Rant about modern elementary education

[cyclohexane]

the 2 methods are identical, you're just not writing out all the zeroes in the 1st one.

 

[Engineer]

My daughter (10) is being taught method #2. I was taught method #1. I've been through enough math (Calc 1, 2, 3 and 4 and DE + others) and absolutely think that method #2 sucks donkey balls. That is all.

 

[DrPizza]

Method 1 makes more sense in the context that method one is more similar to the algorithm used when dividing polynomials. Thus, using method #2 is short-sighted.

So, if your daughter does end up being penalized for using method #2, complain. Insist that they show research that method 2 is pedagogically superior to method #1. Show how method #1 is what is used for division of polynomials. Have the teacher demonstrate long division of polynomials using method #2. When he/she can't, have the teacher do long division using method #1.

Pronounce that the teacher can't do either method with polynomials, probably as a result of learning method #2 him/herself. Complain that your child's teacher can't even perform at an 8th/9th grade algebra level & is incapable of selecting algorithms which will enable her students to not end up math innumerate.

 

[Engineer]

the 2 methods are identical, you're just not writing out all the zeroes in the 1st one.

While true, you have to think in terms of 1000's, 100's, 10's and 1's (or whatever you start with) instead of simply dividing the fist number (few numbers) and pulling the next number down.

Method #2, as I said before, sucks donkey balls.

 

[BoomerD]

I learned method #1 about 50 years ago. It made sense then, it makes sense now, BUT, I can also understand why method 2 may be easier for some kids because it "fills the blank spaces" instead of letting them "drift" accidentally.

I'd expect that once they get the hang of method 2, the teacher would move them to method 1 for speed.

 

[eLiu]

I "learned" method 1 (it's... obvious?), though my paper usually looked more like method 2 b/c I'd make marks to hold place. Otherwise my shitawful handwriting could have me interchanging digits all over the place.

Also, method 2 is more mathematically consistent. If I want to divide A into B, where B is written a*10000 + b*1000 + c*100 + d*10 + e*1, then long division has you doing:
1) find alpha (btwn 0 and 9) such that A*alpha*10000 <= B <= A*(alpha+1)*10000 (0 in this case)
2) find beta (btwn 0 and 9) such that A*beta*1000 <= B - A*alpha*10000 <= A*(beta+1)*1000 (9 in this case)
etc

The whole point is that 9*6000 = 54000. That's the closest you can get with only units of 1000; then you remove 54000 from the dividend and re-ask the same question w/the remainder. Method 1 just drops the 0s b/c this is obvious & doesn't need to be repeated.

I totally disagree about polynomial division. Method 2 is consistent with polynomial division. Say I'm dividing (x+1) into (x^2 -9x - 10) (example taken from first google hit).
Step 1: how close can I get using only units of x^2? Well (x+1)*x^2 = x^3 is not in the dividend, so 0*x^2.
Step 2: how close can I get using only units of x? (x+1)*x = x^2 + x. I can eliminate the x^2 term, leaving me with -10x - 10
step 3: how close can I get to the remainder using only units of 1?
etc (well we're done but you get the point)

The numbers long division asks the same questions: how close can I get using units of 1000? Units of 100? Units of 10? 1? It's basically the same problem but with a different "basis": in one case, 10^n, 10^(n-1),..,10,1; in the other, x^n, x^(n-1), ..., x, 1. You are NOT asking (as with method 1) "how close can I get to 56 using units of 1?" That's a simplification that helps you write down less stuff.

edit2: Oops, in addition to a different "basis," the polynomial division case doesn't have the restriction that the coefficients lie between 0 and 9. If you think about it more generally, it's still the same deal. Because 1*10, 2*10, ..., 9*10 cannot be expressed using (integral) units of 100. Similarly a*x cannot be expressed using (no coefs of 1/x or x allowed) units of x^2.

edit: AND since so many people here seem to think being college educated lends credence to their opinions, let me weigh in: i was a double major in aerospace & math. i'm getting my phd in computational fluid mechanics. I've had more math classes than most people in this thread... and that makes me an expert in division...!


That said, I've definitely run into teachers trying to tell me that my way of doing X is suboptimal/wrong/whatever and I'll lose points if I don't do it the way they were teaching. I can't remember how we were taught to find GCD & LCM in school, but the method my mom taught me was way faster. Or when we first learned systems of equations in middle school. I realized you could multiply an equation by something & add it to the other equation(s)... b/c of the equals sign. But I'll tell you I failed some assignments b/c I didn't do the substitution method we were being taught.

edit3: who cares that the numbers are large or small? If 54000 is scary, then the issue that needs addressing is... why is 54000 scarier than 54? They're just numbers. And again, the numbers are the same size in method 1, because method 1 is a simplification of method 2.

 

[guyver01]

I was taught method #2 ... and i went to elementary school during the 70's
Maybe elementary schools in queens were just more advanced than the rest of the country?

 

[x-alki]

I was tuaght methed #2 in late 60's. My dad was a math teachar and that's the way we lerned. To bad he wasnt a spellin teachar.

 

[Brainonska511]

Learned method 1, but was also taught to draw arrows to "bring the next number down" in long division, which would be similar to leaving zeroes as place holders.

 

[guyver01]

Why is it that basic long division is hard for me to assist my daughter with?

because despite your argument to the contrary, you're a complete idiot... if something isn't done how YOU were taught... it's wrong... and you can't figure out how to do it another way.

You and your child's teacher are identical... stubborn in their way... its their way or its wrong.

 

[Triumph]

i had no problems understanding method 2 at first inspection. but i'm also good at math, so i'm not the best at determining what is "right" for the people who can't understand it.

the only benefit I see to method two, though, is that it keeps things in line for children who may have sloppy handwriting. i'd say that's useful. i've done that myself when trying to do quick long division on scratch paper, messing up the placement of the subtracted values. purely a practicality issue.

 

[911paramedic]

youre just mad that method 2 made you look like a punk infront of your kid

LOL

#1 is easier imho, and the way that I learned it.
#2 makes sense to me but I hate the added math it requires

Is this new method for people that can't figure out how to line numbers up correctly and require placeholders? I don't like it...

 

[Matthiasa]

When using numbers they are the same.

 

[Eli]

Um, I learned method #2 and I was in elementary school 20 years ago..

 

[Jeff7]

LOL

#1 is easier imho, and the way that I learned it.
#2 makes sense to me but I hate the added math it requires

Is this new method for people that can't figure out how to line numbers up correctly and require placeholders? I don't like it...

My brilliant method, which didn't seem to draw the wrath of any teachers, was to draw vertical lines to keep the columns in line.
And I didn't need any expensive educational studies or doctoral degree in psychology to come up with it.

 

[Matthiasa]

Ah Jeff7's method is best.
Though grid paper has built in lines so not always needed.

 

[eLiu]

Damnit people, the zeros in method 2 are not place-holders. They do have meaning, even if it's extremely trivial. Method 2 also doesn't necessitate any additional math, unless you think computing (n-0)=n is hard.

Read my earlier post. Method 2 is more mathematically & conceptually consistent with what you're actually doing when you work out long division. The logic also generalizes to division in other bases (e.g., base 16, base 2), polynomials, etc.

 

[Triumph]

Damnit people, the zeros in method 2 are not place-holders. They do have meaning, even if it's extremely trivial. Method 2 also doesn't necessitate any additional math, unless you think computing (n-0)=n is hard.

Read my earlier post. Method 2 is more mathematically & conceptually consistent with what you're actually doing when you work out long division. The logic also generalizes to division in other bases (e.g., base 16, base 2), polynomials, etc.

your post is tl;dr.

 

[Ben90]

Your little spiel about it causing her to lose confidence isn't justified on your part, she should lose confidence if method 2 is enough to throw you off to the point that you don't know how to do it, then she should lose confidence if your ability to help her with math. I can't even imagine how bad you'd be at algebra, let alone calculus if something like that can throw you off so much.

I agree with this. Its obvious she doesn't really have a grasp on what is going on, just following steps if she doesn't understand how #1 and #2 are the exact same thing. You need to find a way to explain it to her.

While this single event in the grand scheme of things could be small, if it gets repeated a whole bunch, her mathematical base could end up being very weak and she will have problems with intermediate+ math.

I'm not saying your child is an idiot. I strained more than anybody else in my fourth grade class learning long division.

 

[Cogman]

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.

 

[Cogman]

Just teach her Fourier division and be done with it.

 

[Turin39789]

I learned both. Method 2 is just Method 1 except that you add the trailing zeroes after you have solved 56\9, there is no extra math invovled unless, as eLiu has pointed out, 7-0 is a problem for you.

 

[tokie]

Aren't they trying to teach kids multiplication using some confusing cross-table chart thing now?

 

[eldorado99]

Method #1 is da bomb.

 

[dennilfloss]

I was taught Method #1 except that the dividend is on the left (with the side-stepped operations below), the divisor in an L-shaped box on the right of the dividend, and the resulting quotient just below the L-shaped box. No need to add extra zeros as they are implied by the position of each digit in the side steps. Makes more sense to me to have the quotient below & on the right as it's the result and we are taught also to write words from left to right and top to bottom, so it's consistent with the way we were taught to write.