In which I rant about an illiterate from Daily Kos
So I notice a handful of people came to this blog from the Daily Kos, which doesn’t happen, ever. So I go look. And I’m there.
In a discussion about education, a commenter named “Punditician” decides to give an example of a math teacher who went to education school and doesn’t know math. And he uses? me? What?
This week I blogged:
I know how to multiply matrices. I can teach kids how to multiply matrices.
Punditician cites it as some sort of proof about dumb math teachers. Girlfriend’s a moron.
- She’s badly off topic. Trolling doesn’t require a whole lot of intelligence, just patience to keep stoking the flames. Read the essay, if you really want to. The comment, even if it were accurate, doesn’t follow.
- She’s badly mistaken. I’m not an education major.
- She didn’t read. It takes about 5 minutes of poking around this blog to figure out both who I am and what I’m doing here.
- She’s wrong about the math. It is not particularly complicated (I’ll return to that), but basic? Absolutely not.
And she’s wrong about my math. I am not the best, far from it, and I have gaps (including linear). But I consider myself fairly solid.
So why don’t I have a good grasp of matrix multiplication?
First, I can multiply. It is the “why” question that I asked. And frankly, I don’t multiply matrices. Not daily, or weekly, or once a year. It’s not something I need to do.
My first linear course was in 1984, and my last was in 1986. The first was one of my least favorite math classes. Can’t say I gave it reasonable attention. And the second was just meh. That part of my education was at an engineering school. Not an excuse. But an explanation, at least a little bit. Our math courses, some of them, were weird. One day I still need to take a normal pde. That was the weirdest. (Ask me why?)
I’ve encountered matrix multiplication, occasionally, since, but have not given it much thought. Perform the operation, move on.
A lot of what I do well, I have reconsidered as I begin to teach a topic for the first time. My arithmetic is better than when I started teaching. As is my algebra. Trig. Geometry. Let’s not start on counting. And logic.
This year I am teaching precalc. Two of us redesigned the course, and we decided to expand a unit on systems of equations, early. It helps for the kids to see something new that turns out to look wildly different, but is accessible. And we packed the end of the course (Spring) with things they will need for calc (series, sequences, limits, a second, harder look at trig, etc). In any event, I am actually teaching matrix multiplication for the first time.
So why left to right? Why row by column? Why non-commutative? And what is a model that is accessible to kids? The transformations will follow, not precede, teaching the operation. (if you are not sure why, try writing a set of lessons that develop the topic from scratch. You’ll see.)
Why didn’t I just check wikipedia, or my old notes (which I might have?) or an old text (there’s one on my shelf) or the kids’ text book? First, kids’ text book for resource? Never. And as for the others, I could have. But I appreciate the richness of the discussion that often happens here. Finally, I like to tell the kids that I ask for help. They sometimes see me as the authority in the room, rather than the math. It’s good to remind them.
Not everyone can get away with that. The kids need to think I know my stuff before I can admit to gaps. But they do. Parents do. As I was checking my anger at Punditician’s ignorant comments, I remembered how many parents have tried to get their kids into my classes. I thought about how many scientists, engineers, and even mathematicians have wanted their kids to learn from me.
And then I went back to her comments. Just more lousy teacher bashing. And off-topic at that. I shouldn’t have taken so personally.
JD2718 
I am so not going to even look over there. Sorry you got bashed. It always feels bad. (And thanks for being in my corner when I got bashed by someone who may have incorrectly pegged me as a math ed person who didn’t know math.) Sounds like a troll to me.
You’re one of the people who knows enough math to make me feel inadequate (if I let myself). I have to remind myself that math is that way. We need to see its pleasures and not let its hugeness intimidate us.
I’m looking forward to seeing responses to your previous post. (I’ll have to post there so I can subscribe to the comments.)
How irritating! You’d think some people would be too busy listening to the wind whistling through their ear holes to bother hard-working math teachers with their ignorant rants and inane quibbles.
As for linear algebra itself — I, too, would enjoy seeing a good conceptual description of what’s going on with matrix multiplication. Dot products of row vectors with column vectors? Yeah, sure, but what’s a good way to motivate the definition and visualize the result? What would make it clear to students (as opposed to “just do it, it’s useful!”)?
I took an upper-division linear algebra class in grad school some thirty-five years ago. Maybe I should have listened more closely because I didn’t get much from it. (But I’m culpable: I spent most of that class sitting quietly in the back row scribbling on my master’s thesis.)
Now, I don’t have an education degree. I’ve always understood, however, that if someone doesn’t understand a concept, you don’t respond by saying that it’s “so fucking basic, it’s mind-boggling.”
It’s bad form. It’s disrespectful. It teaches nothing.
Basics, indeed.
I have no words for the ignorance of this person. Don’t take it too hard. Your students are so lucky to have you.
Thought of you this weekend. We took some Canadians tubing. They had so much fun. Thinking it might be our last float of the season :(
I hope it brought in a lot of traffic from more sensible people, particularly ones who read the entire entry and not just that excerpt. Those that choose to read will be better educated and make better judgments.
But there’s a reason why some of my friends refer to the site as Daily Kooks.
Wow. As Bugs Bunny might suggest, what a maroon.
I would add “ignorant” to that description, but I’m sure that Bugs would tell me it is implied.
That’s ridiculous. I’m so sorry this happened to you.
This woman used you as an example of an incompetent teacher, when in fact your willingness to be vulnerable and ask for help pegs you as an exceptional teacher.
I too will not bother to go over there, though I was tempted. I have to remember the most valuable piece of advice on the internet:
“Please don’t feed the trolls.”
Yeah, that person is a jack*ss. (Not sure why you think it’s a woman; but this question has made me realize that I reflexively assume complete *ssholes on the internet are always men…)
He/she is also representative of something bigger and more troublesome than isolated jack*ssity: the use of math to make oneself feel superior to other people.
I was actually totally going to leave a comment at Daily Kos (I know you’re not supposed to feed them, but sometimes I just gotta drop that science…) but I guess you can’t do that without a user account.
That person was definitely an asshole, but she was actually right on the math side. It *is* really just the composition of linear transformations that tells us to multiply matrices as we do. It’s a flaw in how linear algebra is taught (i.e. what was available for you to learn) that that knowledge isn’t commonplace.
Now how to break that bit of knowledge down so that kids can understand it, is a quite different issue….
Ah–you see. Another reason why the Daily Kos isn’t on my list of blogs I follow.
“Finally, I like to tell the kids that I ask for help. They sometimes see me as the authority in the room, rather than the math. It’s good to remind them.”
This is, perhaps, more important than any other single lesson, IMO.
“She’s wrong about the math. It is not particularly complicated (I’ll return to that), but basic? Absolutely not.”
Agreed. By this logic, one would need to have studied linguistics before teaching first-graders how to read!
somewhere around the fifth time i taught the “inversion” procedure, it suddenly became clear to me that the “moves” of “row reduction” were accounted for by “left multiplication by elementary matrices”—and that the “inverse matrix” was the straight-up *product* of these “moves” literally. this is obvious once you notice it. wow. the left-to-right (& row-time-column) notation is indeed annoyingly arbitrary-seeming. “permutations” are worse (since *both* possible notations are in common use & one can never “just get used to it”). i linked here in fb. great post.