Phthursday Musings: Tower of Hanoi

My wacky offspring embarked upon his third grade adventure this week. This got me to thinking a little bit about “what third grade is like”.

Third grade was when the district switched schools on us. My old school, Beyer, was practically my neighborhood school, and was only a few blocks from my grandmother’s house. My new school, King, was in a part of town that I don’t think I’ve ever even heard referred to as being a particular part of town. It was west, but too far south to be west side. It was south, but too far west to be south side. And I’ve never heard anyone refer to Rockford as having a southwest side.

And while I was probably still closer to the new school than almost anyone else in my class, it was far enough that it meant I got to start riding the bus.

So for me, although most of my classmates were familiar, it was a new school, and I was newly riding the bus, and our classroom was on the second floor, and so I guess I’d say that in retrospect, the jump from second grade to third grade was the biggest jump since starting school at all, until jumping to junior high after sixth grade.

And I guess I’d also say that third grade was the first time I feel like we were expected to already know things? By which I mean that sure we’d been learning in school all along, but like, we were already supposed to know how to spell and how to do math and whatnot. There were a priori expectations.

Now this is of course me reflecting back some 35 years ago without knowing exactly what the hell I’m talking about… but you’re a regular META-SPIEL reader, so you already knew this, yes?

I find it interesting how little we as parents today are cognizant of what a priori expectations might exist for third graders, or for kids in general. I spent the last two years as the PTO President, I try to pay attention to what’s going on, and I still find school to be a total black box. More specifically, I guess, I find the overall pedagogy to be a black box. I sincerely feel that I have a better fundamental understanding of what doctors and lawyers and other professionals do than I have of what elementary school teachers do.

Our third grade teacher, Mrs. Eaton, had this puzzle in her room. I don’t remember ever learning its name at the time. In my memory, it took the class a while to eventually figure it out. Many years later I learned that the common name for the puzzle is Tower of Hanoi. It looks like this:

The idea is that you need to move all of the discs from the center peg to one of the other pegs, so that the tower steps the same way. But you can only move one disc at a time, and you can never put a bigger disc on top of a smaller disc.

Wikipedia refers to Tower of Hanoi as a “mathematical game or puzzle” but I don’t know that I’d call it mathematical. I see it more as an exercise in patience.

At some point in third grade I figured out how to solve it. It is a little hard to describe the solution - much easier to demonstrate! - and ok SPOILER ALERT - but basically the idea is that you have to first make a tower two tall, then three tall, then four tall… you have to very ploddingly tear the big one down and keep building up bigger versions of the new one.

When our house had baby stuff in it, we had, like every good American household, one of these (though this one is a little more old school and looks like one from the ‘80s):

This isn’t quite a Tower of Hanoi because it’s just one tower. But if you haven’t seen one of these recently, you might forget, the peg is sloped, the holes in the rings aren’t all the same size. So you can’t put every ring on the peg unless in the correct order.

And so it was about 7-8 years ago that seeing this around got me to thinking about the puzzle from third grade. And the way thinking about the puzzle intersected with other things in my head, what I realized was that the methodology of the puzzle solution has stuck with me for decades. There are in fact times to this day when I am confronted with a “real life puzzle” where multiple things have to get done, and I find myself in effect stacking and re-stacking “rings” in order to construct a completed “tower” of work.

This is a little easier to explain in physical terms: If you’ve got five things to bring in from the car, you might be able to do it if you pick up certain objects first (like bags with handles) and certain objects last (like smaller things with little loops that can be picked up with one finger.) But, try and do it in reverse, and you’ve got bigger rings on top of smaller rings… you can’t do it.

In non-physical terms, it goes kind of like this: If you’ve got five work tasks to complete, how do you arrange the order of completion in a way that will facilitate success? As a programmer, sometimes you can’t solve one bug without solving another one first. But as a manager - and not just a manager of people but indeed a manager of time - sometimes you can’t get to a more critical situation without getting smaller nagging ones out of the way, because the critical solution requires a lot more concentration. To stretch the metaphor, it’s not quite like having a tower and moving it… it’s more like having the pieces of the tower laying around, but you can’t rely on visual size cues. You have to weigh the rings, because the heavier rings have to go on the bottom.

The metaphor might have collapsed by now but I think the core metahdological impetus has not: the way to solve the Tower of Hanoi, ultimately, is not exactly through calculation, but rather through deliberate process. And while you can simplify and say the yellow ring is smaller than the green ring and call that a calculation, calculations aren’t solutions here. They’re inputs to the overall process.

And, maybe, third grade is about the right time for a new appreciation of process to awaken in the young mind. Maybe this is the right time for more complex puzzles, not so much because you can finally solve them, but because you can finally learn better lessons from them.

But I don’t know that. I don’t have any kind of deep pedagogical understanding of how the young mind works. Therefore I, like so many others, must rely on my own experience as once being the possessor of a young mind.

Here, I might add, is part of where I think there is such a fundamental lack of appreciation for teaching as a profession. When you go to a lawyer, you need a lawyer. It is a situation all about the law and process, and you need an expert in law and process. When you go to a doctor, you need a doctor. You need an expert on the body. With education, though, we have all been students. We tend to understand education from the perspective of the student, from the perspective of having learned as opposed to having been educated. This is different from having been a patient or a client, where your role is more passive, where the doctor or lawyer is doing the work. In a classroom, everybody is doing the “work”. So I think it’s a lot easier for some people to reason that “anybody can teach” because they think it’s ultimately about the learning and not about the teaching.

I think it’s absolutely true that the relationship between teacher and student is fundamentally different than the relationship between doctor and patient, or lawyer and client, or any number of other relationships. But rather than bumbling to a conclusion that this different kind of relationship somehow lessens of cheapens the relative role of the teacher, I see the fundamental differences as being of kind and not degree, and I believe that a lot of people utterly fail to understand this. I’m sincere in saying that I don’t feel I “understand” pedagogy, and I say this as someone who has taught (three years as a graduate teaching assistant) and trained (in software) and parented (one wacky kid) and interfaced with “the school system” in multiple capacities.

But even though I might not “understand” that doesn’t mean I won’t listen and that definitely doesn’t mean that I don’t appreciate. As a society we don’t value teaching and we don’t value teachers the way we should. Teaching is fundamental to the human condition and if we can orient our thinking more along those lines, if we can understand it more as a deliberate process as opposed to a series of calculations, then we can better appreciate the profession, and in the process the people who perform it, and, well, we can better appreciate ourselves, our fundamental humanity, as well.

While on the subject of third grade, this seems an appropriate time to share something I first wrote back in… my god, 2012. It’s actually still up on my old blog site at huckelberry.org if anyone is tempted to go see old crap.

I paste the whole thing in below for your enjoyment and amusement.

the day I came down with the chicken pox

March 7, 2012

This was spurred on by a recent discussion I randomly started about 11th Street in Rockford. This is the story of the day I came down with chicken pox. I am not sure if I should say the chicken pox.

I want to stress, though, that this story is not really about chicken pox. It is about 11th Street. Really, it’s more about 20th Avenue, and important lessons people learn in their lives.

So. I was in third grade! We had a substitute teacher that day – a substitute we’d never had before, and by my recollection she was kind of cranky.

I can’t remember exactly what happened, if I said I was feeling bad, or if somebody asked why I had red bumps all over me, I don’t know. School had only just begun, or maybe it hadn’t even begun yet, who’s to say. But I was in my classroom and all of a sudden it was like, oh hey, you’ve got chicken pox. I don’t really remember anything else about all of this except that I remember putting my coat on and the substitute was cranky and was all like, you should be doing that out in the hall. Okay.

So, my dad came and got me. At this time our car was a Ford Pinto. I don’t know what year it was and I doubt it mattered. The reason we had a Ford Pinto is because our AMC Gremlin had been totaled in the previous year. The Gremlin had been brown, kind of a metallic poop color. The Pinto, I think, was kind of a faded orange-brown, but I may be getting the exact color confused with my grandfather’s Mercury Bobcat, which was kind of a burnt orange. The Bobcat, of course, was the step up from the Pinto. I swear I am not making any of this up.

Now my school was King, and King was on the west side. We lived on 6th Street. So for us to have been on 11th Street doesn’t really make sense – we must have stopped somewhere else.

Anyway, it was a school day, and it was the morning, and it was cold enough for me to have a coat, so it was probably early in 1985 though maybe it was late in 1984, and I had come down with the chicken pox, and my dad picked me up, and now we were driving south on 11th Street, just past Bowl-Mor, and yes, that was the actual name of the bowling alley. And so we turned right onto 20th Avenue.

And as we turned, my door flew open. Not like, immediately it was wide open, just like, it came unlatched, and just kind of started to open. So when I say flew, I mean “fly” in the graceful, birdlike sense, not in the speedy, timelike sense.

We were not going that fast. As the door started to fly open, and I think I said something, but who knows for sure what was or was not said, and my dad realized that my door was flying open, he naturally stopped the car. That is when I fell out of the car.

I really do not remember if I had tried to reach for the door at some point and failed… I just know I fell out of the car, onto the street. It was not a violent fall. I was not injured. I did still have the chicken pox.

And so all of this is how I came to be sitting on the street, on 20th Avenue, alongside my father’s stopped brown/orange/tan Ford Pinto.

All of this was not far from our house. I am pretty sure that I got up and back in the car, and we locked the door, and I held onto the door as we continued slowly home.

Several important lessons were learned that day:

First, wear your seatbelt! In 1985 this was not exactly standard practice, not even for an 8 year old in the front seat. I know this sounds crazy but I was wearing my seatbelt long before most people I knew.

Second, do not drive a Ford Pinto! Now, this was before it was widely known that upon side impact a poorly located fuel tank would cause such vehicles to explode. Pintos were still common then, even though they hadn’t been made since 1980.

Third, maybe do not drive a Ford at all!

Fourth, quarantine yourself when you have the chicken pox! Or, alternately, visit people who wish to receive it themselves, or who wish to have others receive it. My mother was keen on having me give chicken pox to my sister, then age 3, and she did indeed receive it. She therefore missed out on ever getting to go home from school because she had come down with the chicken pox. Jessie, I am sorry.

All of you fall into three camps: those of you who know nothing about Rockford, those of you who know precisely where I’m talking about but haven’t seen the area in many many years, and those of you who are intimately familiar with the area as it stands today. 11th Street, in the vicinity of 20th Avenue, is a post-industrial hovel. Bowl-Mor has been shuttered for years. Most of the nearby factories are not operating. It is not the worst part of the city by far, but it is, as was pointed out earlier tonight, “vaguely creepy”, and this is the case both by day and by night.

Whatever else may happen, though, that corner, of 11th Street and 20th Avenue, that part of 20th Avenue specifically, from now until the end of time, it can be said, Phil Huckelberry Sat There, and I can say, Yes, I Sat There, The Day I Came Down With Chicken Pox.

As a bonus to the bonus, this may or may not be what that Pinto looked like, though I’ve got to admit, I don’t remember it being this freaking ugly: