Teaching Math Through the Decades...

sketerpot · Post by **sketerpot** » 2005-08-01 10:10am

Plushie wrote:
MariusRoi wrote:
Plushie wrote:Long division's useless, anyway >_>
Ah, My guess is you haven't taken a Calculus class in a while . Without it I would have been sunk on last weeks DiffyQ quiz.
I, *ahem*, kind of ignored calc. Well, not so much ignored as ran on auto-pilot. My concious mind slept while the rest differentiated. I couldn't for the life of me tell you anything about it (well, anything of importance) but I can still do the math itself.

How about integration? You need long division for integration of rational expressions by partial fractions. (Actually, you can use synthetic division too in some cases, and there's an alternate method which doesn't require so much solving of simultaneous equations... but I digress.)

Gil Hamilton · Post by **Gil Hamilton** » 2005-08-01 10:30am

Son of the Suns wrote:Incidently, I went to a private school where we were not allowed to use calculators in math. We had to do everything by hand. As a result, I was way ahead of everyone else in college as far as my algebra and trig abilities go, however, when I got into the higher levels of math I found it difficult to keep up when the instructor said, "Ok now that you've seen how to set it up, just plug the numbers into your calculator." I really wasn't that proficient with a caluculator, but I understood how the problems were worked and whether or not the answer I got was reasonable far better than the majority of my classmates. I also noticed that students that had always used a calculator to do their algebra more often had the attitude that they were "not smart enough to learn math."

I had a different experience with calculators. Once I started higher math classes, they didn't do very much for me or many of my classmates. Texas Instruments hasn't invented a calculator yet that will tell you what to put into it when solving a math problem. People bombed tests using TI-89s, while I used a dinky pocket calculator that wasn't much more advanced than trig functions* and scratch paper and did just fine. The difference is if you don't understand the math, the most sophisicated calculator in the world won't make the problem any easier for you. It's a tool, not a substitute brain. That's why I think that it doesn't matter whether kids use calculators or not in class; as long as they have a good teacher that doesn't spend more time teaching them how to press buttons than math, a calculator doesn't make a difference in how a student performs except for saving them time doing things by hand that they should, by that point, be perfectly capable of doing already.

At most, a calculator is good for speeding things up and preventing brain farts when doing basic arthmetic (99 out of 100 math errors I've made in all my trig and calculus classes have been arthmetic based). Even then, it hasn't helped that much, because they also haven't invented a calculator yet that has stopped me from being distracted by a pretty girl walking by while I'm doing my homework and entering in the wrong buttons.

*incidently, in the private school, how did you do trig functions without a calculator? Did your math books have trig tables in the back? Doing such things completely by hand without a calculator or a trig table is a vicious pain and a complete waste of time.

Gil Hamilton · Post by **Gil Hamilton** » 2005-08-01 10:33am

MariusRoi wrote:Ah, My guess is you haven't taken a Calculus class in a while . Without it I would have been sunk on last weeks DiffyQ quiz.

However, I think they've stopped teaching long division in school. It's fallen into the same category of doing square roots by hand I've heard.

sketerpot · Post by **sketerpot** » 2005-08-01 10:44am

Gil Hamilton wrote:*incidently, in the private school, how did you do trig functions without a calculator? Did your math books have trig tables in the back? Doing such things completely by hand without a calculator or a trig table is a vicious pain and a complete waste of time.

I'm certain they used trig tables. In order to find, say, sin(x), you have to have to approximately sum up

Which takes a lot of multiplication, division, and addition. To get the kind of precision you have with trig tables, you need a nasty number of terms (11 should do for a decent approximation for -pi/2 <= x <= pi/2), and the students wouldn't be able to understand where the Maclaurin series comes from then anyway. Nobody is that insane.

TimothyC · Post by **TimothyC** » 2005-08-01 10:46am

Gil Hamilton wrote:
MariusRoi wrote:Ah, My guess is you haven't taken a Calculus class in a while . Without it I would have been sunk on last weeks DiffyQ quiz.
However, I think they've stopped teaching long division in school. It's fallen into the same category of doing square roots by hand I've heard.

Yeah, well I was lucky enough to have a relatively high IQ and ADHD, and thus I sort of got kicked out of the public school kindergarden

(There was no way in hell that I was going to spend 5 hours a day finger painting), upon which I was enrolled by my parents in a Montessori school for the rest of my kindergarden experience where I learned to do long division in my head.

Gil Hamilton · Post by **Gil Hamilton** » 2005-08-01 11:53am

MariusRoi wrote:Yeah, well I was lucky enough to have a relatively high IQ and ADHD, and thus I sort of got kicked out of the public school kindergarden (There was no way in hell that I was going to spend 5 hours a day finger painting), upon which I was enrolled by my parents in a Montessori school for the rest of my kindergarden experience where I learned to do long division in my head.

They were still doing it when I was learning arthmetic (second grade-ish), where I learned to do long division. Some time after that I think they stopped. I'm a bit hazy about the exact details, but I'm certain about doing long division back then which is where I learned to do it mentally (which is kind of funny, because I visually picture a piece of paper in my head and do the problem there).

Alyeska · Post by **Alyeska** » 2005-08-01 01:02pm

Gil Hamilton wrote:
Son of the Suns wrote:Incidently, I went to a private school where we were not allowed to use calculators in math. We had to do everything by hand. As a result, I was way ahead of everyone else in college as far as my algebra and trig abilities go, however, when I got into the higher levels of math I found it difficult to keep up when the instructor said, "Ok now that you've seen how to set it up, just plug the numbers into your calculator." I really wasn't that proficient with a caluculator, but I understood how the problems were worked and whether or not the answer I got was reasonable far better than the majority of my classmates. I also noticed that students that had always used a calculator to do their algebra more often had the attitude that they were "not smart enough to learn math."
I had a different experience with calculators. Once I started higher math classes, they didn't do very much for me or many of my classmates. Texas Instruments hasn't invented a calculator yet that will tell you what to put into it when solving a math problem. People bombed tests using TI-89s, while I used a dinky pocket calculator that wasn't much more advanced than trig functions* and scratch paper and did just fine. The difference is if you don't understand the math, the most sophisicated calculator in the world won't make the problem any easier for you. It's a tool, not a substitute brain. That's why I think that it doesn't matter whether kids use calculators or not in class; as long as they have a good teacher that doesn't spend more time teaching them how to press buttons than math, a calculator doesn't make a difference in how a student performs except for saving them time doing things by hand that they should, by that point, be perfectly capable of doing already.

At most, a calculator is good for speeding things up and preventing brain farts when doing basic arthmetic (99 out of 100 math errors I've made in all my trig and calculus classes have been arthmetic based). Even then, it hasn't helped that much, because they also haven't invented a calculator yet that has stopped me from being distracted by a pretty girl walking by while I'm doing my homework and entering in the wrong buttons.

*incidently, in the private school, how did you do trig functions without a calculator? Did your math books have trig tables in the back? Doing such things completely by hand without a calculator or a trig table is a vicious pain and a complete waste of time.

Thats the way things worked in my college math. The teacher said that a calculator was required, but not even a scientific calculator. She never taught us how to do the math on a calculator. Instead she taught us the method of doing the math. This left the minor work to be done with the calculator while you crunched the equations. It worked briliantly, for me that is.

SyntaxVorlon · Post by **SyntaxVorlon** » 2005-08-01 03:42pm

Actually I had an experience with this problem myself not too long ago. One of my housemates was wearing his "There are 10 kinds of people in the world, those who understand binary and those who don't."
He, I and our other housemate where in the store checking out groceries when the cashier, looking at his shirt asked, "What's binary?" Hearing this, the cashier on our other side said, "Yeah what is that?"

It really is sad that people can get through so much school and not know their 1000's from their 8's.

StarshipTitanic · Post by **StarshipTitanic** » 2005-08-01 05:06pm

SyntaxVorlon wrote:It really is sad that people can get through so much school and not know their 1000's from their 8's.

Binary would be a rather trivial bit of knowledge for most people.

WyrdNyrd · Post by **WyrdNyrd** » 2005-08-02 04:26am

StarshipTitanic wrote:Binary would be a rather trivial bit of knowledge for most people.

I'm sorry, sir, but the Pun Police will be visiting you soon. You are not expected to survive.

Lusankya · Post by **Lusankya** » 2005-08-02 05:50am

I actually find long division quite useful of you use polynomials. You just turn 78,123/16 into x^5-2x^4-2x^3+x^2+2x+3/x+6, and then once you've solved it like that, you just replace x with 10. I never quite understood the point of it before I learnt how to do it like that, and then it all suddenly became clear to me.

Otherwise I'd just use short division, since I never quite saw any difference between short and long division in primary school, except that in long division you had to write stuff down, wheras in short division you'd just do it in your head.

Tiger Ace · Post by **Tiger Ace** » 2005-08-02 06:13am

Long division makes the head hurt, I think in case of division, I'm reliant on calculators, I've tried learning it, every time I either forget or just get confused to hell.

Lusankya · Post by **Lusankya** » 2005-08-02 08:11am

Hurts much less with polynomials.

Maybe I'm just odd though.

Varmint Al · Post by **Varmint Al** » 2005-08-07 01:23pm

SLIDE RULES RULED…. When I went to college, all engineering students had slide rules. I used a Log-log duplex deci-trig. It was carried in a case that fit on my belt like a pistol holster. I was good at the "fast draw". Achieving the correct numerical answer was straight forward, but a simple hand calculation was necessary to set the decimal place. For really accurate calculations I had a circular slide rule where the C & D scales were approximately 20" long. Those were the good old days. On my first and only engineering job, lasting 30 years, at LLNL, it was 2 or 3 years later that the first calculators came out. It was easy to switch over to the calculators, but much better was programming in BASIC or FORTRAN. We had access to one the best computer complexes in that world at that time.

Sarevok · Post by **Sarevok** » 2005-08-07 01:31pm

When working at home I use my calculator extensively for solving problems that have became mundane. But at school when doing work that will be checked by the teacher working manualy to show all the steps takes priority. Still having read the entire calculator manual I do maintain a slight advantage, not many people I know realise the power of modern scientific calculators.

Zadius · Post by **Zadius** » 2005-08-07 10:28pm

The Shadow wrote:Still having read the entire calculator manual I do maintain a slight advantage, not many people I know realise the power of modern scientific calculators.

My calculator's (TI-83+) manual is literally the size of a Bible. Needless to say, I have not read the entire thing. I've had this calculator since December 2001 and I still am learning about more things that it can do.

Netko · Post by **Netko** » 2005-08-09 03:01am

Over here calculators are looked at as something dirty basicly - whenever and whereever they can be taken out they are. All my math has to be done by hand (on the other hand, numbers are usualy really small and the problems are designed to be "easily" solvable by hand). The only class that allowed calculators fully was physics, and only then since they had multiple answer tests where the answers differed by less then a percent so that roughly solving it was useless since a lot of people were smart enough before they implemented that system to just figure out roughly what the answer should be and select the correct one among several very diffrent ones, thus outsmarting the old stuffy proffesors who made the test. We could not have that, now could we?

. This is college level mind you.

High school was pretty much the same, calcs outright forbidden for most of the math (including trig, however it was made sure that all problems were solvable if you knew the basic table, in your head of course - sin, cos, tg, ctg of Pi/6, Pi/4, Pi/3, Pi/2). Thankfully I just cannot fathom something like the op happening here especialy with the cashiers - hell, over here they always nag you for change so that they can give you a simpler amount back.

Oh, and (half of) the semester when we did systems other that base 10, including base whatever-the-hell-I-like was the happiest time in math class for my nerdy computerloving head, unlike for everyone else. Especialy when that made an impression on the teacher so that she, from then on, thought about my math skills as better then just mediocre which really helped me out in the grade area when I hit areas that were more problematic for me.