Join 3,554 readers in helping fund MetaFilter (Hide)


Math Education: An Inconvenient Truth
September 6, 2008 3:02 AM   Subscribe

Math Education: An Inconvenient Truth. How children learn (or: don't learn) math today.

The video explains the new ways children are taught division and multiplication and what is wrong with new new math (not to be confused with the new math that was taught in the sixties) or whole math.

From the textbook in the video:The authors of Everyday Mathematics do not believe it is worth students’ time and effort to fully develop highly efficient paper-and-pencil algorithms for all possible whole-number, fraction, and decimal division problems. Mastery of the intricacies of such algorithms is a huge endeavor, one that experience tells us is doomed to failure for many students. It is simply counter-productive to invest many hours of precious class time on such algorithms. The mathematical payoff is not worth the cost, particularly because quotients can be found quickly and accurately with a calculator.
posted by davar (130 comments total) 28 users marked this as a favorite

 
Awesome, I get to use a rant I've been saving up.

Cheap fast computers have allowed for professional quality video editing, and modern networking has enabled the sharing of this video to a global audience. It pains me to see that people use it for propagandist pieces, just like those in the past have.

In the first seconds of the film we have scaremongering music coupled with an ominous pan. There are no links to a transcript, making it difficult to verify claims. The organization that sponsored and created the movie isn't listed, I had to go find it myself:

Where the Math


It just seems like, whenever one of these videos comes up, they use the capabilities of the medium to obfuscate and prey on the emotion. It leaves a bad taste in the mouth, especially when I agree with them. Perhaps amateur video hasn't developed the artifice to make the sell not seem like a sell.

I also don't personally like them because I can read much faster than they can talk,
posted by zabuni at 3:38 AM on September 6, 2008 [2 favorites]


Oh, and here's a nice critique from the other side.
posted by zabuni at 3:43 AM on September 6, 2008


When I have to multiply things in my head when I'm in a store I use the nasty TERC method, which nobody ever taught me but is an effective way of doing it when you can't write anything down. I think it should be taught to children because it makes them think and reason through a problem rather than doing it by rote.
posted by Turtles all the way down at 3:44 AM on September 6, 2008 [4 favorites]


Oops, that a critique from another video by the same people, here's a critique on the video in question.
posted by zabuni at 3:46 AM on September 6, 2008 [1 favorite]


I use the TERC method to do things in my head (which I was never taught either) and I do think it should be taught, but only to supplement algorithms.
posted by ValkoSipuliSuola at 3:52 AM on September 6, 2008 [3 favorites]


I use the TERC method to do things in my head (which I was never taught either) and I do think it should be taught, but only to supplement algorithms.
Me too. I also think there is some value in new math. Sometimes estimates are enough. If I am in a store, and a 69.95 dollar dress is 30% off, I don't need to know exactly how much it costs now, it is good enough if I understand that 30% of 70 dollars is approx. 20 dollars. But sometimes accuracy does matter and sometimes you do not have a calculator.

I used to work as a cashier. If a customer had to pay 5,15 and they paid with a 10 note, we would ask if they had 15 cents, so we could give them a 5 note back. Sometimes the customer did not have 15, but did have 20 cents. We would then, of course, give 5,05 back. I see more and more cashiers who do not grasp this concept (both as a customer and as someone who worked in a shop). Their cash register tells them what to give back, and even if that is 4.99, they do not want to take my 1 cent to make it 5 dollars and they sometimes even look at me as if I am crazy for suggesting it because the machine said 4.99.

I thought the video was a nice, though skeptical, introduction to new math. It was really strange for me to realize that I cannot help children with math anymore, because I have no idea what they are doing with all the boxes and the lines. I had no idea that children do not learn long division anymore. Now at least I understand how it is supposed to work and I will be able to understand my child's homework a little better.

One of the examples in the book was: 36/6. You had to give two methods to calculate that, and show the in-between steps. I have no idea how to do that. 36/6 is just 6 in my head, that's not something I "calculate".

I agree the video was propagandistic (unlike zabuni, this is one of the things I love about the web, that anyone with an opinion can make it known to the world, and I do not see how things were better when only certain people had the privilege to do that), but I think the conclusion is useful: if your child is struggling with math, it may help to teach him/her yourself with traditional algorithms.

We also discussed thread math education before.
posted by davar at 4:32 AM on September 6, 2008 [1 favorite]


Please read 5.15 and 5.05 instead of 5,15 and 5,05 if you live in a country that uses dots as decimal seperators (and forgive my other typo's).
posted by davar at 4:37 AM on September 6, 2008


I don't see the problem with partial products compared to the standard algorithm? To me they look like the same method written slightly differently; if anything with partial products makes place value a bit clearer.

Likewise with partial quotients division - same method, slightly clearer presentation.

If the methods aren't being taught satisfactorially I agree that's a problem, but I don't think the methods being taught are at fault.
posted by Mike1024 at 4:43 AM on September 6, 2008




I agree with the metereologist, the most efficient and least error prone method is the one she showed first. All the others methods are much more error prone as they involve more steps.

If I am in a store, and a 69.95 dollar dress is 30% off, I don't need to know exactly how much it costs now, it is good enough if I understand that 30% of 70 dollars is approx. 20 dollars.

Personally, I do like this:

Considering the 70 bucks, which is a reasonable rounding, you can quickly estimate that 10% is one tenth or 7 bucks (70/10=7) as we get much used to base 10 arithmetic. 20% is just two times that, so it's 14 bucks (7x2). 30% is three times that, or 21 bucks (7x3)

Now for 33% , you know 30% is 21 buck so all you need 3%. But 3% is just 3 times 1% and 1% is 70/100=0.07 , times 3 it's 0.21 or 21cents. So 33% of 70$ is 21.21$

36/6 is just 6 in my head, that's not something I "calculate".

That's the effect of rote multiplication table learning, I concour it's useful for many small numbers. It is a good foundation, but one shouldn't just "know in head" how to obtain the result, an algorithm allows to do without a calculator should the need arise and it's a good practice for small number operations.
posted by elpapacito at 4:51 AM on September 6, 2008


If a customer had to pay 5,15 and they paid with a 10 note, we would ask if they had 15 cents, so we could give them a 5 note back. Sometimes the customer did not have 15, but did have 20 cents. We would then, of course, give 5,05 back. I see more and more cashiers who do not grasp this concept (both as a customer and as someone who worked in a shop). Their cash register tells them what to give back, and even if that is 4.99, they do not want to take my 1 cent to make it 5 dollars and they sometimes even look at me as if I am crazy for suggesting it because the machine said 4.99.

You should see the looks I get when the total is $4.27 and I give the poor cashier $10.02. I swear sometimes I think the girl's head is going to explode!
posted by ValkoSipuliSuola at 5:20 AM on September 6, 2008 [6 favorites]


That's why I only pay with plastic these days...
posted by zwemer at 5:28 AM on September 6, 2008 [1 favorite]


I teach the Everyday Math curriculum to 4th graders. I hear (a few) complaints from parents because we aren't teaching kids "the right way," which you may translate as "the way I learned how to do it." (Oddly enough, this often corresponds to parents who say they hated math.) That's pretty much what this woman's argument amounts to.

Note, in the video that she says of the partial products method: "This works, and it gets you the right answer every time, but I get confused about which number to add to what." It's new and unfamiliar to her -- and therefore wrong.

In defense of partial products, I'd say this: It gives you the magnitude of the problem right away. I am very heretical and I teach kids to multiply left to right. So 26 x 31 equals, roughly, 20 x 30, or 600. Now we know the answer is of the same magnitude as 600. This is more useful than knowing that the answer ends in 6.

In other words, there's a continuum from orders-of-magnitude estimates to precise answers. Also, you can do partial-products in your head (try it), which few people can do with the traditional algorithm. I've seen kids who were ready to jump ahead do this, taking on the tough ones in their heads instead of on paper.

I will say that kids love the lattice method. Love it. Personally, I think it's a gimmick -- it doesn't take you inside the number the way partial-products does. But the traditional algorithm doesn't either.
posted by argybarg at 5:43 AM on September 6, 2008 [9 favorites]


I agree the video was propagandistic (unlike zabuni, this is one of the things I love about the web, that anyone with an opinion can make it known to the world, and I do not see how things were better when only certain people had the privilege to do that

Quantity != quality. Especially for information. Misinformation is worse than no information at all. I wouldn't put the genie back into the bottle, as I feel that empowering people is a good in it's own right but I don't believe that world wide video creation by amateurs has lead to a greater amount of good content, and any good content that has come from it is overshot by the sheer volume of bad content.

I think part of it is the medium. Give people the ability to distribute text around the world, and you get awesome link upon awesome link, as metafilter has surely shown. Global distribution of sound gives us the likes of podcasting and metafilter music. Global distribution of video gets us youtube.

I don't see a flowering of useful political discourse coming from movies like these. Just extremist viewpoints sandwiched between propaganda. Just by a few simple word searches I was able to find several rebuttals to the above piece, the group's website, and a newspaper article about the group. In comparison, the video's informational bandwidth sucks and the signal to noise ratio is through the roof.

I love the ability for everyone to post their opinion online. It just seems that most people who do so in a video fall into the trap of preying on the emotions. They seem to do so less in other mediums.
posted by zabuni at 5:44 AM on September 6, 2008


argybarg: as a teacher, do you recognize the concerns that children cannot do simple sums in their head anymore? In the Time article someone said that her straight A algebra student child reached for a calculator to find 10% of 470. To me, after seeing the video, this seems like something that they should be very good at, better than children who learn with the traditional method, but apparently not?
posted by davar at 6:08 AM on September 6, 2008


My mom taught me the "traditional algorithm" before we did long multiplication at school. I could do it and solve the problems just fine but I had no idea how it worked. We learned the "partial products" method at school and it turned on a lightbulb in my head. I still used the old method but I was much better off later in math knowing how my algorithm worked.
posted by martinX's bellbottoms at 6:17 AM on September 6, 2008


A college math professor did a video response to these (part 1, part 2) that said all I wanted to say. It is really important for students to get a basic understanding of what's going on, a basic theoretical grounding, or they're going to come up with answers that aren't remotely sensible. And when they start using calculators, as they inevitably will, they won't be able to realize that their answers aren't sensible. So, yeah, teach them about orders of magnitude and estimation and why things work the way they do!
posted by Jeanne at 6:18 AM on September 6, 2008 [1 favorite]


her straight A algebra student child reached for a calculator to find 10% of 470.

Doing this problem via pencil-and-paper algorithm would be as bad as reaching for a calculator. Either one demonstrates that the student is missing a fundamental mathematical skill: recognizing easy problems.
posted by escabeche at 6:42 AM on September 6, 2008 [6 favorites]


From the response video:Oh, and interestingly, the "standard algorithm" isn't really standard after all. Talk to folks from other countries sometime and ask them to multiply and divide for you.
The reason that I found the video so interesting was that I recognized these boxes and lines and suddenly realized that they are not yet another Dutch school reform test-thing, but an actual international new method. In the Netherlands we were taught long division (though maybe in a different way, I don't know that), and since the first video recommends Singapore math, I assume that people in Singapore learn it that way too.

And when they start using calculators, as they inevitably will, they won't be able to realize that their answers aren't sensible.
But if they now use a calculator to calculate 10% of something, do you think they really have a grasp about which answer is sensible?

So, yeah, teach them about orders of magnitude and estimation and why things work the way they do!
But didn't they do that before in the US? In my country, there were no calculators in elementary school (until age 12), but calculators were required in high school (age 12-18). In elementary school you learned the basics, in high school you learned how and why it worked and how to apply it. We also did math games. I don't see the dualism here, but it seems like people who are in favor of new math say old math was just rote learning and boring sums that had no relation to reality at all and people who are in favor of old math say new math is only scratching the surface of calculating things. Surely there is a way to make math interesting and relevant, while still making sure that children can easily calculate things without a calculator?

I think I also heard about the lattice method in school, but that was more for children who had trouble with math, as an extra, different method.
posted by davar at 7:12 AM on September 6, 2008


This makes me grumpy. Schoolboy multiplication isn't the best algorithm for big numbers (Karatsuba algorithm), but more to the point, I suppose, is that spending the first n years of one's mathematics education having addition, multiplication, subtraction, and division hammered into one's skull is a stultifyingly drab way to learn some very uninteresting mathematics. And then to have poorly informed high school teachers who tell you that you should still run away shrieking when there's a pole in a function definitely numbs the brain.

I once talked to a superintendent of a school district who believed in teaching to the test -- well, he seemed to believe that tenth graders ought to be minimally able to solve linear equations. I'd like to believe that by twelfth grade, mostly anyone could solve the quintic (yes, it doesn't have a solution in root extractions and algebraic operations, I know, but add some theta functions into the mix, and you can do some nifty things.

Start kindergardners on one-two-three and you're going to fall into the same tired nonsense that pervades school districts and math education in general today. Start them on rubik's cubes, and they'll have group theory in their bones.
posted by oonh at 7:15 AM on September 6, 2008


zabuni: I do agree with you that videos are sometimes irritating as a medium. I liked the video I linked to, because it helped me understand what this new math is, and seeing her write out the sums was different and more clear than reading it in an article, I think. But the rebuttal video's that Jeanne linked to are just someone talking. In that case, I much rather read a transcript, because indeed, I do read much faster than I listen.
posted by davar at 7:23 AM on September 6, 2008


First -- her rationale for why she got involved just doesn't hold water. She says she was upset by her classmates lack of mathematical proficiency when she went to UW in 'the late 1990s.' But if you look at the TERC website you learn that the book she is complaining about was developed around 1990:

In 1990, TERC’s leadership in mathematics research and curriculum design led to National Science Foundation support for Investigations in Number, Data, and Space, a comprehensive elementary mathematics curriculum, published by Scott Foresman.

So her classmates, mostly 18-year olds, were about 10 years old when the TERC curriculum was developed. Uh-oh. In all probability their lack of mathematical proficiency correlates with precisely the instructional strategies she is advocating. Most of them were taught using a more traditional, algorithmic approach.

But we already knew that. We have ~100 years of evidence that traditional approaches to mathematics do not in general foster mathematical literacy. I am sure that this woman means well. But advocating for a return to the good old days based on shoddy reasoning and anecdotal evidence is not a recipe for progress. Lee Shulman: "It seems that in education, the wheel (more usually the flat tire) must be reinvented every few decades."

I once heard Alan Schoenberg talk about education. His claim was that education research today is where medical research was in 1915: There is a whole lot more that we don't know about education than what we do know. But -- NSF-funded curricula like TERC is based on what we do know about what works and what doesn't. And so it is an attempt to base curriculum development on a scientific or engineering approach. As the website says, the materials are in revision. That is, they are looking at how the materials are being used and are revising based on what is working and what isn't. If we can continue to do this -- if we are able to keep the culture warriors at bay -- your kids will have better math education than you did, and their kids in turn.
posted by Killick at 7:24 AM on September 6, 2008 [2 favorites]


Here's my thing I'm of the opinion kids should have complete mastery of Multiplcation and Division before they leave 3rd grade. 5th is a bit late to me. I mean damn if kids can do Literature analysis in the third grade they can be done with multiplication that's possible. In fact for me none of the ways shown is the most intuitive way to understand multiplication for me its understanding the X in multiplication is analogous to the words "groups of".

I think so many people have the illusion that math is a science and that it is taught in a symbolic language as opposed to the native language of the people speaking. In America, Math is taught in english. It is a formal language with logical construction and that means its implications are stronger than other languages but if we add something illogical due conjecture, the math is right but the answer is still wrong. I think Math and Modern English both have the same problem. The need to educate both structure and subtle form, the need for both brute force mastery and a subtle grasp. In English to have the grasp of both Logic and Grammar but also the ear and the mind to make what is logical intuitive and harmonious sounding. In Math, A sound computational founding but also the ability to pull out the heart of a problem, find your own patterns and form elegant solutions. Given that these two are literally the foundations for all other classes this is a very serious issue.
posted by Rubbstone at 7:31 AM on September 6, 2008


All the methods have their uses. It seems like what she called the 'standard algorithm' would be the easiest starting point, but I know I'm biased because that's the way I learned it. I'm pretty sure that learning any one method and just being able to grind through it is not very useful.

On paper or with a calculator - these are pretty low-value scenarios in which to be able to solve a problem. In my life, I want to figure something out on the spot in my head, or I have a full-blown computer available. The calculators found in classrooms today are defined by whatever is allowed to be used on standardized tests. There has not been one single math problem I came across since college where I would have thought to reach for one of those convoluted anachronisms.
posted by Bokononist at 7:52 AM on September 6, 2008


I teach incoming freshmen in college calculus, and yes, I've seen kids reach for a calculator to do 4 x 20, and it hurt me in the bottom of my soul. But this isn't because they didn't know that (4 x 2) x 10 = 8 x 10 = 80, it's because the calculator was "easier".

So, while I think the demonization of calculators is a complete non sequitur, I still don't disagree entirely with this (shrill, vile) woman. The TERC method is neat - for kids in high school or middle school. For grade school kids, teach them the fastest, most efficient, least error-prone algorithm. And that algorithm is the standard one.
posted by TypographicalError at 7:56 AM on September 6, 2008


An earlier MetaFilter thread discusses a long essay about the lamentable state of mathematics education, in which both the reform curriculum and the traditional drilling of algorithms come in for much derision.
posted by escabeche at 7:57 AM on September 6, 2008


The division algorithm states that given two integers a and d, with d ≠ 0

There exist unique integers q and r such that a = qd + r and 0 ≤ r <>

Proof

posted by metastability at 8:17 AM on September 6, 2008


should be "r < |d|"
posted by metastability at 8:19 AM on September 6, 2008


Is our children adding?
posted by Saxon Kane at 8:20 AM on September 6, 2008


I learned the "standard" algorithms in school, but I switched to the TERC method (on my own, as it wasn't taught) so long ago that I wasn't really sure what the woman was doing in the video at first. The standard algorithm for multiplication does give you the right answer, but it gets you to that answer with little understanding of why you've arrived at that answer. It simply isn't intuitive and it isn't useful at all for doing calculations in your head (long division is even worse). I wish I'd learned the TERC method in school instead of wasting my time with silly algorithms that I'll never use.

It makes much more sense to teach the TERC method because as soon as children have access to calculators, they are going to use the calculator unless they are able to multiply in their heads fast enough that using the calculator would be a bother. No one is going to write out some silly algorithm on paper instead of just punching it in.
posted by ssg at 8:23 AM on September 6, 2008


you aren't going to fight this believe me. the teacher's union is the strongest around. just teach your own children the real way to do math (and this advice was given to me by several math teachers)
posted by caddis at 8:24 AM on September 6, 2008 [1 favorite]


We learned the "partial products" method at school and it turned on a lightbulb in my head. I still used the old method but I was much better off later in math knowing how my algorithm worked.

That is, in fact, the reason these methods are used. A fundamental, intuitive understanding of How Math Works is invaluable.
posted by five fresh fish at 8:24 AM on September 6, 2008


As a teacher, I teach my students several methods and let them use the one they find easiest and most comfortable for them. As long as they get the right answer and know why, I'm cool with that. Although, one thing I did insist on was memorization of basic addition/subtraction/multiplication and division facts (up to 12 x 12), no way around that.

I do find these non traditional methods discouraging for parents though as it makes it much more difficult for them to help their own children with their homework and studies.
posted by NoraCharles at 8:34 AM on September 6, 2008 [6 favorites]


I agree with the metereologist, the most efficient and least error prone method is the one she showed first. All the others methods are much more error prone as they involve more steps.

When I tell people how to get to my house from the airport, I do not give them the most efficient directions, because the the quickest way to get to my house also makes it very easy to miss my house. Approach my house from the west, and I can tell people to turn right after the only wooden fence on my street between the second and third light. The most efficient route would have people coming from the other direction, and there is nothing to get people to notice my house from this direction until it's too late. Go the long way, and you will get to my house. Go the short way and you will miss it.

Having fewer steps doesn't make an algorithm less likely to produce incorrect answers. Several of the alternate algorithms shown in this vid are much more likely to produce correct answers when used by kids who haven't completely memorized their multiplication tables yet.
posted by 23skidoo at 8:38 AM on September 6, 2008


I expect my kids to think about things mathematically, and as a result of this, inevitably they will be able to multiply and divide by fifth grade... because how could you not? This woman wants her kids to DO MATH because you are SUPPOSED TO, and by god, if they didn't, her head would explode and shatter that helmet of hair.
posted by selfmedicating at 9:03 AM on September 6, 2008 [1 favorite]


The main point of the video is: "kids learn math differently than you did, shouldn't that be a problem?".
posted by dobie at 9:16 AM on September 6, 2008


you aren't going to fight this believe me. the teacher's union is the strongest around. just teach your own children the real way to do math (and this advice was given to me by several math teachers)

Could you fill in a few steps for me, caddis? Because although it's probably unfair of me, without a little more detail my best guess as to how your comment was generated is this:

Check playbook:
Problem with education? Cause --> Teacher's unions.
Solution: --> Home schooling.

And what does the real way of doing math even mean?
posted by Killick at 9:17 AM on September 6, 2008


Math Education: An Inconvenient Truth. How children learn (or: don't learn) math today.

This tempest highlights a pet peeve of mine. Notice that the teachers and parents are arguing about methods, because math is different, and methods matter. Secondary Math education is a failure because kids associate fear and anxiety with math and hardly anyone notices even when they pile into college courses to relearn it all. The anxiety problem is related to deadlines, because math is abstract and isn't an extension of memory and language like most courses rely on when communicating the information. Students simply fail to comprehend math in a certain amount of time, and instinctively they know it will ruin their other grades if they try. So they do what they can. Most of them reach out to a tutor somewhere. The school-based solution would be to never fail anyone at math and only pass them at mastery level by testing, no matter how long it takes. This can be cheaply accomplished in tutor labs under teacher supervision, by having the gifted kids tutor the average ones at school, regardless of age or grade.
posted by Brian B. at 9:18 AM on September 6, 2008 [1 favorite]


Math? I just carry an iPhone so I can google the answer to 26 * 31.
posted by blue_beetle at 9:37 AM on September 6, 2008


so I can google the answer to 26 * 31.

Googling 26 * 31 returns only 1 result. I'm not sure if I can trust it.
posted by daniel_charms at 9:52 AM on September 6, 2008 [2 favorites]


Secondary Math education is a failure because kids associate fear and anxiety with math
I don't know about other countries, but I do know that I see this MUCH more in US children (and parents) than in the Netherlands. When I was researching homeschooling as an option, I read a few homeschool mailing lists, and American people honestly seemed terrified about math, even if they were not worried at all about teaching their children to read and write.
posted by davar at 9:53 AM on September 6, 2008


Ugh, what a bitch. She's basically arguing that we need to go back to the "old way" of teaching "math" (actually, arithmetic) which kids hate. Kids taught the way she wants math taught won't become fluent users of math, rather they will grow to hate it, and never peruse higher types of math, and as adults, they'll use calculators.

We don't need a world full of people who can 'efficiently' use a pencil and paper to solve problems. Why would we? The TERC example is taught because it's much easier to do that kind of math WITHOUT a pencil and paper.

Anyway, people like here are the ones who are holding back mathematics education in this country.
posted by delmoi at 9:56 AM on September 6, 2008


Well, there is that, and the problem that public school curricula are forced into using a single textbook and methods with a cohort of 30-odd students at different stages of development.
posted by KirkJobSluder at 9:57 AM on September 6, 2008


This woman is the Sarah Palin of math education.
posted by delmoi at 10:21 AM on September 6, 2008 [1 favorite]


I don't think that this video was in any way like propaganda. It proposed a hypothesis - that the two curricula presented did not lead to mastery of and confidence in math by a certain point - and in the course of its 15 minutes it presented a series of well-supported arguments, based on the curricula themselves including direct quotations, as well as directly demonstrating what it was talking about by presenting and analyzing the math itself. Characterizing expository persuasion that doesn't attempt to misdirect or deceive as "propaganda" is pejorative and silly.

argybarg: I teach the Everyday Math curriculum to 4th graders. I hear (a few) complaints from parents because we aren't teaching kids "the right way," which you may translate as "the way I learned how to do it." (Oddly enough, this often corresponds to parents who say they hated math.) That's pretty much what this woman's argument amounts to.

It amounts to far more than that - she quotes directly from the authors:
The authors of Everyday Mathematics do not believe it is worth students' time and effort to fully develop highly efficient paper-and-pencil algorithms for all possible whole number, fraction, and decimal division problems.
They're intentionally teaching a less effective and incompletely developed understanding of mathematics, in their own words. And later they actually cite "you could just use a calculator" as a justification for teaching arithmetic more poorly. (She doesn't point this out directly, mind - she just reads the quote and lets the viewer decide if that's a valid approach.)

When I was in school and when I've taught math, the Standard Method of multiplication and long division were integral parts of the way subsequent topics in higher math were presented - for multiplication and division of polynomials, for example. I am curious as to how the TERC and Everyday Mathematics authors deal with that kind of stuff, or whether they just leave it for other people to teach.

selfmedicating:I expect my kids to think about things mathematically, and as a result of this, inevitably they will be able to multiply and divide by fifth grade... because how could you not? This woman wants her kids to DO MATH because you are SUPPOSED TO,

I do not think that this is inevitable as you imagine it to be. In 2001 I taught high-school math in a New England public school for a semester. One of the classes I taught was Algebra I to some of the top-level freshmen and it was a horror show. Many of them seriously needed remedial training in arithmetic, it was a while before we could even get into reviewing the algebra they'd learned in previous grades. And these were the very best students in a school of 3000.

She didn't get into the reason why mathematics is an important part of education. But it's pretty imputing to suggest that she just thinks you're "supposed to" learn math, I doubt she would answer the question that way.

The reason we need kids to be proficient and confident in mathematics is because we need to have an educational system that provides the foundation for a 21st century economy.

I think mathematics needs to be taught in much better ways in the US but the tack taken by these curricula is just punting in response to the problem: it's meeting the challenge of teaching math by teaching less of it to make it less challenging for the teachers and the people with textbook authoring contracts, not for the good of the students. This is a method of screwing our descendants as certain as not dealing with climate change.

I work in the computer industry here in the US and this is one of the reasons that we keep having to import large numbers of Chinese and Indian programmers and scientists to keep the industry chugging. Right now we're getting the best people from those places and others (as we've been for the last couple decades and more) but they aren't always going to want to (or have to) move to the States to get the kind of job they want.
posted by XMLicious at 10:31 AM on September 6, 2008 [4 favorites]


They're intentionally teaching a less effective and incompletely developed understanding of mathematics, in their own words. And later they actually cite "you could just use a calculator" as a justification for teaching arithmetic more poorly.

Arithmetic is not all there is to mathematics. You can very easily teach mathematics better while teaching less arithmetic. That this woman doesn't differentiate between mathematics and arithmetic is pretty damning.

Putting the words "less effective and incompletely developed understanding of mathematics" in the mouths of the authors when they wrote no such things is just silly.
posted by ssg at 10:38 AM on September 6, 2008


Can someone explain to me what the metrics of "Efficiency" are? I get the feeling that she is doing the whole let-me-use-technical-sounding-jargon-to-give-a-veneer-of-science move, but I could be wrong.

ps - that partial product technique seems pretty cool.
posted by Hypnotic Chick at 10:42 AM on September 6, 2008


Arithmetic is not all there is to mathematics.

Arithmetic is the foundation of most of the types of mathematics used in science and industry. We need to teach more of it and teach it better, not less.

Putting the words "less effective and incompletely developed understanding of mathematics" in the mouths of the authors

I didn't do any putting words in anybody's mouth: I quoted exactly what the authors said themselves. If you don't like what I said about it, go ahead and say so and articulate a disagreement with me rather than throwing out rhetorical implications that I've lied.

Can someone explain to me what the metrics of "Efficiency" are? I get the feeling that she is doing the whole let-me-use-technical-sounding-jargon-to-give-a-veneer-of-science move, but I could be wrong.

Efficiency is the term that the authors of the textbooks are using as well as her.
posted by XMLicious at 10:47 AM on September 6, 2008


She's basically arguing that we need to go back to the "old way" of teaching "math" (actually, arithmetic) which kids hate.
But why do American kids hate arithmetic, while children in other countries, who get teached arithmetic using the same algorithms, do not hate arithmetic? I am not saying that we loved it, but it was just another class, just like reading and writing.

The TERC example is taught because it's much easier to do that kind of math WITHOUT a pencil and paper.
But why then, do today's children grab a calculator to calculate 4x20? Shouldn't children who are brought up with those new methods see instantly that 4x20=80?
posted by davar at 10:51 AM on September 6, 2008


Ugh, what a bitch. She's basically arguing that we need to go back to the "old way" of teaching "math" (actually, arithmetic) which kids hate.

Yes, a difference in education philosophy is worthy of being referred to with a sexist epithet. Your point is so well made.
posted by Dreama at 10:53 AM on September 6, 2008 [2 favorites]


All the multiplication algorithms in the video are equally valid. If a student really understands multiplication, they will easily see the methods are all isomorphic. If they understand the underlying concept, who cares if they use calculators for everything?

And this comes from the Texas Mental Arithmetic champion of 1979.
posted by king walnut at 11:11 AM on September 6, 2008 [1 favorite]


Interesting discussion. I remember that the New Math version of long division killed me way back when in Grade 3 because I just couldn't "get" the logic of it. Finally, with a little help from my dad, I improvised a variation on the TERC method ... and voila it all just clicked and has never troubled me since (ie: I now happily use the New Math algorithm).

Bottom Line: algorithms are great for machines but growing minds need to first grasp the concepts which under-lie them. Who f***ing cares if a 10 year old can't quickly calculate the answer to 91 X 73? Let him use a calculator.
posted by philip-random at 11:11 AM on September 6, 2008


I should say, I don't think that the conventional progression of mathematical topics is necessarily all that great and in general I think there's all kinds of room for innovation in mathematics education. For example, I think it's kind of absurd that we wait until after completely spelunking through algebra before starting or even touching on calculus; you could teach quite a bit of introductory calculus to someone who just has arithmetic and the concept of a variable down.

But arithmetic is broadly foundational, not to mention instrumental, and should not be neglected. A solid ability and acumen in arithmetic is as important in mathematics as knowing the periodic table is in chemistry or as having a versatile vocabulary is in composition.
posted by XMLicious at 11:14 AM on September 6, 2008


I didn't do any putting words in anybody's mouth: I quoted exactly what the authors said themselves.

Where are you getting this quote from?
posted by ssg at 11:26 AM on September 6, 2008


They're intentionally teaching a less effective and incompletely developed understanding of mathematics, in their own words.

That's completly false. In fact, it's the reverse of what's true. They are trying to create a greater understanding of mathematics, but focusing on the fundementals, at the expense of mastery of a particular, arbitrary algorithm for doing arithmetic. And by the way Arithmetic is only a small part of "mathimatics" which covers elementary algebra, calculus, linear Algieba, computer science, statistics, etc, etc, etc.

Having an understanding of arithmetic is important for learning math, but being able to do base-10 addition/subtraction/multiplication/etc with a pencil and paper using a particular algorithm that was developed for people who's job it was do do that kind of math all day because computers had not been invented yet is not really important.
posted by delmoi at 11:37 AM on September 6, 2008


The central issue seems to me to be whether we're trying to prepare children to do arithmetic in daily life as adults, or to learn higher math as teenagers. If with the new methods they're getting an intuitive understanding of the distributive and associative laws early on, that's going to help them learn algebra and calculus in high school, which is vital if they're going to have the option of becoming engineers.

On the other hand, the idea that "kids who don't need higher math skills don't need arithmetic either" seems dismissive of the advantages of being able to do sums and find areas accurately by hand if you're a carpenter, or selling rugs, or splitting the check. Maybe all that's needed is an arithmetic elective in high school for the students who aren't taking calculus?

(I myself got 800 on the math SATs back in the '80s when that wasn't so easy, and was a math major in college, and I don't remember any of those "real" arithmetical algorithms; that long division example in the video was opaque to me.)
posted by nicwolff at 11:37 AM on September 6, 2008


Where are you getting this quote from?

The quote that I presented above and commented on, the indented portion of the text here (my commentary, on the other hand, being what you asserted I was putting in their mouths) is from 10:15 in the video, where it is both displayed on-screen and read aloud.

The (spoken) citation within the video says that it's from page 132 of the Teacher's Reference Manual For Everyday Mathematics, Grades 4 through 6. This video was very carefully and empirically made and for the most part just directly presents what it says in the curricula themselves, without the kind of commentary l and others have been making here; that's why I think calling it "propaganda" or calling the narrator a bitch is ridiculous and pejorative.
posted by XMLicious at 11:44 AM on September 6, 2008 [1 favorite]


A solid ability and acumen in arithmetic is as important in mathematics as knowing the periodic table is in chemistry or as having a versatile vocabulary is in composition.

As in, it's not really that important at all.

Being able to do elementary arithmetic on paper is nowhere near as important as understanding the Peano numbers in actual mathematics.

Knowing the periodic table is nowhere near as important in Chemistry as understanding that it is a rhetorical construction — and like all others, it's at its best a clever abstraction and at its worst a misleading indirection.

Having an expansive, orthogonal, vocabulary is nowhere near as important in composition as having read a great deal in order to develop a knowledge of the corpus of possible structures.
posted by blasdelf at 11:51 AM on September 6, 2008 [1 favorite]


But arithmetic is broadly foundational, not to mention instrumental, and should not be neglected. A solid ability and acumen in arithmetic is as important in mathematics as knowing the periodic table is in chemistry or as having a versatile vocabulary is in composition.

Well, obviously people should know the basic idea of multiplication, division, etc but I've taken some pretty advanced math and I don't recall a situation where I've needed to do basic arithmetic on paper in order to solve a an algebraic, or calculus problem. You either had a situation where you could use a calculator, or you'd just need to 'set up' the problem. And often the final result would simply be another equation.

I haven't done multiplication longhand like that since elementary school. Seriously. Like many people I 'discovered' the TERC method or something like it on my own. Rather then applying an algorithm, I decompose the numbers on my own and multiply them that way. There may be more steps but the components are much easier to remember.

Those methods were developed at a time before computers were prevelent, and there were a lot of jobs where people just sat around and crunched numbers all day, with pencil and paper. Obviously you'd want to use the least error prone, most time efficient way to do it -- but in today's world that's pointless. The "math jobs" out there are things like engineering -- you need to be able to apply really advanced math and you'll be using a pretty hard core computer to do the grunt work. Or computer engineering where you'll be programming math circuits in base-2, or doing other exotic math.

Basic pencil and paper math is really pointless in today's world. It serves no purpose, If you watch the response video someone posted, you can see how talks about how being able to do that really gives you no deeper understanding of the core numbers, while the TERC method does.
posted by delmoi at 11:51 AM on September 6, 2008


This video was very carefully and empirically made and for the most part just directly presents what it says in the curricula themselves, without the kind of commentary l and others have been making here;

Bullshit, they're extracting the most inflammatory stuff, and pulling out the most difficult and confusing examples. Just because you present 0.01% of a book does not mean you're giving it a fair hearing.

And if she thinks this stuff is so horrible, why does she think the worlds mathematicians and scientists are pushing it? is it some conspiracy to make kids stupid in order to reduce the supply of scientists and thus increase their salaries?

that's why I think calling it "propaganda" or calling the narrator a bitch is ridiculous and pejorative.

Of course it's propaganda, and if this woman had her way more kids would grow up hating math.
posted by delmoi at 11:54 AM on September 6, 2008


Okay, I teach math at the college level, including remedial courses, so I will jump in.

I blame teachers who are forced to pass students who have not learned the material because their principals tell them they are failing too many students.

Until teachers are allowed to give students the grades they actually deserve, I think the issues being discussed here are irrelevant.

As far as the topic at hand is concerned, underprepared students seem to need very straightforward, one approach teaching. When I teach Beginning Algebra, and I am teaching students how to solve equations, I teach them the way that I have found easiest for THEM to understand, not necessarily the way I know to be more efficient, and the method I might teach if I was reviewing solving equations in a higher level course.

Also, different students find different approaches to be easy; I am skeptical that "one method" of teaching arithmetic algorithms will necessarily be the best approach for every student.

What we really need are math specialists teaching math in elementary schools, to take some of the pressure off elementary school teachers who consider math to be their weakness. (Not a snipe at Elementary Shcool teachers; it is very tough to be able to teach all subject areas. Since Math is a problem in the U.S., however, it might be nice to have a specialist be responsible for all the teaching at a school in this one area.)
posted by wittgenstein at 11:57 AM on September 6, 2008 [3 favorites]


Would someone kindly and briefly explain the TERC method to me? I can't seem to find any kind of description, and now it's driving me mad. I'm not very mathy, so I've not heard of TERC before this thread.
posted by Stewriffic at 11:58 AM on September 6, 2008


This might be a relevant link while this topic is being discussed.


I link to this article because I think it emphasizes the degree to which what we do in Elementary School really can have serious effects when students get to higher level math courses.
posted by wittgenstein at 12:01 PM on September 6, 2008


Would someone kindly and briefly explain the TERC method to me?

It's explained rather well in the first few minutes of the lead link. First she gives the "traditional form" of long multiplication, then the TERC version.
posted by philip-random at 12:11 PM on September 6, 2008


I'm afraid I began watching the video, noticed it was 15 minutes long, got through the part about her being a local meteorologist, was distracted by her bangs, and then clicked it off.

I'll go back and soldier on. Thanks.
posted by Stewriffic at 12:14 PM on September 6, 2008


Since you don't seem to be picking up on it XMLicious, I'll spell it out:Basically, she's a sophist hack. She reserves self-awareness for herself and her audience, and refuses it to students and parents.
posted by blasdelf at 12:19 PM on September 6, 2008 [3 favorites]


I think I use a simple version of TERC all the time, despite having learned math in school using traditional methods. I never mastered the higher numbers of the multiplication table, for example, and I've forgotten most of the entire table now.

If I had to multiply 23*40, for example, I'd double 23 in my head and then double it again. But if I had something more like 23*42, I'd use the traditional multiplication method.
posted by Stewriffic at 12:33 PM on September 6, 2008


delmoi: Having an understanding of arithmetic is important for learning math, but being able to do base-10 addition/subtraction/multiplication/etc with a pencil and paper using a particular algorithm that was developed for people who's job it was do do that kind of math all day because computers had not been invented yet is not really important.

Having an understanding of arithmetic is definitely important for learning math. I don't think that anyone in this thread is saying that it's not, nor are authors of this video saying it's not.

However, a solid ability to do the calculations of basic arithmetic is the efficacy of a good understanding of that arithmetic. I think that conceptual comprehension should be the paramount goal overall in mathematics education and should take precedence over calculation ability but that's not the same thing as saying that calculation ability is irrelevant.

Calculation ability within more basic math is important in being able to follow along in the derived forms of math that are taught in the later years of school. (And it's similarly important within the many science subjects that depend heavily on math.)

Sure, if all students ended up being able to effectively calculate using methods other than "Standard Multiplication" as they call it and Long Division, and were able to effectively apply those methods in the course of their later education, I would be okay with it. But my personal experience and the reading I've done in math education during the past decade appears to indicate that this is not the case and that students keep reaching for the calculator to do more and more basic problems.

Curricula at this level should not be using calculators as a deus ex machina to make the teaching easier. For the sake of the rest of their own educational careers, students need to be weaned off using calculators for basic arithmetic (or better yet, never started) the same way that chemistry students need to be weaned off of constantly doing lookups on a paper copy of the periodic table.

Or take the parallel in composition: even if a student properly cites so that it's not plagiarism, they shouldn't be allowed to turn in papers that are mostly verbatim copying from another source because they would never learn to write on their own. The point isn't to punish them for taking the easy way or something, it's to ensure they have the basic skills.

delmoi: And if she thinks this stuff is so horrible, why does she think the worlds mathematicians and scientists are pushing it?

Can you provide some kind of citation that the world's mathematicians and scientists are pushing this? I ask because I haven't heard this and it's contrary to my experience. Most of the mathematicians and scientists I've had the occasion to discuss this sort of thing with are even more critical of calculator dependence than I and the math teachers I've know are and think that the ability for hand computation of half of higher math ought to be de rigeur, much less basic arithmetic.

Also, she isn't saying that all of the methods discussed are "so horrible". She thinks that the two curricula she's discussing are inadequate in an of themselves to ensure proficiency in elementary school math, due both to their reliance on the methods she presents and the stated intentions of the authors.

wittgenstein: What we really need are math specialists teaching math in elementary schools,

Amen.
posted by XMLicious at 12:33 PM on September 6, 2008 [1 favorite]


It amounts to far more than that - she quotes directly from the authors:

The authors of Everyday Mathematics do not believe it is worth students' time and effort to fully develop highly efficient paper-and-pencil algorithms for all possible whole number, fraction, and decimal division problems.

They're intentionally teaching a less effective and incompletely developed understanding of mathematics, in their own words.


Your understanding of the above quote is poor. The purpose of math instruction is to teach students how to get correct answers reasonably fast. The methods outlined in this video will give you a correct answer in a reasonable amount of time. The methods outlined in this video are not less effective than traditional methods, they are just more efficient when solving problems using paper and pencil. But that's not the only way to solve problems, and math is not a race.

No where in the above quote do the authors say that they are teaching methods that are built upon incompletely developed understanding of mathematics. Every single algorithm presented in this video is based on a completely developed understanding of mathematics.
posted by 23skidoo at 12:38 PM on September 6, 2008 [1 favorite]


Basically, she's a sophist hack.

blasdelf, I really think the mockery you're seeing and your belief that she expects viewers to accept her conclusions about the curricula a priori is your own imagination. You and others talk as if the video is some kind of hate fest about the methods she's demonstrating but it just isn't. She isn't saying that those things are horrible and should never be taught, she's just presenting them as the primary teaching methods in curricula she's claiming is inadequate for a variety of reasons, including the stated aims of the authors themselves. She doesn't throw them up there and say "ha ha, look at these, look how silly these methods are!" she merely makes some pretty mild, but salient, criticisms of them.
posted by XMLicious at 12:46 PM on September 6, 2008


I think there are two issues here:

1) What methods to use to teach arithmetic processes like multiplication. The speaker in the video argues against newer, less traditional methods because they seem less efficient, and because "what's wrong with the old way?" But she herself points out that the new methods promote a greater understanding of place value - they are more transparent in terms of why they work. I think having exposure to many methods is a good thing as long as kids have adequate time to absorb them all.

2) Whether or when it is important for students to master certain arithmetic processes and facts. I personally am in favor of mastery because I think that feeling successful motivates kids like nothing else - in my experience as an elementary math teacher it is extremely frustrating for kids to move on to a new topic before they have experienced mastery. I have found the older version of Everyday Math to be too casual about mastery - the assumption is that because the curriculum sprials, if they don't get it this time they will get it the next time they are exposed to a concept. But because many teachers expressed concerns about this mentality, it is one of the things they are revising in the new edition.

So, basically, both of her points are pretty easily refuted.
posted by mai at 1:02 PM on September 6, 2008


Your understanding of the above quote is poor.

I do not think so. I think that quote is stating that what the curricula is teaching will not be effective on all possible whole number, fraction, and decimal division problems and will not fully develop ability on those problems, but implicitly (via the claim it's not worth it) they think their approach on concepts can trump any consequent issues. It seems pretty straightforward to me, I don't see why they'd have that clause in there otherwise.

I'd really like to see how many students come out of that program being able to do fractions on a calculator, for example. From my own experiences teaching mathematics I'm just very skeptical that they're accomplishing their goals, noble though those goals may be.
posted by XMLicious at 1:05 PM on September 6, 2008


However, a solid ability to do the calculations of basic arithmetic is the efficacy of a good understanding of that arithmetic.
Using a pencil and paper to solve math problems using a method drilled into you is no more of an "ability" to do calculations then using a calculator. Well, not really, but understanding that there several different ways to solve a problem, how those ways fit together is much more important then being able to run one particular pencil-paper algorithm quickly. Especially when there are lots of times when you might want to do math but don't have quick access too pencil and paper. For example, say you're driving and you want to figure out how fast you need to drive to get to your destination in X amount of time. You're not going to be able to whip out a pad and start writing.

On the other hand, most of the time when you'll have paper and pencils, you'll also have access to some kind of computer, and you can just type the equation into Google and get your result, or use the built in calculator.
the same way that chemistry students need to be weaned off of constantly doing lookups on a paper copy of the periodic table.
What is it with you and this periodic table stuff? Most chemist don't need to memorize the table, they'll have an intimate knowledge of the periods that define the table, how atom shells are filled out and what the likely properties of various elements are going to be at certain locations on the table. They are not going to memorize every transition metal.

Remember, the periodic table is actually the output of a very complicated mathematical function, and you can actually predict the properties of elements just based on the number of atoms they have. For example as you go from Lithium to sodium to rubidium you get more and more reactive with oxygen, because the outer shell electrons are farther away from the nucleus and easier to pull off (If I'm remembering my high school chemistry correctly).

Real chemical engineers are not going to be sitting there thinking about various elements that they're working with. I'd be curious to hear some real chemists chime in about what they do all day, since I don't really know. But someone who works for a solar energy company is only going to care about a few elements and get very specific about all of their properties. A microbiologist only cares about 20 or so elements, and probably spends most of their time thinking about proteins rather then the atoms that make them up.
Can you provide some kind of citation that the world's mathematicians and scientists are pushing this?
Every mathematician or actual scientist I've ever heard or talked too supports this kind of thing, and the people who oppose it tend to be ignorant math haters who think their kids need to suffer the way they did. Everyone who really loves math, and excuse me if I don't find the local weather girl a compelling critic.
posted by delmoi at 1:05 PM on September 6, 2008


Loved that video. It is clear, direct and made so much sense. Being math challenged, I tend to use the TERC method, without having known the word for it, when I need to do the math in my head, don't have a paper and pen or calculator. But I like having learned the old fashioned multiplication algorithm method.

Why can't a few techniques be taught as possibilities -not rigidly- and let the kids choose what works for each of them? In any given class there will be people for whom math is as easy as breathing and other kids who struggle to get math concepts?
posted by nickyskye at 1:25 PM on September 6, 2008


How Not to Teach Math by Matthew Clavel
Instead of rote learning and memorization, students move haphazardly from one seemingly unconnected topic to another. In Fuzzy Math lingo, it’s called “spiraling.” On this view, teachers shouldn’t use a single method to get addition across to students; they should try lots of approaches—like adding the left-most digits first. That way, the Fuzzy Math approach says, you have a better chance of getting students to understand the concept of addition. In practice, however, trying to teach a host of different methods if students haven’t sufficiently mastered any specific one—as is all but inevitable, since they haven’t spent much time practicing any specific one—can be very confusing.
...
The repudiation of skills in Fuzzy Math also encourages a detrimental overreliance on calculators. The use of these gadgets to replace mental computation raises concerns about learning skills for all school children. According to a 2000 Brookings Institute study, fourth graders who used calculators every day were likely to do worse in math than other students. But it’s minority kids like those in my class who are turning to calculators the most. The Brookings study reports that half of all black school children used calculators every day, compared with 27 percent of white school kids.
This style of teaching doesn't appear to work well with kids that don't have a lot of self-discipline.

Every mathematician or actual scientist I've ever heard or talked too supports this kind of thing, and the people who oppose it tend to be ignorant math haters who think their kids need to suffer the way they did. Everyone who really loves math, and excuse me if I don't find the local weather girl a compelling critic.

Anecdotal evidence is next to worthless. Here's some for the opposite side:
“Cooperative” learning that leads to classroom chaos, schizoid lessons that fail to impart mastery, ill-conceived and overly difficult homework assignments, lousy results, parental outrage—shouldn’t every teacher have done as I did and thrown Elementary Mathematics into the garbage? I certainly wasn’t alone in hating it. Indeed, I never heard a good word for it from my fellow teachers. At a grade conference one day, one our most respected fourth-grade teachers, a veteran who worked hard and cared deeply about the achievement of her students, summed up the general frustration with the new program: “I can’t teach it.”
posted by Axle at 1:30 PM on September 6, 2008


I do not think so. I think that quote is stating that what the curricula is teaching will not be effective on "all possible whole number, fraction, and decimal division problems" and will not fully develop ability on those problems, but implicitly (via the claim it's not worth it) they think their approach on concepts can trump any consequent issues. It seems pretty straightforward to me, I don't see why they'd have that clause in there otherwise.

You're imagining that the quote uses the word "effective". It doesn't say that. At all. Anywhere.

Also, nowhere does it say that they think their approach will trump any consequent issues. It doesn't say that. At all. Anywhere.

To me, the reason you put that clause in there is not to imply that your approach on concepts trumps any subsequent issues, it's to own up to the fact that for big ugly math problems, it makes more sense to use a calculator. Adults use calculators all the time for calculations that are tiresome to do by hand. Why is it "worth students' time" to develop the most efficient algorithms for "all possible whole number, fraction, and decimal division problems" when most adults (even ones who learned the traditional long division algorithm) do not sit around doing long division all day long? Sure, I *can* divide $583.12 by $1.99, but if I need to know that exact answer, I'm going to use a calculator. Why is insisting that students learn crap that adults don't use worth their time?
posted by 23skidoo at 1:31 PM on September 6, 2008


Also, this:
I do not think so. I think that quote is stating that what the curricula is teaching will not be effective on "all possible whole number, fraction, and decimal division problems" and will not fully develop ability on those problems, but implicitly (via the claim it's not worth it) they think their approach on concepts can trump any consequent issues. It seems pretty straightforward to me, I don't see why they'd have that clause in there
You're missing the point as to why your comment was wrong. They said "fully develop algorithms" and you said "understanding" There is no indication that they don't think students should understand arithmetic, rather then being able to do it quickly with a pencil and paper. (and in particular, they were only talking about division, they think students should be able to divide most numbers, but they're not worried about some tricky situations)

And by the way, I'd be hard pressed to divide numbers in my head if they didn't fit together well 33/76? Yeah, no. But that's not something that's every prevented me from doing anything. I forgot how to do long division long ago, but I can calculate a triple integral or program a back propagation neural network just fine.
posted by delmoi at 1:38 PM on September 6, 2008


Indeed, I never heard a good word for it from my fellow teachers. At a grade conference one day, one our most respected fourth-grade teachers, a veteran who worked hard and cared deeply about the achievement of her students, summed up the general frustration with the new program: “I can’t teach it.”
So she's too stupid to figure it out, even though gradeschoolers can? How is that an indictment of the program?
posted by delmoi at 1:41 PM on September 6, 2008


Every mathematician or actual scientist I've ever heard or talked too supports this kind of thing
What kind of thing are we talking about here, specifically?
If we are talking about the new, realistic methods of teaching math (and not some specific algorithm that is better or worse), I know that at least in the Netherlands people are not universally enthusiastic about it. Frans Keune, Math professor of Nijmegen University said that realistic math is like abstract football (link is in Dutch). University of Amsterdam's professors Jan van de Craats en VU University's Henk Tijms are also critical (Dutch link).

Since the 70's (I think) math has always been applied in our country and nobody argues that it should go back to just naked sums without any relation to reality. The critics do say that they see more and more children with a fundamental lack of understanding of math (the exact thing those new programs are said to prevent) and they argue that math can also be beautiful on its own, that mathematical proofs are good things to learn.
posted by davar at 1:52 PM on September 6, 2008


delmoi: What is it with you and this periodic table stuff?

Pardon me for presenting analogies from the rest of education about the importance of fundamental skills, somehow I have this crazy idea that analogies are good tools for conveying concepts. Memorizing times tables, memorizing the periodic table - really, what's the relation? Just craziness on my part, I'm sure. I made an analogy with development of basic skills in composition too but I notice you stayed away from that one.

Most chemist don't need to memorize the table,

That's great, but I'm talking about chemistry students, not chemists.

I'm also not saying that Stephen Hawking has some really vital need to be able to do long division, by the way.

I'm saying is that I think thorough understanding and calculation ability in basic arithmetic are an important foundation for learning the math that is taught later, and that reliance on calculators at that stage can cause major problems further down the line. You seem to find this to be a vile opinion based upon the way you've been talking about people who hold it. I do not find your opinion nor the TERC and other methods vile, nor do I think that they shouldn't ever be taught, nor do I think that students should be punished by making math hard. I just think that the most effective curriculum and the one that integrates with and best prepares for later learning would have more emphasis on calculation ability than the ones examined in the video.

Every mathematician or actual scientist I've ever heard or talked too supports this kind of thing,

Some of your best friends are mathematicians and scientists, huh? Mine too. No citation either way, I guess.

the people who oppose it tend to be ignorant math haters

Oh, gee, thanks. FUD like there's no tomorrow.

excuse me if I don't find the local weather girl a compelling critic.

Especially if she's a bitch, huh?

Man, the way you are trying to advance your point of view here is way more like propaganda than anything in that video.

23skidoo: You're imagining that the quote uses the word "effective". It doesn't say that. At all. Anywhere.

Didn't claim it does. In fact, in response to ssg above I very explicitly pointed out that "...effective..." is my opinion on the statements the curriculum authors made, not the quote from those authors. But I'll give you a gold star for dramatic rhetorical use of periods.

Also, nowhere does it say that they think their approach will trump any consequent issues. It doesn't say that. At all. Anywhere.

Hence I said "implicitly". But kudos again for the dramatic rhetoric trying to make it look as if I was claiming otherwise.
posted by XMLicious at 2:00 PM on September 6, 2008 [1 favorite]


No, really, why is worth students' time to insist that they learn crap that adults don't use worth their time? Specifically and non-rhetorically, why is it worth students' time to insist that they learn the most efficient pencil-and-paper algorithm for long division where both divisor and dividend are decimals to the hundredths place, when most adults will use a calculator for problems like that?
posted by 23skidoo at 2:37 PM on September 6, 2008


Especially if she's a bitch, huh?

C'mon, stop being an asshole about this. Our problem with her is that while her demonstrations are efficacious, she does not present any rationale for the opinions she constantly states as fact. She's showing the methods, but she's telling the criticisms, and hoping you don't notice the difference.
posted by blasdelf at 2:41 PM on September 6, 2008


And along the lines of what 23skidoo is saying, when confronted with divide $583.12 by $1.99 why shouldn't the most prominent lesson be that the answer will be a bit less than $300?
posted by blasdelf at 2:46 PM on September 6, 2008


Coming in here late...

My credentials: I have a math degree and have done some teaching of math, and have also read quite a few books on teaching math.

And I barely know where to start.

Let's start with this - if you give kids a real-world problem ("you have 180 terrorists and 30% of them are killed by a bomb, how many are left?") most kids have no idea whether to use addition, division, or take a square root.

If I got kids out of grade school and they always understood which operations to perform to solve problems and why, I'd be quite happy, even if they could barely add without a calculator. So the fundamental issue in mathematics education has nothing to do with which algorithms kids learn for multiplication.

Second, after watching both the old and the first "new" algorithm, I haven't a clue why she thinks the old one is better. The new one seems much more concrete to me - the fact it takes a little longer is fine - and it feels a little less error prone.

Finally, why does she feel she knows better? I'm certainly not hung up on math or teaching credentials, but she doesn't have them. She doesn't seem to be claiming to have taught math to a lot of kids. She doesn't seem to be able to present any form of controlled study, or even give a plausible rationale.
posted by lupus_yonderboy at 3:37 PM on September 6, 2008 [2 favorites]


No, really, why is worth students' time to insist that they learn crap that adults don't use worth their time? Specifically and non-rhetorically, why is it worth students' time to insist that they learn the most efficient pencil-and-paper algorithm for long division where both divisor and dividend are decimals to the hundredths place, when most adults will use a calculator for problems like that?

It's worth it because it's an intermediate and instrumental tool to learning the sorts of mathematics that are taught after basic arithmetic. There are all sorts of things that you learn because they're going to help you learn other stuff, not because the theory is you're going to use it constantly when you're an adult. This is what I mean when I say that developing arithmetic calculation skills is important to subsequent learning.

You could make a parallel argument that there's no reason to teach fractions because calculators today can properly handle infinitely-repeating decimals; all the world's stock markets use decimal notation instead of fractions now, weights and measures can easily be done in decimal because scales are usually digital rather than analog now, et cetera. But day-to-day usage isn't the only reason to learn fractions by far; I would actually say it's much more important for understanding ratios conceptually, rational expressions in algebra, the meaning implied by things like dy/dx Euler notation in calculus, et cetera.

PS thank you for being less rhetorical.

> Especially if she's a bitch, huh?

C'mon, stop being an asshole about this.

Not only did delmoi not retract the "bitch" thing, he has in fact continued marshaling the ad hominem arguments: that the evidence and reasoning presented in that video is less valid because the narrator is just a "weather girl", or that people who might agree with me and others here on this topic "tend to be ignorant math haters". I am not the one being an asshole here.

(People with actual degrees in meteorology really find the "weather girl" thing pretty offensive, btw, both male and female. It's kind of like calling a paramedic an "ambulance driver".)
posted by XMLicious at 3:42 PM on September 6, 2008 [2 favorites]


Pardon me for presenting analogies from the rest of education about the importance of fundamental skills, somehow I have this crazy idea that analogies are good tools for conveying concepts.
Yeah, but it just doesn't make that much sense, I mean, it's not like chemists actually memorize the periodic table.
That's great, but I'm talking about chemistry students, not chemists.
So why would chemistry students need to memorize the periodic table? Either they are going to become chemists, in which case the periodic table would come naturally too them and they wouldn't need to memorize it, or they won't become chemists, in which case they won't need to have it memorized either.

Most chemistry classrooms have giant periodic tables on the wall, and while students might need to memorize some parts of the table, memorizing all of the transition metals seems really pointless. At they very most, they might memorize it once, for one test, and gradually forget it over time. A rote memorization of the periodic table just doesn’t seem very necessary to either study or practice chemistry.
I'm saying is that I think thorough understanding and calculation ability in basic arithmetic are an important foundation for learning the math that is taught later
Understanding, sure. But there is a difference between understanding something and being proficient in one specific method of doing something. In fact, I would argue if you only know one way to add and subtract numbers, then you don't understand it.

In fact, you keep using the word "understanding" but the entire point of the TERC method is to increase fundamental understanding, at the expense of being able to do the problems quickly.
I just think that the most effective curriculum and the one that integrates with and best prepares for later learning would have more emphasis on calculation ability than the ones examined in the video.
Well, how the hell would you know which methods are more effective? The person presenting the video hates them, because they are more difficult for her because she was taught the other way, and now she can't wrap her head around the fact that there are other ways to do it. The other ways may not be as efficient in terms of how many pencil marks you need to make, but the components of the problem are easier to remember, making it easier to do without a pencil and paper, which seems even more useful.

And yea, I do think the idea that children should be painfully forced to memorize obsolete, useless pencil and paper algorithms for solving arithmetic problems kind of vile. It is, I think, one of the main reasons why people end up "hating math"
Some of your best friends are mathematicians and scientists, huh? Mine too. No citation either way, I guess.
Look in this thread, you have a video produced by a local weather girl on one hand, and a response from a mathematics professor, who teaches both advanced math and remedial math. Which one do you think would have a better idea how to teach math effectively? I've talked to one friend of mine who has a math degree about this very issue, and she agreed with me. What do you want, my facebook page as a citation? On the other hand, when I hear people complain, they are mostly people who don't understand math very well at all, and certainly don't use it on their job. That's been my experience.
posted by delmoi at 3:58 PM on September 6, 2008


(People with actual degrees in meteorology really find the "weather girl" thing pretty offensive, btw, both male and female. It's kind of like calling a paramedic an "ambulance driver".)

How does a degree in meteorology give you any particular insight into how mathematics should be taught? maybe if she had a degree in developmental psychology or a PhD in education (i.e. someone who studies education techniques, rather then a teacher).
posted by delmoi at 4:02 PM on September 6, 2008


"No, really, why is worth students' time to insist that they learn crap that adults don't use worth their time? Specifically and non-rhetorically, why is it worth students' time to insist that they learn the most efficient pencil-and-paper algorithm for long division where both divisor and dividend are decimals to the hundredths place, when most adults will use a calculator for problems like that?

It's worth it because it's an intermediate and instrumental tool to learning the sorts of mathematics that are taught after basic arithmetic. There are all sorts of things that you learn because they're going to help you learn other stuff, not because the theory is you're going to use it constantly when you're an adult. This is what I mean when I say that developing arithmetic calculation skills is important to subsequent learning.


Specifically, for which topics in mathematics is mastery of the most efficient pencil-and-paper algorithm for long division where both divisor and dividend are decimals to the hundredths place an intermediate and instrumental tool?
posted by 23skidoo at 4:08 PM on September 6, 2008 [2 favorites]


lupus_yonderboy: Finally, why does she feel she knows better? I'm certainly not hung up on math or teaching credentials, but she doesn't have them. She doesn't seem to be claiming to have taught math to a lot of kids. She doesn't seem to be able to present any form of controlled study, or even give a plausible rationale.

I don't think that the idea of this video is to present her as an authority on math, nor to vindicate any one teaching method. I really think it's just a brochure-type presentation of part of what's probably a broader criticism and curriculum evaluation. My guess would be that she's probably the narrator because they didn't want to have just math teachers and education professionals doing presentations.

Googling seems to bear that out; the Preston Productions mentioned at the end led me to the group that appears to be the author of the video, "Where's The Math" of Washington State, which has considerably more material on its web site and does not appear to simply be a bunch of ignorant math haters as delmoi insists people holding this position generally are.

You're very correct that studies and research should be part of this sort of discussion, lupus_yonderboy.
posted by XMLicious at 4:09 PM on September 6, 2008


XMLicious: "I didn't do any putting words in anybody's mouth: I quoted exactly what the authors said themselves. If you don't like what I said about it, go ahead and say so and articulate a disagreement with me rather than throwing out rhetorical implications that I've lied."

Perhaps your English teacher failed to impress upon you the meaning of the word 'quote' in school, but there is absolutely no way in which your summary* is a quote, let alone an exact quote, of what was written in the book.

This is the quote:
The authors of Everyday Mathematics do not believe it is worth students' time and effort to fully develop highly efficient paper-and-pencil algorithms for all possible whole number, fraction, and decimal division problems.
This is falsely attributing your opinion to someone else:

They're intentionally teaching a less effective and incompletely developed understanding of mathematics, in their own words.

You'll note that the authors' own words, which you claim to be reporting, do not include anything remotely like the words you have written. Almost none of the words you are attributing to the authors even appear in the actual quote!

* Totally incorrect and opinionated, but that's beside the point.
posted by ssg at 4:28 PM on September 6, 2008


I used to work as a cashier. If a customer had to pay 5,15 and they paid with a 10 note, we would ask if they had 15 cents, so we could give them a 5 note back. Sometimes the customer did not have 15, but did have 20 cents. We would then, of course, give 5,05 back. I see more and more cashiers who do not grasp this concept (both as a customer and as someone who worked in a shop). Their cash register tells them what to give back, and even if that is 4.99, they do not want to take my 1 cent to make it 5 dollars and they sometimes even look at me as if I am crazy for suggesting it because the machine said 4.99.

Thanks for giving an opening to my math rant. I'm on the outskirts of OKC at a Love's gas station. The total is say $4.57. I give the cashier a 20 dollar bill. He rings it up as a 5. As soon as he hits total and the till opens, he knows he's screwed up. But wait! The golden machine of knowledge has spoken! Please O Great Machine! Reconsider! PLEASE tell me how much of this green stuff and coins I'm supposed to hand her! He is giving me a completely panicked look now. I wait, watching the scene unfold. He picks random bills and coins out, shakes his head and puts them back. I can literally see the wheels turning in his head and boy, are they grinding. People are stacking up behind me. He's mumbling and looking and counting and looking and pulling bills and counting...Finally I tell him, step by step, "Give me 43 cents, ok now that makes 5 bucks." (He's not catching on, but at this point I could have told him hand me that hundred and he would have to get me out of there.) "Now a five, that makes 10 bucks. Now give me a ten and we are up to twenty."

He never picked up what I was saying at any point. And he looked like he wanted to sink through the floor. Darn it when those machines don't give us the right answer.
posted by CwgrlUp at 4:38 PM on September 6, 2008 [2 favorites]


Did anybody else play math games in school? It seems most of the Americans I talk to (who are, I agree, terrified of math) did not. We used to do competitive games like calling out the answers to flip cards for the times table to 12x12. In French class, we used to play a game which I remember as being called Bump, although it was probably named a French word? The class would, in seating order, call out numbers in French, except for any number with a 3 in it, or which was a multiple of 3, you said "bump" (or whatever the French word was that we actually used which I can't remember). 1, 2, bump, 4, 5, bump, 7, 8, bump, 10, 11, bump, bump, 14, bump...

I still don't disagree entirely with this (shrill, vile) woman.
posted by TypographicalError at 10:56 AM on September 6


Shrill? I found her voice to be quite pleasant.
posted by joannemerriam at 4:40 PM on September 6, 2008


But let me reiterate: she's barking up the wrong tree whether or not her algorithms are better or not.

What is key is understanding how to do simple mathematics. Now, part of understanding simple mathematics is understanding basic arithmetic and if you don't know your times tables and how to do additions and such then you really don't understand basic arithmetic. I think the new books are better books - the key is starting much, much earlier with much better teaching.

I'm frankly in favour of rote training for part of this - paradoxical though it may be. I learned all these stupid number songs for multiplication and did them endlessly just like playground games. I just know A x B for any numbers from 1-12. But I think then leading people right to the formulae for long multiplication is wrong, wrong wrong.

We have calculators for this!

I think the next stage should be large numbers. This is ten - this is a thousand. Look at all these tens making a thousand. There are 4,000,000 people in Manhattan and Brooklyn. If I give $30 to all of them, how much is it?

And introduction to units. This is a gram. This is a kilogram. This is a centimeter and this is a meter. This is what 0 degrees and 50 degrees feel like. 100 degrees C is very hot. (or use Imperial if you must, I think that's not so important, surprisingly enough...)

Estimation, analysis of a problem. "How much does that building weigh?" "Well, it's about 100m by 100m by 20m, that's 200 thousand cubic meters or 200 million liters. If it was filled with water it'd be 200 million kilos or 200 thousand metric tons. Suppose building materials were twice water, it'd be 400 thousand tons. But most of the building is empty space, say 40 thousand tons."

At that point you could go back to arithmetic and say, "Now, here's how multiplication really works behind your calculator." Paradoxically, once kids knew what they could do with it, they'd be psyched to learn -- even if it were rote training.

Now, frankly, I've learned a ton of techniques and I think long division is way overrated. I mean, I can compute square roots without a calculator (in several ways in fact) but the way I learned in school (looking a little like long division) was one of the stupidest wastes of time ever. In fact, despite a degree in mathematics, I realize I never got to go back to that algorithm and discover how it worked... today I'd just use Newton's method.

The key skill is understanding how to use mathematics to solve the problems you need to solve in the real world. Whether or not someone's algorithm for doing multiplication is a little better or worse is pretty unimportant in comparison to understanding the big picture, particular in a world of ubiquitous calculators.
posted by lupus_yonderboy at 4:42 PM on September 6, 2008 [3 favorites]


I dont think these algorithm methods help students to really reason out mathematic computations- its just a cookbook approach.

Im an engineer and we have to do quick calcs in our head all the time, typically reasoning it out by the TERC method. I dont see anybody using the algorithms that were taught in school.

Besides, this woman was terrified by one year of calculus? Moron!
posted by freshundies at 4:44 PM on September 6, 2008


If I have to work out something in my head, I'll probably use those partial problem methods, but if I have a piece of paper, I'll use the efficient algorithms, and finish way faster. There is no reason kids need to be experts at doing math in their heads. When is a calculator or at the very least a piece of paper unavailable in a business or academic setting?
posted by tehloki at 4:58 PM on September 6, 2008


delmoi: I mean, it's not like chemists actually memorize the periodic table.

Funny how you follow that up a little bit later by saying "students might need to memorize some parts of the table". You appear to understand what I'm saying just fine.

In fact, you keep using the word "understanding" but the entire point of the TERC method is to increase fundamental understanding,

How completely unlike every single other formal curriculum under the sun.

Yes, I know their stated intention is to achieve understanding in the student. I just don't think they're correct that they are prescribing the optimal approach, for all the reasons I have articulated above.

Well, how the hell would you know which methods are more effective? The person presenting the video hates them, because they are more difficult for her because she was taught the other way, and now she can't wrap her head around the fact that there are other ways to do it.

I guess I "know" which methods are more effective (yeah, as if I've claimed anything like that) about as well as you "know" all these details about the motivation for this video to be created.

In fact, I would argue if you only know one way to add and subtract numbers, then you don't understand it.

That would be a really fabulous argument if anyone in this discussion was actually suggesting that students should only know one particular method - but I think you know very well that no one here has advocated such a curriculum.

Look in this thread, you have a video produced by a local weather girl on one hand, and a response from a mathematics professor, who teaches both advanced math and remedial math. Which one do you think would have a better idea how to teach math effectively?

...and as seemed pretty obvious to me, a little bit of research (links above) demonstrated that the video is the product of a large group of people with all kinds of math education and probably curriculum design experience too. I don't even get why you were trying to frame this to be some sort of credentials pissing contest between YouTube users or something.

23skidoo: Specifically, for which topics in mathematics is mastery of the most efficient pencil-and-paper algorithm for long division where both divisor and dividend are decimals to the hundredths place an intermediate and instrumental tool?

Specifically, where the hell did I even argue anything like that? This seems like a straw man. I even said ^ that it would be perfectly fine if students were developing solid arithmetic calculation skills with one of these other methods - I just don't think that's happening.

ssg: Almost none of the words you are attributing to the authors even appear in the actual quote!

Except of course the text of the quote, which was right there above what I wrote. You've characterized what I said as a "totally incorrect and opinionated" summary; which is it, did I quote and summarize them and opine in my summary, or did I put words in their mouth? I'll grant you that to be clearer I should've used a word other than "understanding" there or moved the "in their own words" clause further up in the sentence. But since I quoted them verbatim I think it's at least as deceptive as you're accusing me of being for you to state that I "put words in their mouth".
posted by XMLicious at 5:08 PM on September 6, 2008


I've taken some pretty advanced math and I don't recall a situation where I've needed to do basic arithmetic on paper in order to solve a an algebraic, or calculus problem

Wow.

I have to do basic arithmetic by hand all of the time. I'm in college right now, and have only ever been allowed to use calculators on exams and quizzes for very specific types of problems.

I had to take remedial algebra when I began college because my math education was so poor. (I'm not "bad at math" at all.) I saw many of my classmates fail quizzes, exams, and even the entire class, because they didn't have the basic skills they needed in order to solve problems. They would know that they had to factor an equation, for example, but be unable to determine the factors. Or they wouldn't understand the logic behind fractions, meaning that when they came across anything but the easiest fractions, they were stumped.

What do you think the impact of that failure will have on their choice to go into math or science?

It's too easy to draw the conclusion that you're bad at math when you lack basic skills that everyone thinks you should have. And of course,if you get your ass whooped by remedial algebra due ot not having those skills, it takes a persnickety sort of student to ignore that and continue on to the more advanced math required by a lot of the sciences.
posted by Kutsuwamushi at 5:15 PM on September 6, 2008 [2 favorites]


The F.O.I.L. method teaches something they will reuse, by establishing grouping signs:

(26)(31) =
(20 + 6)(30 + 1)
600 + 20 + 180 + 6
= 806

And a larger problem:

(1234)(6789) =
(1000 + 234)(6000 + 789)
(6,000,000) + (789,000) + (200 + 30 + 4)(6000) + (200 + 34)(700 + 89)
6,789,000
1,200,000
xx180,000
xxx24,000
xx140,000
200(80 + 9)
xxx16,000
xxxx1,800
(30 + 4)(700)
xxx21,000
xxxx2,800
(30 + 4)(80 + 9)
xxxx2,400
xxxxx,270
xxxxx,320
xxxxxxx36
---------------
8,377,626
posted by Brian B. at 5:20 PM on September 6, 2008


Math education is overrated. I can add, subtract, multiply and divide. For anything else, I'll go find a computer or a nerd.
posted by jonmc at 5:27 PM on September 6, 2008


I'll grant you that to be clearer I should've used a word other than "understanding" there or moved the "in their own words" clause further up in the sentence.

If you put "in their own words" in the sentence at all, you are wrong to put anything other than their own words. You can't write your own summary or opinion and then append "in their own words". You aren't reporting their words, so you shouldn't claim to be doing so. You can have whatever opinions you want, but please don't attribute them to other people.
posted by ssg at 5:49 PM on September 6, 2008


Tom Lehrer
posted by Sparx at 6:04 PM on September 6, 2008


Killick, are you a member of the a teacher's union? Sorry if you are. I don't know about where you live, but around my area the teachers union is basically detrimental to education. They have become so strong that they can dictate what they want, but that is not usually stronger schools, but more like stronger benefits etc. I used to scoff at the idea of charter schools, but now I have become convinced that they are the only solution for failing inner city schools. It's the only way to cut through the corruption. Of course, the teachers unions hate this idea. Also, their needs to be a better way to rid the system of bad teachers. Once someone gets tenure it becomes essentially impossible to get rid of them. No other area of employment has such protection (except perhaps federal judges). A good twenty percent or so of our local school teachers, and this school is considered one of the best in the state, deserve sacking for outright incompetence. There are also lots of smaller issues, like having the teenagers start school at shortly after 7 am despite this being quite difficult for most teens, just because the teachers like to get home early, schedules, and some pretty incredible benefits packages. If they had used their incredible power to actually help the students, such as fighting the No Child Left Behind Act successfully then I would perhaps feel better. However, they would not rock the boat. They will strike for themselves, but not for the kids. Fuck the teacher's union. Oh, I forgot to mention, get off my fucking lawn.
posted by caddis at 6:06 PM on September 6, 2008 [1 favorite]


Yes, I know their stated intention is to achieve understanding in the student. I just don't think they're correct that they are prescribing the optimal approach, for all the reasons I have articulated above.-- XMLicious
You haven't outlined that at all, you've simply argued over and over again that being able to do calculation is important, and then I guess said you thought the video (which is (drumroll...) propaganda) made some good arguments.
That would be a really fabulous argument if anyone in this discussion was actually suggesting that students should only know one particular method - but I think you know very well that no one here has advocated such a curriculum.-- XMLicious
That's exactly what the video advocates. That students should be drilled in what they call the "Standard Algorithm"

23skidoo: Specifically, for which topics in mathematics is mastery of the most efficient pencil-and-paper algorithm for long division where both divisor and dividend are decimals to the hundredths place an intermediate and instrumental tool?

Specifically, where the hell did I even argue anything like that? This seems like a straw man. I even said ^ that it would be perfectly fine if students were developing solid arithmetic calculation skills with one of these other methods - I just don't think that's happening.
-- XMLicious
Maybe you should go back and re-read your own comments. You said here "it's an intermediate and instrumental tool to learning the sorts of mathematics that are taught after basic arithmetic." But what does

The "it's" refer too in that sentence? You quoted 23skidoo saying
No, really, why is worth students' time to insist that they learn crap that adults don't use worth their time? Specifically and non-rhetorically, why is it worth students' time to insist that they learn the most efficient pencil-and-paper algorithm for long division where both divisor and dividend are decimals to the hundredths place, when most adults will use a calculator for problems like that?
So, in other words 23 very clearly and specifically asked you about division to a hundredths place, and you said it was "it's an intermediate and instrumental tool to learning the sorts of mathematics that are taught after basic arithmetic." Again It's all in this comment.
Funny how you follow that up a little bit later by saying "students might need to memorize some parts of the table". You appear to understand what I'm saying just fine. -- XMLicious
Actually I have no idea. I just recalled once that my highschool chemistry teacher covered up the big periodic table on the wall once when we had a test. Maybe we had to memorize some parts for that particular test, or maybe there was some other reason.

But the question is, you used the periodic table as an example of something that chemists needed to memorize, but in general, I don't think chemists need to memorize the periodic table.

Your arguments are getting convoluted and you seem to be forgetting stuff you've said earlier, which makes it difficult to argue with you. You're also making quite a few unsupported claims about the necessity of arithmetic.

Your basic argument seems to be this:
1) Understanding arithmetic is an important part of being able to do math.

2) Understanding arithmetic and being able to do lots of calculations quickly with a pencil and paper are the same thing.

3) Teaching math in the old-school way -- with lots of drilling and memorization of the 'standard method' is the best way to do teach kids how to do lots of calculations quickly with a pencil and paper.
Now, certainly, no one disagrees on point number one. And point number three seems pretty plausible. But, what about point number 2? I don't think it's true. I see no reason whatsoever why it's true, and almost all of your posts in this thread are simply restating points 1 and 3 over and over again.
I have to do basic arithmetic by hand all of the time. I'm in college right now, and have only ever been allowed to use calculators on exams and quizzes for very specific types of problems.

I had to take remedial algebra when I began college because my math education was so poor.
-- Kutsuwamushi
Whereas I tested out of algebra and took Calc-I my freshman year. I once took a section of Calc-II where the professor didn't allow the use of calculators on tests, at which point I dropped it and took it again another semester, where I could use calculators. I'm quite sure I got all the way through college without needing to do base-10 arithmetic. Now, base-2 arithmetic on the other hand I did need to learn, since you do need to know how to do it if you're going to design a digital circuit to do it, which is something that I've done.

Despite that, I've never really been good at long division, and I haven't even tried doing it since elementary school, or maybe middle school.
posted by delmoi at 6:37 PM on September 6, 2008 [1 favorite]


It's pretty amazing to me that you can explain all that stuff to me about my opinion on this matter, even boil my beliefs on it down to a three-point list that I'm evidently repeating over and over again, all without using the word "curriculum" which I thought figured pretty largely in what I've said here. Seems like a whole field of straw men you're setting up there, but what do I know, I'm just a math-hating ignoramus.
posted by XMLicious at 7:58 PM on September 6, 2008


Before Metafilter I rarely saw the words 'straw man' or 'ad hominem.' Is that really the best argument you can muster? Next you'll be pulling the ol' "I'm rubber, you're glue.." nugget.
posted by CwgrlUp at 8:16 PM on September 6, 2008


That is pitiful. If I ever manage to have kids, I would yank them out of public school in a heartbeat if I found that crap being demanded of them. Those methods are interesting and everything, but do nothing to train the mind...
posted by eener at 8:30 PM on September 6, 2008


It's pretty amazing to me that you can explain all that stuff to me about my opinion on this matter

Well, if I couldn't, wouldn't that mean you've failed to communicate them? And if I haven't, what are they?
posted by delmoi at 8:39 PM on September 6, 2008 [2 favorites]


Those methods are interesting and everything, but do nothing to train the mind...

What are you talking about? The film compares several mechanisms to do multiplication - they all work to teach arithmetic, they all expose different aspect of the truth behind it, they all train the mind. Perhaps one is better than the other but to claim any individual one is worthless is not a defensible statement.
posted by lupus_yonderboy at 8:41 PM on September 6, 2008


Before Metafilter I rarely saw the words 'straw man' or 'ad hominem.'

Now you're in a better world where people have to logically defend what they write! Not that I believe XMLicious's straw man argument - seems to me that delmoi pretty well sums up the consequences of the statements - but I'm happy to be in a somewhat rarefied dialog world....
posted by lupus_yonderboy at 8:47 PM on September 6, 2008


Just to clarify: I'm not saying that I would not want my kids to know these methods—it is just that I do not see them as a substitute. When I am doing calculations in my mind, I often use methods somewhat similar to these methods, but learning multiplication tables is not just about learning how to do math; it is also about mental discipline, which the more efficient algorithms (as well as memorization of basic multiplication tables) encourage. Learning to discipline one's mind is a part of education (or at least, it should be). Obviously everyone learns in a different way, so those other methods might very well be better for a subset of individuals, however IMHO, it lowers the bar overall.
posted by eener at 8:55 PM on September 6, 2008


So, basically what this comes down to:

Do we want to train students to be able to sit down at standardized tests, or in a job, and be able to plug numbers into a opaque formula, or do we want to train them to think?

Schools have always served the needs of business for workers. It used to be that factories needed workers to show up a 7am, and work until a bell range, and so schools opened at 7am and taught students to go to a different classroom whenever a bell rang.

Now in the "knowledge economy", we need people who can consistently and without much thought plug data into computers and forms, and schools teach that.

If you're middle-class, and you have a kid of merely normal intelligence, you want to train him or her to be a good little test-taker and later a good little worker, and so math that asks him or her to think really is a threat. Any thinking is just going to make him or her disatisfied to be a cog. Job security is learning to apply an algorithm without questioning how it works or even if it's right.

Real understanding of what the algorithm does isn't for little Johnny or Jane Middle America Public School Student. Leave that to the long-hairs and the the pointy-headed academics.
posted by orthogonality at 8:58 PM on September 6, 2008 [1 favorite]


XMLicious writes "Not only did delmoi not retract the 'bitch' thing, "

Well, in fairness to delmoi, having watched the video, she comes off as a total church-lady, a traditionalist, a proud Know-Nothing convinced her "common sense" trumps those pointy-headed scientists who have actually, you know, researched this topic. In short, she's a bitch.
posted by orthogonality at 9:07 PM on September 6, 2008


but learning multiplication tables is not just about learning how to do math; it is also about mental discipline, which the more efficient algorithms (as well as memorization of basic multiplication tables) encourage.

It may very well be that the other techniques require memorization of tables. As far as mental discipline goes, well, I would prefer kids get that somewhere else so that they can see the beauty in mathematics, rather then seeing it as punishment (or 'discipline').

Being a great (realist) artist requires discipline -- you need to spend hours and hours practicing. Being a great musician requires discipline, to learn your instrument, but imagine if we taught art and music the way we teach math (and the way this woman advocates we do), where rote techniques were drilled into kids heads over and over again.

So if you want your kids to learn mental discipline, teach them how to play the guitar.
posted by delmoi at 9:07 PM on September 6, 2008


delmoi, writing as a chemist (variously theoretical, physical, analytical and now environmental), I think that you've got very strange ideas of what chemists should and shouldn't know.

I would consider a chemist who did not know the periodic table and be able to use it to predict and understand a whole host of behaviours bizarrely uneducated, possibly incompetent. It's true that it's a simplified representation and that there are many exceptions to the trends implied in the table, but it's such a powerful systematizing tool, that to not know it intimately is beyond belief. Synthetic chemistry, organic and inorganic, would be near impossible without it. How would a physical or analytical chemist remember trends? We'd be back to stamp collecting!

Some systematizing tool is needed and the table is the simplest one based on our current best understanding of elemental electronic structure. It works really well for many, many pruposes. Why wouldn't you learn it?

And absolutely first-years uni students are made to memorize the elements (at least in first-year Canadian schools they are). We had a department-wide competition for the best song mnemonics in my year.
posted by bonehead at 9:16 PM on September 6, 2008


I would consider a chemist who did not know the periodic table and be able to use it to predict and understand a whole host of behaviours bizarrely uneducated, possibly incompetent.

And I'd consider a mathematician who didn't know the multiplication algorithm similar - but that isn't what we're talking about. We're talking about young people who are not specialists. It's just the same with the periodic table - if a kid got to grade 5 understanding how the periodic table worked and with some idea of how compounds were made, I'd think whether e actually had any of it memorized would be irrelevant.
posted by lupus_yonderboy at 9:49 PM on September 6, 2008


Don't many, most, secondary school kids get along just fine without any knowledge of the periodic table at all? It's hardly necessary for the day-to-day. Chemistry isn't required in US schools, is it? In any case, I was simply commenting on the analogy being tortured to death above.
posted by bonehead at 10:18 PM on September 6, 2008


I would consider a chemist who did not know the periodic table and be able to use it to predict and understand a whole host of behaviours bizarrely uneducated, possibly incompetent. It's true that it's a simplified representation and that there are many exceptions to the trends implied in the table

bonehead: what I meant wasn't that chemists shouldn't know the periodic table, but rather that they wouldn't need to memorize it by rote. Like there's a difference between sitting down to memorize something, and using the same information over and over again because you use it so much. For example, I know hundreds of classes in the Java API, not because I sat down and memorized them, but because I use them every day. I figured it would be the same way with chemists and the periodic table.
posted by delmoi at 10:41 PM on September 6, 2008


Specifically, where the hell did I even argue anything like that? This seems like a straw man.

As delmoi already pointed out, here is the exact comment where you argue that. I asked specifically about the most efficient pencil-and-paper algorithm for long division where both divisor and dividend are decimals to the hundredths place.
posted by 23skidoo at 6:07 AM on September 7, 2008


Besides, this woman was terrified by one year of calculus? Moron!

I've found out that many people I've talked to who didn't get math, were dissuaded by their teachers' methods of teaching (or by the program the teachers had to adhere to).
posted by ersatz at 7:02 AM on September 7, 2008


This is a pretty mesmerizing argument. Sorry I'm so late to it, but I couldn't write a thing at 2:00 am.
As a parent, it's a BIG problem if you can't help your kids with their work. It can put a kid in a terrible position when they are in a high stakes environment. Also, particularly with math, if you fall behind, you're screwed. Not accounting for parental support as part of a child's education is a giant pedagogical failure. I've experienced this first hand with my kids.
Math is interesting because you have both techniques which can be applied directly without knowing the underlying principles and abstract principles themselves which lead to a higher order understanding of mathematical relationships. People can clearly excel in either one independently. This is the heart of this problem. I can't tell you how many test answers I missed because I dropped a "-" sign. But I'm pretty good with math. I hit my intellectual limit with complex partial differential equations.
I'm more sympathetic to XML's argument. Being able to "do the math" is intellectual power, regardless of ones understanding. My 91 year old mother still does double entry accounting without a calculator, and she takes great pride in the power of her mind. She knows jack about the principles. She's not an abstract thinker.
In general, it seems educators want to skip the boring part and go right to underlying principles in all subjects, not just math. I'm seriously skeptical about this.
posted by Carmody'sPrize at 8:53 AM on September 7, 2008


caddis, I am no longer a member of a teacher's union, because I no longer teach in a K-12 public school. But not only was I a member when I was teaching, I helped form a local. Why? Because I got fired after the end of my first year of teaching. Why did I get fired? Because they fired _all_ of the first year teachers in in the entire district in May, and then rehired them in August _if_ they needed them. I was told not to take it personally.

The reason teacher's unions exist is because without them teachers get treated like shit even more than they do now.

But your rant about teacher's unions didn't get at the question. Your original post implied that teacher's unions have control over curricular issues such as which math texts to use. That is certainly not the case here in New Mexico, and I was wondering whether it is the case elsewhere.
posted by Killick at 9:24 AM on September 7, 2008


As a parent, it's a BIG problem if you can't help your kids with their work.

I don't mean this personally, but I'd think that most parents could either figure it out on their own pretty quick or learn what they needed by dipping into the textbook for a few minutes. We are talking about math for kids in grades three to five here. It isn't rocket science.

Math is interesting because you have both techniques which can be applied directly without knowing the underlying principles and abstract principles themselves which lead to a higher order understanding of mathematical relationships. People can clearly excel in either one independently.

In my experience, this is not at all true. You can excel at memorizing formulae for a while, but if you don't understand the underlying principles, you will reach a limit sooner or later where memorizing is no longer effective. A lot of kids get good grades in grade school by memorizing formulae, but they tend to hit a wall once they get to university math.
posted by ssg at 9:29 AM on September 7, 2008


According to some claims, TERC is measuring poorly.

In the Ridgewood Public School System, TERC has been introduced into two of the village's elementary schools. Contrary to the claims made on the TERC website, math scores on statewide standardized tests for students in these elementary schools have declined ever since the introduction of TERC. Supporters of TERC point to the high math scores of the district as a whole but conveniently omit the fact that the other four elementary schools in the village do not use TERC.

If the idea is to teach problem solving, they haven't solved this one.
posted by Brian B. at 11:06 AM on September 7, 2008




There is one big problem with the general discussion both here and elsewhere.

This issue isn't what is the best way to do math. The issue is: what way are we going to choose to teach an entire generation of public school kids? Whether it is the best method for solving problems is decidedly a secondary issue in this debate. There are issues of teaching ease, testing, etc, which factor into the method chosen. I may not like it either, but that's what matter to the education system.

The reason that's the important question is because it answers the subtext: who are we going to leave behind? For example: immersion is the best method for learning languages, but public schools don't do it that way. Consequently, four years of French for most kids = very little French. However, my guess is that immersion would yield a very bimodal distribution of proficient speakers and completely non-speakers. Maybe that's not acceptable to a bell curve education system.
posted by TheLastPsychiatrist at 11:52 AM on September 7, 2008 [1 favorite]


According to some claims, TERC is measuring poorly.

But how are they testing the kids? If the tests simply test efficiency in solving problems with a pencil and paper, you would expect them to test better using the "standard algorithm" Do the tests measure how much they enjoy math, or how much they understand the underlying principles? I'm sure you could come up with a test that TERC taught kids would do better on.
posted by delmoi at 4:20 PM on September 7, 2008 [1 favorite]


In my experience, this is not at all true. You can excel at memorizing formulae for a while, but if you don't understand the underlying principles, you will reach a limit sooner or later where memorizing is no longer effective. A lot of kids get good grades in grade school by memorizing formulae, but they tend to hit a wall once they get to university math.

Yep. Not everybody is going to do University math. This is exactly the point. Everyone is not infinitely teachable. But we all need to function in the world. People have different needs and capacities. For concrete thinkers, skills are good.

I don't mean this personally, but I'd think that most parents could either figure it out on their own pretty quick or learn what they needed by dipping into the textbook for a few minutes. We are talking about math for kids in grades three to five here. It isn't rocket science.

Maybe. I'm not sure you've met most parents. Many adults do no math. This problem is exactly why this video was produced in the first place.
posted by Carmody'sPrize at 8:06 PM on September 7, 2008


I'm sure you could come up with a test that TERC taught kids would do better on.

Perhaps they should do it then, to avoid the special education stigmatization. Right now they seem bent on selling supplies to their approach.

Here's a recent study on calculator usage in the classroom.

posted by Brian B. at 8:28 PM on September 7, 2008


Maybe. I'm not sure you've met most parents. Many adults do no math. This problem is exactly why this video was produced in the first place.

The problem is that many adults are scared of and hate arithmetic. These adults were educated with the old methods that the video is promoting. If we keep using the old methods that result in some percentage of adults hating arithmetic, we should expect that the kids will hate arithmetic too. We shouldn't keep repeating a failure just because it is a familiar failure.
posted by ssg at 8:37 PM on September 7, 2008 [2 favorites]


But your rant about teacher's unions didn't get at the question. Your original post implied that teacher's unions have control over curricular issues such as which math texts to use. That is certainly not the case here in New Mexico, and I was wondering whether it is the case elsewhere.

In the southwest the teacher's unions are nothing like they are here in the northeast. In the southwest they ar weak and emaciated, too much so, and I think education suffers. Here in the northeast, they are all powerful, too much so, and education suffers. Politics is local. My rant against the teacher's union applies only to that brand of it around here that holds the democratic party by its balls and never fails to squeeze.
posted by caddis at 11:04 PM on September 7, 2008


Another chemist here - though a very uneducated one by bonehead's reckoning. Just last week I was doing some rare earths work, and discovered that there is an element called Gadolinium. Never heard of it before. Never needed to know it existed before.

Actually, I think it'd be cool to know the periodic table, but mostly because just it would make me feel smug, not because I foresee the knowledge of the rare earths in to ever be useful. In fact, memorising the list of elements isn't going to help with the fundamental use of the periodic table - the periodicy of elements. The fact that Niobium comes after Zirconium and before Molybdenum isn't going to give me any information about it's relationship with Tantalum unless I wrote the whole thing out. Which is why I have a periodic table as a mouse pad.

So, as a professional chemist which apparently gives me the right to an opinion on this, I would like it all to be taught. Everything in the old and the new syllabus. In a perfect world, kids would memorise their multiplication tables, learn multiple algorithms to do all four basic arithmatic functions, do lots of approximation and prediction techniques and put all of it into practise with real world problems. But, there is a limited amount of time between Kindergarten and Year 12, by which time some kids need to be learning calculus, and so priorities have to be made. So I would like to put in a plug for being able to do a single algorithm that can deal with any number, letter or base. Then I would prioritise memorising basic facts, then approximation in real world problems. (And then I would prioritise hunting down the bastard who stole the lab calculator again)

The multiple algorithm stuff is pretty cool, but seems more of an extension thing for kids who can do it one way well. Two major advantages I can see - you don't confuse the kids who are already confused with one algorithm (the kids who are good at maths are going to figure out other algorithms by themselves), and you don't need to have teachers that are good at maths. (we need the teachers who are good at maths for calculus)

But I am happy to be proven wrong by people who do this stuff for a living. I'm also happy to accept that there is no one right way of doing this stuff. Education does not have one correct algorithm.

delmoi - I'm sure we're all very impressed you taught yourself to do base-2 arithmatic. Turns out I can do it too. I used the base-10 algorithms you went to such pains to avoid learning. And then I checked them with my calculator.

elpapacito - nice demonstration of how understand the maths is more important than getting it right (33% of 70 is 23.1)

(this got longer and snarkier than I had planned....)
posted by kjs4 at 11:38 PM on September 7, 2008


delmoi - I'm sure we're all very impressed you taught yourself to do base-2 arithmatic.

I didn't teach myself, I learned it in class.
posted by delmoi at 1:43 AM on September 8, 2008


« Older Right at the Edge....  |  The Cornell Evolution Project,... Newer »


This thread has been archived and is closed to new comments