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I've spoken with many people about these systems and methods. The interesting thing that I've found is that lots of adults are dead set against them, even thou

I've spoken with many people about these systems and methods. The interesting thing that I've found is that lots of adults are dead set against them, even though some research shows that they are far more effective than previous methods. (No, sorry, I can't cite the research off-hand, it's been shown to me by others and I don't have the references) Adults don't learn in the same way children learn. Much of the criticism levelled by adults against these systems (and others) is based on their own ability (or more accurately, inability) to use or understand them. Such a basis for criticism is fundamentally broken. We need to know how children learn, and how they can learn in a way that enables understanding, and enables future progress. "Chunking" in particular seems to work especially well as a basis for moving on and developing a deeper understanding of division and related processes. We need fewer fads and more evidence-based child-specific learning systems, especially those that take into account and control for effects such as teacher enthusiasm/understanding and the Hawthorne effect. (Note: we also need to understand that there is a huge variation even amongst children, but that's another rant.)

KoZeN 16y ago
We need fewer fads and more evidence-based child-specific learning systems Couldn't agree more. My partner is a science teacher and this is one of her biggest complaints. Every week, teachers are faced with new research indicating that what their doing is either wrong or can be dramatially improved through dramatic change. Less criticism, more evidence.
- tonygonz 16y ago
  Please allow me to cast a bit of skepticism on this topic. I have an MA in Math Education, and am currently working on a PhD in Education, so I have had a lot of first-hand experience with "how the sausage is made" with regards to education research. Teaching fads are all coming from research-oriented schools of education like those that I am getting my degree from. While the new methods that are being introduced are "research based", I find much of the research being conducted as highly questionable. Since around the 1970s there has been a strong shift away from quantitative research towards qualitative research in education, which IMHO allows researchers to pretty much "prove" anything that they want. I think that when most people hear the phrase "better teaching methods" they tend to assume that this means "better ways of getting students to learn the target curriculum", but in my experience actual mastery of, say, math skills now takes a back seat to, for example, higher self esteem or even just hating math less. The result is that over the past several decades students in the US, at least, where such trends towards new teaching methods seem to be the strongest, are performing worse and worse on international comparisons of math and science skills (see, for example, the TIMMS: http://nces.ed.gov/timss/ http://nces.ed.gov/timss/). Meanwhile the countries that now have the best performing students in terms of mathematics ability are largely from Asian countries that predominantly use methods now considered passe here. The elephant in the room is that the biggest reasons for poor math skills are not related to teaching methods, but rather are cultural issues---starting especially in the middle school years, most students just don't want to be seen as being good at math, as that can be a social stigma for many students of that age (I'm sure that many readers of this site can relate...). A student who wants to learn will do so, no matter how bad the teacher or the teacher's methods. A student who doesn't want to learn will not, no matter how good the teacher or the methods.
  - RiderOfGiraffes 16y ago
    How much research is done on "Drill (and kill)" methods versus the more "modern" alternatives? Probably none. The dogma is that "drill and kill" is really bad, so no one actually does research on whether it works. It seems to me (not in the math education research field, but not that far away) that the "research" being done is often bedevilled and ham-strung by these preconceived dogma. (Primarily I'm agreeing with you) I raise a cautious note about one of your points though: > A student who wants to learn will do so, no matter > how bad the teacher or the teacher's methods I used to believe this, and I want to believe it, but I've now seen several instances of otherwise bright children with bad teachers making no progress. Then a brief intervention by a gifted tutor has led to the child catching up and surpassing the other in their class. You might claim that this is a gifted tutor by-passing the cultural issues by providing enough interest to make the child engaged despite the peer pressure. Perhaps. But I now do believe that a poor to middling teacher in math will actively prevent many otherwise perfectly capable students from achieving their potential. That's why I'm heavily involved in math enrichment programs.
  - deleted 16y ago
    [deleted]
tel 16y ago
I'm not sure that adults learning differently from children is vital here. I think it just comes into play that adults already learned these things and have an expectation to know them; children are looking fresh and are allowed to not know things. I think many adults would benefit from relearning math to use grids and chunks. To this day I think about arithmetic using my own analogues to the grid and chunk methods. They're far closer to the intuitive meanings of the operators and are more useful when you start generalizing. They get at the heart of the divide between meaning and representation. (And for that, see GEB) Algebra is representation of abstract objects via formal computational procedures (sort of). The formal procedures are the mechanism for proof, but really have no weight of meaning. I to this day cannot long divide (without regenerating the rules anyway) and get weird stares when I tell people that. But then I stare back: how many ways can you describe what division means?
wiredfool 16y ago
At least a few of the people dead set against these methods are college professors seeing new students come in with no math skill whatsoever. See: http://cliffmass.blogspot.com/2010/01/how-good-are-uw-students-in-math.html http://cliffmass.blogspot.com/2010/01/how-good-are-uw-studen... The 'classic' methods are algorithims. They work. They aren't any more complicated than the various other methods, but at least they work in all situations. The other methods, while they may be useful for fermi problems, don't always have a clear way to progress when the problems become harder. And the kicker is, they're no simpler when you account for all the 'non-easy' numbers. See: http://www.youtube.com/watch?v=Tr1qee-bTZI http://www.youtube.com/watch?v=Tr1qee-bTZI Whatever the reason, there's a dramatic decline in the understanding of basic math by students at reasonably good universities over the last 20ish years. I've done the math, and I think I was on the tail end of a conservative swing. There's been one new math swing in that time, and I think we're heading back again. (This as the parent of small kids who's done way too much reading about the various curricula that are available, and how even the best ones used in classrooms pretty much suck. Jump and Singapore are the two that I know of that are pretty good, but they're not not USAian, so they don't get used in the schools. It is kinda funny going over problems in Jump and seeing the canadian cultural content.)
- seltzered 16y ago
  Came in here to post that exact video, it made perfect sense to me. I learned with the classic algorithms, and have kindof self-realized some of the newer methods after college when needing to solve some basic math in my head to "eyeball" whether something will work. It's convenient, but not exact. You can't use it in areas where exact answers are required to make sure you're right, and the classical equations serve as "debug/trace information" to see where you went wrong.
  - Someone 16y ago
    I disagree with that video. The alternative methods for multiplication and long division are fine. For long division, the classical one doesn't even work on harder problems. Listen carefulley, and you'll hear several "because we know two times six equals twelve"; for most, that will not work when dividing by say 4367. Also, I doubt that price of books is part of this problem. There is one argument that I think is valid: kids get insufficient exercise to master these. Even that need not be a bad thing. I cannot recite the bible, but the time I gained by not even attempting to master that (I think) gave me time to read a zillion other books.
godDLL 16y ago
There is a part in the article where it says that some children feel long division is a pointless chore. I still feel like that. When I had to do this long division stuff in school, I'd split up the numbers into chunks in my head, and calculate the result with these small chunks (27x43 = (27x40) + (27x3) = 1080 + 81 = 1161); just to be sure. My head could not get around long division back then. I can now, but it would feel like a pointless chore – why do that when I can just chunk it and sum it up in my head?

KoZeN 16y ago

We need fewer fads and more evidence-based child-specific learning systems Couldn't agree more. My partner is a science teacher and this is one of her biggest complaints. Every week, teachers are faced with new research indicating that what their doing is either wrong or can be dramatially improved through dramatic change. Less criticism, more evidence.

tonygonz 16y ago
Please allow me to cast a bit of skepticism on this topic. I have an MA in Math Education, and am currently working on a PhD in Education, so I have had a lot of first-hand experience with "how the sausage is made" with regards to education research. Teaching fads are all coming from research-oriented schools of education like those that I am getting my degree from. While the new methods that are being introduced are "research based", I find much of the research being conducted as highly questionable. Since around the 1970s there has been a strong shift away from quantitative research towards qualitative research in education, which IMHO allows researchers to pretty much "prove" anything that they want. I think that when most people hear the phrase "better teaching methods" they tend to assume that this means "better ways of getting students to learn the target curriculum", but in my experience actual mastery of, say, math skills now takes a back seat to, for example, higher self esteem or even just hating math less. The result is that over the past several decades students in the US, at least, where such trends towards new teaching methods seem to be the strongest, are performing worse and worse on international comparisons of math and science skills (see, for example, the TIMMS: http://nces.ed.gov/timss/ http://nces.ed.gov/timss/). Meanwhile the countries that now have the best performing students in terms of mathematics ability are largely from Asian countries that predominantly use methods now considered passe here. The elephant in the room is that the biggest reasons for poor math skills are not related to teaching methods, but rather are cultural issues---starting especially in the middle school years, most students just don't want to be seen as being good at math, as that can be a social stigma for many students of that age (I'm sure that many readers of this site can relate...). A student who wants to learn will do so, no matter how bad the teacher or the teacher's methods. A student who doesn't want to learn will not, no matter how good the teacher or the methods.
- RiderOfGiraffes 16y ago
  How much research is done on "Drill (and kill)" methods versus the more "modern" alternatives? Probably none. The dogma is that "drill and kill" is really bad, so no one actually does research on whether it works. It seems to me (not in the math education research field, but not that far away) that the "research" being done is often bedevilled and ham-strung by these preconceived dogma. (Primarily I'm agreeing with you) I raise a cautious note about one of your points though: > A student who wants to learn will do so, no matter > how bad the teacher or the teacher's methods I used to believe this, and I want to believe it, but I've now seen several instances of otherwise bright children with bad teachers making no progress. Then a brief intervention by a gifted tutor has led to the child catching up and surpassing the other in their class. You might claim that this is a gifted tutor by-passing the cultural issues by providing enough interest to make the child engaged despite the peer pressure. Perhaps. But I now do believe that a poor to middling teacher in math will actively prevent many otherwise perfectly capable students from achieving their potential. That's why I'm heavily involved in math enrichment programs.
- deleted 16y ago
  [deleted]

tel 16y ago

I'm not sure that adults learning differently from children is vital here. I think it just comes into play that adults already learned these things and have an expectation to know them; children are looking fresh and are allowed to not know things. I think many adults would benefit from relearning math to use grids and chunks. To this day I think about arithmetic using my own analogues to the grid and chunk methods. They're far closer to the intuitive meanings of the operators and are more useful when you start generalizing. They get at the heart of the divide between meaning and representation. (And for that, see GEB) Algebra is representation of abstract objects via formal computational procedures (sort of). The formal procedures are the mechanism for proof, but really have no weight of meaning. I to this day cannot long divide (without regenerating the rules anyway) and get weird stares when I tell people that. But then I stare back: how many ways can you describe what division means?

wiredfool 16y ago

At least a few of the people dead set against these methods are college professors seeing new students come in with no math skill whatsoever. See: http://cliffmass.blogspot.com/2010/01/how-good-are-uw-students-in-math.html http://cliffmass.blogspot.com/2010/01/how-good-are-uw-studen... The 'classic' methods are algorithims. They work. They aren't any more complicated than the various other methods, but at least they work in all situations. The other methods, while they may be useful for fermi problems, don't always have a clear way to progress when the problems become harder. And the kicker is, they're no simpler when you account for all the 'non-easy' numbers. See: http://www.youtube.com/watch?v=Tr1qee-bTZI http://www.youtube.com/watch?v=Tr1qee-bTZI Whatever the reason, there's a dramatic decline in the understanding of basic math by students at reasonably good universities over the last 20ish years. I've done the math, and I think I was on the tail end of a conservative swing. There's been one new math swing in that time, and I think we're heading back again. (This as the parent of small kids who's done way too much reading about the various curricula that are available, and how even the best ones used in classrooms pretty much suck. Jump and Singapore are the two that I know of that are pretty good, but they're not not USAian, so they don't get used in the schools. It is kinda funny going over problems in Jump and seeing the canadian cultural content.)

seltzered 16y ago
Came in here to post that exact video, it made perfect sense to me. I learned with the classic algorithms, and have kindof self-realized some of the newer methods after college when needing to solve some basic math in my head to "eyeball" whether something will work. It's convenient, but not exact. You can't use it in areas where exact answers are required to make sure you're right, and the classical equations serve as "debug/trace information" to see where you went wrong.
- Someone 16y ago
  I disagree with that video. The alternative methods for multiplication and long division are fine. For long division, the classical one doesn't even work on harder problems. Listen carefulley, and you'll hear several "because we know two times six equals twelve"; for most, that will not work when dividing by say 4367. Also, I doubt that price of books is part of this problem. There is one argument that I think is valid: kids get insufficient exercise to master these. Even that need not be a bad thing. I cannot recite the bible, but the time I gained by not even attempting to master that (I think) gave me time to read a zillion other books.

godDLL 16y ago

There is a part in the article where it says that some children feel long division is a pointless chore. I still feel like that. When I had to do this long division stuff in school, I'd split up the numbers into chunks in my head, and calculate the result with these small chunks (27x43 = (27x40) + (27x3) = 1080 + 81 = 1161); just to be sure. My head could not get around long division back then. I can now, but it would feel like a pointless chore – why do that when I can just chunk it and sum it up in my head?