Rant about modern elementary education

[jchu14]

eLiu totally hit it on the head.

Method 2 is much more mathematically consistent. Method 1 is quicker and more probably less error prone, but the algorithm have steps that may not be obvious when you're first learning division. For example, if your daughter asks you 'why' you're bring down the next number down, would you be able to answer that? Just because that's the way that it's done or because it gives you the right answer is not a good reason.

It should be obvious that method 1 is just a shorthand version of method 2. It's relatively easy to teach kids the algorithms of doing math, but actually get them to think about math and why it works is the much more beneficial in the long run.

 

[Ronstang]

I learned method #2, but that was back in the late 60s early 70s. Why is it so hard? They are both exactly the same except in #2 you actually write in the zeros. Considering how stupid kids are these days thanks to technology I see no problem with going back to method #2 as it keeps people from getting confused.

 

[nanette1985]

I also learned method #2 back in the 60's. When they were spending lots of money on math and science education because of all the space stuff. But before they went loco and invented new math.

The thing I noticed when my kids were in school is that many elementary school teachers really don't know arithmetic, let alone mathematics. They're fanatical about whatever process they use because they don't understand what's really going on and get totally lost when you change things. To my kids' elementary teachers, Method 1 and Method 2 are totally different animals.

Fortunately, the kids learned math anyway, in spite of their teachers.

 

[ScottyB]

I drew lines down from the numbers.

 

[Adrenaline]

I drew lines down from the numbers.

I did this with method #1.

Method #2 is not to bad though.

 

[Bryophyte]

I thought long division was taught in 3rd grade, not 5th.

They are still teaching method 1 around here, from what I see, but I think method 2 makes more sense in demystifying the process.

 

[lupi]

method 2 sucks donkey balls.

 

[Fayd]

Just teach her Fourier division and be done with it.

that'd been great to have in 5th grade math class.

fuck this long division bullshit.

 

[PieIsAwesome]

I use the calculator method.

 

[Dekasa]

You want to see confusing? Look at elementary rounding. That is borderline retarded.

Now, to most, 23.530493 rounded to the 1's place is 24, right? Well in my home town they decided that was too simple. so they introduced rule like "If the number following the five is even then round up, if odd round down" or something along those lines. ah, the wikipedia has it. Look up rounding and the "Round Half to Even" method. Most retarded and unnecessary thing ever invented.

b, b, but that's wrong. I mean, it's absolutely wrong. If you're rounding to the A digit from A.5(any number) the number is absolutely closer to A+1 than to A. Rounding A.53 to A is WRONG. I'm sure glad I'm out of school and don't have to learn things in math that are absolutely wrong.

 

[Mr. Pedantic]

You want to see confusing? Look at elementary rounding. That is borderline retarded.

Now, to most, 23.530493 rounded to the 1's place is 24, right? Well in my home town they decided that was too simple. so they introduced rule like "If the number following the five is even then round up, if odd round down" or something along those lines. ah, the wikipedia has it. Look up rounding and the "Round Half to Even" method. Most retarded and unnecessary thing ever invented.

Surely this kind of thing is too retarded to be true...

 

[Matthiasa]

b, b, but that's wrong. I mean, it's absolutely wrong. If you're rounding to the A digit from A.5(any number) the number is absolutely closer to A+1 than to A. Rounding A.53 to A is WRONG. I'm sure glad I'm out of school and don't have to learn things in math that are absolutely wrong.

I'm pretty sure he is just remembering it wrong.
I recall that for a x.50.... it was round up if x was odd(or even can't quite remember but it was one or the other not both).
x.5(a lot of zeros)n was always up.

 

[Born2bwire]

i learned method #1 and method #2 makes more sense.

This. I learned method #1 but method #2 makes more sense. Plus, method #2 has the advantage that it is probably less prone to mistakes (since you explicitly rewrite the full term out each time instead of having to go back up to the dividend) and it more explicitly shows what you are doing in terms of the math. Method #1 will get you the right answer but I think method #2 is better because it better shows the mathematics of what you are doing. When so many people complain about school consisting of rote memorization I don't see why we should be complaining when they start to add more theory back into the lesson.

 

[jchu14]

Surely this kind of thing is too retarded to be true...

it's not true.

Round half to even is only a tie breaking scheme which means that if a number is exactly _.5, the value is rounded to the nearest even number. A 23.53 is still rounded up to 24, but a 23.5 is rounded to 24 and a 22.5 would be rounded to 22. This scheme reduces bias versus the always round _.5 up scheme.

example, given a sample of numbers:
1, 1.5, 2, 2.5, 3, 3.5, and 4 the average is 2.5
with a _.5 round up scheme, the average is ~2.714
with the round half to even scheme, the average is ~2.571

 

[Aikouka]

I used method 1, but either look fine to me.

 

[Born2bwire]

You want to see confusing? Look at elementary rounding. That is borderline retarded.

Now, to most, 23.530493 rounded to the 1's place is 24, right? Well in my home town they decided that was too simple. so they introduced rule like "If the number following the five is even then round up, if odd round down" or something along those lines. ah, the wikipedia has it. Look up rounding and the "Round Half to Even" method. Most retarded and unnecessary thing ever invented.

You should be glad that your school complied to IEEE standards and taught you a better way to do the tie breaker.

EDIT: Wait, jchu14 has it right. This is only for the tie breaker so it only applies when it is exactly X.5 not X.5Y .

 

[AznAnarchy99]

Who cares, in high school you start using the calculator for all the basic math anyways.

 

[eLiu]

You want to see confusing? Look at elementary rounding. That is borderline retarded.

Now, to most, 23.530493 rounded to the 1's place is 24, right? Well in my home town they decided that was too simple. so they introduced rule like "If the number following the five is even then round up, if odd round down" or something along those lines. ah, the wikipedia has it. Look up rounding and the "Round Half to Even" method. Most retarded and unnecessary thing ever invented.

So for elementary school, yes this is ridiculous.

However, rounding is a very interesting question when you're dealing with say, pseudo-random number generation & you really care about the 'good'ness of the resulting distribution. That is, when you take a pseudo-random output & divide by RAND_MAX, in x87 arithmetic (calculate in 80bits, round to 64 bits), a large portion of resulting floating point numbers will have been rounded. If all x.5 values are rounded to (x+1).0, then that introduces a bias that some people care about. Luckily other people (i want to say IEEE but I'm not sure) are out there caring about this kinda shit so I don't have to.

But oh god why would you teach that in elementary school? 20.5 -> 21 is good enough for just about everyone in the world D:

jchu14: yeah exactly. I don't think most students understand what they're doing when it comes to long division. I certainly didn't realize what was going on when I first realized you could do multiplication backwards. It seemed very coincidental that you only had to look at the first few digits & bring in the later digits as you progressed from right to left. Once I became more familiar with numbers in other bases, I realized what was going on with division. But it was definitely never explained in school.

Anyway If students did fully understand division, then polynomial division, division in arbitrary bases, etc. should be trivial... and somehow it isn't. You always have a "vector" of input coefficients (a,b,c,d,e) & you're trying to generate a vector of output coefficients... the only things changing are 1) the set that the coefs in the quotient can come from (for base 10: integers 0 to 9; for polynomials: complex numbers); 2) the "basis" multiplying the input/output coefs (10^n,10^(n-1),...10,1; x^n,x^(n-1),...,x,1, etc).

damnit, I see you already covered the rounding thing. I'm not going to delete what I typed though

edit: c'mon Mr. Pedantic, gotta be living up to your username! Though while Cogman quoted the wrong technique, googling 'round half to even' as he suggested would've shown the right result.

 

[Suspicious-Teach8788]

Who cares, in high school you start using the calculator for all the basic math anyways.

eh. i use it so much that on Friday, i spent 5 min trying to figure out how they got from ln T to 1/T until it finally hit me that integrating a ln T => 1/T. Sigh. My friend with her TI-83 laughed at me because I'm too dependent on the 89 nowadays.

sigh. and i completely destroyed high school calculus and college calculus... lol. how times have changed.

 

[NoCreativity]

I learned method 2 first. It was the "proper way" to do it, i.e. the long hand way. I think the idea was to show that you had to keep track of place. Method 1 is a short cut that we learned afterward once we understood the purpose for method 2.

All my math classes were like that. We learned the theory behind the concept and had to do things the long way. Once we understood the theory, we were shown the short cuts that we could use from that point forward.

 

[IndyColtsFan]

I don't get what the problem is. They are essentially the exact same method except method 2 uses 0's to help keep track of place. I learned one way and easily switched back and forth.

This. It looked funky at a first quick glance, but that is all they're doing and shouldn't cause any problems.

 

[edro]

I learned Method 1, but I like Method 2 better!
I remember my columns leaning pretty bad, so the place holders would have helped that.

 

[yhelothar]

Rant about education, especially the oppressive one that still remains in place today.
http://www.comminit.com/en/node/27123/348

 

[Colt45]

they are the same

 

[acheron]

Method 1 is obviously better (though 2 is basically the same thing, even if it looks stupid at first glance), but the bigger problem is that your child's teacher is a moron. For whatever reason, we let people who hated math and probably never learned algebra become elementary teachers, rather than something more appropriate such as cavemen*. (Ask any college math professor who has to teach elementary ed. students.)

* Calvin: I can get along fine without math!
Calvin's Dad: Oh yeah? What do you want to be when you grow up? Every job requires _some_ math.
Calvin: That's not true. I'll be a... caveman!
Calvin's Dad: That's not really a job.