[mycroft]

I agree with kenberg here - ballparking doesn't mean "figure out the answer by mental manipulation" to me, it means "get a close enough first approximation to make judgements with/know if the result quoted is so Wrong it's 'out of the ballpark'".

A ballpark approximation of 180 miles (a distance that often comes in handy in Alberta) is 300 km. It's not right - I wouldn't put in a quote for road-building time based on it - but if you try to tell me that the distance between Edmonton and Calgary is 500 km, "50 is 80 and 30 is 50" means that I know you're way out.

[kenberg]

mycroft, on Jul 22 2008, 05:59 PM, said:

I agree with kenberg here - ballparking doesn't mean "figure out the answer by mental manipulation" to me, it means "get a close enough first approximation to make judgements with/know if the result quoted is so Wrong it's 'out of the ballpark'".

A ballpark approximation of 180 miles (a distance that often comes in handy in Alberta) is 300 km. It's not right - I wouldn't put in a quote for road-building time based on it - but if you try to tell me that the distance between Edmonton and Calgary is 500 km, "50 is 80 and 30 is 50" means that I know you're way out.

Some years back I was driving in Canada converting all speed limits into mph. After a couple of days I noticed my speedometer had a second circle of numbers. kph! Much easier.

[kenberg]

jtfanclub, on Jul 22 2008, 05:25 PM, said:

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.

3 gozinta 50 about 17 times.
3 followed by a bunch of zeros, and 50 followed by the same number of zeros. Technically cancellation I guess, but I didn't really think of it that way.

I wasn't so much suggesting testing them on these approximations but more just showing how numbers can be brought down to size that way. Everyone has heard the old Ev Dirksen quote "A billion here, a billion there, pretty soon you are talking about real money". But what is a billion dollars? Impossible to imagine really. Rephrase it as 3 dollars and change from each person in the US and it starts to become a manageable amount.

[ASkolnick]

I think everyone here was missing the point of the article. It's not a matter of what the best method is, but is it OK to teach alternate methods. This is not to do instead of the methods they are currently doing, but say they are other ways to solve the problem

I think parents should supplement there kids education, since school is not the only place of learning. You learn at home, playing with friends, on computers, and yes even by watching TV.

I have a background in secondary school mathematics and once had an educational teacher say you couldn't learn things from the TV. So I posed the question, "who knows the preamble to the constitution?". The only ones who seemed to know it were the ones who learned "School House Rock". So, I think it is important to broaden learning.

The math problem is easy since I can say "you can either solve it via method A or via Method B". Neither method is wrong, it is just a different approach you can take. The problem will occur, when the two methods are in direct conflict with each other "Creationism (Intelligent Design) from Religious School vs Evolution (Public School). My son has had the Religious school background, but not the public school background (He is only 6). That is the time when I will have the issues.


But the problem of concepts versus rote skills, it is sort of teaching someone to run before they can walk. No matter what you do, you still need the basic building blocks of math, reading, and writing before you can move forward.

[matmat]

ASkolnick, on Jul 29 2008, 10:03 AM, said:

I think parents should supplement there kids education, since school is not the only place of learning. You learn at home, playing with friends, on computers, and yes even by watching TV.

Right. I think my original implication was that some teachers seem to not think this way and believe that what they show is gospel and parents shouldn't meddle

[kenberg]

matmat, on Jul 19 2008, 09:51 PM, said:

Quote

Morey, on the other hand, feels no guilt. She says her son was relieved to learn long division. "He wants a quick and easy way to get the right answer," she said. "Luckily, he had a fabulous teacher who said long division wasn't in her plan, but we were free to do what we wanted at home."

http://www.cnn.com/2008/LIVING/wayoflife/0...s.ap/index.html

Is the implication here that, in general, you shouldn't supplement your kids' education at home?

It seems you are asking a compound question: Explicitly you are asking whether the article implies that parents should not supplement their kids' explanation and then I take you to be asking, and most are responding to, the question of whether we agree with such an implication.

As to the article, no, I don't think that the article implies that you should not supplement your kids education. To the extent that it passes on the wishes of educators, it seems to be pleading for some communication and coordination. For example, if a teacher is teaching the standard algorithm for multiplying two digit numbers, I suppose that s/he would be disturbed if a kid pulled out a calculator and announced that his father told him that the algorithm is stupid and that everyone uses calculators now and his father said he should just use his calculator like he showed him. Similarly, to use an example from the article, if the kid was told to multiply 5 times 88 the teacher probably doesn't want to hear about multiplying by 10 and dividing by 2.

Now I realize I have done a little role reversal here since it is the educational system that appears to be advocating the multiply by 10 and divide by 2 approach.

The article, imo, was dashed off with very little thought. When an educator supplies an example such as
"Thus, when a parent is asked to multiply 88 by 5, we'll do it with pen and paper, multiplying 8 by 5 and carrying over the 4, etc. But a child today might reason that 5 is half of 10, and 88 times 10 is 880, so 88 times 5 is half of that, 440 -- poof, no pen, no paper."
then I believe an intelligent interviewer should ask "And how does this modern child multiply 7 times 83?". Perhaps the educator has an answer, perhaps not, but an interviewer who let's someone get away with the sort of stupidity quoted in the article should be reassigned to writing stories about Britney Spears.

The point of the standard algorithm is that once you master it, and it is not difficult to master, then it applies to 5 times 88, to 7 times 83, to 27 times 39, and, if you need it, to 573 times 8472. Those folks, such as myself, who enjoy thinking logically about mathematics can exxplore and understand the logic behind the algorithm. Others can just learn it.

A friend of mine, a very fast thinker and a very creative guy, wrote an article some years back called "In defense of rote learning"

http://www.nychold.c...kin-rote01.html

He begins with a quote from A N Whitehead which I will reproduce:

It is a profoundly erroneous truism repeated by all copybooks, and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of operations which we can perform without thinking about them. Operations of thought are like cavalry charges in battle - they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
- Alfred North Whitehead, Introduction to Mathematics


Anyway, the Math Wars go on. To borrow from Bill Maher, I'm Swiss.

[kenberg]

For whatever amusement value it may provide:

We just returned from the grocery store. Apparently we are enrolled in something like a frequent eaters program and the cashier said we get 15% off our total bill of $179.57 . No one had a calculator but fortunately the cashier was approximately of my generation so she took out a pen and did it my hand. Correctly. Yes I can do it mentally by figuring 15% of 180 dollars is $27 and then subtracting 15% of 43 cents, to get the discount of $26.94 (the cash register then does the subtraction from the total). But we dinosaurs enjoy seeing a fellow dinosaur do her stuff.

This is in contrast to an experience a while back (I may have told this elsewhere):
I was in a fast food place, the lady in the line next to me got her change and said "No, I gave you a hundred dollar bill not a twenty". The cashier, a young thing, checked and indeed this was true. The change for the twenty was, let's say, $7.38. Now things got stuck. No one knew how to void the cash register entry so that the $100 could be entered to find the right change. The cashier asked the adjacent cashier who also had no idea what to do. They went back to the guy frying the fries, maybe he would know. He shrugged his shoulders. I finally intervened with the suggestion that since the lady had given $80 more than was entered, the change should be $80 more than was shown. I looked mature and confident so this was accepted by all. I don't think this plan of teaching the concepts is working out very well in practice.

[matmat]

kenberg, on Aug 18 2008, 10:02 AM, said:

I looked mature and confident so this was accepted by all. I don't think this plan of teaching the concepts is working out very well in practice.

Would you like fries with that?

[matmat]

kenberg, on Jul 30 2008, 05:30 PM, said:

It seems you are asking a compound question: Explicitly you are asking whether the article implies that parents should not supplement their kids' explanation and then I take you to be asking, and most are responding to, the question of whether we agree with such an implication.

It's been a while since i've read this thread.

I think what I had originally in mind was the question whether there is a substantial fraction of teachers who believe that parents should not interfere with their own child's education, and that the existing curricula are the alpha and omega of what a kid needs to know. That seemed to me to be the implication from at least one of the quotes in the article.

As to the cavalry charges etc, yeah, I agree. In that sense we're a lot like ants. one l individual will stumble upon something (either through wit or luck), then they will lay a chemical trail that the rest of us will follow blindly..

[Trinidad]

To reply to the question whether parents are allowed to interfere with their child's education:

Absolutely! I think this is blatantly obvious. Teachers do not own a monopoly on education. And to be absolutely clear: in my opinion, education is the parents' responsibility. In practice, most parents delegate part of the educational task to the specialists: the teachers. Nevertheless, it is the parents' job to manage their children's education (until the children are able to do that themselves) and not the teachers'.

Having said that, it is also clear that 'interfering' shouldn't be the way to go. Supplementing is good, counterbalancing is good, but interfering sounds slightly destructive to me. The best way to go is to communicate with your children's teachers and have something like an educational strategy. What do you want your children to know and what skills should they have (and keep checking whether those goals match their talents)? Communicate that to the school and decide who does what part. If you communicate well, there won't be much interference and a lot of supplementing. Then parents and teachers don't get into each other's way.

Since both parents and teachers are there for the benefit of the children, it seems natural that they cooperate, rather than 'interfere'.

Rik

[kenberg]

I agree with everything Trinidad just said. Supplementing and interfering are quite different. The Boy Scouts supplemented my education. For example I got some sort of merit badge for researching and writing about the history of the town I lived in (St. Paul). Parents vary from minimal involvement (my parents' approach) to "I just have to go in and straighten that teacher out on what's what". And of course teachers vary. Some are very rigid, others more open to input from the home. It would be great if all teachers, all parents, and all children were perfect. Maybe in the next world.

I have always thought the important thing is to not to get into a battle, with the child caught in between. Ultimately, while the child is with the teacher, that teacher has to do things as s/he believes to be right.