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Author Topic: doing the math on education
LetterRip
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Here is why the US has such disparities in education outcomes amongst public schools.

Two primary reasons

1) Local funding - thus wealthy districts can attract better quality teachers

2) class size reduction - which requires more teachers and thus shifts the average quality significantly downward.

If we look at a normal distribution representing teacher skill - an average teacher achieves 1 year of educational attainment for 1 year of education time. One standard deviation above the norm achieves 2 years; Two SD above the norm 3 years. Conversely those below the norm achieve less than a years worth of education in a year of time half, or even a quarter of a year. (These aren't exact, can find the exact numbers if interested - but the point is the top teachers and top half of teacher drastically outperform the teachers at lower percentiles)

So the more teachers required - the more teachers you must draw from the bottom of the distribution to meet the total teacher demand. Thus reducing classroom size - surprisingly - leads to lower average teacher quality, and thus a net decrease in learning.

This decrease in learning isn't distributed uniformly. The wealthy districts will just increase the number of individuals they draw from the top of the distribution, so overall will experience little or no decrease in education quality and might achieve a slight gain. However, the impact on poorer districts will be devastating because the good teachers that were at the poor schools will be pulled away to fill the slots at the wealthy schools created by the reduced class size and thus those will be replaced by less skilled teachers. Then due to reduced class sizes will require even more teachers and those will be drawn from even further down the distribution.

The net result is that poor districts fall behind two to three years or more of that achieved by wealthy districts in terms of education achieved.

To quantify this lets do a simplified thought experiment of two schools a poor school and rich school of equal size. We start with a pool of 100 teachers, and we only hire half of them. School Rich picks the top 25 teachers. School Poor picks the next 25 teachers.

School Rich - average percentile rank score of teachers is 87.5 percentile ( (75+100) / 2 )

School Poor - average percentile rank score of teachers is 62.5 ( (50+75) / 2 )

So both schools have above average teachers for all of their students.

Now let us double the number of teachers.

School Rich - average percentile rank score of teachers is 75 percentile ( (50+100) / 2 )

School Poor - average percentile rank score of teachers is 25 ( (0 + 50) / 2 )

Now we see that the average teacher quality fell for both schools. School Rich - the decrease in average quality is modest (7.5 percentile) which is probably offset by the 50% reduction in class size.

School Poor though - the decrease in average quality is an enormous - a drop of 37.5 percentile. They have gone from having almost all teachers above average, to having almost all teachers below average.

Note that pupil/teacher ratios have gone from 27.4 in 1955 to 14.7 (projected) in 2013.

So we have literally had an almost halving in class sizes.

http://nces.ed.gov/programs/digest/d09/tables/dt09_064.asp

My thought experiment doesn't perfectly hold (we aren't at 100% demand for teachers so some from the very bottom of the distribution are excluded; etc.).

[ December 03, 2013, 04:51 PM: Message edited by: LetterRip ]

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PSRT
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quote:
Note that pupil/teacher ratios have gone from 27.4 in 1955 to 14.7 (projected) in 2013.

So we have literally had an almost halving in class sizes.

This actually doesn't follow. A huge amount of the increase in staffing has come as we integrate children with special needs into public schools, and make accommodations for those children.

I am making no comment on the rest of the post at this time.

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Pyrtolin
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quote:
So the more teachers required - the more teachers you must draw from the bottom of the distribution to meet the total teacher demand. Thus reducing classroom size - surprisingly - leads to lower average teacher quality, and thus a net decrease in learning.
This assumes that the the pool of teachers is both effectively saturated and has an even distribution, such that it's impossible to find sufficient teachers to meet the smaller class requirements without dipping into objectively poor quality rather than by moving the center up above a reasonable baseline standard for good results.

Less good than the best is not the same as bad, and is seems rather fallacious to assume that better than average is more important than having the average be better than a certain reasonable minimum standard such that the returns on overall difference in quality isn't as significant..

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Seriati
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I agree with Pyrtolin on the statistical points. You can't assume an even distribution here. I'd suspect that most teachers are actually above average, such that you can staff the majority of schools at or slightly above the total average quality, even at comparitively high usage rates.

However is correct that smaller class size, and another union contract favorite - tenure - can definitely supress the average quality in a school. All it takes is a slight decline in effort post tenure to effectively "lock-in" a below average result for most schools, and that's magnified greatly where truly awful teachers achieve tenure.

By the way it's interesting to me L-R, that you get the impact this could have for teachers but don't believe the same principals apply for doctors.

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KidTokyo
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Local funding is only a problem because wealth inequality is pervasive. If the economy was flatter, locality need not create such imbalance of outcomes.
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PSRT
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quote:
However is correct that smaller class size, and another union contract favorite - tenure - can definitely supress the average quality in a school.
Fortunately, on average, the availability of job security raises the talent pool available for hiring, and correlates more strongly with increased teacher quality than decreased teacher quality.
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LetterRip
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Seriati,

it does apply to doctors however, most doctors are over trained/over qualified for most functions that we have doctors perform.

Ie say we have 10 different functions of doctors, requiring skill level from 100 to 1000. Average doctor skill level is 800. So when they do a task requiring a skill of 100, they are wasting 700 skill points. So if we substitute individuals with skill level 500 or 400, or 300, etc. (PAs, Nurse Practitioners, Medics, etc.) They are still overqualified for the 100 level tasks and thus we can expect the same outcome quality for the low level tasks. Freeing up more highly trained doctors to do 500+ level tasks. Since we free up highly trained doctors for the high level tasks - they can spend more time per high level task improving outcomes, thus by allowing less trained individuals for easy tasks, we get an overall increase in quality of outcome at all levels.

There are many many tasks that doctors are currently used for on a regular basis that could be done by someone with one year of basic schooling.

Note that I view teachers in a similar capacity - divide the 'teacher' task into subtasks - (lecturing, test supervising, tutoring, mentoring, test and homework grading; emotional support; daycare supervision, etc.) Right now we have teachers doing all of those tasks - so the quality of the teacher is their 'weakest link'.

So we have teachers that are overqualified for the 'easy tasks' (test administration) wasting their time; and we have teachers who are underqualified for the tough tasks who are wasting students time.

I'd like teaching reorganized so amazing lecturers have huge classes (ie video lecturers teaching millions of students); test supervising can be done by quite unskilled individuals; test and homework grading mostly need little skill and can often be automated; daycare supervision of modest skill/training; etc.

Pyr,

quote:
This assumes that the the pool of teachers is both effectively saturated and has an even distribution, such that it's impossible to find sufficient teachers to meet the smaller class requirements without dipping into objectively poor quality rather than by moving the center up above a reasonable baseline standard for good results.
Objectively 'poorer quality' - we can readily quantify relative difference in effectiveness, an absolute qualification is a lot more subjective. As stated at the beginning different deciles/quartiles have drastic differences in expected outcome for students. With top decile gaining multiple years of ground relative to median teachers, and bottom decile teachers losing multiple years of ground relative to median.

quote:
Less good than the best is not the same as bad
Yes, but the distribution isn't 'skewed' in reality. So the differnce it outcomes by quartile or decile is drastic.

quote:
and is seems rather fallacious to assume that better than average is more important than having the average be better than a certain reasonable minimum standard such that the returns on overall difference in quality isn't as significant..
Yes it would be good if there was a small gap between the least qualified teacher by increasing the average quality of the least qualified teachers. In reality though the quality gap is enormous - multiple years worth of learning per year.
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yossarian22c
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quote:
Originally posted by LetterRip:
Here is why the US has such disparities in education outcomes amongst public schools.

Two primary reasons

1) Local funding - thus wealthy districts can attract better quality teachers

2) class size reduction - which requires more teachers and thus shifts the average quality significantly downward.

As a teacher I can say that smaller class sizes make teaching easier and more effective. Small classes allow for lots of teacher/student interaction and questioning. Students can work together in small groups and be easily observed and allows for productive conversations. It allows for more meaningful assignments. A long in depth assignment that requires a multi-page write up is almost impossible to grade if one teacher has 200+ students.

It seems like you think every classroom is a teacher standing at a board and lecturing for 50 minutes. There is a critical mass of students that makes that style of teaching much more appealing to the teacher but a great lecturer with 100+ students isn't as good as a good teacher interacting with 20 students. As others have pointed out we could raise the average by making the profession more appealing instead of simply eliminating 1/3 of teachers. A raised average with small class sizes will produce better outcomes than a raised average from restricting the supply of teaching positions.

After writing that I realized I may have misread your intent. Are you suggesting that basically the number of educators remain constant but roles are dividing into just lecturing, just classroom management, just one-on-one/small group tutoring and just grading? Getting those teams to work harmoniously would be a challenge but could lead to some good outcomes. Most of those roles require a high skill level. So I'm not sure what this will accomplish.

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LetterRip
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yossarian,

quote:
As a teacher I can say that smaller class sizes make teaching easier and more effective.
And if the effectiveness of the individual teacher were the only factor at play it provides a slight net benefit in terms of student outcomes for current class design. However it isn't the only factor at play. Smaller class sizes require you to hire teachers from the lower end of the skill spectrum for the additional teachers. For instance 100 teachers with 30 students each - for a reduction in class size of 1 student to 29 students, requires 3% to 4% more teachers all drawn from the bottom of the distribution of teacher quality. So you get a marginal benefit of 1 student less in a class for 2900 students, and you get 100 students - 33 who went from being in the top 1/3 of teachers to worse than the previous worst third; 33 of which who went from average teachers to the worse than the worst third; and 33 of which went from the previous worst third of teachers to even worse teachers.

The smaller the class size, the more students who go to the worst teachers. So class size reduction of 1 is 3% of students (if starting class was 30); of 2 -is 6% of students; so a 50% reduction in class size, moves half the students to the worst teachers.

quote:
A raised average with small class sizes will produce better outcomes than a raised average from restricting the supply of teaching positions.
Individual teacher quality has far greater impact than class size. So the net impact is a drastic decrease in outcomes for each slight reduction in class size. So if you look at same teacher with same class size - you will see a very slight improvement in that teachers effectiveness. If you look at all students, you will see a drastic decrease in cumulative teacher effectiveness. The only way that isn't true - is if you have the teacher quality so high for such a large percentage of teachers that the worst teachers that you are adding have only a slight gap in effectiveness from the best teachers. However we know this isn't the case - the worst teachers have an enormous gap in effectiveness - so each teacher you add significantly drags down the average teacher effectiveness.

quote:
After writing that I realized I may have misread your intent. Are you suggesting that basically the number of educators remain constant but roles are dividing into just lecturing, just classroom management, just one-on-one/small group tutoring and just grading? Getting those teams to work harmoniously would be a challenge but could lead to some good outcomes. Most of those roles require a high skill level. So I'm not sure what this will accomplish.
I have two different things that I've written. If we are to stick with the existing structure - we should probably increase class size and reduce the number of teachers so get better student outcomes.

The second proposal is who I think schools 'should' be done (well partially - I have a more radical proposal that involves teaching via three integrated classes - a 'cooking' class, an 'engineering' class, and a 'communications' class - eliminating all of the traditional courses that students take - history, english, math, science, etc. but having some of the same material covered).

It could end up using the same number of teachers with a redistribution in roles.

quote:
Getting those teams to work harmoniously would be a challenge but could lead to some good outcomes. Most of those roles require a high skill level. So I'm not sure what this will accomplish
There isn't any need for coordination. MOOCs + online tutoring already covers all of this except the 'babysitting' function and mentoring/coaching function. Grading for almost everything that a computer can't grade (and the subset of material that a computer can't grade is actually quite small and shrinking) can be rubric based.
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AI Wessex
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"The smaller the class size, the more students who go to the worst teachers. So class size reduction of 1 is 3% of students (if starting class was 30); of 2 -is 6% of students; so a 50% reduction in class size, moves half the students to the worst teachers."

I confess I find this thinking a little over-precise. If you assume that all teachers are qualified, then you are contrasting the difference between a great teacher and a good one. Even so, the difference in outcomes is driven by other factors that perhaps overwhelm the teacher effect. Exceptional students (ones with an unquenchable curiosity and drive to learn) will prosper in almost any environment, and conversely those with debilitating home environments will suffer no matter how brilliant the teacher is. The latter effect is most noticeable in inner city schools or poor rural areas, where having poorly trained teachers potentially compounds other bad influences.

I'm not saying there aren't bad teachers, btw. Just that without a metric to correlate teacher ability to student outcome in isolation makes your point hard or impossible to prove.

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yossarian22c
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LR people become teachers for multiple reasons. Most because they enjoy it. Also it typically provides job security and decent benefits. Reducing the number of available positions long term doesn't do much to change the average teacher. Smart students in college will shy away from teaching if there are no positions available. By severely constricting the availability of positions you will lose many potential teachers to other majors (and not just the ones who would be below average). So while increasing supply short term could temporarily boost the average I see the long term effects to the quality of teacher as small. Then we have the same differential in teachers as today but they all have bigger classes.

Raising salaries would probably be the most effective way to ensure quality teachers in every classroom. Make the job more appealing not less.

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TomDavidson
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Allowing teachers to anonymously vote to fire one non-teaching administrator in their school district every year would do wonders for retention, too. [Wink]
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OpsanusTau
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quote:
it does apply to doctors however, most doctors are over trained/over qualified for most functions that we have doctors perform.
This is such an interesting statement to me that I have been intermittently thinking about it for days.

For teachers, it is easy to see some opportunities to unload low-skill tasks from qualified teachers - test proctor, study hall monitor, homework grader, etc, as you said.

This would necessarily lead to a pretty radical restructuring of how education works, but I think you're comfortable with that.

For instance my own recent and high-end medical-field education consisted of a combination of some large lectures, some applied skills development, and a lot of small-group discussion with and without faculty guidance.

The idea of 15-30 young people sitting quietly in a room either listening to an adult talk, working on individual or group projects, or engaging in group discussion in 30-70 minute time units as the pinnacle of education is objectively pretty weird and not necessarily optimized for any desirable outcome.

But in something of a digression, I'm very curious about what you think the things doctors do that ought to be done by people in lower-skill positions are.

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yossarian22c
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quote:
Originally posted by LetterRip:
quote:
Getting those teams to work harmoniously would be a challenge but could lead to some good outcomes. Most of those roles require a high skill level. So I'm not sure what this will accomplish
There isn't any need for coordination. MOOCs + online tutoring already covers all of this except the 'babysitting' function and mentoring/coaching function. Grading for almost everything that a computer can't grade (and the subset of material that a computer can't grade is actually quite small and shrinking) can be rubric based.
MOOCs + online tutoring are great for people motivated to learn. Typical teenagers need the mentoring/coaching and motivating function in order to take learning seriously. While computers can grade lots of things reasonably well, it is not easy to make a computer grade an assignment that a teacher writes. A suppose it would be possible to standardize a class to the point where every student (across a state or the nation) was getting the same assignment so that it would be cost effective to have a computer grade an essay or written assignment. The current algorithms for grading essays I'm aware of aren't all that good at actually evaluating students thought process and reasoning ability. From my understanding of what the GRE and SAT computer grading does is look at use of vocabulary, good grammar, and some sense of flow in the paper. Also I imagine that they spend a decent amount of time and money changing the assessment algorithm for each prompt. If you have details as to how they work or a link to a paper describing them let me know.

Also in mathematics it is almost impossible to have a computer grade anything other than multiple choice. To grade while giving partial credit the work has to be in a format that the computer can read and correct answers can be scored incorrectly simply due to syntax errors. To my knowledge the hurdles are still quite large to a teacher writing an assignment that can be graded by a computer effectively.

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scifibum
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quote:
But in something of a digression, I'm very curious about what you think the things doctors do that ought to be done by people in lower-skill positions are.
I trust that LR will respond with details but I think he's thinking of things like dispensing antibiotics and other straightforward prescriptions (or telling people that they aren't needed).

I suspect that some of the value in having a doctor who is overqualified to diagnose an ear infection and prescribe some antibiotics consult with the patient ANYWAY is found in situations where there's no ear infection and no need for amoxicillin but something else wrong that isn't going to be caught by someone substantially less qualified.

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AI Wessex
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quote:
Originally posted by TomDavidson:
Allowing teachers to anonymously vote to fire one non-teaching administrator in their school district every year would do wonders for retention, too. [Wink]

That's why Shirley Jackson wrote her story [Wink]
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LetterRip
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Ops,

quote:
I'm very curious about what you think the things doctors do that ought to be done by people in lower-skill positions are.
Not necessarily 'lower skill' per se, but trained as specialists, not generalists (To use the skill points analogy - if you allocated 200 points to cardiology, 200 to pulmonology, 200 to dermatology, 200 to general surgery, 200 to radiology, 200 to psychiatry, 200 to opthamology - you have total skill points of 1400 for the MD. But if you allocate 200 to dermatology and then little or none to the other areas you still get someone competent in dermatology). Any 'ROAD' specialty - radiology, opthamology, anasthesiology, dermatology - could probably be replaced with someone doing a one or two year training program for most tasks performed by those specialties.
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Seriati
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quote:
Originally posted by LetterRip:
it does apply to doctors however, most doctors are over trained/over qualified for most functions that we have doctors perform.

And most doctors have incredibly large staffs of both medical and non-medical assistants to perform delegable tasks.
quote:
Ie say we have 10 different functions of doctors, requiring skill level from 100 to 1000. Average doctor skill level is 800. So when they do a task requiring a skill of 100, they are wasting 700 skill points.
I think this is the crux of our disagreement. I think you believe the majority of tasks are closer to "100" level than "800" level. I personally think that is not the case. First - diagnostics - the up front meeting with your doctor and their determining of what's wrong with you is by far the task that fills most of our interactions with doctors. You probably see this as a 100 level task, because most people have simple illnesses and the staff person could "pass on" the complicated cases to the doctor. I see this as the reverse, this is 1000 level work, even if the majority of cases are common illnesses. The value add is in correctly distinguishing the less common cases, incorrect identification can be permanently damaging or even fatal.

I don't think anyone disputes that surgery and less common tasks are high level work.

So where is it you see 100 level work being stuck to doctors?

I really think your argument is based on an idea that doctors and hospitals are not being run efficiently and this is because they are prohibitted by law or regulation from doing so. I don't see it. The only thing I know that doctors wish they weren't doing is paper work.
quote:
There are many many tasks that doctors are currently used for on a regular basis that could be done by someone with one year of basic schooling.
Name them.
quote:
Originaly posted by Tom Davidson:
Allowing teachers to anonymously vote to fire one non-teaching administrator in their school district every year would do wonders for retention, too.

And allowing administrators to fire one Tenured teacher a year as if they were non-Tenured would do wonders for motivation among the tenured and quality control.
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PSRT
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quote:
Allowing teachers to anonymously vote to fire one non-teaching administrator in their school district every year would do wonders for retention, too.
I'm not sure how much of this and which part was supposed to be a joke (the smiley conundrum, I guess), but...

The biggest gripe that most educators that I know in Massachusetts have with our new evaluation system (aside from the fact that it basically makes us collect the evidence that our superiors need if they want to fire us) is that there's no teacher evaluation of administrators. Problem is, in the school systems that I've worked in here, the problems are almost entirely caused by poor administration, and to the extent that those problems are not completely destructive to the district, it has been because strong teachers can cover up the mistakes of administration. Bad teachers are highly publicized, and teachers are under fire publicly for "underperforming" schools (when the reality is that controlled for wealth we kick the crap out of most of the rest of the world), but its almost always bad administration that wrecks a school. A few bad teachers can be a problem, but not enough to cause a school to underperform, particularly given that administrators can turn over a teaching staff very rapidly (yes, even with tenure, which is only a bar to firing a bad teacher for administrators who don't follow process). But to get a school or a district to underperform? That has to be systematic, and that only comes from administration.

I wouldn't suggest letting a teaching staff vote to fire an administrator, but I would certainly suggest putting teacher evaluation of administrators into systematic processes for district determination of the quality of its administrators.

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JoshuaD
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I tend to think this problem originates from the idea that we need to micromanage teachers and school administrators. These people are being denied one of the most fundamental rights and important aspect of being a human: the right to make decisions (and the ability to fail).

I think our attempt to micromanage these schools and the school's inability to push back against micromanagement, comes from the fact that school is obligatory. Children (and parents) are subjected to the schools of their district, whether they like it or not. It only seems fair that they should get a say in how that school is run.

But the end result is madness. The teachers can't teach and the administrator's can't administrate. They all have guidelines which come from someone far away, which are designed to limit liability, meet a very small and narrow set of metrics, and inadvertently dehumanize the people whose job it is to educate our children.

I don't know what the solution is. This appears to be the problem to me, though.

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LetterRip
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AI,

quote:
I confess I find this thinking a little over-precise. If you assume that all teachers are qualified, then you are contrasting the difference between a great teacher and a good one.
Qualified is a rather slippery term. All teachers are qualified in that they have passed whatever basic hoops are required to teach in their state - that doesn't mean the baseline teacher is 'good'. That said - even if the worst teachers currently can be called 'good' - they are so much worse than the 'great' teachers that they are relatively speaking 'awful'.

quote:
Even so, the difference in outcomes is driven by other factors that perhaps overwhelm the teacher effect.
Teachers act as a multiplier effect. Yes other factors impact student outcome, but that is really irrelevant to the discussion.

quote:
I'm not saying there aren't bad teachers, btw. Just that without a metric to correlate teacher ability to student outcome in isolation makes your point hard or impossible to prove.
We can already quantify teacher impact ('fixed teacher effect') seperate from other factors (individual endowment, family input - 'fixed student effect').

And 'teacher effect' remains consistent even when teachers switch schools (ie switching to a more advantaged or disadvantaged school where the average student characteristics can be dramatically different - the teacher impact in consistent).

yossarian,

quote:
MOOCs + online tutoring are great for people motivated to learn. Typical teenagers need the mentoring/coaching and motivating function in order to take learning seriously.
Not really - teacher characteristics and course design will dominate motivation - instructor enthusiasm for the material; well organized material; providing of analogies that are relevant to the student; usage of humor; proper vocabulary (so neither using overly sophisticated nor dumbed down language); appropriate feedback; adequate but not overwhelming challenge level (so sense of increasing mastery is achieved).

quote:
While computers can grade lots of things reasonably well, it is not easy to make a computer grade an assignment that a teacher writes.
Of the hundereds of millions or billions of students worldwide - how many 'unique' assignments do you think there are? Of those how many could be trivially consolidated without loss of effectiveness? We have unique assignments not because there is pedagogical value in it, but simply as a gratifying factor to teacher ego and 'not invented here'.

quote:
A suppose it would be possible to standardize a class to the point where every student (across a state or the nation) was getting the same assignment so that it would be cost effective to have a computer grade an essay or written assignment.
We already have that to a large degree - there probably aren't more than 500 or so books that students get assigned to write essays on, and predominantly will be focused on 20 or so books.

quote:
The current algorithms for grading essays I'm aware of aren't all that good at actually evaluating students thought process and reasoning ability.
Critical thinking is far easier to evaluate with other tools. While expressing critical thinking in an essay is an important skill. Writing ability and critical thinking can be assessed independently. Also we don't need to use computers to evaluate everything - rubric based graders can do some work where computers fall down (ie SAT and GRE do use human graders also).

quote:
From my understanding of what the GRE and SAT computer grading does is look at use of vocabulary, good grammar, and some sense of flow in the paper.
It is quite a bit more complicated than that.

quote:
Also I imagine that they spend a decent amount of time and money changing the assessment algorithm for each prompt.
I doubt it - they've probably switched to machine learning using the human ratings and essays as input vectors.

quote:
If you have details as to how they work or a link to a paper describing them let me know.
See this report, it underestimates the state of the art by quite a bit, but gives a decent overview.

http://www.ets.org/Media/Research/pdf/RD_Connections_21.pdf

Also part of limitations can be addressed by peer assessment.

quote:
Also in mathematics it is almost impossible to have a computer grade anything other than multiple choice. To grade while giving partial credit the work has to be in a format that the computer can read and correct answers can be scored incorrectly simply due to syntax errors.
Actually computers can 'read' human writing better than humans can, partial credit would be pretty easy to implement. Students would need to be 'trained' to write in a standardized layout (many of my engineering and physics classes required such standardization).

Here is one such system, but yeah grading math/physics/engineering/etc. is a pretty trivial task for modern programming.

http://www.theexpertta.com/

quote:
To my knowledge the hurdles are still quite large to a teacher writing an assignment that can be graded by a computer effectively.
Not really, see

http://stateimpact.npr.org/ohio/2012/04/12/computers-can-score-student-essays-as-well-as-humans-study-finds/

http://s3.documentcloud.org/documents/335765/contrasting-state-of-the-art-automated-scoring.pdf

[ December 06, 2013, 05:05 PM: Message edited by: LetterRip ]

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LetterRip
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Interesting quote from the last paper,

quote:
If one were to simply focus on the
performance of the majority of vendors across all the measures described in this demonstration,
the results meet or exceed that of the human raters.

Also as further pointed out in the articles, the machines likely performed better than is represented due to the request that only interger scores be returned. Had decimal scores been returned their performance would likely have been event better.
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Charles in Charge
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There's pretty good evidence that shows teacher aptitude has fallen in the US over the past 40-50 years.

My own guess is that pay explains more of the difference than falling class sizes, but both probably contribute. Real pay for teachers has increased, but not at the same pace as other job opportunities, especially for educated women who are much more likely to become lawyers, doctors, etc... today than in the 60's. In addition pay compression within teaching has made it relatively less attractive for high aptitude teachers in particular.

Some data and links:

In the 1960's 40% of teachers came from the top 20% of students (as estimated by SAT scores). By the 80's that number had dropped to 20%. link

The pay ratio of high aptitude teachers to average teachers went from 1.6x to 1 between 1963 to 2000. The pay ration of the low aptitude teachers to average teachers rose from 0.7x to 1. Today high and low aptitidue teachers receive approximately equal pay.link

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LetterRip
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Charles,

compensation and alternative opportunities determine the baseline curve (its mean, mode, distribution).

If we would have kept the number of pupils per teacher constant, we could have increased the compensation about 200% for teachers instead of doubling the number of teachers.

Regarding your numbers. If we had held the total number of teachers constant as opposed to doubling the number of teachers - it would still be 40% who can from the top 20% of students. The reason it has drop to 20% is because we doubled the number of teachers, and all of the expansion comes from the low end.

The same thing has happened in programming - the number of programmers has expanded enormously in the last 20 years, but almost all of the expansion happens from people who are interested in the paycheck, not programming - and so almost all of the growth has been dominated by a much lower quality of skill programmers.

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PSRT
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quote:
If we would have kept the number of pupils per teacher constant, we could have increased the compensation about 200% for teachers instead of doubling the number of teachers.
We haven't doubled the number of students in a regular classroom. Again, a large part of the reason we have an increased teacher/student ratio is because of the expansion of special education programs over the last 50 years.

Class sizes have been declining at about half the rate as student/teacher ratios. Again, mostly due to special education. The actual number of students in a self-contained elementary classroom has been declining at a very slow rate.

The number of students per classroom has declined from about 29 to about 23 since 1961. A decrease, yes, but not a halving. And, even here, class sizes going down has been driven by a number of factors, including safety standards in science classrooms, but primarily the inclusion of students with special education needs in regular education classes. Reducing the number of teachers to increase class size is going to strongly impact special education.

Finally, while there is indeed research saying that reduced class size doesn't always increase learning, there is also research saying that classsizes, particularly at the elementary level, increases learning, and that the achievement gap lasts for several years after a single year of being in a smaller classroom.

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Charles in Charge
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quote:
Originally posted by LetterRip:
The reason it has drop to 20% is because we doubled the number of teachers, and all of the expansion comes from the low end.

I think the interesting question is why it comes from the low end.

Even if we had kept larger class sizes and doubled average teacher salary, pay compression means that high aptitude teachers would only have seen an increase of 25% rather than 100% in their pay. In contrast low aptitude teachers would have seen a 185% jump in their pay. My guess is that a 25% increase in pay for the best teachers wouldn't have been sufficient to keep all of them from going to other job opportunities (the starting wage for a corporate lawyer increased by 200% since 1970) so we would have still seen a higher percentage of teachers coming from the low end.

I agree that teacher quality has declined, that this decline hits poor schools particularly hard and that we shouldn't have shrunk class sizes. In addition I think we shouldn't have stopped rewarding better teachers for being better.

Imagine if you had to pay all programmers the same pay regardless of work quality. This is approximately the case in some large, especially bureaucratic firms such as defense contractors. The average skill level is very low at those firms because the best programmers all leave for better opportunities elsewhere. I've worked with some of those programmers who left and they described an environment where no one was very motivated despite relatively high average salaries.

[ December 08, 2013, 03:41 AM: Message edited by: Charles in Charge ]

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PSRT
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quote:
that we shouldn't have shrunk class sizes.
We haven't done so to nearly the extent necessary to reach optimum learning outcomes, especially at the elementary level. Sadly, shrinking class sizes has sometimes come at the expense of teacher quality, largely because teacher pay has not kept up with the cost of living over the last 35 years, which has masked the benefits of having elementary class sizes around 17 pupils per room compared to the current 22.
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Charles in Charge
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quote:
Originally posted by PSRT:
quote:
that we shouldn't have shrunk class sizes.
We haven't done so to nearly the extent necessary to reach optimum learning outcomes, especially at the elementary level. Sadly, shrinking class sizes has sometimes come at the expense of teacher quality, largely because teacher pay has not kept up with the cost of living over the last 35 years, which has masked the benefits of having elementary class sizes around 17 pupils per room compared to the current 22.
How big are those benefits? Would the optimal class size be 1?

I don't have anything against small class sizes. I should have said that we shouldn't have shrunk class size at the expense of teacher quality.

Why do you say that teacher pay has not kept up with the cost of living? The inflation adjusted salary averages show a (small) increase. And my guess is the value of benefits has risen more than the salaries. It's the decrease relative to other options which seems to be the problem.

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yossarian22c
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quote:
Originally posted by LetterRip:
quote:
The current algorithms for grading essays I'm aware of aren't all that good at actually evaluating students thought process and reasoning ability.
Critical thinking is far easier to evaluate with other tools. While expressing critical thinking in an essay is an important skill. Writing ability and critical thinking can be assessed independently. Also we don't need to use computers to evaluate everything - rubric based graders can do some work where computers fall down (ie SAT and GRE do use human graders also).

Reading from your link here is the summary of the automated grading.

quote:
Notwithstanding its strengths, it must be recognized that automated scoring systems generally evaluate relatively rudimentary text-production skills (Williamson et al., 2010), such as the use of subject-verb agreement evaluated by the grammar feature in the e-rater engine, and spelling and capitalization as evaluated by the mechanics feature. Current automated essay-scoring systems cannot directly assess some of the more cognitively demanding aspects of writing proficiency, such as audience awareness, argumentation, critical thinking, and creativity. The current systems are also not well positioned to evaluate the specific content of an essay, including the factual correctness of a claim. Moreover, these systems can only superficially evaluate the rhetorical writing style of a test taker, while trained human raters can appreciate and evaluate rhetorical style on a deeper level.
Also the link about computer grading being as effective as humans was for standardized test grading. A teacher grading their students writing can be more effective. In addition to getting a grade they provide feedback on what the student did very well and what they can improve. It is one of the ways teachers get to know their students needs. Computer grading is a long way from being able to provide that level of feedback.
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yossarian22c
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quote:
Originally posted by LetterRip:

quote:
Also in mathematics it is almost impossible to have a computer grade anything other than multiple choice. To grade while giving partial credit the work has to be in a format that the computer can read and correct answers can be scored incorrectly simply due to syntax errors.
Actually computers can 'read' human writing better than humans can, partial credit would be pretty easy to implement. Students would need to be 'trained' to write in a standardized layout (many of my engineering and physics classes required such standardization).

Here is one such system, but yeah grading math/physics/engineering/etc. is a pretty trivial task for modern programming.

http://www.theexpertta.com/

I looked at that. There are several issues there. The students need a computer to input the formulas (not all schools are 1-1 computer to student). Also in addition to learning the material students must learn the syntax of inputting the material into the program. That isn't a big deal for physics and math majors in college but it is an unnecessary complication for kids struggling with Algebra 1.

Many of the things you have suggested would work well for you and people like you (highly intelligent and highly motivated) these reforms would not work nearly as well for a significant portion of school age kids.

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AI Wessex
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Many software programming houses use "pair programming" on projects and find that productivity and correctness both improve. The simple idea is that no one writes code by themselves. You even have to pause when the other person goes to the bathroom.

I would like to see this tried in classroom settings more. Students will learn how to share the work and rely on another person. It won't always work, but we're talking about a system that is broken in many schools, anyway. It's well past time to try new things.

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Seriati
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quote:
Originally posted by Charles in Charge:
There's pretty good evidence that shows teacher aptitude has fallen in the US over the past 40-50 years.

***

In the 1960's 40% of teachers came from the top 20% of students (as estimated by SAT scores). By the 80's that number had dropped to 20%.

Both of these factors are probably linked to increased opportunities for women and not to anything we're arguing about. The simple fact that women were artificially limited in their choices of career forced more high quality students into teaching than would otherwise have occurred. I don't see that as a trend that is likely to reverse, so I see limited value in trying to encourage high end students to select a career as a teacher, particularly in light of this:
quote:
The pay ratio of high aptitude teachers to average teachers went from 1.6x to 1 between 1963 to 2000. The pay ration of the low aptitude teachers to average teachers rose from 0.7x to 1. Today high and low aptitidue teachers receive approximately equal pay.
That's a damning statistic if true. I honestly can not think of a single legitimate reason to compensate quality in such a manner. That's a strucuture that's designed to incentivise mediocrity, and when you couple it with tenure and small class sizes the end result makes it clear that the goal of the educational system has been a least partly corrupted into providing jobs for teachers and not top quality education for students.
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Charles in Charge
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quote:
Originally posted by AI Wessex:
Many software programming houses use "pair programming" on projects and find that productivity and correctness both improve. The simple idea is that no one writes code by themselves. You even have to pause when the other person goes to the bathroom.

I would like to see this tried in classroom settings more. Students will learn how to share the work and rely on another person. It won't always work, but we're talking about a system that is broken in many schools, anyway. It's well past time to try new things.

This is a great idea. My mother teaches CS at a public university. Recently she's been replacing lectures with group work. She'll assign a problem at the start of class and then students will form groups of 2-3 to work on it. So far it seems to increase understanding and lower frustration significantly. It does take more work on her part since she had to throw out her prepared lectures from previous years. She's been very pleased with the results.

At my own work we get a lot of feedback simply through asynchronous code reviews. Before you can check anything in another developer has to read and approve of it. It turns out to be an effective way for good style and other knowledge to spread.

I'd like to see education take on some of the characteristics of an apprenticeship - where novice and experienced practitioners work together on real problems.

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AI Wessex
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"I'd like to see education take on some of the characteristics of an apprenticeship - where novice and experienced practitioners work together on real problems."

Same here. Since you're a programmer you appreciate that it's exceedingly rare that someone comes to a software job knowing how to code for the application they're going to work on in the coding style or within the constraints (e.g., repository process, check-in rules, code reviews) of the new company. It's even pretty common these days that newcomers have to learn a new language and/or bone up on the application/system domain. We hire for potential to succeed, not to reward past success (we pay for that [Wink] .

I've been programming a looong time, and of all the things I've done I perhaps derive my greatest satisfaction from the success I've had as a mentor.

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OpsanusTau
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Wow, that was not at all the answer I expected about doctor jobs that could theoretically be done by someone with less training. In my opinion you are mostly wrong about those tasks.

Unless I am misunderstanding - always possible.

For instance, doctors do not generally take radiographs themselves, and they also do not perform ultrasound exams. These things are done by trained technicians, and the interpretation is done by specialist doctors. (In medicine, specialists are not people with less training than generalists as you seem to be suggesting, they are people with some differences in training - and in many cases, more training.) Similarly, nurse anesthetists exist; they are trained more than regular nurses and less than doctors, and practice under the supervision of an MD. So if these kinds of things are what you are talking about, then they already exist and are wonderful. Replacing whole specialties (dermatology? ophthalmology? as though there are no ocular and dermatologic manifestations of systemic disease, and no systemic ramifications of ophthalmic and dermatologic treatment) with non-doctors is a terrible idea.

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PSRT
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quote:
How big are those benefits? Would the optimal class size be 1?

I don't have anything against small class sizes. I should have said that we shouldn't have shrunk class size at the expense of teacher quality.

Why do you say that teacher pay has not kept up with the cost of living? The inflation adjusted salary averages show a (small) increase. And my guess is the value of benefits has risen more than the salaries. It's the decrease relative to other options which seems to be the problem.

Yes, the optimum class size is probably 1. But the benefits of 17 compared to 22 are very, very significant, and in most cases that I can find in the literature, outweigh the costs associated with slightly reduced overall teacher quality.

But, again, I want to make a point about the class size numbers, and special education. Since this isn't something you've responded to yet, I'm going to give a specific example.

My wife teachers kindergarten right now. In her school, there are three classes of kindergarten, with a total of 42 students (slightly made up, because I only know the exact size of her room, but the point will remain). The average class size is 14.

30 years ago, the difference would have been this: 2 fewer students, the two students in my wife's classroom, who both have autism, and my wife would not be employed by the school. They would not have been in public school. So there would have been 20 students per class.

Most of what we are talking about with class size is higher enrollment due to students with often severe special needs attending public schools, and the additional staff (at significantly lower teacher/student ratios) to support those students. Unless you separate the numbers, and most national data on class size and students/teacher do not, you aren't getting any sort of meaningful comparisons between eras divided by implementation of special education laws.

In terms of teacher compensation: SInce the mid 80's, the last time there was a large bump in teacher salary, teacher salary is flat or below cost of living increase, in most parts of the country. Benefits are down as well. Compensation for continuing education is down, health coverage is down, and stipended positions have their benefits increase more slowly than actual salary.


30 years ago, a single teacher could support his family in most parts of the country at a middle class life style. That isn't true anymore. Its not true for a large number of professions. The cost of living has risen faster than compensation for most workers since the early 1980's, and that includes teachers. The problem with teacher compensation is a part of a larger problem with salary and wages for historically middle class professions and industries.

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PSRT
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quote:
I'd like to see education take on some of the characteristics of an apprenticeship - where novice and experienced practitioners work together on real problems.
I think this is happening, and has been happening for a while. However, there are limits, unless we want to redefine what we mean by a public education.

In my previous district, seniors had an internship for the last quarter of the year. THe students that I mentored in my final year there worked for an architecture firm, Raytheon, did a student teaching, and worked at a funeral home.

In my current district, students have an option for course credit for spending two periods of the day in a work environment during their junior or senior year.

However, if they were to spend more time out of the school than they do for these internships, it would come at the cost of their broad liberal arts education that is the primary purpose of public education in our country. So if we want to add more internship than what exists in many places, we have to have a full blown conversation about what the purpose of providing a k-12 education is.

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LetterRip
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Charles,

Optimal class size is probably slightly larger than one if you can choose the students (ie some students will perform far better with peer competition).

PSRT,

quote:
But the benefits of 17 compared to 22 are very, very significant, and in most cases that I can find in the literature, outweigh the costs associated with slightly reduced overall teacher quality.
Source? The best analysis I've seen suggests that class size reduction doesn't even begin to have impact till around 15, and sizes between 15 and 40 are largely the same in terms of student outcome - only when you use tiny sample sizes where random noise can provide ridiculous effect sizes do you see any significant 'effect' for class size reduction. We are only getting effect sizes of around .08 (The paper I looked at actually showed .13, but he had made a math mistake that weighted all studies equally, even a simple per student weighting reduces the effect size to .08, and with more 'correct' weightings (quadratic, etc.) where larger sample sizes are weighted far more than small sample sizes results in even lower effect sizes), also almost every intervention asside from class size have much larger effect sizes

http://wewe2025292.wikispaces.com/file/view/The+paradox+of+reducing+class+size+and+improving.pdf

yossarian,

the papers I provided aren't based on the 'state of the art' in AI for grading essays - I stated that when I posted the links that they missed important developments, but just gave a general idea of what can be done. Also I didn't say that computers could completely eliminate every single task in the universe that humans are used for evaluation of students. You also failed to answer my question of why standard assignments couldn't be standardized - and my point that the questions used already are in fact fairly standard due to the small universe of books and topics on which essays are assigned - they just aren't done so in a coordinated fashion. Also even if there are some essays which computers couldn't handle, if we eliminate 95% of tasks that teachers are spending their time on related to grading that is still a substantial time savings.

PSRT,

regarding teacher student ratios. It is true that 'special needs' student 'mainstreaming' distorts the numbers. However, a huge number of those 'special needs' students are students that would not have been counted as special needs historically - ADD/ADHD, emotionally disabled, dyslexia, etc. Very few of them are profoundly disabled students that would not have been taught or who would have historically been classified as 'special needs'.

Of course schools also try to mislead parents by giving really low 'student faculty ratios'

1) ie a teacher who teaches 4 classes and each student takes six classes a day. Results in an increase in student teacher ratio without change in class size.

2) Counting some administrative faculty as teachers by having them teach a single course out of a 6 or 7 course day. (Or for instructors on sabattical for colleges)

(The first one will inflate some public school figures - I believe many teachers get one 'prep' period per day - though it is unclear what the historical figures are so perhaps no effect in general)

(The second I'm not sure how often this happens in public schools - private schools and colleges definitely use it to improve their student/teacher ratios though)

However, average class size is misleading as well (ie team teaching, or teaching with an assistant provides similar individual time, etc. to students for a doubled class size).

Note however that student teacher ratios in government sources tend to use 'full time equivalent' teachers and 'full time equivalent' students - thus they tend to not exaggerate the STRs.

Regarding 'internships' they tend to be pretty useless unless they are quite long. If they are short, then the student will generally do very little of use. I don't think they are useful in general - apprenticeships are fine if someone already has significant knowledge in the topic and needs hands on - most students aren't ready for any sort of internship coming out of high school and will be little more than gophers.

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LetterRip
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Interesting that you talk of a 'liberal arts' education - the 'classic' liberal arts education is quite the opposite of modern liberal arts education.

Classical would be grammar, logic, rhetoric, arithmetic, geometry, music, astronomy. Which in modern time would translate to a STEM based education.

However I suspect you mean a modern 'liberal arts' education - ie with a heavy focus on 'the humanities', which receive far too much time in both grade schools and at universities while providing little or no benefit to the student.

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LetterRip
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Ops,

quote:
For instance, doctors do not generally take radiographs themselves, and they also do not perform ultrasound exams. These things are done by trained technicians, and the interpretation is done by specialist doctors.
Yes I'm refering to replacing radiologists who interpret the ultrasound/CT/x ray/MRI/etc.

quote:
(In medicine, specialists are not people with less training than generalists as you seem to be suggesting, they are people with some differences in training - and in many cases, more training.)
I'm aware of the role of technicians.

I'm not implying that currently specialists are less trained than generalists. However, much of the generalist training is not useful for the specialist.

If someone will never perform major surgery, then the training for major surgery is a waste of their time. As is memorizing the massive pharmacology information that isn't revelant to their specialty.

quote:
Similarly, nurse anesthetists exist; they are trained more than regular nurses and less than doctors, and practice under the supervision of an MD. So if these kinds of things are what you are talking about, then they already exist and are wonderful. Replacing whole specialties (dermatology? ophthalmology? as though there are no ocular and dermatologic manifestations of systemic disease, and no systemic ramifications of ophthalmic and dermatologic treatment) with non-doctors is a terrible idea.
There are systemic implications of opthamologic and dermatological diseases. However the systemic effects will only cover a modest percentage of the training, and the individual can be passed on to other experts when necessary. I also don't think that the individuals need to 'practice under the supervision of an MD' - in large part that has developed for MDs to maintain control of the economics to prevent being undercut by non MDs - just trained to recognize when they are outside of their training and to refer the individual when that happens.

Ie detailed knowledge of the structure and function and biochemical pathways of most of the other major organs is not needed for either of these specialists - ie pancreas, liver, kidneys, heart, lungs, etc. Knowledge of diseases of these organs will be needed for both but the degree of knowledge can be quite superficial and still adequate. Similarly knowledge of infectious diseases and of cancer will be needed; of various histology - but only a subset of the knowlege will be needed.

Right now they learn a significant amount of minutae for every organ and most diseases, which are utter wastes of time.

If we were to compress what is needed to be the best possible radiologist (especially one who deals with only a subset of all radiology). Ie a lower limb x-ray radiologist. What is the minimal knolwedge needed to practice as a specialist with that singular focus? Design programs to that minimalist need, if the individaul wishes they can steadily add other specialtys (MRI, CT, PET, ultrasound - or particular region - head, upper limb, heart, lung, etc).

I'm not refering to replacing every specialist in ROAD specialities with individuals with less training. However most of their current workload is either routine or could be handled with sub specialists with far less extensive training - that individuals with far less training could do and do well, and then use referals for those areas where someone with full systemic knowlegde is required.

Here is another example - instead of a general 'nurse training' - have many much briefer specialties - ie an 'alzheimers nursing specialist' a 'diabetes nursing specialist' etc. These could require substantially less training than a nurse currently requires, yet provide superior nursing care to those afflicted; and the training could be provided in a substantially abreviated time frame and thus the services delivered at a lower price.

I also think a similar thing should happen to law schools. The general 'law' degree should be broken apart - someone doing contracts has little overlap with someone doing patent filings, who have little overlap with criminal trial law, which has little overlap with family law, etc.

We needed these generalists historically because there wasn't enough work to keep someone with a narrow specialty busy and there was some overlap between what was learned to practice in one specialty to practice another.

These are merely historical economic accidents and speaks nothing of the actual training needed.

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