New Math vs Old Math

Paybacksays...

What the fucking fuck is that all about?
That's ridiculous. All she's doing is spreading the equation apart.
Turning a compact process into a Gordian knot.

Mordhaussays...

It's part of common core. Supposedly it makes it easier to understand the theory behind math so later in higher level classes (algebra, trig, etc) they can easily break the harder equations down.

Beats me, I learned the old way and it worked for me through algebra 1/2, and geometry.

Paybacksaid:

What the fucking fuck is that all about?
That's ridiculous. All she's doing is spreading the equation apart.
Turning a compact process into a Gordian knot.

Paybacksays...

I would piss off my teachers, and later profs, by never showing "my work" on complex algebra. Kept doing it in my head.

"Find for X"

X=3.56

WRONG!!!

It isnt 3.56?

Yes, but you didn't show your work.

Meh.

Mordhaussaid:

Beats me, I learned the old way and it worked for me through algebra 1/2, and geometry.

JiggaJonsonsays...

I have asked math teachers about this and they seem to be behind the line that it helps kids understand how they got to a solution. I am yet to see any credible research that illustrates that this improves skills or thinking or critical thinking.

I will admit, I do THINK about numbers this way. If I come across a problem that's too difficult to do immediately, I start breaking things up in my head.

Sometimes when I'm bored and walking I whistle, sometimes I recount the digits of pie, sometimes I recite the To be or not to be speech from Hamlet, sometimes I start multiplying (really)

2x2 = four
4x4 = sixteen
16x16 = uhhhh <<<< and this is where I start breaking it up --->16x10= 160
----->10x6= 60
------>6x6= 36

Then I have to remember the 36 as I add up the 6 n 6 for 12 dont forget the zero so it's 120 + 100 + 36
so it's 256

256 x256 is like 250x250 or 25x 25 (at this point it's helpful to think of quarters and money) and then add 36 (6x6)
so if there are 4 quarters in a dollar or 100, 25/4 = $6.25
then i need the zeros still

62500 + 360??? = 663? no that's not right, 65? Im losin' it somewhere in there, cant keep track a whole lot further without some paper in my hands or digital transcription (I'm trying to simulate what I actually think of)

>>>>>>>> 65k? estimation <<<<<<<<<
ALL that said, I do that but I learned math the old way and worked as a cashier for 5 years. I never would do regular calculations this way all the time, it's just handy for some fast math. It was easier to commit to memory a lot of my multiplications tables than it would have been to think through this stuff when i didn't know anything about it.

a lot of the education community shits all over the idea of memorization, but I think there's something to be said for it and would be interested if anyone had any studies of memorization as a teaching method and its efficacy.

Mordhaussaid:

It's part of common core. Supposedly it makes it easier to understand the theory behind math so later in higher level classes (algebra, trig, etc) they can easily break the harder equations down.

Beats me, I learned the old way and it worked for me through algebra 1/2, and geometry.

eric3579says...

I guess i kinda do the new math when seeing that problem. I do it in a couple seconds in my head though. 35x10 + 35x2. I always just assume everyone's doing it that way.

psycopjokingly says...

So if I'm getting this right, teaching children something is slower than an adult doing it? What!? Why even bother teaching children, why not just have adults do things?

newtboysays...

They tried this crap in my geometry/pre trig class....they called it "proofs"....forcing us to do mental gymnastics to spread out a problem from maybe three quick steps into 20. Asinine.
My last high school math class was advanced placement B/C calculus....I never found this a bit useful, because I was taught real math. By second grade we were expected to know up to 12 X 12 multiplication tables without hesitation, if they taught us by this method, we would have been years behind.

Since next to no one today is doing even moderately difficult math without a calculator/cellphone, I can't fathom why they bother at all anymore with more than basic math skills for non math or science majors...that said, my cousin still can't add 3 digit numbers or multiply or divide at all thanks to Waldorf schools, and that's really sad.

@Payback, I was accused of cheating in trig because I refused to show my work or do homework. I was separated from the class for a big test, and my score remained an A while the class average dropped by around one full grade. I never had to do homework or show my work in that class again, but did have to separate myself for tests so the class wouldn't cheat off of me. That was in boarding school.

Mordhaussaid:

It's part of common core. Supposedly it makes it easier to understand the theory behind math so later in higher level classes (algebra, trig, etc) they can easily break the harder equations down.

Beats me, I learned the old way and it worked for me through algebra 1/2, and geometry.

Paybacksays...

Had a high school math teacher who was awesome, but had a small aneurism and had to be replaced for a few months second year by a fricken PE teacher with delusions of grandeur.

Was so certain I was cheating, wrote out a problem on the board hoping to humiliate me in front of everyone, but i just wrote down the answer, tossed him the chalk and walked out.

This was long before mic drops were a thing, but it was the same idea.


newtboysaid:

Payback, I was accused of cheating in trig because I refused to show my work or do homework. I was separated from the class for a big test, and my score remained an A while the class average dropped by around one full grade. I never had to do homework or show my work in that class again, but did have to separate myself for tests so the class wouldn't cheat off of me. That was in boarding school.

RFlaggsays...

I get wanting kids to understand what is going behind the scenes of the math problems. It's a good goal, but I do think they spend too much time on this portion. Show how to do it the shortcut way that most people know, show how it works, using the above, then back to the shortcut. Unless the person is entering a math field, they likely don't need the number theory.

It's not dumbing down, it's making it too complex for what most people need. Especially for those taught the old methods... of course "new math" is more like really old math, before we found shortcuts that we use now. The people who'll need number theory, will need to know how numbers actually work behind the scenes of what you are doing, will likely have a more intuitive understanding of the processes.

What needs to be done more is order of operations, so 6 / 2(1 + 2), isn't calculated as 1, and properly as 9... if I see somebody argue 6 / 6 is 1 ever again... There's another famous one that really messes up many calculators, because they do as entered, and don't wait for the equal sign to be entered. With a proper understanding of order of operations, they can use a calculator and get a correct answer. And that is more or less what "new math" is trying to teach in a very odd way...

Minute Physics covered Order of Operations well.
https://www.youtube.com/watch?v=y9h1oqv21Vs

Jinxsays...

Honestly, lets be real. The only problem here is when you try and help your kid with their maths homework and you both insist the other is doing it the wrong way. And long division is really where the proverbial hits the fan.

scheherazadesays...

"Get the answer faster" is not the point.

The left explains why multiplication works, whereas the one on the right is a process for multiplying.

The left makes it visually obvious that scalars are separable.

That : (35*2) = (30*2) + (5*2) = (30+5) * 2


The only thing missing (which may have been covered elsewhere) is that : 35 'IS" (3*10^1) + (5*10^0), and that multi-digit-numbers are already presented as separate scalars in sum.

-scheherazade

bcglorfsays...

The problem is that it's confusing theory with the method. The right hand method(henceforth referred to as right method) shows that 35*2+35*10=35*12. It takes all of a couple minutes to show a class that. Spend a little time reminding them of the theory, put have them practice the right method. This isn't a mathematical theory exercise, this is performing basic arithmetic. It's why you segway into algebra later and show kids a(x +y)=ax+ay

scheherazadesaid:

"Get the answer faster" is not the point.

The left explains why multiplication works, whereas the one on the right is a process for multiplying.

The left makes it visually obvious that scalars are separable.

That : (35*2) = (30*2) + (5*2) = (30+5) * 2


The only thing missing (which may have been covered elsewhere) is that : 35 'IS" (3*10^1) + (5*10^0), and that multi-digit-numbers are already presented as separate scalars in sum.

-scheherazade

vilsays...

Segway.. is that still a thing? I thought everyone was riding those damn electric scooters now.

I like the graphic representation of multiplication as rectangles, works for me. Theory or method, I like to understand how things work so i can reinvent them myself whenever I forget the formula.

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