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Wednesday, November 15. 2017
Great, if you assume that inside each little brat is a hidden Euclid or Archimedes or Newton just waiting for the chance to emerge. Since the odds are strongly against that, we have instituted the concept of "education," meaning learning what much smarter people have already figgered out.
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That's how the third world learns arithmetic...and why they are still third worlders.
Well said, Barrister!
AS a mathematician I am completely disgusted by the way math is 'taught' in schools now. If you can't add a column of numbers without a calculator, you are innumerate. Period. If you can't figure out a 15% tip without a calculator, you are innumerate.
Our glorious educators have spent the past 60 years torturing student's minds with 'new math', then the next new thing and finally some liberal arts scoundrels came up with some breathtakingly stupid 'form' that puts the others to shame... Sign. It is no wonder most kids are intimidated by simple fractions.
Give me a reasonably intelligent kid of 16 with no previous math and I will teach them all they need to know through Calculus in less than 2 years, in less than an hour a day. They have to study, by which I mean practice! of course.
Any road, rant mode off... I always pay attention to your posts, Barrister. They are cogent and well written.
Here's my theory of how we got here: They studied intelligent adults and older students to see how they arrived at answers for simple arithmetic. What they learned was that most people who perform calculations quickly and flawlessly have shortcuts such as estimating the answer first or counting by 5s or 10s or using tricks like knowing that the digits of multiples of 9 below 100 always add up to 9. Now here's where they go stupid: they conclude that to be good at arithmetic you must know all these shortcuts.
So that is what they are teaching in K through 5th grade. They teach them to estimate first, to use shortcuts, to think in 5s and 10s and 2s and, the stupidest of all, to work the problems in their head instead of on paper.
This is also what they PhDs in education have done with reading. They noticed that proficient readers do not decode each word through phonetics. And why would someone who has been reading for decades? They do not need to phonetically decode words they've seen millions of times, they've developed automatic reflexes to certain word shapes. But that is what the "educators" are now teaching, sight words and de-emphasizing phonetics.
I think you're spot on. (Estimate of 100% right).
Clever people do what I call "arithmetic exploration" They play around w/ numbers and learn some tricks. Clever people do that b/c that's what clever means.
Other's struggle with those subtleties and abstractions, for them there are straightforward rules that can be internalized by PRACTICE (just like TheCaptain said). That's how schools used to do it, and it worked quite well.
Geniuses take a field farther, using insight and persistence that is far beyond the norm; so it's absurd to expect the norm to be able to approach things in that same way.
I believe even non-clever people build up a supply of shortcuts and reflexes if they perform the same action enough. Everyone, except for prodigies, must learn and practice the basics before going beyond. You wouldn't take a 15 year old on their birthday to Richard Petty Driving School; that's something adults do after they've learned and practiced the basics of driving for years. But here we are taking that 15 year old out to a track and telling him or her how to take fast lines through the corners when they can't even take off in 1st without stalling the car.
From what I've read, even prodigies (John Nash and others) practice A LOT.
Clever people don't need as much rote practice before things become automatic, which misleads some education professionals into concluding that they don't use rote at all, and that therefore everyone can dispense with it.
Clever people also notice when they try something and it gets terrible results, in which case they try something else. Not so many education professionals.
Bingo. I've been saying this for years about reading. They have their binoculars backwards and have confused aptitude with results. More or less they have cause and effect reversed.
"[t]he first standards gave a strong call for a de-emphasis on manual arithmetic in favor of students' discovering their own knowledge and conceptual thinking."
Bing search: discovery learning doesn't work. Over 52 million hits.
Which brings forth a long standing pattern in Ed Schools. Latch onto the NEW THEORY THAT WILL EXPLAIN EVERYTHING. Teach the NEW THEORY THAT WILL EXPLAIN EVERYTHING in the Ed Schools before it has been thoroughly tested. Five to ten years later, the research informs us that the NEW THEORY THAT WILL EXPLAIN EVERYTHING doesn't work. No problem. The OLD NEW THEORY THAT WILL EXPLAIN EVERYTHING is dead. Long live the NEW NEW THEORY THAT WILL EXPLAIN EVERYTHING. Rinse and repeat.
There is a need for pedagogy, as it is not intuitively obvious how to teach a given material to a given age group. Instead of teaching prospective teachers what HAS WORKED in 2,500 years of formal classroom instruction, the Ed School profs try finding the NEW THEORY THAT WILL EXPLAIN EVERYTHING.Considering the idiots populating the Ed Schools, it is a wonder that any Ed School student becomes a competent teacher. For the most part, they become competent teachers by ignoring all they were taught in Ed School.
A couple of things, math has always been hard for some and almost 50 years ago when I was in college I had an evening job running all of the front end of a large store with 16 cash registers employing high school girls who worked from 4 to 9 each day after the day cashiers went home. I had to teach those young ladies how to make change and figure discounts on sale merchandise and this was before the neat handheld calculators.
Very few of them had any idea that multiplying the sales amount by .8 would yield a 20% discount. They also had preprinted charts they could use for reference but without understanding the basics of percentage they were lost.
Today it is much worse and my wife who is old like me and retired has a degree in accounting with a CPA and she tutors math most days of week and she hates the 'new math' which she tries to understand in order to help the students learn. She thinks its nuts.
When I ask one of my good friends who is a retired grade school principal what he thought he said it has been nutty for a long time. His take is that the school book people always have to come out with a new and better book to improve scores which are not very good. Now in order to repair all of the nut job math they have been teaching for decades they make it new which just causes more confusion.
All I know is that when I get a cup of coffee, pull out a five while the kid enters it into the register and then give him the exact 71 cents to add to the two dollar price plus tax and all I need is three bucks back he is lost. No idea how to really make change.
Got o learn the basics first; without calculators or other aides. Just repetitive BS , until you get it! Then you can work out the shortcuts.
As for reading, used to love debating the "see-and-sayers" among the elementary ed crowd, most of whom couldn't find their asses with both hands, but they had an opinion on that, usually "inherited" from one of their favorite Dewey-ite profs!
I think the answer to the impossible common core question is 12 or any positive multiple of 12. Easy enough to figure out but likely was beyond my skills in the 4th grade.