Class sizes and achievement...

An interesting article on the subject here:

One of the obvious corollaries about small class sizes is that it’s easier to give individual feedback, which may be ideal for some students. The guy that has no clue what the divine sign means isn’t going to benefit from long division, nor is the guy that is 20 questions ahead going to be enthralled if the teacher practices the ten times table.

The article points out that a better student to adult ratio doesn’t necessarily matter if the students are housed in the same class since the focus of the lesson will likely be the same and the larger the population, the higher the standard deviations to either end of the curve.

Neither are qualifications a good predictor of academic success. The above article has one flaw though: it points out that hiring teachers in the 85th percentile is as effective as cutting class sizes by two, but assuming a normal distribution only 1/6th of currently employed teachers are that adept. Assuming you fire anyone below the mean, half of the teachers are unemployed. It may be worth hiring low qualified, below average teachers and giving them fewer kids (assuming money can also be spent on premises to house these several new classes) because they’ll achieve as much as the kid in the next class with a genius teacher with a PhD.

Also, with over $1T spent on military and healthcare this year, would it really be that hard to find space for a few classrooms? I think Cuba had 1/10th of the healthcare expenditure with the same mortality rates… With 9/10ths of the healthcare budget, one could use cocaine instead of chalk in the classroom.

Divide sign, of course. I’ll assume it was a Freudian slip until a halo appears around my computer screen and a ray of light starts to drag me out of my window… In which case I’ll lay off the alcohol.

You don’t have to assume any particular distribution to reach that conclusion. That’s just how percentiles are defined (though of course your statement has some rounding in it).

Anecdotal, but the best experience we had for our kids was 26 kids to one (good) teacher and one (good) trainee teacher. But the key to this 13/1 ratio working was that the kids could be grouped differently for different activities, depending on level.
In fact, it was cooperatively taught with another class one level up (e.g. 1st/2nd grade combo) so it was a pool of 52/4 but the 4 groups could be broken out flexibly, by ability, and moved between groups through the year.

I think if you had 13 random kids (random in terms of ability) in a single class, and taught towards the median (or as more often happens, towards the slower performers), it wouldn’t make a difference what your class size was, in fact it might be worse without the positive reinforcement of peers on your level.

“Flexible” was important; isolating the groups into set ability levels for the whole year (i.e. a bright class and a slow class with no movement between) would have been counterproductive and unfair as well, IMO.

Quite right, I’m sorry. I posted a more coherent critique on Gladwell’s site, namely to do with the possibility that the teaching population is an accurate sample of the general population; thus it would be difficult to attract good teachers that happen to not be teaching, as applications will be in the same proportion. Not to mention that those that are absolutely confident of their ability to teach are probably doing so already. The other issue is that should standards increase, teachers previously in the top percentiles of ability would shift towards the mean. That way if one decimates teachers (or comes up with any measure of expulsion however many standard deviations from the norm) based on performance, a child is just as likely to have a teacher in the bottom 10%, the teacher will just be better than the one that got fired (or executed), while classroom sizes presumably increase due to the lack of accredited teachers.

To think I just handed in an essay on statistics… No wonder my lecturers are always looking at me funny.

You can’t just look at class size from the teaching perspective. There’s also the learning perspective. I think students in a smaller group are going to work harder than those in a larger group. In a small group there’s no anonymity - the students will all be know as individuals so there’s a greater incentive to shine (and a greater disincentive to fail). People respond when they feel their efforts are being recognized.

Does no one here any more remember to post the link to Uncle Cecil’s column??

Are smaller elementary-/school class sizes better?

And speaking as a teacher, of course they are. They make individualized instruction easier. But, more importantly, they make class discipline much easier to maintain. And I’ll maintain that it’s most important for students at either end of the spectrum, those who are the brightest, and those for whom school is most difficult. BUT it’s only one of a complicated and numerous set of factors impacting classroom results.

Since most of my students are below reading grade level (I teach high school; so I’m talking 3-4th grade here) and they’re ‘socially promoted’ until they reach high school…I’m pointing fingers at the younger years.

At my son’s school, they have a teacher and an assistant teacher in every classroom, so the adult-student ratio is 1:10.

Interesting to note one of Cecil’s criticisms about California’s implementation was the need to hire so many teachers at once that the teacher standards dropped. So that helped keep the improvements of smaller class sizes from manifesting.

So what that shows is lowering teacher ability combined with reducing class sizes does not provide improved results, but that is adjusting two variables at once. Not the ideal scientific method, no?

Basically what that says is that California’s real world implementation of the reduce class size plan was flawed. It wasn’t reducing class sizes that didn’t work, it was failing to reduce class sizes in the poorer districts (because they didn’t have room) and hiring less qualified teachers for the places you did implement doesn’t lead to improved performance gains. Um, duh!

But his criticism was along the lines that a reduction in teacher qualifications necessarily meant reduced academic achievement, when Gladwell’s article points out that there may be another variable (interpersonal intelligence?) which better matches classroom achievement. Then when one considers that in order to replicate the effect of having a class half the size one’s teacher must be in the 85th percentile, academic performance would be increased on a wider scale by halving class sizes for the majority of students. One can’t just duplicate the consistently top performing teachers since there isn’t really a good predictor of teaching ability other than past performance.

Okay, I just read the two articles by Gladwell. You make a valid point - is it easier to only hire teachers that perform in the upper 70% (or rather, hire and evaluate, then weed down to the top performers) or to spread the existing teachers and make the best use of them you can? It’s an optimization problem, but one where some of the variables are poorly understood if even acknowledged.

I think Gladwell’s main point was that the criteria for training and certifying teachers has little correlation with the actual skills that teachers require, and so there is little ability to predict how a teacher will do based upon the current hiring criteria. Add to that the current practices of tenure and seniority over performance measures, and that’s why our system is weak overall.

But he seems to be stuck looking at the “quarterback problem”, i.e. the mismatch between how we train and evaluate teachers vs what really determines success, without realizing that by studying that breakdown, people are trying to identify better evaluation criteria. I suppose it’s the difference between (a) trying to define a whole new set of criteria to train to and evaluate by, or (b) changing the evaluatiion process to screen by performance and let the system self sort.

A separate issue is how to define performance criteria such that they make sense. As you say, firing the bottom 50%, then hiring new teachers that are presumably better, would shift the mean. If you fire at 50% on wave 2, that’s actually a tighter performance criteria than wave 1, because average performance is at a higher level.

All of which is irrelevant to my point, which was that California’s implementation of the “reduce class sizes plan” isn’t a fair tool for evaluating the effect of reducing class sizes, because the execution had major flaws that prevent that variable from being measured. If you, in fact, don’t cut class sizes where they are most needed (poorer schools), cut programs where you do cut class sizes (reducing the overall quality of the education in those schools), and higher a bunch more less-experienced and less-prepared teachers, then you can’t really say what the effect of reducing class size from 30 to 22 really is. What you can say is that reducing class size in some schools didn’t improve conditions overall when mixed with several other changes.

There is a fair criticism that one study in Tennessee does not mean the results are directly relatable, and that rolling out the program in more controlled stages would have mitigated many of those issues as well. It would have allowed more selective teacher hiring for the classes that were added, it would have allowed selective addition of classes, focusing money to allow creating new facilities instead of retasking existing overcrowed facilities and thus increasing the crowding problem, and it would have provided tighter controls to allow evaluating the effects of class size reduction better. Hell, they could have done it in the more traditional manner of taking the most crowded districts and building new schools in them.