The following came out of a phone conversation I had this weekend with Joseph. I'll need to get back to this later but for now here's a thumbnail version just to have something on the record.
When we talk about the achievement gap in education, there are two distinct but valid ways of approaching the question:
The first is in terms of variability. The people in the bottom quartile are, by most measures, getting a much worse education than the remaining three quarters of the population;
The second involves correlation. People in that bottom quartile are disproportionately likely to be poor, to be black or Hispanic, or to speak English as a second language.
You address the first by raising scores for those at the bottom. You address the second by changing the order. Reducing the gap is still desirable regardless of the definition used -- we don't want any of our schools to be bad nor do we want an education system that entrenches the class system -- and there are many things we can do that will improve both, but it is important to remember that we are talking about two distinct objectives.
To further complicate the picture, proposals that are meant to improve educational outcomes in general are often pitched as ways to address the achievement gap.
All three goals (improving overall outcomes, reducing variability and breaking the correlation) are important -- I'd argue the third one is absolutely vital -- but whenever we need to be clear about what we are trying to do.
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