Bad teachers are a fact of life. I recall sitting in class during the second grade in Philadelphia (where we lived for a year while my father worked as a consulting engineer at Eddystone Generating Station), having the teacher pull the globe down from the shelf to show me that the USA was larger in land mass than Canada…
Right.
I can tell you this for fact: I had to play catch-up when I got to Grade 3 back in Montreal. I was lucky: I had at least 4 very good teachers in public school and high school.
My history teacher taught us that Native Americans got to North America by riding the continents as they drifted apart from Pangea. My science teacher said there were canals on Mars. My gym teacher . . . gave me a bunch of Asimov novels and talked to me about Existentialism while waiting for my turn to bat. I had a weird, weird education.
Is vector calculus advanced mathematics? Maybe barely, but if it is, I’m going to say right now that this would not have helped me at any point in a math career with that as my current pinnacle.
Guess how I dealt with the fact that the cross-product is not-commutative: I just went, “Why?” Then I rationalized it, convinced myself of the fact, and then remembered it. It’s a process that maybe took a minute- and I’m hardly a math genius. This is an incredible amount of effort to go through to prepare a kid for what amounts to little more than a factoid. One they may never use, and if they do, it will be a decade on. In the meantime, commutativity remains the bread and butter in solving virtually every mathematical problem until then, and well after.
Meanwhile… and this is something I’m not sure a lot of teachers understand: YES! Grades don’t matter in the long run. I get it. However, it is a fact of human psychology that we are shitty long term planners and that human beings live very much in the present. Grades can hugely incentivize and disincentivize students in an almost Pavlovian way. Right now, the lesson they are learning is to defer to authority when it comes to accepting new information, rather than make sense of it on their terms. There is an entire business model based on this:
I never memorized the multiplication tables. I remember in sixth grade, every day we had a “quick multiplication” sheet with 25 2-factor problems to solve. We were given 10 minutes to solve all of them. I was the only kid in class who couldn’t mentally regurgitate all the answers. They weren’t from the 12x12 table, but were simple enough.
I always sucked at mental arithmetic. It just doesn’t click for me. I can do math on paper till the cows come home, but time pressure + ADHD + Everyone thinking I was stupid = Me spending 10 minutes every day on the edge of tears, frusterated out of my mind, with no help.
And what was really unfair was that everyone who could get the thing done got a hershy kiss, but because my brain doesn’t work well for rote memorization of 144 tuples, no amount of motivation or reward would “make the stupid kid do math faster”.
Joke’s on them. I went to many years of math tutoring, of my own accord, because I refused to let an abstract concept beat me. I indeed never got faster at mental arithmetic, but I did become really good at math.
By the time I was in high school, I was doing the job of all our sucky, despondent math teachers. None of them were actually math teachers. They were all coaches, and really only cared about the star athletes and the upcoming game. So while everyone demanded to cheat off me, I instead proposed a deal: I’ll teach you what I know, and you can earn grades as good as mine. I taught math for four years, successfully to burnt out potheads, pretty girls who thought they could get by on being given the answers, jocks who didn’t care, other guys with ADHD because I figured out how to make it interesting. It was probably the most fulfilling work I’ve ever done.
Sometimes I wonder if teaching is what I should really be doing.
I genuinely didn’t understand why I was expected to memorize certain values in basic organic chemistry. It boggled my mind for a time. It made no sense: You never have to memorize the first three rows of the periodic table. That’s something that you could legitimately argue a student has to memorize. You are however expected to memorize the pKa of various substances. Which I always thought was odd. Why not throw it into a table and let me look it up? The answer, as it turns out, is that the MCAT and DAT don’t let you do that. And even though I never want to become a doctor, here I am, being prepared for the MCAT anyway. I don’t know about the GRE, but honestly fuck the whole alphabet soup lot of them. I hated memorizing the stuff.
I can point to which is more acidic or basic and give you a ballpark pKa most of the time, but often tests would pit two entities that were fairly close. What annoyed me most is that working with chemistry over time, I would inevitably memorize this stuff, anyway, much like I can rattle off the atomic weights and proton numbers of the first four rows of the periodic table. My opinion is that if you can look it up on a table, it should be given, and if it’s something people who regularly work with it tend to need to know, then I guarantee you don’t need to teach it.
This is how I learned to solve stoichiometric equations back in general chemistry. Other students memorized that it’s moles divided by mass or vice versa. I just learned to do dimensional analysis and I never had to remember “the rules.”
YMMV, but do you want to get paid like shit and be treated like you’re the enemy of humanity? Go ahead. My girlfriend is one of those very fortunate people who realized early on in life what she wanted to do for a living, and that was to teach. She is currently unable to find a way to make it worth her while in the state we live, which actually has an emergency shortage of teachers.She’s waiting for me to finish my degree so we can leave this stupid state and move somewhere where they value education. I told her she should consider teaching abroad. Plenty of other countries would kill to import qualified teachers from the US.
Always better to ask why or state your confusion than… you know, scream and shout obscenities. Although there is definitely a time and a place for screaming and shouting obscenities.
I was going to say almost the same story. I got held back a year because rather than just stare at a boring repetitive table until my brain died, I was actually trying to understand multiplication (and make it work for numbers other than 1-12).
Years later, the school had nothing for me to do because I had tested above the class, so I got assigned as a tutor to help kids that were having trouble with math. I’m still friends with one of them who “could never do math” at the beginning but was able to ace algebra, geometry, and trigonometry after a few months.
At least, that was kind kind of answer I’d give in those situations, and was usually insistent enough to pull it off.
@japhroaig: “Don’t teach kids wrong things, they’ll make fun of you in their thirties.” - Not about planets, but in 2nd grade my teacher mixed up the different Apollo missions, and I insisted she let me go down to the school library and bring back a book that had it right. Not need to wait until my thirties.
My initial instinct would be to go over the teacher’s head, but you’re correct that he or she deserves a chance to defend such idiotic teaching first. Of course this is why my kids (we’re still working on making the first of the two we plan) will not be subjected to public school unless and until they reach middle school and really prefer it, which will mean a lot more curriculum monitoring for us. During elementary school we’re going with a combination of community and home schooling.
We don’t know if the students were taught the method that goes multiplier x multiplicand (which seems to be a thing now).
We don’t know if the teacher was emphasizing that arrays go row x column (which also appears to be how it’s done).
We don’t know if there is a value in being taught that way that we don’t understand simply because we weren’t taught that way.
Some of us seem to be ignoring that the point of the assessment was to demonstrate multiplication strategies, not to solve multiplication problems by any means necessary or to simply know by rote our times tables.
I don’t presume to know whether the underlying strategy being taught is a strong one, but the idea that teaching is emphasizing useful strategies over rote knowledge shouldn’t be dismissed with knee-jerk reactions by people who have no context.
I can see both sides here. On one hand I do remember being criticized and being told I was wrong when I did a math problem in a non-approved way but still came up with the correct answer. I did think that was ridiculous. On the other hand I do understand that there is value in being precise and explicit in giving and following instructions.
This reminds me of the show on NPR that has people call in with cooking questions. A guy was asking about a recipe that would say, for example, 1/2 cup chopped nuts. So his question was, “Do I measure the 1/2 cup nuts and then chop them or do I chop some nuts and then measure out 1/2 cup?” The answer seemed painfully obvious to me - chop and then measure. Otherwise it would have said 1/2 cup nuts, chopped.
So while, yes, the total of 5X3 or 3X5 is the same. The result of five sets of three vs three sets of five are definitely not the same.
I dunno, putting them in junior high can be problematic, too. My 8th grade math teacher refused to recommend me for geometry for 9th grade in spite of my points totalling 105% in her class. I learned that women can be sexist, too, and her biases nearly prevented me from completing calculus before graduation. No math teacher should ever enter the year thinking “girls can’t be that good at math.”
My goodness I hated being told to show my work. But then I also didn’t care when my teachers docked me marks. I figured it said more about them than about me.
