After seperate public schools for black and white students were established to be unconstitutional by state laws in Brown vs Board of Education, there has been no change. It hoped to bring together white and black children to learn with, and from, each other, and end the disparities that blacks suffered under decrepit buildings, lower-paid teachers, and the lagging achievement. If schools are now equal, then the difference between their achievements should be much less or equal. Keep in mind that Brown vs. Board of Education ended more than 60 years ago.
According to statistics, education between blacks and whites still isn’t equal because of its achievement gap. In these statistics, it provides possible factors that may contribute to the disparities and data in order to make the possible factors believable and then support their statement that education is still unequal and hasn’t changed. Some possible factors include, lower wealth, lower parental education levels, and lower health. For example, a white adult’s basic reading skill was 102 but of a black adult, it was 85. Also, 91% of white children aged 3 to 5 who weren’t enrolled in kindergarten were read to by family members three or more times per week, 78 % of black children were read to with the same frequency. This can then lead to fewer black children demonstrating proficiency in development skills like vocabulary, counting, colors, and shapes.16 % of black students drop out compared to 8% of white students which means that fewer black students graduate from high school and aren’t eligible for college enrolment.

These achievement gaps are a problem and can be solved. This time, no Brown vs. Board of Education can attempt to solve it. This time, it could be the parents or guardians making a change. If this isn’t taken care of, the achievement gap could soon grow instead of shrinking.
You raise a lot of issues in this post, which is great. You do a good job laying out possible causes of the issue. You need to identify what the metrics are for achievement disparity you mention at the start of your post. The causes that lie with parents and the home may also have deeper causes. If families also had a terrible educational experience than that will create a cycle. We will study Brown v Board around April. One interesting thing to look at is the loss of jobs for Black teachers in the aftermath of Brown v Board. Take a look at this podcast if you are interested in learning more:
http://revisionisthistory.com/episodes/13-miss-buchanans-period-of-adjustment
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