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> If you explain well enough the concepts of > place-value and multiplication, most children > can independently invent an algorithm for long > multiplica

> If you explain well enough the concepts of > place-value and multiplication, most children > can independently invent an algorithm for long > multiplication. You're going to stare at your screen in disbelief, my experience suggests otherwise. A small number of gifted children have, in my experience, been able to work out their own methods, and they've become more efficient over time, and eventually converged to something isomorphic to long multiplication. But this is not the norm. Evidence suggests - and my experience agrees - that correctly teaching process creates the ground-work for moving to understanding. Correct methods, practised over time and in different context, result in an internalisation that leads to an ability to generalise and apply in wider contexts. This is my point about research and evidence-based teaching systems. The existing fads are borne of insufficiently researched and poorly developed methods, badly applied. They are often driven by dogma, and then delivered by teachers who don't properly understand what they're doing. There has to be a better way, and unfortunately, nearly everyone has an opinion, and none of them are supported by anything like enough evidence. And so we continue to damage our children. In parting, much of what you say I agree with, but not all. This isn't really the place to have a lengthy debate, but our positions aren't as far apart as my comment might have you think at first sight.

lmkg 16y ago
> This isn't really the place to have a lengthy debate To the contrary, this is Hacker News! Unfortunately, the situation that I'm referring to with children inventing their own long-multiplication algorithm was presented at a talk, so I can't point to the specific results, if they're even published yet, but my contention is based on an academic research study. The punchline of the experiment was that a full class of approximately-average grade-schoolers were taught math in a novel method, and developed their own multiplication algorithms, and went on to have above-average improvements in math test scores. The development of those algorithms were probably guided to a certain extent, but they looked to me like someone who was working the problem out from the first principles based on the concept of place value. That said, I'm definitely willing to accept the evidence you claim to have (especially since it leaves open the meaning of "correct"). I definitely agree that education should be based on science and not on dogma. Just because we think something ought to work doesn't mean that it works (it usually doesn't), and education is something you don't want to fuck up because the stakes are high and you only get one chance. But, I'm not sure we're even at the point where we can do research yet. Before you can measure results, you need to decide what results you're looking for and how you're measuring them. I'm a mathematician, and I'll be the first to admit that being able to perform long-multiplication isn't actually that useful of a skill, and yet that's mostly what we measure on standardized tests. Understanding what multiplication means and being generally numerate is far more useful and not measured very often (the best we have is word problems). The more desirable side-effects, such as the ability to abstract concepts, to generalize processes, and to apply knowledge from one domain to another, aren't being measured at all, and those are really the only things from my math education that I use in my day-to-day life. Similar things happen across other subjects--knowing what year the War of 1812 happened in isn't useful, while understanding the social, economic, and political conditions that led to that war is useful for the average citizen in a democracy (but doesn't fit well in a scantron). I think we as a society need to first have a big sit-down and figure out what the point of education is. We know it's important, but we've never coherently stated particularly why, and that lack of explicit direction is what lets politics, dogma, and fads more easily take control of the process. Once we've done that, we can let science guide the structure of education. Or rather, we should. There's a bit of a chicken-and-egg problem that without solid backgrounds in quantitative and logical thinking, most people have difficulty making data-driven decisions, and people in general won't get better at that until the education system improves.
- Alex3917 16y ago
  "Unfortunately, the situation that I'm referring to with children inventing their own long-multiplication algorithm was presented at a talk, so I can't point to the specific results, if they're even published yet, but my contention is based on an academic research study." I've read that before too, and I'm guessing that there is a cite for this in Alfie Kohn's book The Schools Our Children Deserve. However, it's been a few years since I've read it now so I can't remember if it's actually in that book or if it was Eleanor Duckworth's book The Having of Wonderful Ideas.
wiredfool 16y ago
Evidence suggests that if my oldest were to come up with a method for multiplication it would involve: scissors, a stapler, and a stick, 5 complicated steps, 2 requests for materials from one of the parents, and it would be abandoned halfway through for some method of making a crane that involves an even bigger stick and rope. On the other hand, going through 100 lessons on reading, spelled out to the word what I was to say and do, and 9 months after starting he's reading 100 pages of books like The Way Things Work when he's supposed to be sleeping. Sometimes rote methods work _really_ well.
- WalterBright 16y ago
  We have a 1000 years of history of what works in education, but people keep ignoring that.
joe_the_user 16y ago
Evidence suggests - and my experience agrees - that correctly teaching process creates the ground-work for moving to understanding. Considering you are talking about evidence, where is yours? I agree that a lot of people make unsupported generalizations about "what works" and "what doesn't work". I'm simply doubtful you can really propose a practical alternative, not even hypothetically practical alternative. I would assert that part of this how extremely difficult it to really determine better teaching methods scientifically, controlling for expectation, controlling for multiple socio-economic factors, controlling for each child's background, etc, etc. The rather rough experiments that anyone can point to show at best that "X works reasonably with teacher of X ability with student of X socio-economic position". Inherently, just about every teaching method is "insufficiently researched". Just about every way that we deal with human beings is "ready, fire, aim" because we simply don't have the resources to fully, scientifically tease out what's the best dealing with the many, many dimensions of human behavior. I'm not against social science because it's better to try to be a systematically as possible. I am against deluding oneself into thinking social science will work like natural, that it will come up with generalized laws that one can follow without constant adjustment.
- RiderOfGiraffes 16y ago
  You ask the very reasonable question: > Considering you are talking about evidence, > where is yours? As I say in http://news.ycombinator.com/item?id=1679203 http://news.ycombinator.com/item?id=1679203 > 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 We're not really arguing different points here - we're both saying it's bloody difficult to do "proper" research in this area, and even harder to come up with anything that's guaranteed to work. I've seen a lot of papers written and witnessed a lot of different techniques. I've seen first hand several fads, and most things work for some children with the right teachers. But I am concerned with the way the whole thing is approached, in part because I have a PhD in math and I know that "research" when in an area that involves people is really, really hard. Especially with children. I know that things have to be done differently in education research, and people who do the work are doing their best. I observe that the situation is still appalling - there's more that needs to be done. I have my personal opinions about what might work, but they are unsupported by anything like scientific evidence, and I'm working closely with both teachers and education researchers to see if my ideas can be tested, and if so, whether they can be made to work. But I won't air them here. ADDED IN EDIT: Wow - a down-vote. Wonder what I said that made someone feel that this comment is of negative value. Interesting.
SiVal 16y ago
"Evidence suggests - and my experience agrees - that correctly teaching process creates the ground-work for moving to understanding." Yes, but this discussion can't really be understood without understanding what it is that the US education system is trying to optimize itself for. In the US, teaching methods are NOT optimized for mathematical proficiency. They are designed to implement a "progressive" social agenda, "social justice," that puts "closing the achievement gap" ahead of all other considerations. The more rigorous the math curriculum, the more obvious our achievement gap, so the progressive ed schools have decided to de-emphasize objectively measurable math performance and emphasize other things that reveal less of an achievement gap. Instead of reasoning through geometry problems and "finding the measure of angle A," which can be easily graded for correctness, we have them increase the amount of time spent "engaging in mathematical discourse." ("Who can name a job that uses math?") Of course all answers are correct so, voila, no more achievement gap. We de-emphasize calculational proficiency--too likely to produce an achievement gap--and emphasize "conceptual understanding," which sounds great and can mean whatever you need it to mean for political purposes. "Do we all understand that there are many ways to multiply?" Sure we do! Instead of "find the answers to these problems," our kids are assigned to "find pictures in magazines of math being used in real life, cut them out, and bring them to class." This is called "engagement." Who can't cut pictures out of magazines? Bye-bye achievement gap, hello social justice. While the East Asians train their primary math teachers in techniques that have been found to maximize math proficiency, our teachers get a very different sort of preparation for teaching out kids: http://www.city-journal.org/html/8_2_a1.html http://www.city-journal.org/html/8_2_a1.html Read the above article, consider what the proficiency-focused Asian schools are doing instead, and imagine the implications for our future.
- jleader 16y ago
  I'm not sure what to say about this; my son is in 5th grade (in California), and his experience doesn't really resemble what you describe. A plurality of his classmates are 1 or 2 generations removed from East Asia, but relatively few of the teachers or administrators are Asian and nearly all were US educated.
  - SiVal 16y ago

lmkg 16y ago

> This isn't really the place to have a lengthy debate To the contrary, this is Hacker News! Unfortunately, the situation that I'm referring to with children inventing their own long-multiplication algorithm was presented at a talk, so I can't point to the specific results, if they're even published yet, but my contention is based on an academic research study. The punchline of the experiment was that a full class of approximately-average grade-schoolers were taught math in a novel method, and developed their own multiplication algorithms, and went on to have above-average improvements in math test scores. The development of those algorithms were probably guided to a certain extent, but they looked to me like someone who was working the problem out from the first principles based on the concept of place value. That said, I'm definitely willing to accept the evidence you claim to have (especially since it leaves open the meaning of "correct"). I definitely agree that education should be based on science and not on dogma. Just because we think something ought to work doesn't mean that it works (it usually doesn't), and education is something you don't want to fuck up because the stakes are high and you only get one chance. But, I'm not sure we're even at the point where we can do research yet. Before you can measure results, you need to decide what results you're looking for and how you're measuring them. I'm a mathematician, and I'll be the first to admit that being able to perform long-multiplication isn't actually that useful of a skill, and yet that's mostly what we measure on standardized tests. Understanding what multiplication means and being generally numerate is far more useful and not measured very often (the best we have is word problems). The more desirable side-effects, such as the ability to abstract concepts, to generalize processes, and to apply knowledge from one domain to another, aren't being measured at all, and those are really the only things from my math education that I use in my day-to-day life. Similar things happen across other subjects--knowing what year the War of 1812 happened in isn't useful, while understanding the social, economic, and political conditions that led to that war is useful for the average citizen in a democracy (but doesn't fit well in a scantron). I think we as a society need to first have a big sit-down and figure out what the point of education is. We know it's important, but we've never coherently stated particularly why, and that lack of explicit direction is what lets politics, dogma, and fads more easily take control of the process. Once we've done that, we can let science guide the structure of education. Or rather, we should. There's a bit of a chicken-and-egg problem that without solid backgrounds in quantitative and logical thinking, most people have difficulty making data-driven decisions, and people in general won't get better at that until the education system improves.

Alex3917 16y ago
"Unfortunately, the situation that I'm referring to with children inventing their own long-multiplication algorithm was presented at a talk, so I can't point to the specific results, if they're even published yet, but my contention is based on an academic research study." I've read that before too, and I'm guessing that there is a cite for this in Alfie Kohn's book The Schools Our Children Deserve. However, it's been a few years since I've read it now so I can't remember if it's actually in that book or if it was Eleanor Duckworth's book The Having of Wonderful Ideas.

wiredfool 16y ago

Evidence suggests that if my oldest were to come up with a method for multiplication it would involve: scissors, a stapler, and a stick, 5 complicated steps, 2 requests for materials from one of the parents, and it would be abandoned halfway through for some method of making a crane that involves an even bigger stick and rope. On the other hand, going through 100 lessons on reading, spelled out to the word what I was to say and do, and 9 months after starting he's reading 100 pages of books like The Way Things Work when he's supposed to be sleeping. Sometimes rote methods work _really_ well.

WalterBright 16y ago
We have a 1000 years of history of what works in education, but people keep ignoring that.

joe_the_user 16y ago

Evidence suggests - and my experience agrees - that correctly teaching process creates the ground-work for moving to understanding. Considering you are talking about evidence, where is yours? I agree that a lot of people make unsupported generalizations about "what works" and "what doesn't work". I'm simply doubtful you can really propose a practical alternative, not even hypothetically practical alternative. I would assert that part of this how extremely difficult it to really determine better teaching methods scientifically, controlling for expectation, controlling for multiple socio-economic factors, controlling for each child's background, etc, etc. The rather rough experiments that anyone can point to show at best that "X works reasonably with teacher of X ability with student of X socio-economic position". Inherently, just about every teaching method is "insufficiently researched". Just about every way that we deal with human beings is "ready, fire, aim" because we simply don't have the resources to fully, scientifically tease out what's the best dealing with the many, many dimensions of human behavior. I'm not against social science because it's better to try to be a systematically as possible. I am against deluding oneself into thinking social science will work like natural, that it will come up with generalized laws that one can follow without constant adjustment.

RiderOfGiraffes 16y ago
You ask the very reasonable question: > Considering you are talking about evidence, > where is yours? As I say in http://news.ycombinator.com/item?id=1679203 http://news.ycombinator.com/item?id=1679203 > 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 We're not really arguing different points here - we're both saying it's bloody difficult to do "proper" research in this area, and even harder to come up with anything that's guaranteed to work. I've seen a lot of papers written and witnessed a lot of different techniques. I've seen first hand several fads, and most things work for some children with the right teachers. But I am concerned with the way the whole thing is approached, in part because I have a PhD in math and I know that "research" when in an area that involves people is really, really hard. Especially with children. I know that things have to be done differently in education research, and people who do the work are doing their best. I observe that the situation is still appalling - there's more that needs to be done. I have my personal opinions about what might work, but they are unsupported by anything like scientific evidence, and I'm working closely with both teachers and education researchers to see if my ideas can be tested, and if so, whether they can be made to work. But I won't air them here. ADDED IN EDIT: Wow - a down-vote. Wonder what I said that made someone feel that this comment is of negative value. Interesting.

SiVal 16y ago

"Evidence suggests - and my experience agrees - that correctly teaching process creates the ground-work for moving to understanding." Yes, but this discussion can't really be understood without understanding what it is that the US education system is trying to optimize itself for. In the US, teaching methods are NOT optimized for mathematical proficiency. They are designed to implement a "progressive" social agenda, "social justice," that puts "closing the achievement gap" ahead of all other considerations. The more rigorous the math curriculum, the more obvious our achievement gap, so the progressive ed schools have decided to de-emphasize objectively measurable math performance and emphasize other things that reveal less of an achievement gap. Instead of reasoning through geometry problems and "finding the measure of angle A," which can be easily graded for correctness, we have them increase the amount of time spent "engaging in mathematical discourse." ("Who can name a job that uses math?") Of course all answers are correct so, voila, no more achievement gap. We de-emphasize calculational proficiency--too likely to produce an achievement gap--and emphasize "conceptual understanding," which sounds great and can mean whatever you need it to mean for political purposes. "Do we all understand that there are many ways to multiply?" Sure we do! Instead of "find the answers to these problems," our kids are assigned to "find pictures in magazines of math being used in real life, cut them out, and bring them to class." This is called "engagement." Who can't cut pictures out of magazines? Bye-bye achievement gap, hello social justice. While the East Asians train their primary math teachers in techniques that have been found to maximize math proficiency, our teachers get a very different sort of preparation for teaching out kids: http://www.city-journal.org/html/8_2_a1.html http://www.city-journal.org/html/8_2_a1.html Read the above article, consider what the proficiency-focused Asian schools are doing instead, and imagine the implications for our future.

jleader 16y ago
I'm not sure what to say about this; my son is in 5th grade (in California), and his experience doesn't really resemble what you describe. A plurality of his classmates are 1 or 2 generations removed from East Asia, but relatively few of the teachers or administrators are Asian and nearly all were US educated.
- SiVal 16y ago