Tuesday, February 23, 2010

Word Problems

I was going to just rant on Twitter about this, but man, I have been neglecting this blog and need to get my rant on here, so here we go.

A common complaint I've heard regarding math and the learning thereof is the existence of word problems. Instead of "5*12+3" you'd get "You need five apples for twelve people, but you just know your cat is going to eat at least three of them. How many apples do you need?" A REALLY simple example not using complex math, but that's the idea. Not sure what's up with that cat, though.

I appreciate word problems due to their providing a real world scenario and thus a reason WHY you would need to know the formulas they're teaching. There are math formulas I was taught in high school that I cannot recall now, but i suspect I would if they had bothered to give a real world example of what they were for.

I recall a class where these formulas would come up and I had no idea what the purpose of them was, and it seemed like I could never get a straight answer on the subject. Either they assumed my feeble brain couldn't handle it, or I guess those formulas just had no purpose. That alone I found frustrating, much like the rest of high school where I'd question "why do we need to know this".

The thing is, I like math. It's incredibly useful and I like coming up with formulas for things. I suspect I'm not alone in this, and wonder how many math students would do better if more teachers would take the time to explain what the real world use for what they're learning is.

Actually, I think that applies to almost every class. Tell someone why they should care, and maybe they will.


  1. I agree! I'm not sure if there *are* real world aplications for calculus... Though to be fair, I might know for sure if what you're suggesting came to fruition!

  2. As a computer programmer, I use algebra constantly. Trigonometry and geometry are essential for engineering and architecture. As for calculus, a big use is in physics. Not surprisingly, the inventor of calculus was Newton, who NEEDED it to figure out and prove his formulas. Put another way, the world itself runs on math!

  3. It's possible they just didn't teach you far enough into the subject. I was taught Maths and Further Maths at A-level in the UK school system which meant I had one, maybe two maths lessons a day and while initially some formulas were just "You have to know this" like summing to infinite series, eventually their use was revealed. I mean with some things there is no point in saying "Oh, it does this" because you'll then say "Why the hell do I need to know how to do that?" or a variation on the same.

    There is only one formula that I was taught and never saw the use for, even having been told what the use was and shown what do to and that was completing the square. I had to do it for the exam, it made no sense. The quadratic formula made the entire completing the square formula redundant. And that is much more annoying than just not knowing why you do something.

  4. In recent years there's been a bit of a teaching revolution that's pushing more and more for real-life examples, especially in the math and science fields. Things are being taught in ways that make a little more sense to students, at least by some of the younger teachers. Just as an example, I'm a Physics major in university. In my second physics class, instead of just being handed formulas, we've actually started with a real-life example and derived the formula for every single formula we've had, sometimes using mathematical formulas to help do so. Everything seems to have a purpose.

    Now, of course, my little discourse there missed one question, the "will I ever actually need to use this?" question. The answer? Probably not, especially not in today's world. So many techniques are taught in math and science classes today, which before were necessary to solve some problems, but now can simply be plugged into a computer or calculator without a single thought. The point of teaching them is still to spur the brain activity of actually learning how to do it without relying on some program or some machine to do it for you, instead being able to do the calculation yourself. This is the part I believe is being lost though. In older times, many jobs absolutely required some basic math knowledge. I couldn't imagine trying to do carpentry, or construction, or electrical work, without at least a fair amount of knowledge of algebra. Sure, there's times when you can just say "put this here", but if you don't know how much of this you need, or how long this is supposed to be to fit here, or where exactly to cut this and that so it'll all fit together right, things just aren't going to come out quite right.

    I guess my point is, there's some use for everything you're taught, usually. Today, we're slowly shifting to a world where we're telling people why something's useful... except it's not that useful anymore, because there are other ways of doing it now. Confusing and messed up? Yes, but isn't everything nowdays?

  5. I just don't get why people don't write out the word problems as numbers... All the information's in there... it's not made inherently more difficult just because it's "five" instead of "5"... oh the way the mind works. :P

  6. I despise word problems. I can translate math to real life just fine without them. But different methods work for different people. I had a friend who was really good at turning problems into word problems for people who understood better that way.

    My point is, while word problems may work for some people, a course can't be made to fit the way every single student prefers it. I had a teacher who simply ADORED word problems and the painful part for me was reading them. I could get the answers right, but having to read through my teacher's attempts at storytelling was something I would've gladly avoided.

    My Calculus teacher, on the other hand, had the plus of not being a word problem kind of guy (he was also hot. SO HOT) and the reason "you need to know this to pass the course" was reason enough for me. I also believe my mother's motto: "Nothing you learn will ever get in your way."

  7. My problem is now I can't do math in "math", but I can do it in any programming language. The pure math notations just stopped making sense to me a while ago.

  8. Having some education as a mathematician (I'm an old undergrad), I have to agree with what you've said for the most part. Teachers who are tasked with teaching math in schools frequently don't really understand the subject themselves. This is a critical failure in our educational system.

    Those who do understand the math (as opposed to the arithmetic) sometimes have trouble conveying that understanding to students in ways that can make it real for them. Word problems that don't pose "real" problems make it even more difficult for students trying to see the reason for it all, and they wind up watching the clock and thinking about end-of-day activities instead of learning anything.

    I'll stop after one more thing: the biggest failure in mathematical education is that not enough time is spent on the "easy" stuff in Chapter 1 of those expensive textbooks. A student without good understanding of the basics on which math is built will have a hard time understanding higher and more abstract concepts.

  9. Ha! I remember asking my 8th grade teacher about the real-world applications of the stuff we were working on, and she flipped out, started screaming about "only every job on the internet!" She ran out of the room crying and gave me a really bad grade. I still have no idea why.

  10. Actually your right i came up with an equation but can never remember it because it has no aplication

  11. I just learn and apply when needed, which is so infrequently that I usually forget by the time I need it. There are uses, but only for certain jobs. If you hate math, don't get one of those jobs.