Sleep

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.

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.

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!

November

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.

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.

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.

Undecorating

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.