Hand to god, I will finish my post about the reform math fuss I twittered in mid-week, but I am blocked and trying to chop back what I discuss and I want to talk about something fun.

So I will discuss Dale, a fellow math teacher who was a colleague at my last job. Dale is half my age and three days younger than my son. Yes. I have coworkers my son’s age. Shoot me now.

He and I are very different, in that he is an incredibly hot commodity as a math teacher, whose principal would offer him hookers if he’d agree to stay, and gets the AP classes because he’s a real mathematician who majored in math and everything. He turns down the hookers because he’s highly committed to his girlfriend, who is an actual working engineer who uses math every day. I am not a hot commodity, not offered hookers, and not a real mathematician. I also don’t have a girlfriend who is an actual working engineer using math every day, but there’s a lot of qualifiers in that last independent clause so don’t jump to too many conclusions.

He and I are similar in that we both were instantly comfortable with teaching and the broad requirements of working with tough low income kids who don’t want to be in school, and extremely realistic about cognitive ability. We also don’t judge our students for not liking math, or get all moral about kids these days. (Of course, he is a kid).

We are also similar in that we like beer and burgers (he has a lamentable fondness for hops, but no one’s perfect), and still meet once or twice a month at an appropriate locale to talk math. I tell him my new curricular ideas, which he is kind enough to admire although his approach is far more traditional, and ask him math questions, particularly when I was teaching precalc; he tells me that most of the department wants him to be head, despite his youth and relative inexperience. We also talk policy in general. It’s fun.

“I have some news for you,” I told him, “but you will laugh, so you should put down your beer.”

He obligingly takes a pull on his schooner of Lagunitas IPA and sets it down.

“A new study came out,” I said, “and apparently, many high school algebra and geometry courses have titles that don’t actually match the course delivered.”

Dale, who clearly thought I was going in a different direction, did a double take. “Wait. What?”

“The word used was ‘rigor’. Like, some Algebra I courses don’t actually cover algebra I. Same with geometry.”

He looks at me. Takes another pull. “Like, not all algebra teachers actually cover the work formula?”

“Like, not all algebra teachers cover integer operations and fractions for two months. Like not all algebra teachers spend two weeks explaining that 2-5 is not the same as 5-2.”

“Uh huh. Um. They did a *study* on this?”

“They did.”

“They could have just asked me.”

“They can’t do that. They think math teachers are morons. But there’s more.”

“Of course there is.”

“Apparently, the more blacks and Hispanics and/or low income students are in a class, the less likely the course’s rigor will match the course description.”

He sighs. “I need more beer. Ulysses!” (that’s actually the bartender’s name.) “I’m assuming that nowhere in this study did they even mention the possibility that the students didn’t know the material, that the course content depended on incoming student ability?”

“Well, not in that study. But you know what happens when we point that out.”

“Oh, yeah. ‘It’s all that crap they teach in elementary schools!’ Like that teacher in that meeting you all had the year before I got here. ‘Integer operations and fractions! Damn. Why didn’t I think of that?‘”

“Yes. Actually, the researchers blamed the textbooks, which was a pleasant change from the platitude–and-money-rich reformers who argue our standards are too low.”

“Did anyone ever tell them if it were that simple, whether textbook or teacher, then we could cover the missing material in a few weeks and it’d all be over? Wait, don’t tell me. Of course they told them. That’s the whole premise behind….”

“Algebra Support!” we chorused.

“But then there’s that hapless AP calculus teacher stuck teaching algebra support. He spent, what, a month on subtraction?”

“And the happy news was that at the end of the semester, the freshmen went from getting 40% right on a sixth grade math test to 55%.”

“The bad news being at the end of the year, they forgot it all. Net improvement, what–2 points?”

“Hell, I spend the entire Algebra II course teaching mostly Algebra I, and while they learn a lot, at the end of the course they’re still shaky on graphing lines and binomial multiplication. And I don’t even bother trying to teach negative numbers, although I do try to show them why the inequality sign flips in inequalities.”

“But it’s our fault, right?”

“Of course. But that’s not the best part.”

“There’s a best part?”

“If you like black comedy.”

“The Bill Cosby sort, or the Richard Pryor catching himself on fire sort?”

“Someone doesn’t know his literary genres.”

“Hey, we can’t all be English majors. What’s the best part?”

“The best part is that Common Core is supposed to fix all this.”

“Common Core? How?”

“By telling us teachers what we’re supposed to teach.”

I’d forgotten to warn Dale, who was mid-gulp. “WHAT???”

I handed him a napkin. “You’ve got beer coming out your nose. Yes. Checker Finn and Mike Petrilli always use this example of the shifty, devious schools that, when faced with a 3-year math requirement, just spread two years of instruction over three!”

“Wow. That’s painful.”

“Well, they don’t much care for unions, either, so I guess they think that when faced with a mandate that’s essentially a jobs program for math teachers, we teachers use it as an opportunity to kick back. But that’s when they are feeling uncharitable. Sometimes, when they’re trying to puff teachers up, they worry that teachers will need professional development in order to know the new material.”

“How to teach it?”

“No. The new material.”

“They think we don’t *know the new material?*”

“Remember, they think math teachers are morons. On the plus side, they think we’re the smartest of teachers. (Which we are, but that’s another subject.) There’s still other folks who complain because ed schools don’t teach teachers the material they’re supposed to be teaching.”

“But we know that material. That’s what credential tests are for. You can’t even get into a program without passing the credential test.”

“Do *not* get me started.”

“So when the test scores tank, they’ll say it’s because teachers don’t know the material?”

“Well, they’ve got the backup teachers don’t have the proper material to teach the standards, in case someone points out the logical flaws in the ‘teacher don’t know the material’ argument.”

“Sure. If it ain’t in the textbook, we don’t know it’s supposed to be taught!”

“Don’t depress me. Yes, either we don’t know what’s supposed to be taught or we don’t know how to teach it without textbooks telling us to.”

Dale starts to laugh in serious. “I’m sorry, Governor. I *would* have taught vectors in geometry, but since it wasn’t on the standards, I taught another week of the midpoint formula.”

“I’m sorry, parents, I *would* have dropped linear equations entirely from my algebra two class, but I didn’t know they were supposed to learn it in algebra one!”

“Damn. A whole three weeks spent teaching fraction operations in algebra when it’s fifth grade math. I could have spent that time showing them how to find a quadratic equation from points!”

“I didn’t know proofs were a geometry standard. Why didn’t someone tell me? Here I had so much free time I taught my kids multi-step equations because my only other option was showing an Adam Sandler movie!”

“Stop, you’re killing me.”

“No, there’s too many more. Who the hell went and added conics to the standards and why wasn’t I informed? Here I spent all this time teaching my algebra II kids that a system of equations is solved by finding the points of intersection? Apparently, my kids didn’t bother to tell me that they’d mastered that material in algebra I.”

“I can’t believe it! Four weeks killed teaching kids the difference between a positive and a negative slope! Little bastards could have told me they knew it but no, they just let me explain it again. No wonder they acted out–they were *bored*!”

My turn to snarf my beer.

“Jesus, Ed, I’ve wondered why we’re pulling this Common Core crap, but not in my deepest, most cynical moments did I think it because they thought we teachers just might not know what to teach the kids.”

“That’s not the most depressing, cynical thought. *Really* cynical is that everyone knows it won’t work but the feds need to push the can—the acknowledgement that achievement gaps are largely cognitive—down the road a few more years, and everyone else sees this as a way to scam government dollars.”

“New texbooks! New PD. A pretense that technology can help!”

“Exactly. I’d think maybe it was another effort to blame unions, but no.”

“Yeah, Republicans mostly oppose the standards.”

“Well, except the ‘far-seeing Republicans’ who just want what’s best for the country. Who also are in favor of ‘immigration reform’.”

“Jeb Bush.”

“Bingo. You’ll be happy to know that libertarians hate Common Core.”

“Rock on, my people!”

“Yeah, but they want also want open borders and privatized education.”

“Eh, nobody’s perfect.”

“But all that depressing cynicism is no fun, so let me just say that I would have taught sigma notation except I thought that letter was epsilon!”

“Hey, wait. You *do* get sigma and epsilon confused!”

“No, I don’t, or I wouldn’t call the pointy E stuff sigma notation, dammit. I just see either E shape out of context and think epsilon. Why the hell did Greeks have two Es, and why couldn’t they give them names that start with E? Besides, the only two greek letters I have to deal with are pi and theta, and really, in right triangle trig there’s no difference between theta and x.”

“Well, you’re going to have to stop making that mistake because thanks to Common Core, you’ll know that you’re supposed to teach sequences and series.”

“Damn. So I won’t be able to teach them binomial multiplication and factoring and let them kick back and mock me with their knowledge, which they have because they learned it all in algebra I.”

“Here’s to Common Core and math research. Without them, America wouldn’t be able to kid itself.”

We clinked glasses just as Maya, Dale’s girlfriend walked in, a woman who actually uses centroids, orthocenters, and piece-wise equations in her daily employment. The rest of the evening was spent discussing my search for more real-life models of quadratics that don’t involve knowing the quadratic formula first. She offered road construction and fruit ripening, which are very promising, but I still need something organic (haha), if possible, to derive the base equation. So far area and perimeter problems are my best bet, which gives me a good chance to review formulas, because until Common Core comes out I won’t know that they learned this in geometry. I wondered if velocity problems could be used to derive it. Dale warned me that it involved derivations. Maya was confused by my describing velocity problems as “-16 problems”, since gravity is either gravity is either 32 ft/sec/sec or 9.8 m/s/s. Dale interpreted. I’m like Jeez, there are people who know what gravity is off the top of their heads? This is why I don’t teach science. (edit: I KNEW I should have checked the numbers. I don’t do physics or real math, dammit. Fixed. )

But all that’s for another, happier, post.

July 14th, 2013 at 10:24 pm

“since gravity is either 32 ft/sec or 18.8 m/sec.”

Don’t you mean, “since gravity is either 32 ft/sec/sec or 9.8 m/s/s”? (The SI abbreviation for second is ‘s’, not ‘sec’.)

I know this is a minor point, but this math and physics teacher just can’t resist.

July 14th, 2013 at 10:35 pm

18.8 m/s?

July 15th, 2013 at 1:40 am

(1+8).8 m/s^2 maybe?

July 15th, 2013 at 3:18 pm

Why minus 16? Because in physics down is generally considered to be the negative direction. Starting from rest, an object in uniformly accelerated motion will go 1/2 a t exp2. Since gravitational acceleration near the surface of the earth is 32 ft/s/s down, the distance an object falls in free fall is -16 t exp2 (minus 16 times time squared).

BTW: great post.

July 21st, 2013 at 12:32 am

Thanks! I showed it to Dale, and he was cracking up that all the comments were about the techie stuff.

Yeah, I know that it’s half of gravity and going down. She did, too, but she had no idea what I was talking about, because I said “gravity thingy being -16”. Dale knows how I think–utterly divorced from the reality his girlfriend actually works with–so could translate.

The equation is derived with calculus, right? I’ve read up on it and it appears not to be something I can explain easily to my students.

July 21st, 2013 at 11:17 pm

Dear ER !

Equation x=0.5*a*t^2, if it is the equation you are talking about, is derived without calculus. It is just the area of right angle triangle with side “t” and and height “a*t” on the v —- t plane.

Here “a” is acceleration, so that during time “t” velocity goes from zero to “a*t”.

Your avid reader, F.r.

July 15th, 2013 at 10:01 pm

My favorite joke is about a military boss (e.g. a Major), who is deriving the formula for the horizontal length of projectile flight, when the projectile is shot from the artillery gun with initial velocity “v” and at gun’s elevation angle “alpha”.

Correct formula is

L =[(v^2)/g]*2*sin(alpha) * cos(alpha),

where g=9.8 m/s.

In the process this Major has made a typo somewhere, and got cos(alpha) in denominator, instead of numerator:

erroneous L =[(v^2)/g]*2*sin(alpha) / cos(alpha).

Some smart conscript asks:

– Sir, Major, Sir, what if alpha is getting closer and closer to 90 degrees ? Will L become infinitely long ?

Major (after two minutes of intense thinking):

– No, it will not go to infinity, since each big artillery gun has at 88 degrees special stopper.

–

There is important morale of this story for me.

When we speak and listen, there are physical “stoppers”, which do not allow our throats to generate the frequencies above 25 Kilohertz, and do not allow our ears to hear frequencies above 25 Kilohertz.

–

Morale: when using Fourier Series, do not be concerned about the series convergence at high frequencies.

Best to Educationrealist,

your F.r.

July 17th, 2013 at 8:24 am

Typo: “where g=9.8 m/s” should be “where g=9.8 m/s^2”.

Sorry.

August 27th, 2014 at 2:42 am

To F.R., I think you mean “moral” of the story, not “morale”, but that’s English, not math…or is it French? LOL

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November 17th, 2013 at 11:58 pm

“I just see either E shape out of context and think epsilon.”

It is always funny when you see sigma used for “E”. “My Big Fat Grssk Wssding”.

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