[kenberg]

skaeran, on Jul 21 2008, 01:54 PM, said:

kenberg, on Jul 21 2008, 02:59 PM, said:

Long division is easy, harmless, and occasionally useful. It's possible, for example, that a person might want to know the price per widget if 15 widgets are being sold for $255. At least some people feel more confident if they can work this out themselves even if they may have a calculator at hand. Part of education is giving people justified confidence in their own abilities.

Now about the easy part: The procedure is very simple. To carry it out the child needs to know how to multiply and how to subtract. If he finds this difficult, then he has not learned how to multiply and subtract. This should be addressed.

I'd do this in my head like this:

255/15 = 225/15 + 30/15 = 15+2 = 17.

I would do it as 15^2=225 and we need 30=2X15 more so it's 17. But that's me. Of course it can be done in other ways. But so what? It's not like learning long division will do them any harm. It's one more tool and they can use it at their discretion.


As to concepts, I am all in favor of learning concepts. I don't remember learning long division (it was probably on a Friday) but for some reason I do recall the more difficult task of learning my multiplication tables, even though it was earlier. There were concepts galore. I would practice catching a ball, bouncing it off the steps, and intermittently practice multiplication. I had some difficulty with remembering that 7X8=56 while 9X6=54. I would check myself by adding the numbers in my head. This reinforced the concept that 7X8 is the sum of seven eights. It also reinforced the concept that the sum of seven eights is the same as the sum of eight sevens. Similarly for 9X6. Moreover, in an attempt to keep it straight I realized that as you move numbers closer together, keeping the sum the same, the product gets larger. For example 8X4 is larger than 9X3. So 82X93, whatever it is, is larger than 81X94. Another concept.

Setting a mental task for a child is apt to lead to conceptual learning. Learning long division is probably too simple to demand much in concepts, but it is good preparation for learning how to divide one polynomial by another. The child who knows long division can just say "Oh, division of polynomials works just like division of integers". Indeed it does, and in fact the analogy doesn't end there at all. For example, the Euclidean Algorithm (based on division) for polynomials works exactly like the Euclidean Algorithm for integers, and pretty much for the same reasons. This explanation is meaningless to a child who does not have a good grasp of division.

Long division won't damage the child's brain. It may do him some good.

I recall learning in school something along the lines of Hail to thee blithe spirit, bird thou never wert. Now that was useless. Is "wert" actually a word?

[RichMor]

What do you - as a citizen and as a taxpayer - really expect from public education?

I think public education is a basic necessity for a basic purpose; a functioning democracy requires a population that can intelligently participate in the process of governing.

Here is a quote from Thomas Jefferson.

". . . whenever the people are well-informed, they can be trusted with their own government; that, whenever things get so far wrong as to attract their notice, they may be relied on to set them right."

The public schools are not designed to prepare our children for rewarding careers, or admission to good universities, or other personal goals. The schools are designed to deliver a basic minimum level of education to the largest number of people.

Various current 'accountability' programs (No Child Left Behind etc) are based on reducing the number of failing students. There are no rewards for schools that produce a large number of high-achieving students. Please don't expect the teachers or administrators to spend their time and efforts to produce the next Nobel prize winner.

If you don't think the public schools are serving your children's best interests then your reasonable options are private education and/or home schooling. I have a lot of respect for parents who put in the effort to home school their children. We bit the bullet(financially) and sent our son to a private school instead.

I have no respect for the persistent complainers. It's just another case of the 'entitlement' mentality where some parents expect the public schools to take a responsibility that belongs to the parents.

[vuroth]

onoway, on Jul 20 2008, 10:05 PM, said:

http://www.thehumora...ke/Physics_Exam

Classic!

[onoway]

"I have no respect for the persistent complainers. It's just another case of the 'entitlement' mentality where some parents expect the public schools to take a responsibility that belongs to the parents. "


I guess the subject of the thread was too far back for you to remember what it was...

Of course, it isn't every family who is able to manage either private school or home schooling ..such as most single parents..so I guess too bad for the kids with the bad planning to be born to those parents. After all, why should we expect anything much from the school system anyway? It's not like we are paying for it.....oh........wait a minute......

Btw I don't deny there are some excellent teachers out there. My youngest daughter went to a public school where history was taught by a historian, phys ed by an ex olympic gymnast, art by a working artist etc. Some private schools would drool over the staff there. Every teacher there was teaching something he or she had a real interest in and enthusiasm for. That's contagious. That's the way it should be, imo, but so often teachers are in such and such a class because they had some free time in the schedule. Not fair to teacher or kids.

[cherdano]

EricK, on Jul 20 2008, 03:15 AM, said:

I can understand from a teacher's point of view why they would not want the parents to "teach ahead". A child who is bored because he is being taught stuff he already knows can be very disruptive, yet giving that child his own, more advanced, work to do, separate from rest of the class, can lead to that child being picked on by the other kids (and leads to more work for the teachers, who are already overworked as it is).

I agree, smart student's are a pain in the ass for teachers, parents should all raise their children equally dumb.

[EricK]

cherdano, on Jul 22 2008, 05:28 AM, said:

EricK, on Jul 20 2008, 03:15 AM, said:

I can understand from a teacher's point of view why they would not want the parents to "teach ahead". A child who is bored because he is being taught stuff he already knows can be very disruptive, yet giving that child his own, more advanced, work to do, separate from rest of the class, can lead to that child being picked on by the other kids (and leads to more work for the teachers, who are already overworked as it is).

I agree, smart student's are a pain in the ass for teachers, parents should all raise their children equally dumb.

They should teach them to behave themselves in class.

[brianshark]

Lets see... 15 goes into 25 1 time, carry the 10... 15 goes into 105 7 times. 17.

[kenberg]

brianshark, on Jul 22 2008, 04:43 AM, said:

Lets see... 15 goes into 25 1 time, carry the 10... 15 goes into 105 7 times. 17.

Yes. It hardly seems excessive to ask that teachers teach this (in this short form or in the long form) and that children learn this.

The problem, I think, is that teachers are confronted with kids who because of past non-learning are not able to say things such as "15 goes into 105 7 times". The response has been not to correct this deficiency but rather to work around it. Since "work around it" doesn't sound so hot someone with a bright future in marketing decided to refer to the work-around as the teaching of concepts.

[mycroft]

I couldn't care less how you work it out - frankly, LD would work well for me, even if I could work it out in my head. Accurate and timely beats elegance any day (although, elegance is COOL).

Lots of neat tricks - and I wouldn't have thought of the simplest, doubling and making it easy (although I have done it before, in other cases) - but I can do 105/15 in my head, without thinking hard. Yeah, I did it the LD way, but who cares?

What's important for ballpark is, frankly, to get the first digit and within a power of 10 of the result - because 99% of the time, any keypunch errors will be caught by those two. For smaller/money numbers, getting within a power of two works well enough for non-accounting tasks.

I used to go out to dinner with a bunch of Engineering Grad Students; they'd work out the bill to the penny, with tax and tip. By the time they were done, I had my money out and done, and could usually go and start the car; because, even as a student, if I was within 25 cents of it, 'twas okay. I could see Math geeks not getting it, but the first thing they teach you in Engineering is precision and significant digits, and the fact that 10.0m of steel costs $X, but 10.00m costs $5X, and isn't their time worth 12 cents or so?

[kenberg]

Hey, don't dis the math geeks. From my experience we math types are less rather than more likely to just divide the bill by the number of folks at the table. If I have had more to drink than the rest (very likely) I throw in an extra bill of roughly appropriate size. Just because we can do the accounting doesn't mean we want to.
I was, like your friends, once a grad student and with very very limited finances. But then I didn't eat out so the issue of dividing the bill did not arise.

[y66]

re: OP's question: Is the implication here that, in general, you shouldn't supplement your kids' education at home?

The implication, for me, is that reasoning is more important than rote learning and specific procedures.

Here's something I just read by John Holt that made me go hmm:

“The most important thing any teacher has to learn, not to be learned in any school of education I ever heard of, can be expressed in seven words: Learning is not the product of teaching. Learning is the product of the activity of learners.”

I love that.

[P_Marlowe]

y66, on Jul 22 2008, 12:12 PM, said:

re: OP's question: Is the implication here that, in general, you shouldn't supplement your kids' education at home?

The implication, for me, is that reasoning is more important than rote learning and specific procedures.

Here's something I just read by John Holt that made me go hmm:

“The most important thing any teacher has to learn, not to be learned in any school of education I ever heard of, can be expressed in seven words: Learning is not the product of teaching. Learning is the product of the activity of learners.”

I love that.

Brilliant.

How to play a instrument? Using reasoning or rote learning,
tell you what they do a lot of rote learning.
And rote learning is one way of getting the brain to learn.

As it is, you need both:
If you just go via reasoning, most of the guys will node, saying
they got it, but just ask them after while later, and they have
forgotten it, because they never trained it.
... I see this regular in my job, I tell / explain the stuff to the guys
the node, move on, and one week later they ask again.
Rote learning is nothing else than practice, practice and practice.
Of course if you just go via practice, you wont get the grand
picture.

With kind regards
Marlowe

[matmat]

jtfanclub, on Jul 21 2008, 09:07 AM, said:

kenberg, on Jul 21 2008, 07:59 AM, said:

It's possible, for example, that a person might want to know the price per widget if 15 widgets are being sold for $255.

30 widgets sell for 510 dollars
3 widgets sell for 51 dollars
1 widget sells for 17 dollars

Ballpark gives you an exact number that time. Pulling out a scratch pad and a pen so you can do long division on it seems kinda pointless.

With the exception of some savants or really easy problems, long division isn't something you do in your head. Maybe short division? 10 leaves (100+5)/15?

The sad one is when people who know long division start to calculate it when 15 widgets cost $299. Ballpark really is superior for most things.

lol...
you just did a bunch of multiplication and division in your head and call it BALLPARK?!

[matmat]

cherdano, on Jul 22 2008, 12:28 AM, said:

EricK, on Jul 20 2008, 03:15 AM, said:

I can understand from a teacher's point of view why they would not want the parents to "teach ahead". A child who is bored because he is being taught stuff he already knows can be very disruptive, yet giving that child his own, more advanced, work to do, separate from rest of the class, can lead to that child being picked on by the other kids (and leads to more work for the teachers, who are already overworked as it is).

I agree, smart student's are a pain in the ass for teachers, parents should all raise their children equally dumb.

In fact, there should be a mandatory labotomy at age 3.

[matmat]

kenberg, on Jul 22 2008, 11:30 AM, said:

Hey, don't dis the math geeks. From my experience we math types are less rather than more likely to just divide the bill by the number of folks at the table. If I have had more to drink than the rest (very likely) I throw in an extra bill of roughly appropriate size. Just because we can do the accounting doesn't mean we want to.
I was, like your friends, once a grad student and with very very limited finances. But then I didn't eat out so the issue of dividing the bill did not arise.

hehe

it's funny. In my experience you NEVER give the bill to the math major, and you NEVER give the bill to the engineering or accounting student. Typically the physics/chemistry/bio types got stuck with the task of doing the arithmetic...

Also, had some friends visit from Europe last summer. I had to get them a little credit-card sized tip indicator

[kenberg]

I didn't get the idea that the author of the article was advocating either way. He was reporting that some parents in fact do try to teach their kids to learn specific old way academic skills that they believe to be valuable. Some don't.


My parents: Virtually no involvement whatsoever with the schools or in directing my education. One exception: During my high school years if we had a heavy snow my mother would call and say I was sick so I could make some cash shoveling out driveways. It's remarkable how willing people were to believe that the school was closed if their driveway was full of snow and I was there with a shovel.

Me, with my kids: Modest involvement. When my older daughter turned forty I asked her if she remembered the quadratic formula. Sorta.


Grandkids: It varies.

My oldest grandchild is now 15. When she was young her parents watched over her education rather carefully. Like hawks, actually. I was more interested in making sure she knew how to ride a bike. A proper role for a grandparent I think. She took a pretty bad spill when I was out with her and I thought oops, this might be tough to explain. When we got back she somehow forgot to mention this spill to her parents. Last summer she went on a ride from somewhere in Vermont up to Montreal. But I think she is taking calculus or maybe AP statistics this fall so the academics are OK.

Somewhere along the way I am pretty sure that she learned long division.

[mycroft]

I wasn't dissing the Math geeks - at least not that way. I would never assume anyone would split down the middle; I expected the Math people to be more likely than the 'Gearheads (okay, I ride the lightning, and took exactly enough hardware credits to get my degree, but still, I wear the Iron Ring) to work out their bill, plus tax and tip, to the penny.

I expected the engineers to work out that within a quarter is good enough - I was Very Wrong. I don't expect Mathies to work out anything that practical - they stop using numbers in second year, and the English alphabet middle of 4. And remember:

"Mathies can't count, Engineers can't add."

[jtfanclub]

matmat, on Jul 22 2008, 01:19 PM, said:

you just did a bunch of multiplication and division in your head and call it BALLPARK?!

Yes, Ballpark is when you manipulate an unfamiliar equation to one that's familiar to you so that you can solve it, then either you calculate the difference by the remainder or you simply remember that there is one.

It's easier to see with multiplication.

"I don't know what 15x17 is, but I know what 15x15 is, so ballpark is 15x15+2x15"
"I don't know what 15x17 is, but I know what 30x17 is, so I'll do 30x17 and divide by 2"
"I don't know what 15x17 is, but I know what 16x16 is, and I know that N-squared equals (N+1)(N-1)-1. So I'll use 16x16 and subtract 1"

That's how you use ballpark. Takes some knowlege of math, but it's very effective. It's more than just rounding (though rounding is certainly part of it).

[kenberg]

jtfanclub, on Jul 22 2008, 02:47 PM, said:

matmat, on Jul 22 2008, 01:19 PM, said:

you just did a bunch of multiplication and division in your head and call it BALLPARK?!

Yes, Ballpark is when you manipulate an unfamiliar equation to one that's familiar to you so that you can solve it, then either you calculate the difference by the remainder or you simply remember that there is one.

It's easier to see with multiplication.

"I don't know what 15x17 is, but I know what 15x15 is, so ballpark is 15x15+2x15"
"I don't know what 15x17 is, but I know what 30x17 is, so I'll do 30x17 and divide by 2"
"I don't know what 15x17 is, but I know what 16x16 is, and I know that N-squared equals (N+1)(N-1)-1. So I'll use 16x16 and subtract 1"

That's how you use ballpark. Takes some knowlege of math, but it's very effective. It's more than just rounding (though rounding is certainly part of it).

This is in fact how I do a number of simple calculations. I wouldn't myself call it ball parking but it can be useful.

To me, ballparking is more like: A government program is going to cost 5 billion dollars. There are 300 million people in the US more or less. So it will be about 17 bucks a person, man woman and child.

I see this as different from 15 times 17 is (16+1)(16-1) = 256-1 -255.


Both are useful, I think they are different, I call my example ballparking. But I won't insist.


I think children should be taught how to estimate roughly and to know rough relationships. For example, the Sun's diameter is about a hundred times the Earth's. Not anywhere near accurate of course, but it is useful to know that the ratio is not around 10 and not around 1000. The distance from the Earth to the Sun is about 100 Sun diameters, so about 10,000 Earth diameters. The Earth's diameter is about 8.000 miles. OK we get the distance from the Earth to the Sun is 80 million miles instead of 93 million. It's a ballpark estimate.

Children learn too little of this by far. Sure it would be nice if they (and I) knew exactly when the Battle of Gettysburg took place. But placing it in the early 1860s would at least keep them from looking foolish. Most people are forgiving of a little uncertainty here, I certainly am since I make many errors myself, but if someone thinks maybe it was in 1920 he looks like a dodo.



Anyway, I don't want to get sidetracked by a semantic debate but whatever you wish to call the above sort of information I would like to see children learn some of it.

[jtfanclub]

kenberg, on Jul 22 2008, 03:53 PM, said:

There are 300 million people in the US more or less. So it will be about 17 bucks a person, man woman and child.

I see this as different from 15 times 17 is (16+1)(16-1) = 256-1 -255.


Both are useful, I think they are different, I call my example ballparking. But I won't insist.

But how did you get there? It's not fair to take 5 billion and 300 million and say "well, it's about 17". How did you figure that out?

Did you round 5 billion to 5.1 billion so it would come out even?
Did you factor out and end up with 50/3?
Did you notice that 5x6=30 and then take the decimal of 1/6 and multiply it by 100?
Did you use long division?

Personally, if I were a high school teacher, I'd be tempted to give kids 50 questions like these on a test and tell them that they had 500 seconds to solve them +/-10%. And yes, 500/60 would be the first question.