Things that make you go hmm...

[EricK]

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]

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]

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]

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]

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]

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]

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]

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]

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. :lol:

[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]

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]

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]

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]

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.com/akin-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]

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]

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