Getting the students at the low end of the spectrum to "get math" is certainly a noble goal, but in order to have such a low variance in math ability at the end of the year, there's another required component - you have to keep the high end students below their potential. As far as I'm concerned, anyone who claims otherwise has a high burden of proof. Go take a remedial math class and turn it into a winning USAMO team and then get back to me. High end math education (at least in the US) is just as poor as the low end, but because the scores are acceptable not as many people care. Talk of "evening things out" is misguided.
What if we discover some magic new program that improves every student's scores, but it improves the poorest students the most and the gifted students the least relative to our existing programs? Such a program wouldn't be holding the gifted students back relative to existing education, it would improve them, and it would still reduce the variance.
(My comment sonly apply to standardized education, not to streaming students into different programs such as specialprograms for gifted students.)
I don't know why you have to postulate "magic". I didn't say that a program that helps each kid progress as quickly as possible wouldn't reduce the variance. It probably would, as the kids on the bottom have more room for improvement. But I would still expect a large amount of variance. Actually, I just noticed that the "after" graph is clustered near 100%, so it's possible that there still is a large variance, but it's just not measured by the tests that were administered. These are probably standardized test scores and don't really address higher end performance.
So I guess my points are:
1. I'm doubtful that the "paint by numbers" approach is what the young Picasso needs.
2. Maybe I'm wrong about (1), but we certainly shouldn't subject the advanced students to this method until higher end performance has been measured.
3. I find the attitude of the author, who used the phrase "even things out" as if it was a good thing, concerning. Evening things out should be an explicit non-goal of education.
Expressions like "magic" are simply ways of making it clear that the notion of what is or isn't possible is orthogonal to the question of what this specific program does or doesn't do. But as far as your points go, the second one is the most interesting. yes, we should have a good look at what happens when "advanced" students are exposed to any method.
Some advanced students might even get even better and increase the variance! I can't comment on this program, I know nothing about tutoring. But I know that I personally like breaking things down into little steps, and I think I would have enjoyed a program running on these lines if I was allowed to move at my own pace.
Based on the graphs given, it looks like the low variance may simply be a result of having the x-axis be percentile.
Consider Round 2, where sigma=1.2%, mu=98%. Suppose hypothetically that 90% of students are clustered below 100 (an absolute measure of performance), 96.8% of students are below 150 pts, and 99.2% of students are below 300 pts.
In this case, the absolute variation is huge (300 vs 150). But because only 2.4% of students score between 150 and 300 pts, on a percentile graph, it looks like sigma has been reduced.
I think it's unlikely that this has occurred, but the graphs given don't preclude it.
You're missing an important point: there is a built-in ceiling to how good a child can be in a particular math class. There is only a finite amount of material taught and a finite amount of time. So any program like this is inevitably going to greatly reduce the variance as everyone gets pushed towards this ceiling. This isn't keeping gifted students below their potential. It's just not giving them special treatment by accelerating the class material for their sake. Which is the same as before.
This approach seems to benefit everyone, including the top students. If you look at the graphs, in Round 1 the Max went from 80% to 99% and in Round 2 the Max went from 75% to 99%. This occurred not in a remedial class, but in an independent, unscreened school.
Perhaps one side-effect of the overall improvement is that the teacher doesn't have to spend as much time with struggling students and can devote more time helping high end students unlock their potential.
Your assumption does not hold water where my kids go. ...Fortunately They are in small classes and the school has 3 math levels per grade; one for the advanced students, one for the struggling students, and one for kids that fall between these 2 camps. It is great!
