The blog of Luther M. Siler, teacher, author and local curmudgeon
Sometimes you stay home from work because you feel like hell, which means you have to push your Algebra final back a day. But then your son also has an Algebra final on Wednesday, so you end up having to prepare an 8th grader for an Algebra final anyway.
It doesn’t happen often, but it happens.
My classroom is completely ready to go other than a single piece of furniture, which needs to be delivered, removed from its box, and placed in its appointed location. I still don’t have any goddamn textbooks or anything like that, mind you, but the room is ready. I’ll probably go in tomorrow anyway just to see what kind of trouble I can get myself into.
In the “good news/bad news” department, it looks like we’ve got a fully staffed Math department for the first time since I’ve been in this building. This is good news because it means I don’t have to teach an overload, but it’s bad news because it means I don’t get to teach an overload, and I’m vulnerable to getting called for class coverage on my prep period. So I won’t be getting as big a paycheck as the last couple of years, because that bump from overloads is substantial. But I actually get to, like, breathe, and occasionally take a leisurely piss, during the school day. That’s gotta count for something, right?
I think I’ll work on sub plans and early photocopying tomorrow. God forbid I get that shit done before school starts. I’ll also get some pictures; I forgot to do that today.
Spent the last half hour talking a high school sophomore off the ledge, which is what you expect to happen when you teach 8th grade. She’s in Algebra 2 right now, which technically I’m legally allowed to teach, and I can absolutely handle both the mathematics behind and the explanation of that second inequality up there, but she swears up and down they haven’t been working with quadratics at all. That’s the second question of the two she asked me about, and the first of the other pair of inequalities looks like this:
…which is a reasonably tricky PEMDAS problem (a parenthetical with an exponent and a multiplier on it is the stuff of 10,000-comment internet videos) even before you get to graphing quadratics by hand, which I’m capable of with intense concentration but may not be great about explaining very well at the moment. Both pairs of inequalities have a simple linear inequality and a quadrilateral, and long story short, I’m not convinced her teacher gave her the assignment that he meant to. On an e-learning day, no less? You serious, man?
This isn’t a kid who’s going to forget that they just spent a month on quadratics or something like that, by the way. She’s bright. And she took a picture of one of her assignments from last week, which was graphing absolute values. The leap in difficulty from graphing absolute values on a number line to graphing systems of inequalities where one inequality is linear and the other is a PEMDAS nightmare that turns into a quadratic is … stark. There’s gotta be something else going on here.
Anyway, we’ve got the day off tomorrow again, which was the right decision. It’s been 20 below or worse all day, and it’s supposed to warm up significantly tomorrow, but at 8:00 in the morning it’s still going to be 20 below, and even after a two-hour delay it’s still going to be fifteen below– the temperature isn’t going to be conducive to human life until after noon, and you don’t make kids walk to school in subzero wind chills, especially when a lot of them don’t have coats. We will not lose Thursday or Friday, as it will be regular Midwest January cold and not the kind that has you cursing God.
The kids will, of course, find a way to make Thursday and Friday feel like a long week.
Every time my kids took a test last year, I went into a depression spiral, because for some reason my test results were consistently worse than all of the other middle school math teachers in my district. My 8th graders took their first real test of the year on Wednesday. And … well.
Blue bar is best bar, there’s no green bars for anybody because the idiot person who put the test together forgot to set a level for Mastery, and red is Bad, and white is untested kids. The person who has 100% of his kids mysteriously untested is also the guy who wrote the test and screwed up the scoring. He also set the schedule for when we were supposed to test! And just … didn’t.
But my blue bar is way bigger than anybody else’s blue bar, including Mr. I Work At the Honors School to my right, and my red bar is smaller than everyone else’s, so suck it.
Can we talk about Algebra’s last test? Sure, let’s, and be aware that this is what both of their tests look like:
The other teacher is the other Algebra teacher at my school, and yes, I’m still mad that I don’t have both Algebra classes any more, and the reason there are only two is that for some reason the high school teachers aren’t using the system that we’re all supposed to use to keep track of student achievement on the tests the high school teachers wrote.
There’s some inside baseball going on here, obviously, and I’m sorry if this is a little incoherent, but I’m really frustrated with the way this system for common assessments is getting implemented at basically every building other than mine. But y’all know how competitive I am and my kids are kicking names and taking ass so far this year. Which is a fucking relief, after last year.
Oh, and grade-wise? Currently I have one hundred and seventy-four students in my six classes (Algebra has 21, and all of my 8th grade classes but one have 31. My “small” 8th grade class has 29.) and of those 174 kids, only 39 (22%) have Ds or Fs. Considering that last year this happened at the beginning of the third quarter I will absolutely take those numbers. I have way more kids getting As than getting Ds or Fs. That hasn’t happened very often.
So yeah. I’m going to enjoy pretending I’m good at my job tonight.
I have removed the Second Skin from my new tattoo, and the itching is absolutely maddening, so I’m going to distract myself with math. Because that’s why you come here, right? As a reminder, this is the original image, and the question is the ratio of the inner square to the outer square:
The first thing we’re going to do is draw the two diagonals of the inner square. These are, by definition, perpendicular to each other, and they are also equal to the circumference of the circle. Let us define the radius of the circle as x:
What we have now is four right triangles inscribed inside the circle. Pythagoras tells us that the sum of the squares of the two legs are equal to the square of the hypotenuse, which is the line on the left of the square there. Therefore, defining the hypotenuse as Y, we get:
x2 + x2 = y2
2x2 = y2
Take the square roots of each side, and we get:
√(2x2) = √(y2)
And therefore:
√(2x2) = y
Which means that all four sides of the inner circle are equal to √(2x2), thusly:
To get the area of the inner square, all we have to do is multiply √(2x2) by √(2x2), which, conveniently, just gets rid of the square root symbols. The area of the inner circle is 2x2.
Now, we need to realize that since the radius of the circle is x, the diameter of the circle is 2x, and that the diameter of the circle also equals the width and the height of the outside square. So that outer square is 2x high and 2x wide:
Therefore, all we have to do to get the area of the outside square is multiply 2x by 2x, which gives us 4x2. Which, conveniently, is exactly twice the area of the inner square, which was 2x2.
The outside square is therefore twice the size of the inner square, and the ratio of the inner square to the outer square is 1:2.
Or, y’know, you could just rotate the fuckin’ inside square, which makes it visually obvious.
I ended up having some spare time this afternoon, and I found a free practice test online through the same people that sold me my study guide (so I figure it’s at least reasonably reputable) so I went ahead and took it, and if I’m understanding the scoring methodology correctly … it looks like I passed, although not exactly with flying colors– I got 42/66 questions right, or 63.34%, for a final score of 163, and a 159 is a pass in Indiana. I could have gotten a 39 and still passed, so I had a three-question cushion on my first try.
Now, granted, no one is ever going to look at my Praxis score again after I’ve passed the thing, so it really doesn’t matter if I pass it by the skin of my teeth or by flying colors, but I want a little bit more of a cushion than that. I was able to go through the practice test after taking it, and I printed out two categories of questions: questions I had gotten wrong, and questions that I got right but I know good and well that I got right by being lucky. That gave me about 27-30 questions to study tomorrow; in there are a handful that I absolutely shouldn’t have gotten wrong, including one thing I’ve taught fairly recently (!!!) and one where I just flat-out calculated something incorrectly and didn’t notice it, but I figure being fully confident of over half the test is better than I expected going in. I missed nearly all of the calculus questions, of course, but I got a couple of the trigonometry ones right without guessing and there were one or two of the harder ones where I was guessing between, say, two answers instead of all four and managed to get the right one. I figure I’m going to do this twice more– I’ll study my wrong answers tomorrow and see which ones I can get comfortable with (some are a matter of just not understanding certain kinds of notation, so those will be easy points) and do another practice test on Thursday, then maybe one more over the weekend, and if my numbers move in the right direction I don’t see why I can’t move ahead with the real thing next week sometime. Which, on one hand, will wipe out one of my big plans for June, but on the other hand will let me focus more on Arabic, curricular stuff, and Spanish.
The other thing I need to make sure I understand is the actual rules for taking a Praxis from home. I know they have a proctor monitoring you but I’m not sure what the tech rules are and I suspect on at least two questions I may have broken a rule, depending on how picky they are. This organization has made me incandescently angry with them on multiple occasions so I need to make sure I’m prepared for literally anything. Hopefully things go smoothly, but I need to prepare for them not to.
It is Friday night, and I am sitting at my computer, listening to the first concert of Pearl Jam’s new tour, featuring the first live performances of half a dozen tracks from Dark Matter, and interpreting data from charts and spreadsheets.
In other words, this is very close to the perfect evening, and at 47 I may as well accept what I am because it’s not changing.
I am a rock star, ladies and gentlemen. We took the final NWEA of the year on Wednesday and Thursday, and … goddamn. I was elated by last year’s scores. I am fucking ecstatic with these. I have never seen results as good as what I got on this year’s spring NWEA before. And the really awesome thing is that I could go a dozen different ways after that sentence and they’d all be just as awesome.
Let’s back up a bit. The NWEA is administered three times a year and eats up a grand total of about twelve hours of instructional time over the course of the school year. It is primarily a growth test, with no concept of success or failure– the scores are indexed against grade levels, but you can’t fail the NWEA; you only show high achievement or low achievement compared to your grade cohort and high growth or low growth compared to other people in the score band of your grade cohort.
This is the kind of test I want. I get kids all over the map– kids taking a class two years above grade level and kids with 60 or 70 IQs. I don’t care whether or not my kids are successful against some arbitrarily designated cut score that can be manipulated depending on whether the politicians think we’re passing enough kids or not. I want to know whether they got better at math under my instruction. And the NWEA provides me with that data.
And it also provides me with something I really like– the ability to compare my own kids’ performance in Math against their performance in Reading, which I don’t teach, which is as close as I can get to an unbiased check on whether I’m doing my job right. Two years in a row now my kids’ Math growth has kicked the shit out of their Reading growth. It was rough last year; it was staggering this year. Which brings me to that chart up there. That’s my second hour. The pluses are their Math scores and the squares are their Reading scores, so each kid is represented twice on the graph. The farther to the right their boxes are, the better they performed, and the higher they are, the more their growth was. In other words, you want them in the green box and maybe not so much in the red box. Orange and yellow are on-one-hand-on-the-other-hand territory.
Here, let me clear the Reading scores out:
Now, this particular chart shows the two things I want to highlight more clearly than the rest of my classes, but believe me, these are common threads across all of my students. First, look at how many of them are high growth. I have four fucking kids at the 99th percentile in growth– in other words, kids who showed more growth than 99/100 of kids who took this test, nationwide. I have eleven across the 117 kids I have scores for. There were nine of them at the 90th percentile or above, just in that class. There were 26 across all of my classes– in other words, 22% of all of my students were in the top ten percent in growth in America.
I want a fucking raise.
The other thing I want you to notice is that yellow box, the one for kids who are high achievement but low growth. Notice that that fucker is empty.
If we look at my low-achievement kids, 44 of them were high growth and 44 were low growth. Which sounds exactly like you might expect, but “what box are they in” is kind of a blunt instrument. Almost 2/3 of my high achievement kids– 19 of 29– were also high growth. And the high-achievement kids are widely considered to be much more difficult to get to show growth.
This is interesting to me in terms of what it says about me as a teacher. I did a good job with my low-achievement kids. I want to dig into those numbers more and look at averages and medians to get a little more detail, but I’m still pretty damn happy with a 44/44 split. But I did a fantastic job with my high achievers. I am doing a mathematically demonstrably better job achieving growth with my high-achieving kids than with my low-achieving kids. Which, believe me, I’m going to make a point of when I campaign to get a Geometry class and maybe the other Algebra class back next year. I would love to see numbers from the guy who teaches the Geometry class at the only middle school in the district where it’s actually taught. If he’s beating the numbers I put up this year, I need to be sitting in on his class.
God, I love being a numbers nerd, and God, I love it when I get a chance to brag about my kids.
From the “I’d have two nickels, but it’s weird that it happened twice” department: Between Kyne Santos, who wrote this really awesome fucking book, and a simply outstanding TikTok account called Carrie the One, I follow two different math-based drag queen accounts on social media, or at least I did before I killed off my TikTok account. I say an awful lot that you already know from the title and the cover whether you want to read this book or not, but let’s be real here: a book about math written by a drag queen might be the ultimate “you already know if you want to read this” book, and to be honest this is less of a review than a notification that this book exists, and you might have missed it, and if the notion of reading this book rustles your jibblies in literally any way at all you should go spend money right away.
This book is part memoir, part textbook (simultaneously of mathematics, the history of gay culture and the drag movement, and of the history of mathematics) and part adorably unhinged geek-out about how fucking cool math is. You probably need to be at least comfortable with algebra to be able to fully appreciate it, if only because it’s kind of hard to talk a lot about math without getting at least a little bit into the weeds, but Kyne’s going to be explaining what ℵ0 is at some point and if that terrifies you you should at least take a deep breath before jumping in. It’s only 233 pages, though, so even if you have a rough time with it it’s not terribly long.
Each chapter takes on some aspect of mathematics– there’s a chapter on infinity, a chapter on algebra, a chapter on what “proof” means in a mathematical context and what the difference between numbers and numerals are, and so on, and Santos interweaves their own story and the history bits into the more technical (but again, not super technical, so far as it goes) math-focused parts. I picked up a couple of things that I am absolutely going to be bringing up in class, or at least with my Algebra kids– I have my lesson plans for Monday done already, and they’re directly from an anecdote in this book about imaginary square numbers that absolutely set my brain on fire– and Santos is one of those people who can carry a lot of what could be a slog just by sheer enthusiasm for the subject matter. Again, if you’re even the least bit curious, absolutely give this a shot. It’s well worth it.
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