How big is this gap and what are the significance for public schools. Many studies of incoming kindergartners seem to show that gap between advantaged and disadvantaged populations is approximately one standard deviation. Some of you remember the standard deviation from college statistics. Here's a picture of the familiar bell-shaped curve

The idea is that in a so-called "normal distribution," just about one third of the population is within one standard deviation above the median and another third, within one standard deviation below. Put differently, more than two thirds of the normally distributed population is less than one standard deviation of the median. So, what does it mean if we say that the mean score of disadvantaged students is a full standard deviation below the median of advantaged? Consider two populations, advantaged and disadvantaged. The advantage might be economic, linguistic, racial or some other factor that results in a standard deviation difference between the advantaged group and the disadvantaged group.

The achievement gap is not a product of public schools, it is a product of the disadvantages that arise in families where the parents are themselves educationally disadvantaged. Mastering the achievement gap requires improving public schools so that they can overcome overwhelming disadvantages. They need to be massively better, not because they are terrible schools, but because we have set them a mission that is overwhelmingly difficult and challenging. They need to move a group of children who come to school, on the average, a standard deviation behind, and whose disadvantages continue throughout their schooling.

Suppose for example, half of the students who came to school practiced dribbling and shooting a basketball one hour a night throughout elementary school, while another group never touched a basketball at home. How would those two groups perform on tests of dribbling and shooting? I'll have more to say about this in the next post.....

First, randomly selecting one disadvantaged child and one advantaged child and comparing their scores will show the advantaged child exceeding the disadvantaged child 76 percent of the time and the disadvantaged child exceeding the advantaged child only 24 percent of the time. Second, 84 percent of advantaged children will perform better than the average disadvantaged child, while 16 percent of disadvantaged children will perform better than the average advantaged child. Third, if a class that is evenly divided among advantaged and disadvantaged is divided into two equal-sized groups based on ability, then disadvantaged students will compose roughly 70 percent, and advantaged 30 percent, of the students in the lower performing group. Fourth, if a school district chooses only the top-scoring 5 percent of students for “gifted” courses, such classes will have thirteen times more from the advantaged group than the disadvantaged group. Finally, assume that a reading textbook is written so that the average advantaged student will read it at a 75 percent comprehension rate. The implied comprehension rate for the average disadvantaged student will be 53 percent, virtually guaranteeing that such a reader will not engage with the text. Rock and Stenner, Assessment Issues in the Testing, of Children at School Entry (2005).A full standard deviation between advantaged and disadvantaged groups is a huge gap with grave consequences for the disadvantaged group. It doesn't mean that members of the disadvantaged group can't succeed, because some will. But it means that the disadvantaged group faces overwhelming disadvantages right from the start of school, and that these disadvantages compound themselves, year after year, unless the disadvantages are attacked at the very beginning. And, I am arguing that the attack on the disadvantage requires compensatory time -- more time learning during school and after school.

The achievement gap is not a product of public schools, it is a product of the disadvantages that arise in families where the parents are themselves educationally disadvantaged. Mastering the achievement gap requires improving public schools so that they can overcome overwhelming disadvantages. They need to be massively better, not because they are terrible schools, but because we have set them a mission that is overwhelmingly difficult and challenging. They need to move a group of children who come to school, on the average, a standard deviation behind, and whose disadvantages continue throughout their schooling.

Suppose for example, half of the students who came to school practiced dribbling and shooting a basketball one hour a night throughout elementary school, while another group never touched a basketball at home. How would those two groups perform on tests of dribbling and shooting? I'll have more to say about this in the next post.....

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