Engineering school. I forget which class exactly, whether it was fluid mechanics, dynamics, or mech eng design, but anyway, a final exam question had us calculate thrust produced by a snow blower expelling snow, after deriving the formula from basic principles. There was a point in the derivation where, if you made one little mistake with an exponent, you got a snow blower producing roughly as much thrust as an F-18 on full afterburner. I was able to catch myself with the reasonableness test, but I was dismayed to see how many of my classmates didn’t bother to make a reality check. It’s not like engineering school is about reality or anything like that :smack:
The annoying ones are problems where you have no intuitive sense of the correct answer. When I took a Thermodynamics, Acoustics, and Optics course, for instance, I had a problem (known as an “initial value” problem I believe) that was essentially “given this uniform air temperature, how long would a lake <some number of meters> deep take to completely freeze solid?” I mean, obviously lakes don’t freeze solid very quickly, but I have no frame of reference for how long it takes a deep body of water to become a block of ice. Millenia? Decades? I did get the problem right, the answer was somewhere around 460 years (the actual calculations were in seconds, which was even harder to intuit!), but I had literally no way of knowing if that was right or not.
Well, speaking as a student who has faced and surpassed Algebraic challenges… My professors gave partial credit for attempts. A problem worth 10 points got a zero if you didn’t attempt it. I had a problem involving a dog kennel. I tried and tried. My best answer was a dog kennel that was 127 feet long and 3 feet wide. Obviously a wrong answer, but it ended up that I dropped a sign and made another silly arithmetic answer, so i got 7 of the 10 points. I learned right there it’s better to try your hardest to get it as right as possible rather than leave it blank. A couple of silly mistakes were pointed out to me, while the things I got correct were emphasized by my prof. YMMV.
As a physics teacher I came across bizarro answers like this all the time. I always loved it when they would report a velocity that was greater than the speed of light. Or a negative mass. Or a negative time. Or some ungodly amount of charge that if it ever existed in one place in time would rip all the electrons in a 500 mile radius away from it. You get the point.
And no matter how many times I would say, “Examine your answer. If you know the answer you got is IMPOSSIBLE, but you cannot figure out where you went wrong, put a question mark and a note and I will take off fewer points.”
As a student this was always the approach I took to solving problems. If I got an answer that I knew couldn’t POSSIBLY be right, but I had no idea where I was going wrong, I would put some question marks and write “I know this can’t be right but I don’t know where I’m going wrong.” Did all my teachers care? Probably not. But at least I was signalling I had some basic understanding of things.
Reminds me of a fun physics problem we had at high school that went something like this: “A hunter brags that he stopped a charging moose with a single rifle bullet. What is wrong with his story?”. Then you could calculate any one of four possible impossible answers - bullet weight, bullet speed, moose weight or moose speed. Either bullet value would be absurdly high and either moose value absurdly low.
One of the best teachers I ever had (this teacher’s name routinely appears in those “Security Question” spots for “favorite teacher”) had a great policy with regard to homework: if you had an A or B on the most recent test, you were not required to hand in homework. Obviously, he thought, you understood what was going on.
If you got less than a B, you needed the rote practice and should be turning in your homework.
He was also famous for his line, “My students never fail calculus! They fail algebra first.”
This was my problem with topology. I had no problem with linear algebra. But I took a class called something like “Basic Differential Topology,” and quickly realized I was out of my depth, in large part because I had absolutely zero sense of what the answer SHOULD be.
Shortly thereafter, I switched out being a math major. Screw you, Sard’s Lemma.
I took a physics for dummies course my freshman year in college, and I remember a test question I went completely fluff-brain on and realized it about an hour after the test was over. It concerned the density of objects and how they responded to pressure. While I calculated how much a granite formation would compress under a certain amount of pressure correctly, when asked what an object of a certain density would do if dropped in the ocean, it somehow made sense to me that the object would fall until it reached a point where it’s density was the same as the seawater around it, and it would remain at that level. Because, we see inanimate objects floating at 100 km below the surface of the ocean all the time. Sooooooo embarrassing.
Well that’s a silly question. It’s not the momentum of the bullet that stops the moose, it’s friction between the moose’s body and the ground when it falls over, having been killed by the bullet.
A møøse ønce bit my physics prøfessør…
Is the joke here just that the ocean doesn’t ever get that deep?
As to the homework issue people have with math (and physics which is basically all math). As a physics teacher I rarely ever gave any homework at all. Not because I really believed that it was useless or that certain students didn’t “need” it. It’s just that I guess I honestly believe a grade should be based on what you can demonstrate on a test. Homework is rife with cheating in high school. The students who are going to do well don’t need it, and the students who are struggling are going to cheat or they aren’t going to do it at all.
We had plenty of “in-class” practice however to help inflate those grades! 
But yeah I’m not a huge fan of tons of homework overall so I didn’t give much. Most of my homework was honestly “if you didn’t finish this practice in class, you have to do it for homework” and the vast majority of the time they had plenty of time to finish.
That’s the way I see it, too. A lot of students hate math, and one of the reasons could be teachers who pile on boatloads of homework every day. Is it any wonder? I leave half the class time to work on problems, and assign one problem from each section for homework. It’s a harder problem, but as long as they make a reasonable attempt they get full credit.
That might bee a little too generous, but I’m definitely in favor of 5-10 demonstration problems and then several word problems, although it depends on the complexity. If it’s something like calc and you’re allowed to use the shortcuts, you can easily knock them out in seconds each. Whereas, when one giorram problem requires ten minutes, and you’ve assigned 15 of the things, you may have gone a little far.
The word problems help make sure the students actually know what the hell the math does.
Ha! That’s pretty true.
Well, as long as you add “or reaches the bottom of the ocean, whichever comes first”, it seems that your answer is correct.
Yeah, sure, since water is pretty incompressible, there’s a pretty narrow band of densities where something will float in equilibrium at a particular level, so that doesn’t happen often, but IT COULD!
I spent the last semester tutoring high school kids in algebra and chemistry. A lot of times, they were genuinely surprised when I would “remember” a formula or idea. For one example, I decided to show them HOW I"remember" formulas.
They were working on formulas for circles and one of their problems gave them the center of a circle and a point that lays on the circle. To make it extra complicated, the center and the point didn’t line up to make it really easy to tell the distance between them. The student I was working with really didn’t know how to approach it. I had her sketch the two points and asked her what she knew and what she could determine with two points. She correctly guessed that the only unknown she had was the radius of the circle but she didn’t know how to tell how far apart the points were. I asked her if she remembered the formula for the distance between two points and, when she admitted she didn’t, I told her I didn’t either. Then, I walked her step by step through deriving the formula using more basic principles.
When we finished the problem, I told her that this is how I “remember” the formulas. I hope she learned some of what I tried to impart about solving problems (Draw a picture, determine what you know and don’t know, relate what you know to what you don’t know, etc). I know I didn’t get it until I was in engineering school.
[QUOTE=amarinth]
…someone else farms on a 1’ x 80’ plot of land…
[/QUOTE]
Sounds like a perfect place to grow spaghetti.
[QUOTE=Arrogance Ex Machina]
Reminds me of a fun physics problem we had at high school that went something like this: “A hunter brags that he stopped a charging moose with a single rifle bullet. What is wrong with his story?”
[/QUOTE]
It’s not moose season.
[QUOTE=Senegoid]
Let’s not forget about professors too!
[/QUOTE]
Or high school teachers. I remember one problem concerning area - how many gallons of paint will you need to buy to paint a room? The “correct” answer was something like 4.39 gallons, but the question was how many gallons to buy, so the real answer would be five.
One what?
One big difference between school and life is that in life, you get extra, unnecessary data. If only life would be so kind, real problems would be a lot easier to solve. Less fun, though.
I never was graded on homework* during the equivalents of Middle School, High School or College - but I was also never, ever, taught Maths in context by the Math teacher, except for Applied Stats. In fact, my other Maths teachers took offense if you dared ask for context.
That is the part where I think the system failed. I finally understood Set Theory thanks to a Doper who put it in context. Trig and calculus made no sense as explained by the Math teacher, it was the Physics and Chemistry teacher who taught them to us, because he put them in context.
If your students had never gotten any context before, they’re not used to expecting it.
- We had tons of “exercises”, of which the compulsory ones would be demonstrated in class by a student after we’d done them at home (with other students proposing corrections or asking questions, it’s great preparation for real-jobs teamwork and presentation skills), but they were considered part of studying, not part of grading.
I’m a math moron. Numbers don’t make sense in my head, words and letters do. I can do things like double or halve recipes and figure out if the couch will fit in that space if I use a different side table, but it takes serious concentration and a pen and paper. Advanced mathematical concepts are seriously a totally different language to me.
Most of this thread actually is a written version of this to me 