I don’t know about Nava, but I sure as heck did. (high school) Calculus actually seemed to be the most useless math I ever did. It was all memorization: derivative rules and integration rules. It was only when I got to the AP test that I realized I actually understood the subect better than my peers who all got As (while I got a C). I had the lowest grade in the class but was the only one who even passed the AP test. Because I refused to just memorize.
I’m responding to people who seem incredulous that the teacher blew off the question.
In a college course, it’s perfectly understandable that a professor discussing a mathematical formula could display incredulity when asked about something miniscule and tangential to understanding the topic at hand. I would NEVER dare to ask such a question in a college-level physics or math lecture. Talk about setting yourself up to be snickered at and not taken seriously by your peers. I don’t know about the OP of the original thread, but when I was in my university’s Physics 101, I and all 79 of my classmates were concurrently enrolled in at LEAST Calc I, if not Calc II or higher (depending on AP results). To disrupt lecture by asking a question of such an elementary nature would be unheard of. That’s why god invented office hours and/or the internet.
Anecdotally, the salutatorian in my high school class would do this every day. She would frequently interrupt calculus lectures for clarification on some small question that was obvious to the rest of the class. We would always facepalm about it and the teacher got exasperated, but she lacked the self-awareness to stop and ask questions at a time when it wouldn’t interrupt learning for the rest of us. Like, during the 35 minutes of homework time we were granted every period.
While this trait didn’t make her stupid (obviously, she made #2 in the class and was enrolled in all the same APs as I), it made her seem pretty dumb to the intellectual elitists in the class, and it pissed EVERYONE off that she was dragging the class down with her.
I think it’s really bizarre that you take pride in refusing to memorize. It’s not like you couldn’t get a good internal grasp on physics while memorizing things at the same time. That one simple thing would have turned you from a C student who passed their AP exam into an A student who passed their AP exam.
Life is occasionally about playing by the rules of others. If you couldn’t play by a teacher’s rules in addition to educating yourself outside the class, you’re not as smart as you think you are.
Oh, no, I’m talking about waaaaaay beyond that. Heck, the geometry you’re talking about, I had it in 4th grade.
The “calculus for geometry problems” were along the ways of “find the family of curves whose tangent follows the form [blahblah] and whose second derivative has a constant value ‘a’”, the blahblah would change from one problem to another but the second derivative thing was pretty much a given. The teacher was not interested in the solution, only in the process, and it had to be done exactly the way he would have done it (if you took a shortcut or used a different symbol for something, even though you had defined it when you introduced it, you were screwed) because he was one of those who don’t understand the subject. He graded calculus exams like other people grade multiple choice: any deviation from the template bombed you.
One of the few math teachers I had who was a mathematician and not keen on memorization was, sadly, horrid at either discipline or understanding her student’s questions. When something was obvious to her, she couldn’t understand how it could not be obvious to us (A: in most cases, because nobody had explained it to us). She taught me in 10th grade: trig, then limits, then we used limits to deduct derivation. Integrals were next year.
Oh, and I’m a chemical engineer, so sort of both 
What the hell? Are you actually attacking me for posting that my Calculus class sucked? Are you attacking me for getting the highest grade on a test because I bothered to learn outside of class time, rather than waste my time on a pointless grade? Do you really think I even valued getting an A in the class?
And where in the world did you get the idea that I was claiming to be smart? I claimed nothing, except that my class was so stupid that I was able to surpass it by learning on my own. We got hours of homework every night. If I’d have wasted my time memorizing, I would not have had time to learn on my own.
Because memorization is completely useless if you don’t go from there to the point where you actually learn the material. Memorization is exactly what the other people in the class did–because that was the easiest way to get good grades. And that’s why they failed the AP test. They memorized just enough to pass each test. while I actually tried to learn the material. And learn it I did: my C was from never turning a lick of homework because I was too busy learning. I got As on all the tests, because I actually learned the material.
So, go ahead and attack me for not being smart, but I’d say the fact that I don’t have some useless emotional attachment to getting an unnecessary grade (and got an A on my college transcript anyways) means I made the right decision. In fact, that one grade on that test meant I never had to take another math course throughout my undergraduate career. That’s worth a lot more than an A in a useless class that didn’t even cover Calculus 1.
Yeah, yeah, that last paragraph barely makes sense, but I didn’t notice until it was too late to edit, and I’m sure you guys are smart enough to make sense out of it.
I will add that, if I hadn’t made a good grade on that test, I could have dropped the class, and my GPA actually would have gotten higher–an odd quirk of the system at my school. So I fail to see any reason why I should violate my principles that homework after you’ve learned something is useless, and that memorization should only be used as a stepping block until you know the material. Plus, I’ve never been able to memorize worth anything, thus it takes a lot of effort for minimal gain.
This thread is reminding me of when my daughter was in AP calculus in high school. She was always very good at math and enjoyed it until AP calc.
She continued to get good grades but was very frustrated with the class and her teacher because, even though she got good grades she didn’t understand what she was doing. When she would ask for explanations, he would tell her, “You got it right. You’re doing better than most everyone who takes this course. What more do you want?”
He steadfastly refused to explain what it was she was doing. Not only did he encourage his students to learn math by rote, he insisted on it.
Thanks for convincing my daughter that math was too hard and she was bad at it, High School AP calc teacher.
This semester I am teaching MAT 115, Algebra with Business Applications. I have a class at 5:30 PM today, in fact.
During my first class, I discovered most of my students,
- Did not know how to add fractions. (They had never heard of a common denominator.)
- Couldn’t solve for x in an equation like 4x = 12.
- Had no idea what a negative number is.
- Had never multiplied two fractions before.
These are business majors trying to receive 4-year bachelor degrees.
How did these people ever graduate from high school? Hell, how did they pass 6th grade??
There is something very, very, very wrong with our schools in this country.
Agree. And I have a theory about this.
Students learn to hate math in elementary school. Why? Because their math teachers hate math.
Well, when rachelellogram found it bizarre that you’d say something like “I just refused to memorize,” I thought, “Yeah, WTF’s up with that??” If one of my Calculus students told me “I refuse to memorize the Product Rule!” I’d think :dubious: “What are you even doing in this class, then?”
Now, if they had said, “I want to understand why it’s true, rather than just committing it to memory without understanding it,” I would have said “Great!” and done my best to explain it. If they had said, “I’d rather work through a few problems with the Rule in front of me, until it sinks in and becomes automatic, rather than just memorize the rule,” I would have said, “If that’s what works for you, I’m all for it.” But you can’t get very far in math, or I dare say in any other subject, without committing some things to memory.
You seem to be saying that memorization is somehow opposed to “learning” or understanding. I say, you can’t really understand a subject unless you have enough stored in your mind—enough facts and rules and examples and data—to be able to see how it all fits together.
Thudlow Boink, on one hand learning anything requires memorization.
But what doesn’t work, doesn’t really constitute learning, is rote memorization as the only mechanism. There are parts of the multiplication tables that I still can’t for the life of me remember but, because I do remember how to build the tables, I can recreate the missing parts (I can’t remember what 7x8 is - I always go “7x8 = (7x7)+7”).
An example of how memorization vs learning took place in my math classes: set theory; memorize the properties of a Ring without being told what a set is or why are we using Rings in the first place or what might we use them for. Ask “so what is a Ring?” and be told “who cares, just learn its properties”. I can’t remember who was the poster whose explanation in another conversation about math told me that that list of properties is the definition of Ring and that we’re defining the word “Ring” as shorthand for “any set of mathematical entities which happens to have all these properties”, but that was a moment of illumination so big it should have shown in Hubble pics :p. Mind you, I do agree with you that it required me to know the definition of definition.
I’m sure BigT can defend him- or her-self, but “I refused to just memorize” is not the same thing as “I just refused to memorize.” What BigT actually said was that pure memorization was not sufficient. He/she didn’t say that memorization was not necessary.
I have, for all intents and purposes, an 8th grade math education. Almost flunked 9th grade algebra (I think I only passed because the teacher was a giant pervert and he liked my boobs) and failed 10th grade geometry bigger than shit. I’m perfectly fine with what I think of as “life math”; home finances, for example, or fiddling with recipes or knitting patterns, reading maps, stuff like that.
It kind of sucks, though, that when my 6th grader needs help on her math homework I have to call up a friend of mine to give her a hand. (I tried to help her on a homework assignment early in the year; that was the only D she got that quarter :smack:.) And last weekend I took an employment test that included a few math questions that made my brain go “Bwuh?”.
I’m 36; I remember regularly dissolving into tears of frustration in math class from elementary school on because I just could not get it, which of course invited a merry hailstorm of derision from other students and, usually, the teacher. Maybe it was just being poorly taught, or maybe my brain is defective, or maybe I was traumatized by an abacus a a toddler, but for whatever reason, math and I are not friends.
On the other hand, we’ve all heard tales of college students that couldn’t write a coherent paragraph, or thought the cavemen hunted dinosaurs, or had never heard of Hitler. There’s a strong streak of anti-intellectualism in this country; we somehow take pre-schoolers who are lively and curious and eager to know ALL THE THINGS, and turn them into tween-agers who don’t care about anything except who Snooki is screwing this week and how many Facebook friends they can collect, and I’m damned if I know what the solution is.
Okay, you’re right and that’s a good point.
Find a best-fit function in two variables describing the boundaries of Snooki’s boobs and double-integrate to determine the volume.
I hate to generalize this, and add the caveat that my mother was a math teacher, but this is at least somewhat true. Likely aided by the fact that many high school and lower math teachers aren’t good at math. Because if they were they would likely be engineers or scientists or accountants or something.
It’s entirely possible (and based on some of my experiences likely) that these HS math teachers that refused to explain the underlying concepts do so because they don’t even know the underlying concepts themselves.
My favorite teachers - and the ones I learned the most from - were those who were genuinely enthusiastic about the subject material they were teaching. Based on my experience in elementary school, the most serious offenders were the math teachers. Their vibes suggested they ***hated ***math. I excelled at it in spite of them. Most of my fellow students did not.
I now teach math at the college level. Not to brag, but I have received very positive reviews from my students, and some have asked to be placed in other classes I teach. I do not attribute this to me being “good at math.” I attribute it to my attitude toward it. (I am a geek, and genuinely like math. It apparently comes through when I teach.)
So in a nutshell, I don’t think the problem is a lack of skill or knowledge on the part of the math teacher. I think it’s their *attitude *toward the subject matter that is most important.
Yeah, that’s pretty much so. I learned geometry and pre-algebra from a teacher who wasn’t terribly invested in the subject, and it was painful rote memorization.
When I got into calculus in high school, the teacher was one of the top mathematicians in the school district, regularly participated in administering and grading AP exams, and basically knew his shit. Out of a 90 minute class, he only lectured for 30-45 minutes and then let us work on homework for the next 45-60 minutes, providing individual help as needed. I don’t think I’ve ever learned as much in a single class as I did in that one.
I read a suggestion somewhere (I forget where or by whom) that if an elementary teacher hated math, they ought not teach it—that the students would be better off with a year with no math instruction than a year in which they were instructed by someone who was hostile toward the subject.
It’s not just math.
This semester I am teaching HIS 300, History of California.
During the semester, i have discovered that many of my students,
- do not understand subject/verb agreement
- don’t know how to use possessive apostrophes
- believe that a plural made with an s at the end requires an apostrophe
- can’t keep tenses consistent within a sentence, let alone a whole paragraph
- like to capitalize random words
These are education majors trying to receive 4-year bachelor degrees, and intending to become elementary and middle school teachers.
I think, in some cases, universities and teacher training colleges bear some of the blame for all this, because they allow people to graduate who have no business in front of a classroom. Education departments themselves often, in my experience, seem to have incredibly low standards. I have students in my history classes who can barely put together a coherent sentence.
Here are a few sentences copied straight from a student essay i received last semester:
Poor usage, run-on sentences, comma splices, agreement issues, random tense changes, etc., etc. These sentences are not the only poor ones from the paper; they are merely a representative sample.
This student, at the time of submitting this paper, had a cumulative GPA north of 3.7, and had received grades of A or A- in courses such as English Grammar and Syntax, Elementary Teaching and Learning, Intro to Linguistics, and Sociology of Education.
I didn’t find As in high school classes to be useless because I wanted to get into a great college, and transcripts matter at that level of competition (it’s a serious numbers and letters game up there). I will grant, though, that college grades don’t generally matter as long as you get the diploma. Like the old saw goes, “What do you call the person who graduates last in his class at medical school? Doctor.”
It borders on the patently unbelievable when you’re claiming it would have been literally impossible to do your homework every night while simultaneously understanding the material on the level required to pass an AP exam. The two are not mutually exclusive and I don’t think it’s fair to claim they were. Priding oneself on not doing homework is an attitude I come across in a lot of people who say and think they are smart, when really they’re just expressing a self-serving attitude and laziness.