What is Digg?83 Comments
- ownedbytheman, on 10/12/2007, -0/+30Not your typical blog post that I am so hateful of. Valuable and well written.
- multivariate, on 10/12/2007, -0/+16Yegge's point is dead on in his take of the way we teach math to grade school and high school kids. Before they can even see the faintest glimmer of usefulness in math, they are turned off by its seemingly complex and obscure nature. The learning approach primary education takes now, by rote and proofs, is intimidating, overly-complex, and boring. It may have worked for yesterday's generations, but not today. Instead of adapting children to archaic methods of education, education should adapt to their method of learning.
- Herolint, on 10/12/2007, -0/+11I totally agree! math/algebra/etc. are taught so poorly in school it is pathetic.
A few months ago, I picked up a book called "Practical Algebra a Self-Teaching Guide" and as I started reading I thought, what the crap were my grade school teachers doing? There are definitely better ways of learning mathmatics. - geminitojanus, on 10/12/2007, -9/+19Still highly opinionated and, to be blunt, a relatively narrow targeted audience.
Some of his conclusions make sense, I'll grant him that, and I wondered the same things in high school and college. "Why didn't I learn this linear algebra stuff in middle school, where I could have actually /used/ it in high school?"
On the other hand, some of his conclusions are nonsense. Nobody should be learning about Information Theory in high school or they're going to be more lost than a 12 year old girl who's just started bleeding in her pants. It takes a very significant amount of experience with algorithms before you can even start to handle most Information Theory processes, and that's not the kind of experience you can get without being through at least a course of calculus, in my experiences. Arguably it could be because we're not being exposed to math since we were knee high to an Asian grasshopper, but then again, we can't all grow up to be the next Fermat or von Neumann can we? American schools are designed with the average in mind, exceptional students need not apply.
I'm also /appalled/ on how quickly he dismissed Calculus. Calculus is as paramount to anyone in our industries as Algebra is to any middle schooler or English is to any 3 year old. Luckily, some of us have a really good time with it and enjoy it a lot and understand it way before they're even exposed to it. For the other 4/5ths of the people out there, Calculus is worse than cancer, and I've personally had friends contemplate suicide because they couldn't sort out the rules of integration (and when you're an engineer, these things matter).
Next, he completely throws away the learning processes of younger students. We're taught Long Division because it works and because it's provable and deterministic. Of course, I could grab a calculator too, and do any problem you can throw at me just about. But we're building students who build the calculators. If the students who are building the calculators don't understand the processes of how the calculator works, then they can't build effective calculators can they? While it's all good and easy to say now that he's older that algorithms are easier to understand, he's been exposed to them for the past, oh, 15 years of his life (if he's a college grad, could be more depending...).
I'll finish my short tyrade against this guy's theories with my more humorous reason for not trusting him. He's an Emacs user. And everyone knows that Emacs users are maschocists. - TheClone, on 10/12/2007, -0/+7Really? I rarely read full articles in my Slashdot/Fark/Digg browsing, but I actually read the full text of this article. As a new college student, I'll likely have a lot more math ahead, but this article almost makes me want to go out an tackle a lot of it on my own.
- tablatronix, on 10/12/2007, -0/+6heh so true.
I just wrote a coordinate mapping system to map "zones" using double precision spherical/cartesian coordinates, headings and sizes.
I had to relearn all the stuff i was supposed to have in school.
The problem is its very hard to learn something in theory when there is no practical application being used to facillitate it or something to apply it too. As is usually so in textbook curriculum.
The "WHY" you might need to know certain maths is never covered experimentally. - focalrecursion, on 10/12/2007, -1/+6I agree with this 100%. Every time one of my professors go over a proof i zone out from trying to understand what is going on to just repeating what he wrote on the board to my notebook. It is so very boring and it doesn't give me much time to understand the importance of what i am writing down. I remember back in one of my undergrad calc classes were I asked the professor out right where will i ever need this and he said to me if i ever wanted to write a program to solve the problem.
- metalstorm, on 10/12/2007, -0/+5Well you will see a lot of calculus if you program anything that uses physics or something of the sort and need to use some differential equations. Though I don't really see the relation of a lot of math to just general programming. However, I do see a lot of correlation between higher level research programming and say the graph theory and a couple other math courses I have taken. The proof techniques are highly useful also since no one will use your new algorithm if you can't prove that it is better than previous implementations. I will give it a digg to promote the realization that math is still an integral part of programming and shouldn't be overlooked.
- lydon, on 10/12/2007, -0/+5The problem with the way schools have to teach math is that in public schools there is such a wide range of students with such varying levels of knowledge and competence. Sure some of us with higher IQ's can teach ourselves something one way, but Joe Blow sitting beside us in class coudn't teach his ass how to fart without ***** coming out.
The bottom line is that public schools have to teach to the lowest common denominator, which leaves those students with higher abilities at a disadvantage. - quentinp, on 10/12/2007, -1/+6I guess what he is saying though is that you also aren't a good PHP programmer if you know what stripslashes but don't know WHEN to use them.
- inactive, on 10/12/2007, -1/+5One thing would be for highschools to teach advanced math. I lost interest in math because even as a freshman, they were still teaching us how to do BORROWING in subtraction. I mean, what the *****?! That's the kind of ***** you do in second grade!
- jasqwerty, on 10/12/2007, -0/+3"Linear Algebra (i.e., matrices)"
Article fails and falls apart right there...
"It's pretty easy"
Article completely lands on it's face as being dead wrong.
If you want to teach it, you should teach it, not glance over how you do matrix multiplication and move on.
"Quantum mechanics is still beyond me, but calculus is nothing."
Just further grows the ***** pile...
i*h_bar*d/dt*Y = ^H*Y
I know it looks like *****, but if you know anything about QM, then you recognize that, and along with Heinsenberg's matrix formulation is pretty much it. After that ITS ALL CALCULUS, LOTS AND LOTS OF IT, along with some linear algebra, which this guy thinks is jokingly easy. - davidhullster, on 10/12/2007, -0/+3I understand the sentiment, I often find long blog entries difficult to finish too.
However, this blog article is very well written, I had no problem finishing it. I was even a little disappointed to reach the end of it. I'm adding Steve Yegge's blog to my list of regularly-visited sites. - OmegaSeraph, on 10/12/2007, -6/+9I disagree with this article completely. Telling you that proofing isn't the right way to go about learning Maths is very bad. Being able to prove and show why something works is, in my opinion, just as important as being able to use it. You wouldn't consider somebody a good php programmer if they didn't know WHY they were using stripslashes, would you?
- chimona, on 10/12/2007, -0/+3@ Geminitojanus, I agree with you that long division is important. but i think the important thing is that a lot of people have forgotten how to do long division. THe author is just trying to make the point that if we don't understand why long division works, and what division actually is, then none of the lessons will stick.
Human brains are meant to be heuristic, as opposed to algorithmic. we can learn algorithms, but it takes longer. most people understand long division as a series of steps...numerator here, denominator there, move this, bring this down, etc... the problem is that we end up knowing how to do it, but not why it works. if you understand the concept of division, you don't need the steps to divide stuff, but if you want to use them, you at least know what they are doing.
A better example of this is the quadratic formula. if you have an understanding of what it does to the numbers, then you don't have to memorize the equation, you can get the answer with just your concept of squares and square roots.
I haven't done a great job of explaining this here, but i plan to devote my life to changing the way mathematics is taught. So I guess I'll have to come up with better a better explanation. - plod, on 10/12/2007, -1/+4Um, the fact remains.... The education system needs reform in the United States :(
- mikexstudios, on 10/12/2007, -0/+2jasqwerty: Exactly! Although this guy makes some good points, dismissing Linear Algebra and Calculus as "easy" really diminishes his points.
- Harlequn, on 10/12/2007, -0/+2I have like over twenty years in I.T. behind me. being good at math helps, but I only went as far as Trigonometry and Analytical Geometry. Any more math than that probably would have been overkill for me. Take some courses in logic. That's what you really need to know. And make sure you can whip thru those "story problems" in math with ease. Story problems are somewhat similiar to programming problems. They make you rack your brain for a while. Also don't be afraid to take courses in English and Writing. Programmers with good people skills are more valuable. And anybody these days who knows how to write clearly is valuable to an employer. Also - musicians always seem to do well as programmes. Why? don't know, but I have observed that over the past two decades in this business.
- waterandfood, on 10/12/2007, -0/+2We all could spend more time with Math... Math is everywhere! This "rant" is definitely worth the read and could change your life forever.
- mndoci, on 10/12/2007, -1/+3I disagree with the part on how mathematics should be taught in school. The beauty of mathematics lies in being able to derive proofs. Teachers can make that more itneresting, but what I loved most about the subjects was that I did not need to learn anything by rote. A few core equations and theorems and derive the rest. What teachers need to do is show students where the mathematics they are learning will come in use later. That being said, basic mathematics and derivation is a great mental exercise.
As for programming, I am not sure. I suppose some programmers could make do, but most of them (I would guess more than 95%) probably need it in some form or the other). Also, how many people know what they want to do in life in high school. So a well rounded education, which includes mathematics as a core component would be most beneficial.
Disclaimer: I did not go to school in the US. - alterself, on 10/12/2007, -0/+1mine: http://digg.com/science/Learn_Calulus_from_bikini_clad_models is older :)
- d03boy, on 10/12/2007, -0/+1I totally agree on everything this article says.
- trivas7, on 10/12/2007, -0/+1Coming from a liberal arts/English lit background it's only been by slogging through SICP and 'How to Design Programs' that I've kindled a love of math rigor that is to be found in the jewel-like setting of functional programming, particularly the elegance of Lisp. Besides the writing of Douglas Hofstadter I'd recommend the writing of Ellen and Robert Kaplan ('The Nothing That Is') and David Foster Wallace ('Everything and More: A Compact History of Infinity') -- marvelous writers.
- inactive, on 10/12/2007, -0/+1I couldn't stand Discrete Math.
I had to take both the Intro course and the regular course. Maybe the teachers had something to do with it, but I found both classes to be terribly uninteresting.
I understand the relevancy of most of the material taught in the class, but in most cases, without real-life examples concepts are useless. I especially despised the section of the class devoted to Proofs. *cringe*
I'm in Statistics right now and it seems a lot more interesting to me for some reason. This could possibly be attributed to the fact that I've learned the material on three different occasions and it's fairly simple for me to grasp again.
Even though I'm a Computer Science/Mathematics major, I just want to be finished with math. Either that or I'd like to be put in classes that use real-world examples. - noamsml, on 10/12/2007, -0/+1They're prettry bad. After they went along claiming that calculus is the "trick to dividing by zero" and that "we don't need to know what it is, we just need to know how to do it", I promptly closed the tab and returned to my world of nonprocedural math. I like my math hard, not prechewed.
- dBLiSS, on 10/12/2007, -0/+1As a computer engineering student I can fully appreciate his article. Luckily the school I go to does a good job at teaching math necessary for the field, as well as showing how the math is relevant to real life.
Excellent read. Digg. - ctheory, on 10/12/2007, -2/+3I'm sure you're not only a fantastic mechanic, but one hell of a programmer, to boot.
Right? - ThePhilomath, on 10/12/2007, -2/+3You guys need to read more. I read WAY more than this every single day,... damn mathies.
- MrUnderbridge, on 10/12/2007, -0/+1No linear algebra? To me, that's THE most important math course to a programmer. Probably more important to the average programmer than discrete math.
- raccettura, on 10/12/2007, -0/+1I royally stunk at math, but can hold my own at coding.... perhaps it was the way I was taught? Or I just march to the beat of a different drum
- nixcraft, on 10/12/2007, -0/+1Because of its language, notations and symbols it considered difficult by many. According to these people mathematics is closed off from the rest of the world by a high wall. What goes on behind this wall seems to be a secret to them, and therefore they think that math is difficult. To be frank elementary maths is so simple and easy to learn that even a layman can do and enjoy it. However math's tutor needs to put ideas in a clear and interesting manner to all new learners. I will say an ability to reason and the urge to learn are the only prerequisites to learn maths.
- bentwookiee, on 10/12/2007, -1/+2"the simple fact is that the number of programming jobs is rapidly outpacing the demand for all other engineering roles"
Where did the author come up with this gem? If you're going to say something like that you should probably back it up. Yes, there has been significant growth in the programming field over the past 10 years, but does that mean we no longer need roads, bridges, buildings, cars, clean water etc, etc? Sorry, you're always going to need engineers. - iam1e3t, on 10/12/2007, -0/+1because they consist of the 'grade' levels - 1st grade through 8th grade. 9th -12th are just called freshman, sophmore, junior, and senior 'grades'
- ericpp, on 10/12/2007, -0/+1The math I was subjected to in high school was horrible. In the year I entered high school, the state mandated that schools should teach a new math program that emphasized group learning over teacher learning. Rather than have the teacher teach the material, they would instead give a brief introduction to it and have us break up into our small groups to learn the rest. In most of these groups, the students had absolutely no idea what was going on and asking the teacher question resulted in the same "Work it out with your group" response.
I'm actually thankful for the real math courses I now have in college. - stesun, on 10/12/2007, -0/+1Dude this guy is totally whacked. There is a reason that you learn math in this order. Well yes you might take some shortcuts and skip some parts but really. The stuff up to advanced calculus is just to make you understand mathematics. After that, then you specialize and go into discrete math. I don't think i would understand easy stuff like integrals and derivations if i was learned some formula for quadrature or spline interpolation technique's.
- faithnomore, on 10/12/2007, -0/+1Good ***** post! DIGG!
- raccettura, on 10/12/2007, -1/+2IMHO this:
http://www.digg.com/links/Advanced_Math_Girls_in_Bikinis_=_Bikini_Calculus
is the only way to learn math. - yahoofrom, on 10/12/2007, -0/+1math is kinda fun. very true.
- CosmicJustice, on 10/12/2007, -0/+1Spot on! Excellent review of the state of mathematics teaching. For those of you who disagree because you immediately "got it" in your math classes, congratulations. I think everybody else would benefit from a different way of looking at things.
- inactive, on 10/12/2007, -0/+1So, let's say I want to learn math. What is the *right* way to learn if school is crap? Where do I go?
- stesun, on 10/12/2007, -0/+1btw, information theory in high school? to actually understand that field you need to have a firm understanding of probabilities and stochastic processes. Which needs that you understand statistics and a lot of transformation and so on. So no not in high school. The kids would run and hide if they looked at that sort of math.
- inactive, on 10/12/2007, -0/+1So? In the U.S., the abbreviation of hte plural word Mathematics is spelled MATH. That is not WRONG. IT is just different.
- d03boy, on 10/12/2007, -1/+1I think he was talking about the theory behind linear algebra, etc. The little I know about linear algebra isn't very difficult at all but it does take a lot of memorization.
- ShaDoWwork, on 10/12/2007, -0/+0these are all the kids that needed to be punched in the face at school ***** smart asses................
use a calulator - al4444, on 10/12/2007, -0/+0the math is the language and philosophy of programming.
- lumberjack, on 10/12/2007, -0/+0I think he essentially hits the nail on the head with his comments about von Neumann machines and programming, and how we've come to associate calculation with what should be abstract tools that help you model a problem. Unfortunately, it seems that instances where mathematical skills come into play vs. frequency of use cases tends to live on the short end of the "long tail" curve. Most of the time you're stuck with how to engineer widget A to fit into widget B, and with processor speeds and memory the way they are, the kind of complexity analysis you'd do for algorithms aren't *that* necessary in most cases. I'd think that the trend in some communities towards semi/fully formally provable systems, and the rise of stuff like integrating relevance search are going to make the connection between math and coding more apparent. Well, that and game programmers: it seems those guys have to dream in linear algebra these days.
- xravenx, on 10/12/2007, -0/+0Math in high school was integrated into Algebra I & II, Geometry, Trigonometry, and Calculus. They we're actually in this order from your Freshman Year to Senior Year. Also with the DSTP test you we're testing in many different area's the DSTP test was a state test that you had to pass in order to get a diploma. We did many group activities where the teacher would tell you, "Work on the problem together". Most of the time other people slacked off so you I had to be the leader and ask people what they thought we should do and then put in my input. College is a lot different I feel that I'm more so independent now I'm learning theories and all. There is no actual "group work" your on your own learning it and I seem to deal with this very well. Like stated in the article learning math on your own is sometimes the best way!
- stesun, on 10/12/2007, -0/+0Have to thank this blog for introducing me to Kolmogorov Complexity. Seems very interesting and i probably buy a book about it. But i look at the reviews and with reviews like
"This was the second-hardest book I ever read. Honestly, it took me years and years to get through it. I even had to buy a 2nd copy, because I kept getting frustrated and throwing the first copy across the room until it was destroyed. So yes, this book requires a substantial effort to read."
Based on this, i don't really think that a high school student that does not even have a firm understanding of algebra should do. - feshmania, on 10/12/2007, -1/+1I like probability. As in what the ratio of alcohol to body mass a drunk frat boy can handle, or what the amount of disease per sexual partner a slutty girl has.
- GrumpyStoo, on 10/12/2007, -1/+1I think after reading what this guy wrote and complained about, which is most likely the difference between a High Context vs Low Context teaching style. The USA Low Context, China and India High Context. Jobs going over there. Hmmm.
Continuing, people want all their classes spoon fed to them. Math unfortunately you can not spoon feed to people. I doubt I can just sit here and jump right into Linear Algebra, do all the work for a student and expect a student to understand what Nullspace and Nullity is and how it might connect to Differential Equations. Only way these things are comprehended in some facit is by doing a lot of work.
Which unfortunately, takes a few hours out of your week. A class such as Linear Algebra results in doing 3 to 4 hours of work per section and 2 sections per week, so 8 hours of Homework per week. Your average student today not being effecient at doing things themselves, plays WoW, does the MySpace things Txt's msgs, needs to work to get through school, then whines that the class is too hard cause they don't know how to study for it on their own.
The reason they are like this due to the spoon feeding they received in grade through high school.
We all remember "One plus One equals Two"
Where as in a High Context Culture its toss on the board "One plus One Plus one" and wait til someone figures it out. Or a more Socratic method for more complex problems.
I see this and had this was pointed out due to the 20 some hours of Tutoring i do for Basic math to Calc II (Methods of Integration). This is what College professors are griping about right now. Because all you hear about is how many people are avoiding taking harder math courses , and the work force is getting saturated with underqualified individuals who don't have the basic math skills required for jobs in many fields. Those math courses being Calculus, College Geometry, Statistics and Probability. -
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