there’s strong evidence that smaller classroom size really does help a lot with performance across a wide variety of subjects.
A smaller classroom contributes to better results, but how exactly?
Does it make easier to explain (to answer every student’s questions and check every student’s mistakes), or does it make easier to maintain discipline (to keep the class quiet and make sure everyone is really doing the exercises)? I think both these effects are helpful, but what proportion do they have in the outcome?
In my opinion, the difficulty of explaining is not that different. It’s not like 2× more students will ask 2× more questions; many questions will be the same. And having more questions asked and answered could help better understanding. There is always a chance another student will come with an unexpected question and make an original mistake, but on the other hand, you can make a Khan Academy video for the whole planet and many people will get it.
The critical part is maintaining the order in the classroom. If there is too much noise, students can’t learn. If you have one disruptivestudent, that’s bad, but if you have two of them, that’s ten times worse because they will encourage each other. So with a larger classroom there is more noise and a higher chance of disruptive students.
If this analysis is correct, there seems to be an easy fix—just throw the disruptive students out of the classroom, and you can have rather good results with large classrooms too. Unless your population already contains too many disruptive students, in which case pretty much your only chance is to separate the other students in special classrooms and teach only them.
easier to maintain discipline (to keep the class quiet and make sure everyone is really doing the exercises)? I think both these effects are helpful
I realize and confess that my sentiments are unusual, that my thinking on this subject is grossly distorted by ideology and therefore not to be trusted, and that I don’t myself know how to set up a learning environment that will actually work for actual children, but I must beg the community’s forgiveness, because I want to say this anyway: I think this ideal of “discipline” causes tremendous harm (which of course I understand is not to say that it doesn’t also have benefits, but those benefits are not the subject of this comment). I consider it a monstrous tragedy that so many millions of people grow up (as I grew up) without any conceptual distinction between learning important things and being enrolled in a school and obeying the commands of the designated “teacher”, with no idea of there being a difference between morality and obedience.
Personally, I’ve mostly recovered from this phenomenon to my satisfaction. I now have an explicit notion that it is morally righteous to learn great ideas and train useful skills, and some experience of the pleasures and satisfactions to be had from these endeavors—which is not to boast that I’m doing well; I would never be so delusionally arrogant as to think that I’m doing well—but I think I’m doing far better than I was before I learned these ideas. It certainly seems so when I contrast myself to my fellow undergraduate students. Last semester at community college, I witnessed a student passionately arguing with an instructor that surely his paper deserved an A- rather than a B+. (I’m given to understand this is not an uncommon occurrence.) I imagine there are many who would take such incidents as evidence that there’s not nearly enough discipline in “our” schools: how insolent of a mere student to argue with an instructor! I, however, draw a different moral. I wanted to cry out to the student: Don’t you see how silly this is? Your work, your creation is already good or already bad, no matter what letter the instructor writes on it afterwards! But perhaps it was I who was being silly. The student, of course, didn’t care about good writing; he just wanted to get into the University of California at Berkeley. That was the highest goal he had been trained to aspire to, from the days when his elementary-school caretakers rewarded him for being quiet and doing what all the other children were doing. Again, I do not claim that I know how society should be organized; any particular reform or revolution I might propose could very well just make things worse. But can I at least say that it’s sad to see entire generations of human minds systematically crippled in this way?---because it’s sad.
We obviously use the word “discipline” to mean different things. For me it’s something like “stop talking loudly while the teacher is trying to explain a difficult concept to your classmates”.
As an illustration, here is a quote from my favourite blog about teaching:
A teacher in a British school is likely to be used to starting to do something, even something as simple as speaking, and having to stop what they are doing due to deliberate disobedience. If you are not a teacher it might be hard to imagine how frustrating this defiance is. I can only suggest that you imagine that feeling you get when you are in a traffic jam on an important journey. Now imagine how you feel when you think the traffic is starting to move on, only for it to grind to a halt a second later, and imagine that happening repeatedly for hours on end. Now imagine how you feel when you realise that the hold-up is not actually due to an accident ahead, or a busy road, but is in fact due to somebody (probably a caravan owner) deliberately driving at 10mph in front of you and not letting anyone overtake. Now imagine that you are trapped in this situation for two dozen hours a week. Finally, imagine that every so often your boss drives up to your window and tells you that if you are trapped in a traffic jam it must be because you are a crap driver. If you can imagine that, then you have some idea how frustrating it feels to be a teacher.
Are you familiar with the signaling theory of education? I think that, properly considered, it makes sense of a lot of the things you find so aggravating.
Sort of (if ability is hard to directly observe, but higher-ability people find it easier to obtain credentials, then there could be an equilibrium where one needs a credential in order to be taken seriously, even if the process of obtaining the credential doesn’t actually do anything), but not in any substantive detail. But really (notwithstanding a book I had daydreamed of writing), it’s probably better that I don’t look into it. As I keep telling myself (and keep neglecting to take my own advice), it’s much healthier to just focus on doing good intellectual work, rather than waste any more precious time and emotional energy continuing to feel pointlessly bitter and resentful that “society” (whatever that means) doesn’t care about the sorts of things I consider good work.
(Speaking of healthy working habits, I’m going to try taking out a $20 StickK contract and putting “127.0.0.1 lesswrong.com\n127.0.0.1 news.ycombinator.com\n127.0.0.1 reddit.com″ in my /etc/hosts for 14 days to see if I can remember what it feels like to not be constantly distracted; wish me luck.)
I teach writing at a community college (I began in January), and I agree with this.
I wouldn’t see that student as a sign of poor discipline. If the student was arguing solely about the grade, then like you, I would see it as a waste of time and emotional energy—his and mine.
Incidentally, one of the things I like about the class I’m teaching is that, even before I got there, the syllabus was set up to get students thinking about their purposes in writing the various essays they write, and the purposes the authors of the assigned readings had. Many of my students aren’t getting further than “the purpose is to inform” (argh!) yet, but at least I have an opportunity to teach the difference between instrumental goals and terminal goals.
(Meta-discourse note: some time after writing the parent, I worried that I had worded it far too harshly. I usually try to keep most of my comments here very close to being emotionally neutral, on the grounds it’s better to err on the side of being Spock-like than to risk letting my passion tempt me into saying something obviously wrong or harmful (which has happened a few times). But given the karma count and lack of disapproving replies to the parent, perhaps I didn’t actually do so poorly by making an exception this time? Maybe I should even update a little bit in the direction of thinking that it’s okay to express emotion sometimes, as long as you clearly explain what you’re doing? I’m not sure.)
[Edited to add: Actually, I still feel guilty about being non-nice, so I’ve edited out the two instances of cusswords, which, while entertaining, didn’t actually add any substantive content.]
If this analysis is correct, there seems to be an easy fix—just throw the disruptive students out of the classroom, and you can have rather good results with large classrooms too.
The reason this isn’t implemented is that children are forced to attend school. If they could get out of classes without consequent punishment, not just one or two ‘disruptives’ but many students might opt out. A school doesn’t have anywhere to keep such a group; classes are in large part make-work to occupy students.
On the other hand, if you punished disruptive students but did so outside of class, the habitual disruptives would spend a lot of time in punishment sessions, and would definitely not learn their lessons / pass end of year exams / etc. Schools in the US* prefer to have everyone barely pass exams, to 80% passing with high scores and 20% failing irretrievably. The failing students’ parents have too much political power over the schools.
I’m not from the US, but have seen enough people complaining about US schools on the ‘net. The Israeli public schools I went to in the 90s were the same. Every time teachers tried to set up separate classes for non-disruptive students who could be taught instead of disciplined, the non-eligible students’ parents complained.
Schools in the US prefer to have everyone barely pass exams, to 80% passing with high scores and 20% failing irretrievably. The failing students’ parents have too much political power over the schools.
I can’t believe I didn’t think of that before. The unwillingness to risk (localized or individual) failure is the strongest guarantee of mediocrity.
Does it? By many metrics the US does better with gifted and talented education than much of the world. For example, the US has some of the highest per a capita rates of Noble Prize winners and Fields Medal winners, more than Britain or France. If anything, the US is doing badly on the average case but is doing a lot better with the very smart students.
Edit: This claim is massively wrong, see Douglas’s remark below.
Someone a while ago told me this I think and I must have not bothered checking it. Yeah, this is unambiguously wrong as of right now. It is possible that this was true until some point quite a few years ago, but is clearly false today. Thanks for catching me on that.
You shouldn’t reason from Nobel Prize per capita all the way back to gifted & talented education without bringing in many other factors to your regression.
The US is the wealthiest economy in the world with the best elite higher education establishment with some of the largest investments in STEM or R&D in general, with the largest Jewish population outside Israel (which, IIRC, beats the US on per capita measures), and as wedrifid pointed out, for all these factors attracts the best students from across the world. Just off the top of my head.
This means that our G&T programs could easily be underperforming and a simple gross observation of per capita Nobelists not make this instantly obvious. A better approach would be to simply look for experiments, natural or otherwise, on funding for G&T programs and seeing how they do.
If anything, the US is doing badly on the average case but is doing a lot better with the very smart students.
Either that or they are doing well at acquiring very smart students (either by immigration or the genetic inheritance from historic immigration patterns.)
Does it make easier to explain (to answer every student’s questions and check every student’s mistakes), or does it make easier to maintain discipline (to keep the class quiet and make sure everyone is really doing the exercises)?
Your disjunction isn’t complete there: it could be something else, like how many questions are asked. We LWers are of course familiar with the testing effect, but not so familiar with Bloom’s 2 Sigma problem. Alas, I cannot seem to find the reference now, but I recall reading that in tutoring, students are asked 2 or 3 orders of magnitude more questions than in ordinary classrooms.
A smaller classroom contributes to better results, but how exactly?
Does it make easier to explain (to answer every student’s questions and check every student’s mistakes), or does it make easier to maintain discipline (to keep the class quiet and make sure everyone is really doing the exercises)? I think both these effects are helpful, but what proportion do they have in the outcome?
In my opinion, the difficulty of explaining is not that different. It’s not like 2× more students will ask 2× more questions; many questions will be the same. And having more questions asked and answered could help better understanding. There is always a chance another student will come with an unexpected question and make an original mistake, but on the other hand, you can make a Khan Academy video for the whole planet and many people will get it.
The critical part is maintaining the order in the classroom. If there is too much noise, students can’t learn. If you have one disruptive student, that’s bad, but if you have two of them, that’s ten times worse because they will encourage each other. So with a larger classroom there is more noise and a higher chance of disruptive students.
If this analysis is correct, there seems to be an easy fix—just throw the disruptive students out of the classroom, and you can have rather good results with large classrooms too. Unless your population already contains too many disruptive students, in which case pretty much your only chance is to separate the other students in special classrooms and teach only them.
I realize and confess that my sentiments are unusual, that my thinking on this subject is grossly distorted by ideology and therefore not to be trusted, and that I don’t myself know how to set up a learning environment that will actually work for actual children, but I must beg the community’s forgiveness, because I want to say this anyway: I think this ideal of “discipline” causes tremendous harm (which of course I understand is not to say that it doesn’t also have benefits, but those benefits are not the subject of this comment). I consider it a monstrous tragedy that so many millions of people grow up (as I grew up) without any conceptual distinction between learning important things and being enrolled in a school and obeying the commands of the designated “teacher”, with no idea of there being a difference between morality and obedience.
Personally, I’ve mostly recovered from this phenomenon to my satisfaction. I now have an explicit notion that it is morally righteous to learn great ideas and train useful skills, and some experience of the pleasures and satisfactions to be had from these endeavors—which is not to boast that I’m doing well; I would never be so delusionally arrogant as to think that I’m doing well—but I think I’m doing far better than I was before I learned these ideas. It certainly seems so when I contrast myself to my fellow undergraduate students. Last semester at community college, I witnessed a student passionately arguing with an instructor that surely his paper deserved an A- rather than a B+. (I’m given to understand this is not an uncommon occurrence.) I imagine there are many who would take such incidents as evidence that there’s not nearly enough discipline in “our” schools: how insolent of a mere student to argue with an instructor! I, however, draw a different moral. I wanted to cry out to the student: Don’t you see how silly this is? Your work, your creation is already good or already bad, no matter what letter the instructor writes on it afterwards! But perhaps it was I who was being silly. The student, of course, didn’t care about good writing; he just wanted to get into the University of California at Berkeley. That was the highest goal he had been trained to aspire to, from the days when his elementary-school caretakers rewarded him for being quiet and doing what all the other children were doing. Again, I do not claim that I know how society should be organized; any particular reform or revolution I might propose could very well just make things worse. But can I at least say that it’s sad to see entire generations of human minds systematically crippled in this way?---because it’s sad.
[Slightly edited from original version]
We obviously use the word “discipline” to mean different things. For me it’s something like “stop talking loudly while the teacher is trying to explain a difficult concept to your classmates”.
As an illustration, here is a quote from my favourite blog about teaching:
Are you familiar with the signaling theory of education? I think that, properly considered, it makes sense of a lot of the things you find so aggravating.
Sort of (if ability is hard to directly observe, but higher-ability people find it easier to obtain credentials, then there could be an equilibrium where one needs a credential in order to be taken seriously, even if the process of obtaining the credential doesn’t actually do anything), but not in any substantive detail. But really (notwithstanding a book I had daydreamed of writing), it’s probably better that I don’t look into it. As I keep telling myself (and keep neglecting to take my own advice), it’s much healthier to just focus on doing good intellectual work, rather than waste any more precious time and emotional energy continuing to feel pointlessly bitter and resentful that “society” (whatever that means) doesn’t care about the sorts of things I consider good work.
(Speaking of healthy working habits, I’m going to try taking out a $20 StickK contract and putting “127.0.0.1 lesswrong.com\n127.0.0.1 news.ycombinator.com\n127.0.0.1 reddit.com″ in my /etc/hosts for 14 days to see if I can remember what it feels like to not be constantly distracted; wish me luck.)
I teach writing at a community college (I began in January), and I agree with this.
I wouldn’t see that student as a sign of poor discipline. If the student was arguing solely about the grade, then like you, I would see it as a waste of time and emotional energy—his and mine.
Incidentally, one of the things I like about the class I’m teaching is that, even before I got there, the syllabus was set up to get students thinking about their purposes in writing the various essays they write, and the purposes the authors of the assigned readings had. Many of my students aren’t getting further than “the purpose is to inform” (argh!) yet, but at least I have an opportunity to teach the difference between instrumental goals and terminal goals.
Fully agreed!
(Meta-discourse note: some time after writing the parent, I worried that I had worded it far too harshly. I usually try to keep most of my comments here very close to being emotionally neutral, on the grounds it’s better to err on the side of being Spock-like than to risk letting my passion tempt me into saying something obviously wrong or harmful (which has happened a few times). But given the karma count and lack of disapproving replies to the parent, perhaps I didn’t actually do so poorly by making an exception this time? Maybe I should even update a little bit in the direction of thinking that it’s okay to express emotion sometimes, as long as you clearly explain what you’re doing? I’m not sure.)
[Edited to add: Actually, I still feel guilty about being non-nice, so I’ve edited out the two instances of cusswords, which, while entertaining, didn’t actually add any substantive content.]
The reason this isn’t implemented is that children are forced to attend school. If they could get out of classes without consequent punishment, not just one or two ‘disruptives’ but many students might opt out. A school doesn’t have anywhere to keep such a group; classes are in large part make-work to occupy students.
On the other hand, if you punished disruptive students but did so outside of class, the habitual disruptives would spend a lot of time in punishment sessions, and would definitely not learn their lessons / pass end of year exams / etc. Schools in the US* prefer to have everyone barely pass exams, to 80% passing with high scores and 20% failing irretrievably. The failing students’ parents have too much political power over the schools.
I’m not from the US, but have seen enough people complaining about US schools on the ‘net. The Israeli public schools I went to in the 90s were the same. Every time teachers tried to set up separate classes for non-disruptive students who could be taught instead of disciplined, the non-eligible students’ parents complained.
I can’t believe I didn’t think of that before. The unwillingness to risk (localized or individual) failure is the strongest guarantee of mediocrity.
It also explains the state of gifted & talented education, incidentally.
Does it? By many metrics the US does better with gifted and talented education than much of the world. For example, the US has some of the highest per a capita rates of Noble Prize winners and Fields Medal winners, more than Britain or France. If anything, the US is doing badly on the average case but is doing a lot better with the very smart students.
Edit: This claim is massively wrong, see Douglas’s remark below.
What is your source for per capita rates?
France has 4x Fields medalists per capita as the US. (and the UK is the geometric mean). (or try wikipedia) For science Nobels, the UK beats the US, which beats France.
Someone a while ago told me this I think and I must have not bothered checking it. Yeah, this is unambiguously wrong as of right now. It is possible that this was true until some point quite a few years ago, but is clearly false today. Thanks for catching me on that.
You shouldn’t reason from Nobel Prize per capita all the way back to gifted & talented education without bringing in many other factors to your regression.
The US is the wealthiest economy in the world with the best elite higher education establishment with some of the largest investments in STEM or R&D in general, with the largest Jewish population outside Israel (which, IIRC, beats the US on per capita measures), and as wedrifid pointed out, for all these factors attracts the best students from across the world. Just off the top of my head.
This means that our G&T programs could easily be underperforming and a simple gross observation of per capita Nobelists not make this instantly obvious. A better approach would be to simply look for experiments, natural or otherwise, on funding for G&T programs and seeing how they do.
Either that or they are doing well at acquiring very smart students (either by immigration or the genetic inheritance from historic immigration patterns.)
.
Your disjunction isn’t complete there: it could be something else, like how many questions are asked. We LWers are of course familiar with the testing effect, but not so familiar with Bloom’s 2 Sigma problem. Alas, I cannot seem to find the reference now, but I recall reading that in tutoring, students are asked 2 or 3 orders of magnitude more questions than in ordinary classrooms.