Things that make you go hmm...

[matmat]

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?

[HeavyDluxe]

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

I don't know that I got that implication from the article. But I have no sense for the subtle.

 

At any rate, we homeschool... So, no fight with the school district there. The NEA? Well, that's a different matter.

[onoway]

Some thoughts which immediately come to mind:

1) that there is assumed to be ONE optimum way to teach so all kids learn equally effectively, which is an asinine assumption.

2) that using a concept based method of teaching math rather than a practical one will be more effective for most kids, .and I would love to see the studies that came up with that result

3) I'm not at all sure what the goal of it is supposed to be. Most kids won't become mathematicians, and if kids used to say, "what's the point of this"??.. and they did..what can you say to them when even their parents can't find a connection to "real"life?

4) I might be more sympathetic if kids could at least make change without having to rely on calculators and cash registers..if your bill is $6.79 and you give them $7.04 many of them would be totally lost...

 

Home schooling looks more and more like a rational choice.

[jtfanclub]

4) I might be more sympathetic if kids could at least make change without having to rely on calculators and cash registers..if your bill is $6.79 and you give them $7.04 many of them would be totally lost...

I don't mind 'ballpark'.

 

Ballpark tells you immediately...

 

The right answer ends in '5'.

The amount will be less than $1 but more than 0.

 

This is far better to me than the people who could figure out the answer by writing it down, but when they go to the register they try to give me the wrong change because they fat-fingered it. I find ballpark far more useful than column addition or long division in real life. Don't you?

[matmat]

4) I might be more sympathetic if kids could at least make change without having to rely on calculators and cash registers..if your bill is $6.79 and you give them $7.04 many of them would be  totally lost...

I don't mind 'ballpark'.

 

Ballpark tells you immediately...

 

The right answer ends in '5'.

The amount will be less than $1 but more than 0.

 

This is far better to me than the people who could figure out the answer by writing it down, but when they go to the register they try to give me the wrong change because they fat-fingered it. I find ballpark far more useful than column addition or long division in real life. Don't you?

sure the ability to estimate a figure is useful and often sufficient to whatever is required.

but my concern has nothing to do with whether this is math being taught, or biology, or sociology, or chemistry, or history, or religion, or wtf knows what else.

 

my concern is that there is an implication in the quoted blurb that there are teachers out there who tell parents NOT to introduce other aspects of a subject at home. i.e. "we don't teach long division in school, as it is not in the curriculum and therefore you, as a parent, shouldn't either."

 

This reminds me of a somewhat unrelated thought ... back in the equivalent of junior high when we had to learn the various cell organelles some parents were in an uproar that their kids had to learn names like "endoplasmic reticulum" or "golgi apparatus" etc. the kids just couldn't do it... but, of course, if you asked these same kids to name italian sports-cars and whatnot, the mazerattis, ferraris, lamburghinis rolled off their tongues fluently...

[jtfanclub]

my concern is that there is an implication in the quoted blurb that there are teachers out there who tell parents NOT to introduce other aspects of a subject at home. i.e. "we don't teach long division in school, as it is not in the curriculum and therefore you, as a parent, shouldn't either."

 

This reminds me of a somewhat unrelated thought ... back in the equivalent of junior high when we had to learn the various cell organelles some parents were in an uproar that their kids had to learn names like "endoplasmic reticulum" or "golgi apparatus" etc. the kids just couldn't do it... but, of course, if you asked these same kids to name italian sports-cars and whatnot, the mazerattis, ferraris, lamburghinis rolled off their tongues fluently...

I don't have an opinion on that. How about when it's a direct contradiction, such as when the school is teaching that the earth is 5 billion years old. Is it ok for the parents to teach if it's 5,000?

 

We used to write rap songs that would use words like 'endoplasmic reticulum'. This was back when rap first came out, so it wasn't gangsta or anything. But it turns out to be much easier to remember stuff if you put it to a beat.

[onoway]

Insecure teachers have always tried to limit what involvement the parents have with their kid's education. I ran into this when I was in school, when my father corrected incorrect factual information concerning agriculture, much to the teacher's ( and principal's!)indignation. Years later I had one suggest I was a bad parent because my kids were not supposed to be able to read before they got to school.. it wasn't important that for them books were sources of delight and information. The teacher found it inconvenient. Two examples, there are many.

 

It is so much easier if the kids are in lockstep and don't challenge.

 

It isn't just in schools either. I was visiting someone in a university office one day when there was a huge kafuffle next door. Apparently a graduate student had had the temerity to challenge his prof about something. The prof, ( who had tenure), offered the highly pertinent information that if said student didn't shut up and agree he would toss him down the stairs. (This same prof refused to talk to me for several months after I beat him at chess).

 

Good teachers don't need to teach in a sterile environment. Unfortunately really good teachers are not the norm.

[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).

 

Going over the topics they have already done at school and perhaps showing them a different way to do things is less problematic, as is extending that to cover stuff that won't be covered in class at all.

[Trinidad]

I am a scientist in Physical Chemistry in my forties. In elementary school, I learnt long division. Do I find it useful in today's world? NO. And if I, with a daily need to do multiple calculations and a lot of mathematics, don't find it useful, I doubt that it really is useful to anyone else today.

 

My grandfather learnt the method of 'long roots' in elementary school. For those of you who don't know this method (I guess most of you): It is a method to calculate the square root of a number and it is has striking similarities to the long division method.

 

When I was about 15 or so, my grandfather taught me how to calculate square roots with the long root method. Of course, the method wasn't needed since we had calculators for that (and slide rules before that). What was interesting is that my grandfather had remembered the method for 50 years (despite the fact that he surely never used it in real life).

 

But the crucial difference between the two of us was that he could explain how the procedure for the long root method worked, while I could understand why it worked and what the underlying mathematics were (because my grandfather learnt mathematics on a procedure basis and I on a concept basis). But this small lesson by my grandfather taught me how to convert mathematics into procedures, which helped me to learn computer programming.

 

I don't know whether my kids are going to learn long division in elementary school. (In a way, I hope not, what are they going to use it for?) If they don't, I might well teach them when they are 15 or so. I would teach it as a curiosity, which might inspire them to link the new way of looking at math to the old ways. But I wouldn't teach it because I think long divisions are useful in a society where these kids have owned their own computer since they were 2 years old...

 

Rik

[PassedOut]

Some thoughts which immediately come to mind:

1) that there is assumed to be ONE optimum way to teach so all kids learn equally effectively, which is an asinine assumption.

 

<snip>

 

Home schooling looks more and more like a rational choice.

By 1998, our three boys had lost interest in school because of the slow pace of instruction, so Constance and I gave them the choice of switching to home-schooling. They all chose home-schooling and stayed with it for three, five, and six years respectively.

 

For the first few weeks, home-schooling went slowly too, but then the natural drive to learn kicked in and they began to investigate one subject after another as deeply as they chose and without artificial time limits. In a special program for high-schoolers, a small local college agreed to accept our sons for a class or two each semester on such subjects as laboratory sciences. (Our middle son took life drawing classes there too, something he definitely could not get at home!)

 

When it came time to attend college full time, all three were top students. However, our youngest was recruited early by an internet company willing to pay him a lot of money, so he left college before graduating. Of course his mother and I would like to see him finish college, and he says he plans to do so, but nothing yet...

[onoway]

EricK Posted on Jul 20 2008, 04:15 AM

" 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)."

 

This is PRECISELY the point I was trying to make. Where, in that paragraph, is there a concern for that child's education? Are a teacher's only options for the brighter and/or more advanced kid to penalize either by isolating or by trying to force back into the mainstream and pretending he or she is NOT ahead of the class, as though it's something shameful?

 

Definitely there are far too many kids in most teacher's classes. However, there are ways within this which can operate to everyone's benefit, one being to have the kids who are ahead help the kids who are behind. This was very common in the days of mixed classes. Kids learn better from other kids anyway, many times, AND it establishes a value in the eyes of both the kid who is ahead and the other kids. The teacher has demonstrated respect for accomplishment and it brings into play on a very basic level, the concept of social responsibility.

 

. For sure this requires a bit of time and monitoring, esp. at the beginning, but at least this is constructive time which is spent otherwise in dealing with the problems mentioned above. Some teachers still do this naturally, others are horrified at the idea that a kid can do what they do, sometimes better.Also, this is only one way of dealing with the situation, there are others.

 

This whole question brings into focus, exactly what is the point of education supposed to be? Hopefully NOT the idea that there is only one way to get there from here, when there might be any number of ways to do so. Some need the straightest route possible, others enjoy exploring along the way.

[kenberg]

I generally believe in supporting the efforts of teachers.

[onoway]

http://www.thehumorarchives.com/joke/Physics_Exam

[P_Marlowe]

Hi,

 

How do they teach divison "concept" based? What is meant with this?

 

As a matter of fact: I believe that the starting point of Math is boring,

it is similar to learning how to read and write: First you learn the hard way

to speak single letters, than come small words, ....

Of course you can make it more entertaining using competive games,

e.g. who gets the right answer first, ... but it is boring.

 

As a matter of fact: "Long division" is a "concept", and so is simple

formula transformmating, if you cant do this in praxis (and you need

to train this), you will fail, and not only in Math, but in Physics, Chemestry

as well.

 

With kind regards

Marlowe

[kenberg]

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.

[jtfanclub]

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.

[Al_U_Card]

Ballpark really is superior for most things.

Especially franks (Things that make you go .... yuummmmmm) B)

[Trinidad]

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.

Ken,

 

It frightens me that someone would suggest that 255/15 should be calculated by long division. JT pointed out that ball park works just perfect.

 

Anybody with a 'feel' for numbers will 'calculate' this in a fraction of a second:

 

255=256-1=2^8-1=(2^4+1)*(2^4-1)=17*15 => 255/15 = 17.

 

Long division is good for complex divisions when you have paper and pen available but not a computer or a calculator. (And even then, in 9 out of 10 cases, the fastest (and most reliable) solution to the problem is to go and find a calculator.)

 

In essence, you have proven my point. I would prefer that they teach my kids to calculate with binary numbers, and hexadecimals, so that they have a good understanding of what numbers really are. On top of that they need to understand basic mathematic equations, such as (a+b )*(a-b )=a^2-b^2 and how they can be applied, like in your example. I find that much more important than that they can follow a recipe and do long division. I prefer the teacher who can teach my kids the concepts, rather than the recipes.

 

Rik

[Trinidad]

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.

Exactly. If my kid would approach this problem and the first thing he could say about the answer is: "It starts with the number 1", I would most certainly start talking to the teacher. Fortunately my oldest is only 7 and I do get the idea that his school is teaching by concepts. So I'm not there yet and I am fairly confident that I won't get to this situation.

 

Rik

[skjaeran]

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.

[kenberg]

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]

http://www.thehumorarchives.com/joke/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]

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.