that the local grocery was out of pumpkin pie spice (perhaps temporarily), and out of canned pumpkin (perhaps not so temporarily). Did you know there was apparently a pumpkin shortage this year? I hadn't heard anything about it, but I figured I'd make one more attempt this morning to see what I could find.

I stopped at the local grocery on the way out and found at least the spice was restocked, but no canned pumpkin. The store did have pre-made pies and pumpkin bread kits, but I didn't want those. So back to visit Wegmans in the Medium City again. Wegmans was out of most of their pumpkin, but did have plenty of cans of organic pumpkin from a brand I hadn't heard of, so I found what I needed and headed home.

I started setting up the casserole in the afternoon. Let's see, green beans, casserole dish, cream of mushroom soup... hmm, the soup is how old now? Oops, it seems to have a 2003 expiration date. Maybe it's OK? Hmm, no it looks kind of funny. Well, off to the local store one last time for soup. Thankfully they were still open for another hour. For not having done much in the way of cooking, my Thanksgiving turned out almost as hectic as a traditional meal would, complete with multiple grocery trips for missing and forgotten ingredients.

In any case, the meal turned out fine, and I've spent the rest of the day watching my recently arrived Netflix DVDs of Buffy the Vampire Slayer and Charmed. So it was a fairly supernatural Thanksgiving, but that's what I like, so it was good in its own way. I just wish I could have gotten down to Kentucky, too.

Wednesday, November 25, 2009

Baby in a basket

As I passed a shopping cart in aisle at K-mart, I noticed a small foot waving around inside the cart. Laying flat on the bottom of the cart (which was lined with a blanket) was a baby in a sleeper, wiggling about on its back, making that goofy, vaguely smiling face that only babies can. Or at least, when I'm making the face and I think anyone has noticed I stop quickly and look embarrassed. I know people usually say it's just gas, but that's not usually where my gas comes out. Although I guess it can make me smile and giggle afterward, especially if it happens at a really funny time. But how often does one get to meet the pope, anyway? Maybe I should have tried pulling his finger. (The baby's, not the pope's.) But that might have upset the parents. You don't want strangers playing with your baby at the K-mart before you've even gotten it to the checkout yet; they probably went to a lot of trouble to pick one off the shelf that looked fresh.

It's probably a really strange view of the world to the baby in the bottom of the cart. Big orange grids on all sides, and looking straight forward all you can see are ceiling tiles and fluorescent lights. I'd probably be laughing at my gas, too.

Tuesday, November 24, 2009

Winding down

We've stopped briefly for Thanksgiving break. To no great surprise of mine, a number of students were missing in both my Monday and Tuesday classes, since we are off on Wednesday through Friday of this week. We'll be back for two weeks, and then finals, then graduation, then we're hitting the Christmas break, and soon enough I'm traveling again.

I usually like the brief periods of "down time" around a break or between sessions, when most of the students are gone. In the past, I remember spending a lot of time around my office around finals or the last day before a break, getting things done. It's a good time to get last grading done, file, organize my grades, respond to e-mails, and the like. And since nothing in particular is due immediately, the air can be almost festive. It's also a good day to take off for a nice lunch with colleagues. But today for some reason, I just wanted to get out of there as soon as possible. I guess I'm just run down this semester for some reason. So I ran up to town for some brief shopping and dinner after my class (it turns out I teach one on Tuesdays), and I'm looking forward to sleeping in for a few days.

I'm glad for the break. I'm also ready for the semester to be over.

Monday, November 23, 2009

Flu shot

The school just got H1N1 vaccine to offer to faculty, so I called this morning to make an appointment, then walked over to the bursar's office to pay for it. (The last thing I need is to get sick when in about a month I'll be flying all over the place on various trips. Plus, I get my flu shots on general principles anyway.)

When I got back to my office and got back to work, my arm felt a little achy, which is more or less what I always get with a flu shot. Then I remembered I hadn't actually gotten the flu shot, I had only paid for it. I'm taking it tomorrow morning. Talk about psychosomatic. Either that, or I'm developing an allergic reaction to spending money. But since I just booked a bunch of flights and hotels for my upcoming travels without batting an eye, I don't think that's it.

Sunday, November 22, 2009


Last night I dreamed I forgot I had a class Tuesday. It was apparently the elementary education majors class, and they were all sitting in the room with the big tables for the whole period waiting for me. (Yeah, like that would happen.) I finally remembered (for some reason) and was dashing around trying to get ready, when I remembered I had another class after the first one. Since the room was still full of my last class of students, the next class had gone to another classroom downstairs. I had a notion of trying to rush back and forth between the two classes, setting each one to various tasks as I went between them. (Never mind that this would imply I must have been scheduled for two classes at once.) I never got myself organized enough to actually start with either class, 'though, and I was pretty sure time must have run out on the first class by the end.

I don't usually have dreams like that mid-semester, although I certainly know the feeling of rushing around and getting nothing done. I do sometimes have similar dreams at the start of the semester. Usually those don't involve forgetting a class altogether. Pre-semester dreams tend to involve being fifteen minutes late for class and running around trying to photocopy my syllabus and get ready. I understand well the fear of not being ready for the semester. Apparently now I'm also afraid I'll forget classes altogether during the semester.

Of course, by the time I woke up, I had no idea whether I had classes on Tuesdays or, if so, how many. Thankfully I have 'til Tuesday to figure that out again.

Saturday, November 21, 2009

Traveling Academics

Today my Alma mater hosted a conference for undergraduate research in mathematics and computer science. Since that school is a scant two and a half hour drive from our school, my colleague (and partner in crime in the department) spread word and attempted to find interested students to present at the conference. In the end, no students from our department managed to get a paper submitted in time, but three students were interested in going to the conference anyway. I was interested too, but with five of us going, that's a bit more than can be comfortably squeezed into one car for 2.5 hours, even if my car is fairly roomy. So my colleague and I debated whether or not to reserve a van through the university. We both pretty much agreed that the odds favored at least one of the students dropping out before the trip, but she decided (wisely, I think) to reserve a van anyway.

On Thursday, one of the students dropped out of the trip. So we canceled the van and planned to go in my car.

We planned on leaving about 6 am to allow enough time to arrive. One of the two students showed up at 6 am, and we finally gave up trying to find the other around 6:30 and hit the road. When we were about 15 miles outside of town my colleague got a call on her cell phone confirming that the student had indeed overslept, and in fact had just woken up. So in the end the trip with three students became a trip with one. So the van was definitely not needed, just as we suspected. It remains to be seen if it was canceled early enough that we will not be charged for it.

My colleague performed admirably when tasked with keeping me awake on the drive into Ohio, so we arrived without my getting my morning jolt of adrenalin by driving off the road or something. We even had enough time to get settled before the first talk started.

The talks were lovely and interesting. A few were in fields that went completely over my head. I have found in those cases that it is much easier to remain awake and alert looking if one stops trying to follow a talk that sounds like gobbledygook and instead just thinks about other things. Like, for instance, what I was going to write about tonight. This paragraph, for example.

But other talks were understandable and interesting. Even many of the CS talks I found fairly accessible, which was nice. The student who actually came was a CS student (but is also fairly mathy), and he seemed very charged up about a number of the topics, so I'm very glad he got a chance to come. He's actually about to graduate and plans to head off to grad school, so who knows what some of these ideas could inspire him to look into.

An invited speaker talked about art created via operations research, including such interesting projects as Obaminoes (which involved using 44 complete sets of dominoes to make a pretty darn good pictures of our 44th president). It was a neat talk, and the various art projects he'd worked on through operations research were pretty cool.

The student talks covered a wide variety of topics, including dissecting regular polygons into squares, simulating a robot, and solving sudoku and ken ken puzzles using some some algebraic geometry tools. All of the students did a great job. We need to get some students coming out and presenting at this thing.

Besides, our students might not have so far to travel next time. The hosts of the conference indicated they needed a host institution for next year, and my colleague and I talked to them about the possibility. It's a reasonably small conference and sounds like it might be manageable, so we are going to be looking into what resources we have and what support we might get if we wanted to try and host next year. It sounds like a lot of fun in addition to being enough work to make us truly frantic.

We briefly checked out the campus after the talks, grabbed some dinner, and headed home. On the drive, the three of us ended up in a light and fluffy discussion about education, history, social trends, biological engineering, the nature of knowledge, computability, the limits of human thought, and what constituted "writing down" or storing information. You know: the easy stuff. It was almost like being back in college again.

All in all a good day, although it was fairly tiring. And there goes Saturday. Tomorrow of course is Sunday, which means I have to get on the ball on getting ready for the next week, which thankfully only includes two days before Thanksgiving break.

Friday, November 20, 2009


It's registration time at the university again, so (some) of my advisees are coming to see me to get scheduled. Actually they pretty much have to come see me to get scheduled, since I'm the only one with their PIN that allows them to register. The school does that to force the students to actually get advising before they register for classes to help cut down on the students doing foolish things. This doesn't keep the students from doing foolish things, of course, but it might help.

Mostly I advise computer science majors, which I understand because we are a mixed department and most of our majors are CS. Most of the "math" majors are actually secondary education majors, and are advised in the education department. Although I still don't understand why I keep hearing about the few math majors we do have being advised by CS professors. But at least I get an opportunity to see the trajectory of the typical CS major. Or at least, the typical declared CS majors. They really don't have that many more majors than we do, they just get lots of people who think they want to be CS majors. I think some of the students think, "Hey, I love computer games; I'll major in computer science!" For many of those, things don't go so well. I often find myself advising a major who is repeating the introductory programming course and the introductory math class multiple times. Eventually, they usually give up and switch majors. Or fail out.

Some students are not so good at getting around to getting registration done. I had one who stopped by my office suddenly on Monday right before I was about to go to class and want to get his PIN so he could register. (Registration started some time earlier.) I spoke to the student briefly about the fact that he was failing his intro programming class and had withdrawn from his math class (see? I wasn't kidding). He indicated he wanted to change majors. So I took a minute to talk to another professor about a suitable major closer to what he wanted. Then he told me he actually wants to transfer to some other school, so he just wants to take some classes for spring and transfer credits. I asked where he was transferring. He didn't know. I told him I had to go to class, but I could talk to him tomorrow morning. He was worried all the classes would fill up and needed his PIN right away. I wasn't giving in on that, but offered to meet him after my classes finished that night at 8. He decided he could wait 'til tomorrow morning after all. But he didn't actually show up. I didn't see him again until Thursday. Then I could finally sit down and talk to him about what he was going to do, and make some semi-recommendations, which I know he isn't going to take. I suspect he's not going to end up transferring, changing majors, or doing anything else before next spring's registration, when I fully expect him to come rushing into my office towards the end of registration again, telling me he needs his PIN right away.

On the bright side, I do actually have a computer science major graduating this semester. That one, by the way, came to see me early in the registration period, always had a plan, passed his classes, and took what little advice I had the opportunity to give him. I wonder if there's any correlation.

Thursday, November 19, 2009

Student projects again

My numerical class finished up the second (and final) week of student projects tonight, and I am still very pleased. So are the students. They told me they enjoyed it. I enjoyed it. I learned about a number of things that I hadn't before, including some tantalizing glimpses into topics such as the use of quaternions in computer graphics and how GPS works.

I had good students, and I think I structured the assignment well. Early in the semester, I asked everyone to pick (separately or in groups) a tentative topic one week as part of their homework. The next week, I asked everyone to find three sources about their topic. Next came a brief outline, and I started meeting with the students in their groups. We met about once a week, and I think it made a real difference. I got to find out what was going on and direct each group of students a little more each week, refining and refocusing their work. Most of the projects needed to be significantly reduced, but sometimes they needed redirected, too.

Over the past two weeks I also watched each group show me a practice run of their presentation and made some final suggestions for improvement. You know what the number one suggestion I had to give almost every group (including my very best students)? "Make sure you start by telling people what problem you are trying to solve." It was an odd sense of deja vu when I watched each new group during the practice presentations dive in and start explaining how to carry out, say, the Wronski-Schwarzchild Decomposition Algorithm,* without ever mentioning what the algorithm was supposed to accomplish. But this is why asking to see the presentations first is such a wise idea (for anyone who plans to do this); I got to let the students know that they ought to discuss such things. And to my delight, I found that the students by and large took my suggestions when they actually presented to the class.

It's been a good few weeks for this class, and we'll be off next week for Thanksgiving break, so it will be a while before I see them again. It was a good place to take a pause.

*Yes, I just thoroughly made this algorithm up. And it was fun. Although I had a friend who came up with the idea that, should he ever develop some new mathematical operation which he got to name, he was going to call it the "Poopyface matrix," which I also like a lot. I think that also shows that he's funnier than I am.

Wednesday, November 18, 2009

Nighttime reading

There are certain books--only a few--that soothe me as a I read them. They're old familiar friends, and as the words and scenes start to flow around me, it's like slipping into a warm bath. I know the lines and cadences, I know the plot twists and the characters, and I'm not likely to find anything new, but I'm not really looking for it. It's a calming experience, almost like a trance. These books I read to enjoy but also to relax, unwind, and shed the cares of the world.

I finished one of these again just a bit ago. I own a copy now, but I found it first in our town library when I was growing up. I used to visit the library pretty much every weekend, walking out with a precarious pile of books every Saturday. I don't do as much reading anymore I guess, but I still enjoy it. In fact, I still enjoy some of the same books after all these years, those old familiar works that I track down to read again, which sweep me back to my childhood escape. I re-read books back then too, picking out the same books again and again from the library sometimes. Some old favorites haven't weathered time well; I recall them fondly, but don't much care to revisit them. But others form the core of my nighttime reading, the books I pull out when I need to relax, before I try to sleep.

Tuesday, November 17, 2009

Never mind

I mentioned recently that I was slightly panicked because I didn't see how I could finish everything in pre-calculus during the limited number of classes remaining. This week, I had to figure that out. I needed to put together the last assignment sheet that gets the class to the end of the semester.

So I sat down and did a major hatchet job over the weekend. Topics got pared down to almost bone. In the last chapter I cut all exposition and essentially covered two sections by just saying, "here's two equations, now use them." But I finally came up with a schedule that could (minimally) cover everything I needed to by the last day of classes, although I wasn't proud of what I was going to do.

To finish the schedule, I looked up our final exam time so I could put that on too. Then I... oh, look at that: We actually have two weeks after we get back from Thanksgiving break, not one. I can finish the chapter up in a reasonable way after all.

Never mind.

Monday, November 16, 2009

We are Borg now

I joined the ranks of the cell-phone enabled over the weekend. Sort of.

I purchased a cheap phone on a prepaid plan with no contract. For under $50, I got the phone plus three months of service and about 4 hours of airtime. I'm not sure I'll even use the four hours, but it's there for all the traveling that I'm doing over the next few months. Next weekend I'm off to help a colleague shepherd students to a conference in Ohio. After that, it's off to Kentucky to see my partner. A few weeks later and I'm off to Dallas to see my folks. Then in early January I'm off to California for the Joint Meetings of the AMS and MAA, plus some general happy sightseeing. There may be extra trips in there somewhere, but I hope not.

So I'll be glad to have the phone as an option when I'm traveling, and I'm sure there will be other occasionally uses for it. I'll probably keep it active. If I really like it, I may think about upgrading to something fancier. But for the moment basic functionality seems like plenty. After all, I got along this long without having one at all, and generally only had any possible use for one a few times a year. It's always seemed mostly unneeded to me, like just one more thing to have to keep track of and pay for. But I figured there was some point to having it while traveling, so it seemed like a time to give it a try.

Resistance is futile.

Sunday, November 15, 2009


I was happy to find a great sale over the weekend and picked up some more slacks and long-sleeved shirts. (Which is good, because I always have the fear that my students will eventually notice I keep re-wearing the same things over and over. I know it's unlikely, but it still bothers me.) It struck me while I was trying to get everything into the laundry that shirts have way too much stuff attached when sold.

For the standard (folded) shirt, I had to remove: a size sticker on the back of the collar and another on the front, pieces of cardboard and plastic to hold the collar up just so, three clips and a pin from the back of the shirt so I could get to and remove the big flat piece of cardboard and some tissue paper (for some reason), another pin at the neck, and then two tags attached on the front somewhere (one from manufacturer and one from the store). Some shirts had a few extra clips/pins to stick one cuff out on the front of the shirt.

I'm glad I don't feel the need to store shirts this way in my closet, because I don't think I have the origami skills to put it all back the way I found it, either.


Sleep is good. I never seem to get enough, but I like it. My computer has this menu option called "Sleep", and when I select that, the machine goes to sleep right away. I often find myself wishing I had that little menu option. "OK, go to sleep now." I tend to be a little bit of an insomniac. As much as I like sleep, sometimes I just have a hard time making myself actually do it. My mind needs a lot of time to wind down.

And sometimes I find myself having a hard time going to sleep because I'm too tired. I know that sounds crazy. I end up lying in bed, yawning, eyes watering, and essentially being to obsessed with being tired for a while to actually fall asleep.

On the good nights, when I can relax, I tend to think about pleasant things. Like imagining soaring over the world at night, flying on the winds, with lots of twinkly stars and people below sleeping. Or when I was little I used to imagine that my bed was a boat that would gently float down a river as I fell asleep. Then on some nights I would imagine I was paying extra for the "deluxe" sleep river that went through beautiful gardens. (I have no idea what I was paying extra with.) Yeah, I was a weird little kid, but it was a good fantasy.

Sleep is good. I think I'll go get some.

Friday, November 13, 2009

This is so hard, you should get college credit for it! Wait...

Our university has a math sequence for elementary education majors. The courses mostly take a very deep and comprehensive look at the underlying mathematics involved in about K-6 education. Since we have a number of mathematics education professors in the department, the courses are extraordinarily well designed. It meets in a room with large hexagonal tables where students can sit together in groups of six, and we have two large cabinets filled with all kinds of wonderful manipulatives which are used in many class activities. (A manipulative is any sort of physical object which can be manipulated to learn math. We have various types of colored chips, geometric shapes, and other cool toys for demonstrating mathematical concepts.) Many of the activities are actually similar to and based on activities which could be used to introduce concepts to elementary students, although of course the college students are expected to go a little deeper and are asked to do some things that we don't ask elementary students to do. (For example, we have the students in the course perform various operations in bases other than ten to emphasize the basics of a place value system. No one teaches base four or base twelve to elementary students anymore.)

It's actually a really fun class, and full of all sorts of wonderful discoveries waiting to be made. I personally find myself fascinated by the fact that in many cases, the way we explain a concept to our students parallels the abstract definitions which can be used to define that concept in advanced mathematics. So whereas in class we may use groups of red and yellow counters to define the integers, a mathematician might start tossing around scary sounding phrases like "sets of ordered pairs" and "equivalence classes", but ultimately mean pretty much the same thing. I personally found the demonstrations hugely enlightening the first time I did the class. It provided me with very concrete way to think about and explain concepts such as why a negative times a negative is a positive and why dividing by a fraction is done by multiplying by the reciprocal. The idea of the class of course is to provide our future elementary educators with similar insights.

Unfortunately, the class is always a struggle to one degree or another. One particular point which the students never seem to get (no matter how often they are told) is that this is not a class in elementary school mathematics. We obviously expect them to have already learned how to do things like add and subtract integers and fractions, how to multiply and divide multi-digit numbers, and the like. After all, they were supposed to have mastered these topics in grade school. (Except of course we know many of them actually can't do these things reliably, so the course also helps back up these concepts. But I digress.)

As a result, the students sometimes ignore instructions on how to complete an activity. For example, they are supposed to learn how to represent integers with sets of colored counters and then use the counters to add and subtract integers. (This is actually a really cool activity; I'll have to write about it sometime.) But since they know what 7+(-4) is, and following the directions to make representations of the numbers using the colored chips seems complicated, they instead just write down "7+(-4) = 3" and explain to me that "the model was too hard, so we just did it." Since they feel the class is about (or should be about) learning to add, subtract, multiply, and divide just like they did in grade school, there is no need to learn anything else about these topics as long as they know what the right answer is. They sometimes fail to understand that the colored counter model they have been asked to use is, in essence, the content of this course: we want them to learn to use a physical model which represents basic operations on integers, and to use that model to derive various known properties of addition and subtraction with integers. This issue is usually an uphill fight all semester with the students.

But this semester I'm getting even another argument from some students in one class. With almost every activity we do and with almost every mathematical model we describe and learn to use, the students complain to me that "this is too hard for any little kid to understand!" Which is completely irrelevant, since I'm not asking any little kids to do this work, I'm asking my class full of college students to do this work. I've told them I don't address the issue of how to teach their future students, but rather just teach them mathematics. I leave it to other people to teach them how to teach math. This doesn't sway the students.

I tell my students, "I'm not asking your students to to this."

The students respond, "Yes you are!" against all evidence to the contrary.

My students somehow feel that any topic which they consider to hard for a third grader should be too hard to ask a college student to do either. I suppose they want a refresher of third grade math without any of the "hard stuff." Remarkably, I seem to have little success with convincing the students that they are not, in fact, third graders. Do they really think that in a college math class they should learn nothing more than what grade school students are expected to learn?

But do you want to know what the worst part is? Most of the activities actually aren't beyond the grasp of moderately intelligent third graders. I consider it the dirty little secret of the course. Granted, it would take more time, but grade school students could certainly be taught rules for representing integers with colored chips. With practice, they could learn techniques for adding and subtracting with the colored counters and even explain how it works. Eventually they would find patterns in what happened when you add and subtract integers. The same is true for almost every other topic we discuss, from the most basic (addition of whole numbers), to the most advanced (division with fractions, perhaps). You couldn't do all of K-6 in a semester obviously, and children may not make as many connections as a college student ought to be able to, but they could do almost every activity we do in the college course, and learn a lot.

I don't even bother to argue the point with my students 'though, because whether grade school students could do what we do or not is entirely beside the point. My class isn't filled with grade school students. It's supposedly filled with college students. College students who want to be elementary teachers. The same teachers that will lay the next generations mathematical foundations. Which will, in another ten to fifteen years or so, become our next generation of college students sitting in my college classes. And that thought usually fills me with the urge to go lie down for a while.

Thursday, November 12, 2009

There's a pattern to this

It's that point in the semester. Too much is going on. I end up running from early morning to late at night, with stuff to do piling up during the week. Stacks of papers to grade, assignments to write, lessons to prepare, quizzes to write, meetings to attend, students to talk to, e-mails to respond to, and supposedly at some point I'll do some research, too.

And when my week finally ends (which is around 8 or so on Thursday night this semester), I feel worn down and can't stand to look at anything anymore. I usually have a light Friday (usually just a meeting or two, respond to a few e-mails, maybe grade or take care of some minor task), then consider Saturday "off". (Of course off time has it's own commitments, like the need to go to the grocery so I have something to eat, do dishes so I have something to eat off of, and do laundry so I don't stink while I teach the next week. But I still have free time, and I enjoy it.)

But then Sunday creeps up, and off we go again. OK, what do I have to have finished for Monday? Then of course Tuesday will come, and... how long until Thursday night again? Thursday nights are really good. At least this semester.

Happy Thursday!

Wednesday, November 11, 2009


November is NaNoWriMo, National Novel Writing Month. The goal is to try to write a novel (50,000 words) by the end of November. It's an interesting idea, but I'm not really interested in trying to write a novel now. (I actually worked on a novel at one point in my life, but the idea is not really appealing to me now.)

However, there is also a parallel event inspired by NaNoWriMo, the NaBloPoMo, which (of course) is National Blog Posting Month. Here the goal is just to post to your blog every day for a month. (Actually, they now extend NaBloPoMo to every month, but originally it was based on NaNoWriMo.) I thought this sounded like a reasonable idea, so I decided I'd try it this November. (I'm not doing anything official, I'm just posting every day for a month.) It sounded interesting and I figured it would be good for me. And it might make me put together some postings. I'm now just past the one-third mark, so I figured it would be a good time to explain.

So this answers the question on a few people's minds about "Why has he started posting all the time?" Although maybe the answer is really just that I decided to do it.

Tuesday, November 10, 2009

Real facsimiles

I've been reading a couple of books put out by Disney (Disney Treasures and Disney Keepsakes) which give brief histories of Disney works, together with reproductions of various Disney memorabilia. Every page or two there is a removable piece which is a replica of something from long ago--a cartoon panel from a magazine, tickets from the opening of Disneyland, a menu from the studio cafeteria, paper toys distributed as promotional materials, and similar items. The books themselves are light, fun, and filled with pictures. I like perusing these before bed to wind down.

The memorabilia is odd in a way, and I enjoy them more than I thought I would. The replicas are often objects that (in original form) are collectors items, the sort of thing people would pay money for at an auction. I understand some of the allure, although I wouldn't be willing to pay what the originals cost by any stretch of the imagination. There is something about getting to hold and examine some little piece of history, even if it's an insignificant little trinket. I was holding one night a copy of a paper Pinocchio mask that was distributed as a promotion by Gillette (of all people) in 1940-1941. It's a weird feeling to hold that mask. Something that floated around almost unnoticed almost 70 years ago. Some child who is now significantly older than me probably played with one just like it. And here it is again, born anew.

Granted, these are fakes, reproductions rather than originals. But most of the originals were quick promotional gimmicks, not intended to be great works of art in any case. So really how much difference is there between the original and the copy? (Maybe the new copy is even made on better material.) So it's sort of cool to see and hold, and think about these being around so many years ago, seen and then quickly forgotten at the time.

I went through a similar phase with pennies once. Every time I found a penny (or really any coin), I'd check to see when it was minted. Then I'd try to think back to what was happening in my life that year. It's like a connection to that time. But sometimes I'd find a penny made before I was born. It's kind of weird and somewhat disturbing to be holding in your hand a penny, generally thought of as small and insignificant, which is older than you are.

Monday, November 09, 2009

Risk taking

So I heard passed on a complaint from some employers: That the current workforce is too risk-averse, that they only want to do what is "safe". Or I guess in the usual "business-ese", that their employees don't "think outside the box." This is, I suppose, seen to be a failure of educators. (That would include me.)

I'm inclined to call bullshit.

There's no question that US public education has an unspoken agenda to produce docile, unquestioning workers who will sit in cubicles all day doing mind-numbing tasks and avoid asking difficult questions at all costs. That's actually part of the history of what the public education system was for. But it's worth asking why this was ever a goal, and the answer is because that's what employers wanted.

I'm also inclined to think that people have been encouraged to take fewer risks because risk taking because they have so little overall security. Most people today worry about being laid off at every downturn of the economy. There is no long-term job security any more. And in a particularly screwed up twist, no one gets health care at an affordable cost without a really good job. Plus we have an otherwise generally eroding social safety net. So no one feels safe, and I think a lot of that lack of security can be laid at the feet of corporations that decided short term profits could be had by regularly laying off employees and trying to squeeze more out of the ones left. And now they're complaining that their employees aren't willing to take risks? Why would anyone take risks in such a precarious situation?

Plus I doubt they really want risk-takers. Risk takers might try some crazy scheme that no one ever thought of before, and that scheme may fail. Actually the crazy schemes probably fail more often than not. (How many start-up technology companies did not go on to become Google, Microsoft, or Apple?) I suspect what they mean is that they want employees to take risks doing things that turn out successful. But that's not risk-taking! I don't know. Maybe an employee that does try some wild new idea that fails spectacularly really does get a "Congratulations! You failed!" celebration a la Meet the Robinsons. Maybe innovations (including failures) are actually encouraged by some (or all) employers. But that just doesn't ring true. I think it's the businesses that are risk-avoiders, and the employees are picking up on that and following along.

And employees are easy to blame. What employee would disagree with his or her employer's assessment of the situation? That sounds like awfully risky behavior.

Sunday, November 08, 2009


I just took down the last of my Halloween decorations. It occurred to me when I took out the trash I should probably uproot the tombstones outside my apartment before the neighbors think I'm any weirder than they already do. Especially since it's been over a week since Halloween, and I didn't manage to put them out in the first place until the afternoon of October 31. (Does that make the lag taking stuff down better or worse?) Of course, that's just show for the neighbors. Everything is still sitting around my apartment waiting to be packed up.

At least I remembered to take the giant glowing skulls out of my upstairs windows. Plus it's been over three days since I took off my horns.

Saturday, November 07, 2009

Feeding my neuroses with technology

First TiVo, then Netflix. There really is no better way to watch television series if you're a little OCD. Either pick a show and start recording, or (better yet), pick something out on DVD and get it. Then sit down and watch a bunch of episodes at once. Total immersion. It's the only way to watch. (Actually I subscribed to Netflix originally because my TiVo was missing a season of Smallville.) Thank goodness everything comes to DVD now. And if you're looking for more details about a series, there is no greater resource for all your pop-culture trivia than Wikipedia.

At the moment I'm "OCD"-ing Buffy the Vampire Slayer and Charmed, which are oddly enough pretty similar when you think of it. (Basically both featuring somewhat reluctant chosen ones with special powers fighting supernatural baddies of the week. And both featuring kick-ass women as the leads, come to think of it.) It's somehow just easier once you start on one thing to keep watching that one thing. And keep watching. Even previous obsessions drop by the wayside.

Thank goodness there are past shows that I like but didn't already watch.

Friday, November 06, 2009

Where does time dissapear to?

This week I had to get together another set of assignments for my pre-calculus class, and I'm really struggling to get to the end of the material. I keep trying to squeeze (and SQUEEZE) the schedule, cutting out more and more stuff, trying to make a mad dash to the end of the semester. And I'm realizing how little there is left. It's hard to find space for what's required.

It seems like everything drags, but somehow I'm more than halfway through the semester. This was a hell week anyway. I had a flu shot plus two meetings Monday, an academic club fair Tuesday afternoon then College Bowl all Tuesday night, meetings all week with students, plus all the usual stuff. I've started using my PDA again to keep track of stuff. I was glad to get to the end. But how will I get to the end of everything else?

I'm also now looking towards spring semester and trying to get planning done for new courses there. Plus a talk over break at the Joint Mathematics Meetings of the AMS and MAA which has to get done at some point.

Where does all the time get away to?

Thursday, November 05, 2009


I gave my numerical analysis students this week off to work on their projects (which they start presenting next week). I told them I would be available during class time for them to ask questions. The difference between doing this with upper level and lower level students is that the upper level students will actually do it. (I was actually a little surprised at how many people I saw.)

I'm actually really pleased with my numerical students right now. Most of them have been working hard on interesting projects. Most of my work in meeting with the students up to this point has actually been in getting students to scale down their proposals to a manageable size. One group of students was originally starting with an ambitious project of figuring out how to guide a robot through an obstacle course using GPS guidance. I initially got that scaled down to just working with the GPS, then got them to massively reduce the number of factors they include in their GPS model, and finally we have settled on doing linear least squares fitting, which is simpler than the non-linear least squares fitting that GPS requires. I'm relieved, and so are they. I knew at the beginning of the semester that this was simply too big, and I think it's finally something they can finish in a reasonable time. (Actually, they are almost finished now.)

Almost all of the projects are progressing nicely and look really interesting. I have student showing how calculators evaluate functions like sines and cosines, another student solving linear systems using iterative techniques, one studying efficient matrix multiplication for graphics applications, a pair of students working on Bezier curves and their use in graphics, a group of three presenting on a numerical simulation of the Tacoma Narrows bridge collapse, one doing arbitrary precision arithmetic, and one doing on the fly polynomial interpolation to compensate for lag in networked computer games. All of the presentations look good. I just need to make sure they don't run too long.

Sometimes I really like teaching.

Wednesday, November 04, 2009

How old are my students again?

I have a group of students who seem to think it's very funny that one of them saw me having lunch with one of my colleagues a few times. This is not surprising, since she and I probably have lunch more days than not. (I'm reminded of an evaluation from a student years ago which said "I see him out eating all the time." I wondered if that one might have meant that I ate out way to often. Either that, or the student was stalking me.)

My students this semester like to ask how my date was and then giggle. I'm not sure if it's funny to think of their professor having a date at all, or that it's funny to suggest I'm going on a date when I'm not. I'm not sure why either would be that funny, actually. All I know is it baffles me and it feels very much like junior high (or earlier). But then students seem to get younger all the time. Why, every year it seems like the new first years are another year younger than me.

Come to think of it, by this point many of my students probably grew up with Harry Potter, which is in my recent memory. Ack, I just made myself feel old.

Nonetheless, my students' obsessions with my lunchtime habits are just plain weird.

Tuesday, November 03, 2009

The grass is always greener

I subbed a class for someone who was out sick this morning. It was an algebra class and the second day the prof was out, so I was asked to try to actually teach something. Unfortunately, I never found out what he was doing in class, so I ended up having to ad lib something about graphs of transformations. (You know, a little algebra improv. "Now pretend you're a function translated to the left two units! OK, now you're getting stretched, s-t-r-e-t-c-h-e-d... AAAAANNNNND freeze! Reflect about the y-axis!" Well, something like that, anyway. Only less entertaining.)

After class I had several students asking me more about who I was and if I taught various courses. (And not in the "Ye gods, I must be sure of who you are so as to avoid scheduling you at all costs, you weirdo!" way, either. They seemed to like me.) This is always a little weird, because usually my own students aren't that crazy about me. They would probably like someone else who came in to sub for me and did some free-form math jazz better. I can just imagine my students all crowding around the other prof, asking if he ever taught the next course they needed to take.

This is why I don't take sick days.

Monday, November 02, 2009

College students can be less than adorable

I was unimpressed on Halloween night by the number of college students I found trick-or-treating at my door. (Seriously, college students? It's questionable by the time the kids are 13 or 14.) I'm thinking I might construct a more age-appropriate treat for college students next year, like a really interesting pamphlet on a cool math problem, and tell them it's their intellectual treat for the night. If they want candy, they (unlike the six year-olds) can drive down to the grocery store and buy some.

But today my math class for elementary education students was working on an activity involving adding and subtracting integers. It uses a cute little paper copy of a clown who walks forward and backward on a number line "tightrope". It's a nice activity. When I was cleaning up after class I found a left-behind clown that some student had taken upon themselves to add genitalia to and portray performing an obscene act. (These students want to teach grade school?)

I am not overwhelmed with the cuteness of my students at the moment.

Sunday, November 01, 2009

The waiters are younger than I remember

I went to pick up Chinese food for dinner tonight. The family that runs the restaurant has a few children that are usually present, including a small girl. She was entranced to discover I would say "Hi" back when she said "Hi" to me, but I was a little nonplussed when she switched to "Ho Ho Ho". From that point she said many things, but I have no idea what. Possibly because she was speaking Chinese, or maybe because she was about three years old. I don't know which.

I sat down in a chair to wait for my food. The child toddled over, retrieved a melamine plate, and set it in front of me. "Thank you, but I don't need a..." The child was headed across the floor again, returning with a napkin. She kept one for herself to play with for a while. "Thank you, but no I don't..." Shortly thereafter she left and returned with plastic utensils. Then another place setting appears, and she even brings a fried noodle for herself (I don't know where that came from) which she starts trying to cut up with a plastic fork. By this point I'm starting to look around hopefully for someone to re-emerge from the kitchen and at least make some comment on all of this.

Lacking much success with her noodle, the child went over to her McDonald's play set in the corner. (I have to admit there is something that just strikes me as weird that there is a McDonald's play set in the corner of another restaurant.) She returns unfolding an actual dollar bill which she attempts to present to me. (I think some aspects of business may still be eluding her.) Unable to convince me to take it, she gleefully tears an edge from it and laughs. Before too much else happens, the mom comes out of the kitchen with my order, and I get to escape. I told the lady that the waiters here are so young, and pointed out the partly set table and her daughter. She laughed. I didn't mention the dollar.