yeah. look at figuring out tips. what’s easier, trying to sit there and suss out what 15% of the bill is, or looking at the total and thinking “ok, 10% is x, plus half that is 15%.”
Well, of course my way is best. It’s easier to understand. 
The problem with the “old” method is that it’s a process to get the answer, but why you get the right answer is somewhat opaque. If you learn the proper machinery by rote, you do get the right answer, but if all you want is the right answer, you should just use a calculator.
The “new” way of doing it is to teach the kids how to think of the numbers in their head so they can move them around in ways that make sense. When I was in college, I was a waiter in a restaurant, before computerized checks. I would have to write down what was ordered and the price, then total it up and add tax. I could write down the line-item prices, add them all in my head and include tax so the next thing I wrote was the total. Now that was in the days of 5% sales tax which was easier to figure than it is now, but still. And I used the “new” methods back then, all in my head. That’s what they’re trying to teach kids. If you just want to go through a mechanical process that gives the right answer, use a fuckin’ calculator.
Speaking of cashiers and change, it’s happened to me several times when the amount I’m paying is something like $7.86, and I pull out a $10 bill, then hand over 11 cents along with it. But the cashier just entered the $10 as the amount tendered before they saw me also giving change. The confusion generated is pretty comical. If they had learned their “new” math they would have no problem!
Well, “I’m not certain that math teachers are actually taught to do that” is not the same as “they aren’t taught to do that” or “they don’t do that”, is it?
But, leaving that aside, there is in fact a better prospect that the kids will “just see it”, or that it will be easier for a teacher to get the kids to “see it”, because this method of addition and subtraction is intuitive. We know this because generations of cashiers, without anybody telling them to, have arrived at this method, even though most or all of them had already been taught the older method.
Not really.
87 + 93 =
87 + 100 = 187
-7 = 180. (93 is 7 less than the 100 added)
Break it into blocks of 5, 10 or 100 etc. Add those blocks.
225 + 331
225 + 300 + 10 + 10 + 10 + 1 = 556
How laborious would it be to add, say:
4,131,762
8,675,309
using the new method. My brain explodes.
As far as I can tell, most of the concepts behind common core math are sound and actually really, really good ways to teach and think about math. Concepts that are worth learning and can make your life easier even as an adult if you’re not familiar with them. However, a great deal of the actual teaching material (and some degree of the associated esoteric terminology) is dreadful, and the source of a lot of the confusion.
In this case, you’d likely use a hybrid method. If I were to add these numbers in my head, I’d probably add the following:
4+8
131+675
762+309
And then combine the outputs of those, the individual smaller numbers would be subject to a bit of finagling to make them themselves easier to add. 762+309, in my head, is more like 310+761 (much easier to add if you balance one of them to the nearest 10).
Hmmm… That is in fact how I do it in my head actually: both methods.
I remember “New Math” as the “latest thing” when I was in the higher grades in grade school, it was a big deal in the mid-60’s. (Hence the Tom Leher song). At the time, it was teaching math starting with the basics of number theory, then sets, rings, etc. and operations which yielded closed sets and more.
I attribute it to the wave of new graduates in education theory. When someone is writing a thesis on education, or trying to make a name for themselves - “we’ve been doing it just fine for the last few centuries” doesn’t win any accolades. Instead, it is important to come up with something completely different, and that is exactly what the hippy-dippy new thinkers did in that era. It had the added advantage of enhancing the prestige of the apostles of the new method - “all you parents stand aside and let us teach your kids math. You’ve been doing math all wrong and besides, what we’re teaching is so different that you can’t help them anyway. Only we can…”
There was a similar situation with “whole word reading”; apparently learning the alphabet, then syllables, wasn’t “correct” any longer. This apparently rendered subsequent generations challenged when it came to sounding out unfamiliar words.
(I remember in grade 7 being part of a group being given reading tests for whole word. I didn’t know what it was about at the time, but the film-based gizmo would black out the screen except for one word at a time, and you could set the speed with which it flashed each word. At the end was a reading comprehension test. I got one of the highest scores, because one exercise was about Abraham Lincoln and I had been reading about him before that.)
+1 to this.
Perhaps the new curricula are poorly taught or ill-designed; I don’t know. But I know rotely memorizing and drilling the old algorithms is not tremendously useful either. What’s so important about training kids to be calculators, anyway?
Because there are lots of situations in life where simple mathematical manipulation in your head is advantageous.
I can’t imagine not knowing how to add, multiply, divide in my head with minimal effort.
Of course my 17 year old daughter doesn’t get this and is convinced she’ll just take out her phone and get the answer. :smack:
But if you give them a pocket calculator instead, they are completely helpless without it, unlike the “difficult” and “brute effort” methods you deprecate.
Of course, YOU don’t believe that this new way is the One True Way and nothing else is as good or better. Right?
The 1960s “new math” caused a nosedive in math abilities of students who were subjected to it. Lots of skepticism now is completely justified.
Of course they’re all mathematically equivalent. The problem is that the kids may get confused and learn NONE of those different ways well enough.
I got the same impression. I suspect the TEACHERS don’t fully understand it, or their understanding depends on what they know from learning the old way, which new students don’t know. It seems to me it would be much clearer just to teach them to multiply this way:
47
x35
rewrite as
40 + 7
x30 + 5
Then:
5x7 = 35
5x40 = 200
30x7 = 210
30x40 = 1200
----
1645
Not in the earliest grades, if my own memory is correct.
AND learn this separate method. Fine for people who already know algebra, but not for others.
Well then, why the heck are all these complications being chosen at the same time as the introduction of Common Core? Sheer coincidence?
Common Core is simply a standard, and honestly a very good one. However, individual schools and districts are given basically nigh-infinite freedom in implementing course material that will prepare students to meet those standards.
A lot of the course material manages to utterly fail at effectively communicating the concepts in any sane, reasonable way. Plenty of it conveys the concepts just fine, but only if you have sufficient background to understand it (i.e. not good for kids, but would be good for adult relearners). A very small amount of it is much, much better than the old methods for kids.
Common Core isn’t the problem, it’s the fact that they (by design) didn’t provide any real guidance for achieving those standards, so the usual suspects in the textbook and K-12 course plan industry did a race to the bottom in making new course materials.
The mere assertion does not convince me that this is of significance. What’s wrong with taking out your phone and getting the answer?
I don’t see any real reason to add and multiply 20-digit numbers in your head, but surely you see some value in number sense. The newer common core methods provide, if nothing else, a useful framework for seeing how numbers relate to each other. Having some broad sense of how numbers relate to each other is definitely important for combinatorics, statistics, or even things like graph theory sometimes.
I agree that we place way too much emphasis on correctly manipulating symbols under artificial time constraints, but teaching number sense (of which arithmetic is a part of) is pretty important.
Yes, I agree with that. I am not actually arguing against the newer Common Core methods, which I am not terribly familiar with, and which do seem at least intended to develop “number sense” rather than rote rule-following. I am arguing with the small-c conservative (often anti-Common Core) mindset that insists on kids memorizing and drilling the old algorithms.
I’m all for kids " kids memorizing and drilling the old algorithms."
I find it analogous to not teaching kids to spell, and expecting the spell-checker to work things out for them.
What’s really important in life, and neither old math nor new math really teaches, is numeracy or estimating. What’s 148 times 62? Well, it’s about 150 times 60 - 100x60=6000 plus half that - so close to 9,000. yeah, with a bit of finagling, I can get the correct answer but so can a calculator. Know the “Rule of 70” for interest calculations. And so on. There’s about 2080 work hours in a year at 40 hours a week, so $20/hr means $40,000 a year - divide by 50 to get around $800/week. What’s the bit density of a DVD? (It holds 4.5GB per layer, is 5.25 inches diameter) How far between lines of latitude? (Earth is 8,000 miles diameter, c=2(pi)r, 360 degrees in a circle.)
This is the point - you need to know (memorize) the times tables and do addition or division in your head, and memorize some basic formulas, to fiddle with these numbers. If you need exact numbers, a calculator will do it much faster and Google will give you precise starting values. Being able to estimate will tell you if the numbers make sense - did I miss a digit or screw up a formula? (I walked a friend’s son through the DVD question, then made him show me how big a square his area of the DVD was - he’d used D not R for the area calculation.)
Computers or calculators can do incredible precision, but only humans can bring common sense to the question - just ask Siri, she’ll tell you.
Is anyone here aware that there is a difference between the 1960s-era New Math and Common Core standards for mathematics education?
*Annoyed Employee: * “My name’s Myron, not Moron. Next time don’t take the first word spell-checker gives you!”
*Pointy-Haired Boss: *“What’s spell-checker?”
The point of teaching syllable sounding out of words, is that even the exceptions tend to occur in patterns - “-tion”, “ough”, “ph”, etc. Once a child has learned enough, they will see the pattern and can pronounce a new word even with weird English-type spelling. There’s a good chance they will have heard the word before, even if they have never before encountered it in reading. Whole word gives no such clue.
As for memorizing math tables, the human brain has massive capacity for memorization - the epics like the Odyssey and Iliad were recited for centuries before being written down. The key is to not force memorization at the expense of understanding - or vice versa.