Tag: math

On the final

On By Luther M. SilerIn TeachingLeave a comment

I have crunched the numbers, or at least calculated my pass rates, and of the 139 kids who took the 8th grade Math final, 55.4% of them managed to pass it. I curved the test to 20 points instead of 25 before putting it into the actual grade book, and with that adjustment, 66.2% of them managed to pass. This from a test that upon looking at it the first time, I was fairly certain that 2/3 of my students if not 3/4 of them would fail it.

(Only one student failed the Algebra final, before or after the modest two-point curve. I’m not worried about that class right now.)

Furthermore, and I’m not going to post the graphs here because they’re vaguely incomprehensible without the information that I’d have to strip out of them, my kids did pretty respectably compared to the other 8th grade Math teachers in the district. The data I get through the dashboard is incomplete but still a little more fine-grained than just pass/fail rates, but at worst we’re tied for the best performance in the district, at least of the teachers I can see data from, and depending on how you measure, you could make an argument for first or second. I’ll take “tied.”

A couple of other things: first, my 8th graders are unused to the concept of “final exam” or “midterm” to begin with. 7th graders did not have to take either last year. They are also, and I think this might be a place where my current grade policies might be hurting me, not used to the idea of a test they can’t retake in my room. I told them over and over again that they were only getting one shot at this and a bunch of them asked me if they could retake it anyway. I think I’ve managed to create some kids who just sort of breeze through tests the first time, knowing they can redo them if they have to, and if they don’t get a good enough grade the first time, they actually try on the second attempt.

Second, I may need to rethink the way I teach my classes from the ground up, so long as the guy who is in charge of writing these tests remains in charge of writing these tests. I am a big fan of Everyone Who Tries Can Pass, which, honestly, probably shouldn’t be true no matter how much I want it to be. He is a big fan of Rigor, which I generally find to be nothing more than artificial difficulty with no particular instructional utility.

To put this in simpler terms, if the objective is “prove you can multiply,” I’ll likely ask you what 7×8 is. His questions are more likely to be 7.13 x -18.014, that is if he’s not writing something utterly demonic like -7/18 x 8.12.(*) Both are “multiplication,” of course. Mine lacks Rigor. His lacks common sense. I feel like maybe if the kids are seeing a particular mathematical concept in 8th grade, maybe we ask them some simpler questions about that concept to see if they get the idea before we jump to the Rigor shit. Not so for my compatriot; the ILEARN is gonna be Rigorous, so our assessment must be as well.

This is the point where I generally throw my hands up and point out that if you want me to fail half of my students, please have the balls to actually say that. I’d ultimately rather have them feel like they have a chance to pass, and (slightly more importantly) a chance to understand the math I’m supposed to be teaching them. If every test question is high level and Rigorous, I can point at ten kids in every class who are already done before I pass the tests out, and that’s not including the ones who just don’t give a shit one way or another. That’s a whole different conversation, and one I might have sometime during break depending on whether I get around to analyzing my ILEARN data the way I want to.

So what did I do? Detailed guided notes. Detailed guided notes. Here, take a look at them if you want:

8th Grade Final NotesDownload

Basically every question in those notes is a test question on the final that has been slightly rewritten, basically just changing the numbers. In other words, if you paid fucking attention during the four days that we spent going over that nine page document, you had the entire test in front of you. And yes, the test was open notes. 45% of my kids failed with this document in front of them; most of them because they didn’t even glance at it during the test. (You may recall the test I gave a couple of years ago where I literally wrote the answers on the board and 23% of them failed. There is nothing I can do to get some of these kids to pass.)

Anyway. If you’ve read this far, go ahead and look through those notes, and keep in mind that I didn’t exactly keep that document a secret. I shared it with my boss and I gave it to my 8th grade partner teacher. I don’t think she used it with her class; I could be wrong.

You tell me: is this cheating? Meeting the kids where they are? Something else? I don’t know. They did a lot better than I thought they were going to do initially, and there are still a bunch of questions on that test (not all of them, to be clear) that I think are manifestly unfair for 8th graders. Looking at the kids who failed anyway, honestly, I’m not sure how many of them were possible for me to get short of taking the test for them.

The question is whether I just give up on those kids next semester and leave them behind so that I can have the rest of them ready for a test like this without this degree of a crutch, or if I keep providing the crutch. I genuinely don’t know. I really don’t.

(*) To get a little bit further into the weeds, converting decimals to fractions and vice versa isn’t in 8th grade standards, and I don’t have time to teach it. So there is zero chance that I’m going to give my kids a question where that must happen in order to get the right answer. Because it introduces a source of error that is not “do the kids understand this 8th grade standard” and I’m not about that life.

A quick question

On By Luther M. SilerIn Teaching3 Comments

Super busy tonight, but: if you say to another teacher that you expect 75% of your kids to fail the final that was imposed upon you by the district, and 51% of your kids pass it, is that “good news” or just less bad than you expected?

In which today was tomorrow

On By Luther M. SilerIn TeachingLeave a comment

I want to read tonight, so this isn’t going to be long, but I figured it was probably worth it to point out that today was a genuinely good day, for the most part, and the first day at least of the study guide seemed to go over pretty well. I have no doubt that as some routine sets in things will get a little rougher– four days in a row of taking notes, even in guided and somewhat abbreviated form, is gonna get on the kids’ nerves– but today at least went well, so I’ll take it.

Just discovered that the wind chill is supposed to be eight below tomorrow morning, too, so watch us get a two-hour delay on a day where I definitely do not have time for a two-hour delay and an actual cancellation would be a huge pain in my ass.

(There is no chance at all of a cancellation, but still.)

Anyway. Got a book to finish.

In which tomorrow is a new day

On By Luther M. SilerIn TeachingLeave a comment

Today was probably the most demoralizing and exhausting day of the school year so far, to the point where I utterly unloaded on my boss after school, which is not typical of me at all. I’m usually the one talking other people off of ledges even on shitty days, and today the only advice I had was jump, fucker.

I don’t know how to educate people who know nothing and are utterly unbothered by the fact that they know nothing. I just don’t. There may not be a way to do it. You may as well just put some of these fuckers in jail right now, because that’s where people who fail every single class in middle school generally end up anyway, and finding out that one of the six or seven shitheads I wrote up today (!!) already has a PO was the shit cherry on top of the smegma sundae that today served me.

Another thing I said to my boss: “If our district was trying to set up the middle schools for failure, how would it look any different from what they just did to us?”

And then I got home and other than a break for dinner have spent three and a half hours working on study guides for the finals, which I will exhaust myself even more over the next four school days trying to get my kids to understand. I will fail, and they will make no difference, and 3/4 of my kids will fail the final anyway, because I could literally write the answers on the board and a third of them would still fail, and if thought is required those numbers go up. Significantly.

I really wonder what it would be like to work at a good school. I never have. I don’t even know where to find them.

Tomorrow

On By Luther M. SilerIn TeachingLeave a comment

I get to spend my entire day tomorrow giving my students standardized tests, and I mean that literally– every single one of my classes, all day, except for my 30-minute lunch, which is going to be delayed a bit from its usual time because of Reasons. I will have to read several pages of instructions six times and ask over a hundred and thirty students “Do you have a cell phone?” and hope none of them are lying to me, because I get to catch all the bullshit from everybody if we have to invalidate a test.

You’ve all heard the rants before; I’m tired and I don’t wanna. I’m going to predict my sixth-hour kids have the worst test scores I’ve ever seen, though, because giving a standardized test at the end of the day is fucking professional malpractice.

And then Thursday the process will repeat, with the ELA teachers giving their half of the test, and I’ll be in my classroom instead, trying to figure out how to keep the bastards busy and quiet for class periods that are ten or so minutes longer than usual. I’m thinking color by numbers. I’m already pre-annoyed by Thursday behavior issues that haven’t even happened yet– that ten minutes don’t sound like much but they’re going to be. My current ability to tolerate bullshit, as well as the ability of the other adults in the building, is calibrated for 53-minute blocks. There will be a lot of damn referrals during the last ten minutes of class over the next couple of days.

Also, I just ate about two thousand calories of deep dish pizza, and it was a bad idea.

The end.

Some good news in some nerdy graphs

On By Luther M. SilerIn TeachingLeave a comment

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.

Okay, fine, I’ll do the math

On By Luther M. SilerIn Geek, idiocy, TeachingLeave a comment

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.

New tattoo!

On By Luther M. SilerIn art, Teaching2 Comments

It has been, I think, sixteen or seventeen years since my last tattoo. I know my wife was with me; I’m less certain that we were actually married at the time. And while you very well might be looking at that and wondering what the hell I was thinking, I’ve been thinking about this exact design for my next tattoo (that’s my right wrist) for most of that time, and only just now decided to pull the trigger on it.

It is, oh, I dunno, sometime during the first Obama administration, and I am at a training with a bunch of other teachers from my school, none of whom are math teachers. We are presented with three pieces of construction paper, held together in the center by a brass paper fastener, in this shape: a large square, with a circle inscribed in the square, and a second square inscribed inside the circle.

“Figure out what the ratio of the inner square to the outer square is,” they tell us. “You can do whatever you like to come up with the answer.”

My entire group looks at me.

Sigh. Okay, fine, I’ll math this shit. To be entirely honest, I do not, at this time, remember exactly how I got the answer, but there was a lot of Pythagoras involved, and I think at least one place where I solved a set of equations with two variables. It took a few minutes. I’ve considered reconstructing the math, but I think the story is kind of better if I don’t. The ratio is 1:2. In other words, the outer square is twice the size of the inner square.

Anyway, they give us a few minutes, and then ask if anyone wants to share their answer. My group volunteers me to explain my answer, having heard my explanation and apparently accepting none of it. So I attempt to explain my logic to this group, again, none of whom are math people. It takes a few minutes and I may have killed at least one of them. The presenters, now with wide grins on their faces, because they are a step ahead of me and I have walked into their trap, ask if anyone else solved the problem in a different way. A large man on the other side of the room raises his hand. They call on him. He looks like a not-insignificant portion of the people who know him call him Coach, possibly including people he has never actually coached.

He asks if he can use their prop. They say yes, and their grins get larger.

He demonstrates a solution in about a second, by rotating the inner square exactly forty-five degrees to the left.

“S’ half,” he says, and sits the fuck back down.

I start swearing. There’s a moment of disbelief and then the whole room, including me, starts laughing.

Perhaps you have trouble picturing what he’s done. Let me draw this real quick:

I think it is probably immediately clear to everyone looking at this, with the inner square rotated, that the inner square is half of the outer square.

A few days later, I found a second construction-paper shape similar to this one in my classroom, also held together by a brass paper fastener. I kept it in my classroom for years. I don’t think I have it any longer, but I had it for a really long time, across multiple classrooms in multiple schools.

This tattoo is my permanent reminder that sometimes shit does not have to be complicated, which is something I have been fairly accused of in my life, more than once.