We had one professor who was rather infamous for being really sloppy when writing exam questions. On more than one occasion did he accidentally transpose a couple of numbers in a problem, turning an equation that should have easily reduced to a trivial linear problem into a 4th degree polynomial with complex roots.

In a real analysis class, we were asked to give an example of an irrational number, without proof. My friend wrote "sin(1)" and, even though we were all convinced that it was correct, the teacher felt that it was a bit too "clever". My friend should have gone with the old sqrt(2), but he decided to be a little more original.

The teaching basically told us to prove the claim, at home, and to find a convincing argument. Then he went back to the exam and gave my friend the points that he deserved. It's not that he couldn't prove the thing himself, it's that he didn't feel like wasting his time because of some student's funny answer.

It was like a dam broke over night. Everything clicked and I was so pissed off that it took so long to find such a stupid issue. Better late than never I suppose...

TED has had people cover this a number of times, but the problem with math isn't that the the _syntax is too hard to parse_ its that the _problems in math class are stupid_.

"The bucket is depth X, diameter D and full of water. When you open the tap, how long will it take to drain if the water drains out at rate Z?"

I've never had to apply solving a problem like this, in my entire life (and if I were in a job that I _did_ have to, the complexity of a real life situation would mean I would still have to learn domain specific tools to solve the problem (eg. how big is the air intake? Does that limit the rate of flow? etc)).

Tangible problems in the real world require mathematical models (often probabilistic models) to solve them.

How do you take a real world problem, break it down into bits, and then use the mathematical tools available to solve them?

By creating a model, and then guessing what the rules that govern that model are, then comparing the model to reality, and refining the rules; and when you can't figure out the rules, thats when its time to whip out the text book and say, well, guess what, someone has had that problem before and this is how they solved it~

Teaching kids how to create models and reach out into the mathematical library available to them when they need it would be vastly more helpful than trying to creating more abstract alternative ways of understanding obscure math concepts that will never to relevant to them.

I've never been more frustrated than I was the other night when I was at a party and a boiler maker (who incidentally earns 3x what I do. damn mining boom) was telling me about all the cool math he's learnt since he started his job. It's all geometry and rate of flow differentials and he said "why did I have to learn matrices at school? total waste of time. they should have been teaching us useful things"

I'm a CS major. I will never in my life (outside of school) be asked to solve a difficult math problem without having a ridiculously overpowered tool like Mathematica in front of me.

I'm all for teaching hard math to students. But we need to be teaching them how to do things their calculator can't (or better yet) teaching them how to build the calculator. Not teaching them how to add 600 numbers by hand.

1 - Math is rarely taught well. The "ax2+bx+c=0" approach to teaching quadratic equations is rubbish. I never understood what it was they were trying to solve until a few months ago I was at the library and read a book on the history of mathematics. It became crystal clear. IIRC, the Indians used quadratics to make sure that they could increase the size of their altars without losing the proportions.

2 - Many people who get good grades in Math don't get it at a fundamental level. Sure, they can regurgitate the rules of logarithms, and solve worksheet questions that follow a specific pattern, but outside of that, they're sitting ducks. I've asked several people why ax2+bx+c=0. Why doesn't it equal 37? Or 3.456? None of them have a clue. I realize that this logic can be applied to me if someone asked me about branch prediction or out-of-order execution, but I think the logic holds.

I've also realized that I use ratio to solve many problems. I remember in my year at Uni, we were given a problem to solve in electronics class. I realized the answer immediately, knowing that 1 amp is = to 1 volt applied across a resistance of one ohm by definition. The 'math genius' in the class struggled.

I've always believed that those who have a natural talent for programming also have a natural talent for math. It's just not taught well. Me, I've convinced myself that I have the latent ability, it'll just require me to learn it on my own terms, instead of a formula-based approach. In the same history of math book, they showed the history of place value, and it made so much sense. The same approach we take to crafting algorithms can be used to find the solution to math problems. Again, great article. Gotta love YC.

PS. I just noticed that when you enclose text in *s, it gets displayed in italics. Nice one, PG

PPS. Actually, I can speculate about branch prediction and OOE. But that's for another time.

Rule 1: Read all the directions first. Rule 2: Jump up and down on your head Rule 3: Generate a proof which demonstrates that [insert random equation here] ... ... ... Rule 50: See rule #1 ... hand this paper in to complete the assignment within the first X minutes and you get an A. (or something to that extent)

While I gotta agree that the communication wasn't clear, part of me wants to be the grouchy teacher which says "the lesson is this: read the dang directions". This guy just forgot the 1st part which was: read the directions first!

you know you're doing math wrong if students display (1) a lack of initiative, (2) lack of perspective, (3) lack of retention, (4) aversion to word problems, and (5) the few who understand the math just want to jump to a formula.

Math textbooks encourage teachers to teach math wrong. The way they present problems is with a complex visual with mathematical structure already imposed, step-by-step handholding through the problem, and asking a question at the end (a question that can often be solved just by figuring out which number to plug into which part of the formula, without necessarily understanding why.)

Suggested method for teaching right: (1) use multimedia. (2) encourage student intuition. Students will argue with each other about what they see and buy in to the problem. (3) ask the shortest possible question. Don't begin with a page full of numbers, measurements, and individual steps. Let the detailed questions come out through discussion. (4) Let the students build the problem. Students will recognize the need for mathematical structure (labels, coordinates, measurements, etc.) as they decide what information they will need to answer the question. They'll go through the steps on their own. (5) Be less helpful. The textbook helps in all the wrong ways, taking you away from your obligation for developing patient problem solving and mathematical reasoning.

Example: he completely rewrites a question from a math book about filling a water tank. He produces a video of a water tank being filled from a garden hose, which takes excruciatingly long to complete. Students get uncomfortable, complain about how long it's taking, and then put in their guesses as to how long it will take. Then they decide what information they'd need to calculate the end result, ask for the measurements they think are important, do the calculations, and watch the rest of the video to see if their calculation was right and how close their initial guesses were.

I saw a 8th grade textbook that explained how compute square roots by hand - but the algorithm was wrong. It only worked for examples in the book.

His pet peeve was that engineering wasn’t about finding a precise answer at some point, but about finding good enough answers fast.

I liked that this forced you to stay alert during the problems for simplifications and to understand what you were doing, instead of just droning out method A for solving problem type B.

He had a policy of no calculators/computer use, but he relaxed it for this assignment as he didn't want students to needlessly suffer.

All the kids that used software (Mathematica and similar ones) got it wrong. All of them. Each and every one made a typo somewhere.

Thing is, had any of these students done a very simple dimensional analysis, they would have known very quickly that their answer was incorrect. I'm sure they would have done that analysis had they attempted solving it by hand. However, people tend to forget sanity checks when working on a computer.

(Then again, I’ve had uncommonly thorough math courses, and would likely share your frustration.)

I had good math professors. Too bad I wasn't a good math student.