Tag: mathematics

In which I need to figure this out

On By Luther M. SilerIn Teaching1 Comment

Right now this is my new Facebook profile picture, but I felt like it was necessary to share it here too. Sushi hates me so much, it’s adorable.

The kids appear to be having massive difficulties with the assignment I gave them today. I’ve tried to move on a bit from endless review into new material (effectively the entire fourth quarter has been distance learning, so none of the stuff that is supposed to be covered in the last 25% of the year has been taught yet) and something that probably should have occurred to me earlier occurred to me today.

When I’m teaching in a regular classroom setting, if I notice my first couple of groups having trouble with a specific aspect of something or simply not understanding the way I’m teaching it, or a common mistake I wasn’t expecting, I can adjust throughout the day. If kids in 3rd and 4th hour are frequently making the same kind of error, you can bet that 6th and 7th hour are going to hear me specifically address that type of mistake before I turn the kids loose on whatever their assignment was for that day. And in e-learning, not only do I not really have a way to adjust from class to class, but the vast majority of the time I can’t even tell what mistakes they’re making. This could be fixed somewhat if I adjusted how I was instructing– I’ve been defaulting to mostly multiple-choice assignments in a Google form that can grade itself– but it’s difficult to imagine what I could be doing that would let me see their thinking as they’re making mistakes. I mean, sure, I could ask— I could give them a problem, then they answer it, and then maybe explain in a text box how they solved it, but I know my kids well enough to know that that’s not actually going to be as helpful as it sounds like it could be. I’ve only got about 30-40% of my kids even doing the work on a day-to-day basis, it’s tough enough to get them to watch the instructional videos that are showing them how to do the stuff in the first place, and I have no way of telling whether a kid who got a terrible score on an assignment got a terrible score because he doesn’t understand what he’s doing or because he simply logged on and answered “C” for everything– which I suspect at least a couple of my kids are doing.

I need to figure out a way to get this material to teach itself, effectively– because while there’s less than a month of school left, and maybe only 15 days of actual instruction, there is no way that we don’t lose a substantial chunk of next year to this as well, and when that happens I want to be prepared.

If you’re wondering what I mean by “teach itself,” read this excellent article about how– this is not a joke– the first level of Nintendo’s Super Mario Brothers teaches you how to play it. That game is a masterclass of tutorial design; I just need to figure out a way to apply that style of learning to math.

It’ll be easy, I’m sure.

6:52 PM, Wednesday (God, is it Wednesday? Is that right?) April 22nd: 837,947 confirmed cases and 46,560 Americans dead. That is a pretty staggering increase in the 31 hours since I last posted.

Mama cooked a breakfast with no hog

On By Luther M. SilerIn Teaching1 Comment

I’ve talked about this before– my seventh hour class is absolutely my problem children this year, and rearranging about half of them at the semester break somehow made no real differences in the overall attitude and vibe of the class. Yesterday I introduced solving systems of equations with substitution, which frankly is one of the more difficult bits of mathematics they’re going to have to deal with this year, at least in terms of the number of steps involved. And they did a decent job! I’d been warning them in advance that it was going to be tricky and I needed everyone focused while I was going over it, and I more or less got what I needed from them.

Today my co-teacher and I split the group up, if only to keep the noise level down a bit, and I ended up sitting at a table with five of my boys for the majority of the class.

And the five of them spent probably about half an hour working through the assignment with me, with varying levels of teacherly assistance, and after maybe fifteen minutes I found myself wishing I was recording them. They were genuinely working together– not one of the five was waiting for the others to get the answer– discussing their ideas on how to solve problems productively and without arguing, explaining their thinking, and generally doing every single God damn thing I want my students to do when working through math that they find challenging.

Three of the five failed math at least one of the two quarters last semester, too, which made the whole thing even more amazing.

It was a damn good day today.

In which I’ve done 1/3 of my job, maybe

On By Luther M. SilerIn TeachingLeave a comment
I love the visual shorthand that has evolved for pictures of teachers; there are literally dozens of variants on this picture of a teacher rubbing her temples at a desk piled with books with vaguely math-looking chalk notes on an obsolete blackboard behind her.

I received some small amount of evidence today that I have, indeed, been teaching at least seventh grade math for the last, oh, five weeks or so; my kids had a test today on adding and subtracting positive and negative integers and they did, on the whole, a bit better than I thought they were going to. I apparently have not been teaching eighth grade math, which makes me wonder just what the hell I’ve been doing with my time four class periods out of every day for that same five weeks. My students certainly do not appear to have learned anything, or at least they have not learned anything about classifying numbers, which is what I’ve been trying to teach them, and spending yesterday telling them exactly what was going to be on the test as well as providing them with an extensive supply of notes, presentations and videos on the subject (in addition to my own actual instruction) appears to have gotten me absolutely nowhere.

I’m blaming them, mostly.

Okay, that’s probably unfair, but I note that the kids who I can generally count on to give a shit appear to have actually learned something; the problem is that in 8th grade the supply of available Give a Shit is somewhat lower than it is in other grades, and, well, my kids have a bit of a shortage situation going on at the moment. This is, it should also be noted, not the most interesting or immediately useful of mathematics, either; even laying my usual cynicism about the world to the side I can’t really pretend that knowing how to distinguish a rational number from an irrational one is a skill that any of them are ever going to actually need. And while I usually bare my teeth and snarl at the when are we gonna use this school of avoiding acquiring new knowledge, there’s still a spectrum to these things, and this isn’t all that high on that spectrum.

Ah well. This was actually a pretty good week once it got started, and don’t tell anyone I said this but it’s possible that I’m starting to make some headway with the gang of hellions in my seventh hour class. I discovered to my bewilderment earlier this week that despite them being my most behavior-impaired class by a wide margin they are also getting the best grades and have the smallest amount of missing work. This fact rendered me unable to even for nearly a full hour. I was curious to see if it would also lead to them getting the highest grades on the test today; they … did not. I made the mistake of praising them and it went to their heads, I think; I’ll not make that mistake in the future.

I really like my seventh grade classes, by the way. They’re both fun groups even when they’re being more buttheady than usual. I like nearly all of my 8th graders as individuals; as classes … well, we’re still working on about half of them. But we’re only a month in. Plenty of time. I’m sure I’ll have everybody beaten into shape by June.

On actual helpful ed tech

On By Luther M. SilerIn Teaching1 Comment

I am tired– okay, that’s always true, but it’s basically bedtime and I just wanted to take a moment for this– and so this will be a brief piece, but: my lesson for my 8th graders today involved something that I don’t do a lot in my classes: note-taking. I defined and provided a bunch of examples of rational numbers and irrational numbers, mostly me talking and writing on the board and the kids being surprisingly dutiful about writing it all down.

I have a student in one of my classes who speaks basically no English at all. She is– there is some debate about this, and every time I remember to just cut to the chase and ask her about it, she’s not in the room– either from Mexico or Guatemala, or possibly Guatemala via Mexico, I’m not sure, and she only speaks Spanish.

She uses Google Translate to get by in my classroom. I’ve got her paired with another kid who speaks a moderate amount of Spanish and they have their Chromebooks out at all times and the one kid will translate anything important I say into Spanish for her. Unfortunately, this wasn’t working very well today, since I was writing quite a bit and the other girl had to take her own notes as we were going.

She came up to me and told me (in English, which I was impressed by) that she didn’t understand what I’d said after the lecture, and the amazing thing is that between my own limited-but-not-nonexistent Spanish abilities and the translation software I was able to translate all of the notes for her in maybe an extra five or six minutes. At which point she happily– and, I noted, accurately– did her assignment.

I am very old-school in my teaching despite having spent last year literally working as an ed tech advocate. It’s nice when something works like it’s supposed to and actually makes my job easier.

Here we go here we go here we go

On By Luther M. SilerIn Teaching3 Comments

Spent most of the day in my classroom, alternately rearranging desks and staring at the wall. I ended up taking the second classroom from the earlier post, mostly due to some late-breaking information about occasional temperature problems in the other room. The good news is that the other teacher has moved out of the room; the bad news is that she, uh, took a little bit more of the furniture than I was expecting her to, and one of the things I had to do was email the principal and ask for things like a file cabinet and a teacher desk.

I’m going to end up swapping about a third of the big desks for one-piece arm desks, which I think will end up as a best of both worlds situation in my room– I’ll have mostly the larger desks, which are more comfortable for bigger kids (and bigger teachers) and left-handed kids, and still have some of the smaller one-piece desks that will give me a little bit more room to move around the classroom once there are actual bodies at all of those desks. Right now there’s too many places where not only am I convinced I can’t move around between desks, I’m not sure I can have kids seated at both of them without bumping into each other.

I’ll get it sorted. Once I have I’ll post some pictures.

Oh, and I dropped just under $180 on classroom necessities today, too, without touching things like new clothes (not really an expense I can count, but still) and office supplies– just stuff that I know good and well I’m going to need no matter how I end up laying the room out. I do so love having to spend my own money to get my room set up, guys. It’s awesome.

Anyway. All sorts of family stuff going on tomorrow, which means I won’t have time to be in my classroom, so I’ve got Friday and all of next week to get ready for this. I am surprisingly enthusiastic about it, despite how this post might sound. This is gonna be a good year, dammit, if it kills me.

In which I leave the house

On By Luther M. SilerIn Teaching1 Comment

We just got back from Doing a Thing, the annual Science Alive! event at the main branch of the St. Joseph County Public Library in downtown South Bend. This is the third year my wife has taken my son; I didn’t go the last two years because I was working every Saturday. It’s an interesting event; they basically take over the library with tons of booths and exhibits (too many, honestly; there’s stuff everywhere you turn, and tons of people, and I was stressed out from trying to keep from bumping into people or knocking little kids over) and most of them are hands-on in some way or another, which is pretty cool.

The ground floor was basically a mini-4H fair, with a lot of vaguely bemused-looking farm kids letting the terrified city folk do stuff like pet chickens, with the occasional pig or snake thrown in for good measure.

The upper floors were more … science-fair-ish, I guess? Not in the sense of people showing off experiments, but more like lots of table staffed by local college kids demonstrating some aspect of SCIENCE! to the kids. The weird thing was a lot of the time the science they were wanting to talk about was miles beyond the comprehension level of the small kids (my son is 7, and he was about average for the crowd, and there were a lot of kids way younger) who were there. I spent a couple of minutes watching some poor woman who is probably an excellent teacher when she’s surrounded by college students who want doctorates gamely struggling to relate square dancing and mathematics and fractions to each other … somehow? She literally had a whiteboard covered with equations next to her and I had to keep myself from bursting out laughing when she, entirely seriously, asked the group of elementary-age kids in front of her who wanted to square dance what the negative reciprocal of 1/2 was.

I would wager that, if you threw out the actual scientists, no more than 10% of the adults in the building could tell you what a negative reciprocal is. I mean, it’s not a difficult concept, but it’s not one of those things that most folk need to worry about, y’know? Then there was an entire room full of particle physics folks and one lonely astronomer. And, like, okay, radiation’s cool, and particle accelerators are cool, and whatever the spinny ball-balancy thing that my son was so enthralled with was neat, but I found myself wondering if anybody at all was thinking about age-appropriateness when they put this all together. Waving a hand-made Giger counter at a piece of Fiestaware is pretty neat, but I’m pretty certain that despite a valiant effort at explaining radioactivity by the two Ph.D candidates behind the table, it really didn’t get anywhere with my kid.

So. Yeah. Interesting event, but they maybe need to think a bit harder about the age group they’re pitching to and how they’re going to do that in the future.

A quick insight into my personality

On By Luther M. SilerIn Geek1 Comment

Django Wexler, an author I was rather fond of ten minutes ago, just did this to me:

I had a long day at work today, guys.  My last customer of the night kept me at work well past closing time and didn’t buy, I want to curl up in bed with a book, and instead this damn math problem is in my head and fucking with me.

I may need to grab a note pad and oh fuck it I’ll do it on the blog.

Let’s say N is 2.  So two bits, either 1 or 2.  Roll them once.

25% of the time you get both twos.  (so 25% of the time, only one roll)

50% of the time you get one two.

25% of the time you get two ones.

SECOND ROLL

If you have one die left, you have a 50% chance of being done.

If you have both, see the above calculation.

So…

this suggests you have a pretty big chance of being done after N rolls, with diminishing returns after N.  I’m too tired to nail the numbers down, but I suspect N2 is a reasonable answer. Maybe tomorrow I’ll try to figure it out more carefully.

Assuming I can sleep, ever.

DAMMIT.

In which MATH NERDERY DESTROYS THE WORLD

On By Luther M. SilerIn Geek10 Comments

18lp8jstacc0xjpgThe new hotness for the boy lately has been Teen Titans Go!, which works for me because as it turns out I enjoy the program quite a lot.  It’s of that genre of cartoon where at the end of every episode the slate is wiped clean for the next episode, so literally anything can happen and the next episode they just pick up and move on.

To wit: there is an episode where one character blows up the moon.  And they do not all immediately die.  In fact, the blowing up of the moon is more or less passed over a few minutes later once the “YOU BLEW UP THE MOON?!?” moment is over.

“Would that really kill us all?” my wife muses.  “The moon’s awfully far away.”

“I think it would,” I say.  And then I start trying to figure out exactly how bad that might be.

Feel free to correct my math or my thinking if I’ve made a mistake.  HOWEVER:

  • The average distance from the Earth to the Moon is approximately 385,000 kilometers.
  • Assuming that the moon, once blown up, exploded evenly in all directions, by the time the debris field reached the earth it would form a sphere.  That sphere would have a surface area of 1.86 x 1012 square kilometers– or 1,860,000,000,000 square kilometers if you don’t like scientific notation.
  • This is a slight oversimplification, but we shall assume that the Earth presents as a flat disc for this scenario.  The Earth’s diameter is roughly 13,000 kilometers, so the disc has an area of 133,000,000 square kilometers.  That represents .00715054% of the total surface area of the sphere that the moon has exploded into.
  • The mass of the moon is 80,994,200,000,000,000,000 tons.  Or so.
  • Excel tells me that that means that the Earth would be hit by (calculating .00715054% of 80,994,200,000,000,000,000) approximately 5,791,523,012,258,060 tons of broken moon.
  • I don’t even know how to say that number.

Most of those numbers came from Google one way or another and were copy-pasted into Excel or figured out with online calculators.  The mass of the moon, in particular, seems to have a fairly wide range of accepted values.  I can imagine a universe where I ended up off by a factor of ten somewhere but something tells me it doesn’t make a difference.  

I’m still trying to figure out if anyone has estimated the mass of the asteroid that wiped out the dinosaurs, or if I have an easy way to kludge that (I actually can think of one way) but I suspect the following is true:

EDIT!

The generally accepted diameter of the Chicxulub asteroid is six miles.  This means that, assuming a perfect sphere (which isn’t true, I know), it was composed of 113.1 cubic miles of (assuming, assuming, assuming) iron.  That’s 16,648,088,371,200 cubic feet of iron.

A cubic foot of iron weighs 491.09 pounds.

Multiplying, we get an asteroid that weighs 8,175,709,718,212,610 pounds.  Divide that by 2000, and we get an estimate of 4,087,854,859,106 tons for the asteroid that wiped out the dinosaurs.

The amount of moon hitting Earth would be 141,676% of that amount.

So yeah.  We’re fucked.