long division; stifles their creativity

[catskills]

After reading this article I want to stop paying my school taxes. What the hell are we paying the teachers for if they don't teach long division anymore. :angry:

Quote from Six Grade teacher,

"We don’t teach long division; it stifles their creativity.’ ”

Any teachers on this forum please feel free to explain this one.

I figured it out. The CIOs from Enron and Worldcom were trained in Fuzzy Math to encourage creativity.

 

[FridayHiker]

Ahem. PLEASE don't get me started on this. I have two elementary school students who are at the top of their class in math. Why? Because I spend a lot of time with them "unconfusing" them after they have been taught six different ways to subtract, all of which get melded in their minds into one very wrong algorithm. Subtraction was the absolute WORST in this regard, though none of the operations are exempt from the problem (they're not to division yet, so maybe that will be worse than subtraction).

There ARE elements of the program that I like, but the computation elements are very, very weak.

Personally, I don't see any need to reinvent the wheel. I think the US should look to countries that are producing the best math students and adapt their program for use here.

 

[roark]

Personally, I don't see any need to reinvent the wheel. I think the US should look to countries that are producing the best math students and adapt their program for use here.

BINGO!

 

[catskills]

Ahem. PLEASE don't get me started on this. I have two elementary school students who are at the top of their class in math. Why? Because I spend a lot of time with them "unconfusing" them after they have been taught six different ways to subtract, all of which get melded in their minds into one very wrong algorithm. Subtraction was the absolute WORST in this regard, though none of the operations are exempt from the problem (they're not to division yet, so maybe that will be worse than subtraction).

H'mm maybe this does work. Parents recognize how bad the teachers are doing, parents get involved, parents teach children, many children do better on tests, and test scores improve in the state. Minor little problem. There are a lot of single parent children that will not get the extra help from mom or dad.

 

[ctenidae]

What, the Whole Language crackpots have gotten to the Math teachers now, too?

I weep for the future.

 

[FridayHiker]

H'mm maybe this does work. Parents recognize how bad the teachers are doing, parents get involved, parents teach children, many children do better on tests, and test scores improve in the state. Minor little problem. There are a lot of single parent children that will not get the extra help from mom or dad.

I've just got to clarify that I LOVE our school's teachers -- they're really terrific and I would never diss them -- and I don't fault them at all for this. In fact, they seem to recognize the "basic fact" issues, and have added fact drills. Unfortunately, curriculum decisions aren't made by the teachers.

 

[JimG.]

I truly understand your pain...we moved to a new school district 3 years ago and math teaching was part of the reason. My kids are now taught math the same way I was many years ago.

Of course, my wife and I spend alot of time with them, but it's more just checking work; we don't have to re-teach them or explain how to do the problems.

Maybe math is creative for mathematicians, but it isn't supposed to be for school kids. There is a math problem and usually one right way to solve it. Saying you don't teach the correct way to solve the problem because it stifles creativity is frightening and borderline criminal in my book.

 

[jack97]

Personally, I don't see any need to reinvent the wheel. I think the US should look to countries that are producing the best math students and adapt their program for use here.

First, I think teachers are the most unvalued profession we have in our society. Often placed in the most difficult positions and yet they remain devoted to their craft. This level of devotion means a lot to me.


Here’s the negative

Other countries are willing to fail a certain percentage of students who do not perform; they are not promoted to the next grade level. In our school system, we have “social promotion”; every one gets promoted, so we compromise academic performance for self confidence. Other countries don’t give many chances, if a student does not show aptitude in math and science they are put in a remedial program or school. So top students are given more resources to hone their skills instead of waiting for the rest of the class to catch up.

The crux of the issue; our school system is trying to get everyone educated in a mainstream way. Initiatives such as; “No child left behind” or “Disparity in Achievement” tends to dumb down the lessons and lowers the achievement level. In Mass. more school systems are eliminating “tracking”, basically grouping the smart kids in separate subject classes and challenging them with harder problems. Such program are deem discriminatory because the lower half of the class do not get access to equal education. They would rather promote mainstreaming and to dumb down the lessons so that everyone can make the lowest level of achievements. The smart kids are not motivated to do more. And are being taught simple and non rigorous lessons that are targeted for the lower half of the class.

I can go on about certain school districts battling against charter schools for public funds. In addition, my strong concerns about Mass legislation and the Governor elect but this would get into politics.

 

[JimG.]

The crux of the issue; our school system is trying to get everyone educated in a mainstream way. Initiatives such as; “No child left behind” or “Disparity in Achievement” tends to dumb down the lessons and lowers the achievement level. In Mass. more school systems are eliminating “tracking”, basically grouping the smart kids in separate subject classes and challenging them with harder problems. Such program are deem discriminatory because the lower half of the class do not get access to equal education. They would rather promote mainstreaming and to dumb down the lessons so that everyone can make the lowest level of achievements. The smart kids are not motivated to do more. And are being taught simple and non rigorous lessons that are targeted for the lower half of the class.

Tracking is a big reason we moved...it's a big thing in the Arlington school district and my 2 oldest boys are in honors classes in all of their subjects. In addition, they go to school an hour early 2 days a week for enrichment classes which are sort of like electives.

It is not viewed as discrimination because it is available to all students...they just have to be smart enough or work hard enough to be enrolled. Totally determined by the teachers too.

And if any group ever tries to eliminate this because it's "discrimination" (it should be more correctly called recognition of outstanding work), I'll enroll my boys in private schools or we will move again.

 

[jack97]

And if any group ever tries to eliminate this because it's "discrimination" (it should be more correctly called recognition of outstanding work), I'll enroll my boys in private schools or we will move again.

You are fortunate; protect it by fighting for it and voting for it.

We lost tracking a couple of years ago; we just enrolled our daughter in math program outside of the school system.

 

[JimG.]

You are fortunate; protect it by fighting for it and voting for it.

You bet, each and every year!

We are fortunate indeed that we live in a district dominated by relatively young professional couples all of whom have 2 or more kids. Everyone is on the same page educationally speaking, and most of us moved there for that reason. I do not believe our school budget has ever been voted down in the past 2 decades.

That's in comparison to our last neighborhood where the school budget was defeated every year for the 11 years we lived there. The demographic there was skewed more towards DINKs and older couples who were empty nesters.

These are issues that are invisible to you until you have kids.

 

[FridayHiker]

I also miss tracking, which was the norm when I was in school. That said, our school is small enough that it would be a bit impractical. They do pull the kids out twice a week for G&T classes -- basically electives, as you describe, but during their normal school day -- and that helps to add interest to their week.

Personally, it doesn't bother me a bit if child A uses a different algorithm than child B to arrive at the same (correct, obviously) answer; I disagree with this statement:

There is a math problem and usually one right way to solve it.

in that there is often more than one way to solve a problem correctly. But what I don't like is the attitude that "Kids don't need to do this because in the real world, they'll use calculators". I completely disagree. I think that conceptually and mechanically, the kids DO benefit from learning long division, or multiplication of multi-digit numbers. When we worked a bit on two-digit multiplication this summer, the kids didn't know the standard algorithm. They knew two different algorithms, one of which involved drawing a complicated grid (not so complicated for two-digit numbers, but much more so for larger numbers), or involved multiplying each of the digits by every other one, e.g.:

38*64=30*60 + 8*60 + 30*4 + 8*4 = 1800+480+120+32=2432 My son came up with the right answer, but if he were to have to multiply a 4-digit times a 4-digit, there would be sixteen different opporunities for errors, which could be as basic as inadvertently dropping a zero.

And like I said, subtraction was even worse.

 

[JimG.]

Personally, it doesn't bother me a bit if child A uses a different algorithm than child B to arrive at the same (correct, obviously) answer; I disagree with this statement:
in that there is often more than one way to solve a problem correctly. But what I don't like is the attitude that "Kids don't need to do this because in the real world, they'll use calculators". I completely disagree.

Point taken...poorly written on my part. My point was supposed to be that kids need to be taught a correct solution to a problem and a framework or system to solve similar problems. To say that long division (and I'll read between the lines and say any generally accepted method of division) isn't taught because it stifles creativity is insane.

Teach the kids a method and then they can get creative if they want to. We're not looking for creative answers, just the right answer.

And I agree with you regarding the sentiment that kids won't use this stuff and will use calculators and computers instead. This "logic" is what condemns me to watching a cashier fumble trying to give change from a cash purchase even when the register does the math for them...they still have to pull the correct change.

 

[ctenidae]

The value in math is not, strictly speaking, being able to add and subract (though both are extremely useful skills themselves). Math provides a way of thinking, a framework for logically describing, then solving, a problem. How you organize the math in your head, whether it's subtraction, long division, or matrix algebra, is an intensly creative process.

 

[JimG.]

The value in math is not, strictly speaking, being able to add and subract (though both are extremely useful skills themselves). Math provides a way of thinking, a framework for logically describing, then solving, a problem. How you organize the math in your head, whether it's subtraction, long division, or matrix algebra, is an intensly creative process.

I do not believe this is what the teacher in FridayHiker's scenario meant when she said that long division stifles creativity.

Children need to be taught methods of solving math problems. This is the framework wherein the creativity you describe takes place. Without that framework, children will not be successful math students. Period.

Long division is an established method for teaching kids how to solve division problems. It also promotes, not hinders, creativity because in this method each step is broken down and the children can see how the division is done. Creativity grows from this type of teaching method.

 

[FridayHiker]

ctenidae, I agree with that as well -- I was on the math team in high school :nerd: and know that it was interesting to compare notes to see how others had approached problems.

But when push comes to shove, it doesn't really matter how creative the thinking is; if someone knows that they have three minutes to administer meds to save someone's life, and multiplies 3*60 and comes up with 300 seconds, you'd better hope that someone isn't you!

Extreme hypothetical examples aside, complete mastery of and comfort with computation in the early grades is pretty critical to being able to deal with more advanced math, not to mention science. I think that the constructivist math programs have emphasized creativity over accuracy to an extent that the students aren't being well served. While I do agree with some of the developments -- e.g. the use of manipulative blocks/bars to enhance understanding of carrying or borrowing -- I think that the programs need to focus on one algorithm through mastery, and THEN examine other algorithms as an illustration that there are other methods that work, and an extension of number sense. The grid method of multiplication that I mentioned above works because it forces the proper numbers into the proper place values. The reasons that it works would actually be a sort of cool thing for maybe fifth graders to explore once they're completely comfortable with multi-digit multiplication. But the kids in the younger grades have no conceptual understanding of why it works, and it's a pretty labor-intensive method, due to all of the drawing involved.

Here's a link if you're not familiar:

http://mathforum.org/library/drmath/view/52468.html

As for the other algorithm I cited, yes, it works, and obviously it's central to algebra once the kids get there. But for computation purposes, it's pretty inefficient.

 

[ctenidae]

But for computation purposes, it's pretty inefficient.

Rote memorization, I think, lays the most efficient computational groundwork possible. Everyone should memorize their sums and gazzintas. From there, you can figure out your personal algorithms.

 

[jack97]

Extreme hypothetical examples aside, complete mastery of and comfort with computation in the early grades is pretty critical to being able to deal with more advanced math, not to mention science. I think that the constructivist math programs have emphasized creativity over accuracy to an extent that the students aren't being well served.

I agree, it's been my conjecture that educators promoting our present method has completely missed on this point. At times, I question their general understanding of math. Exp with my daughter in the lack of adhering to accuracy has been causing behavoiral problems. She thinks that we are highly critical of her work (nit picking). Hopefully by enrolling her in an outside program where accuracy matters she might get the idea how important this is.

BTW, The lattice math approach is a wonderful method in showing structure to the associative and distributive properties of the multiplication operator however spending alot time on it as a computational skill is a complete waste.

 

[ctenidae]

Dr. Warfield said. “That’s why we have so many parents who see their children having trouble with math and say ‘Honey, don’t worry. I never could do math either.’ ”


I think we may have evidence of at least part of the problem, here. Not dinging on the parents here, but parents, in general, have got to take some responsibility for their children's education. It's good to see a significant group doing so.

 

[JimG.]

Dr. Warfield said. “That’s why we have so many parents who see their children having trouble with math and say ‘Honey, don’t worry. I never could do math either.’ ”


I think we may have evidence of at least part of the problem, here. Not dinging on the parents here, but parents, in general, have got to take some responsibility for their children's education. It's good to see a significant group doing so.

No doubt true...parents have to be an active participant. And that does not mean doing the homework for the kids because I know more than a few families that play this game.

But realistically the groundwork, challenge, and grading standards are totally the realm of the school and the teachers. Because none of my exhortations to strive for success and embrace challenge matters a bit if my kids are being taught nonsense and they get an A for doing work well below their capabilities.