Final answer:
In response to the question, the Supreme Court's 2007 decisions on Parents Involved in Community Schools v. Seattle School District No.1 and Meredith v. Jefferson County Board of Education limited school districts' ability to voluntarily integrate schools using rigid racial assignment methods.
Step-by-step explanation:
The Supreme Court case Brown v. Board of Education of Topeka (1954) was a seminal event in the civil rights movement, leading to the declaration that racial segregation in public schools was unconstitutional, violating the Fourteenth Amendment. This decision overturned the "separate but equal" precedent set by Plessy v. Ferguson. However, later Supreme Court decisions in 2007, specifically Parents Involved in Community Schools v. Seattle School District No.1 and Meredith v. Jefferson County Board of Education, limited how racial diversity could be pursued within schools. Specifically, the Court ruled that public schools could consider race when making assignments but found the systems in these cases too rigid. As a result of these rulings, the Supreme Court ruled that school districts may no longer voluntarily integrate schools in the specific ways at issue in the Louisville and Seattle districts.