Cleveland, Mississippi, is literally a town divided by old railroad tracks. Most white students live on the west side, while many African-American students call the east side home, reports CBS News correspondent Michelle Miller.

A court order to integrate schools in Cleveland was announced Monday, a day before the anniversary of Brown v. Board of Education, the landmark 1954 Supreme Court ruling that declared unconstitutional the principle of "separate but equal" in public schools. While Cleveland School District officials contend they have made big strides since they were first ordered to desegregate back in 1969, the federal judge ruled that wasn't enough.

Deshambra Fields and her brother, Quoindedrick, attend East Side High School, a well-regarded school where the student body is 100 percent black.

"So you think they should not desegregate these schools?" Miller asked them.

"No, ma'am," Deshambra said.

"Why?" Miller asked.

"It's this side of the highway versus that side of the highway. And it's just -- it's been a rival for a long time," Quoindedrick said.

Under the desegregation plan, East Side High School would be merged with Cleveland High School where 45 percent of students are white and 47 percent are black. A nearly-all black middle school would also be combined with a racially mixed one.

Less than a third of students at the new schools will be white in a district where nearly half of residents are.

"We have kids learning side by side with each other, different races," Cleveland School District attorney Jamie Jacks said.

Jacks fears the plan will spur a white flight out of the public schools.

"Unfortunately, when you do a mandatory reassignment plan, the results statistically tell us it's not good in terms of maintaining diversity," Jacks said.

"This is not a country that in 2016 wants to be perceived as having deeply segregated communities anymore," said Vanita Gupta, head of the U.S. Department of Justice Civil Rights Division.

The Civil Rights Division formulated the desegregation plan.

"Children deserve to be educated in the kinds of environments that we as adults face, which are mixed race, mixed religion," Gupta said.

Even though Brown v. Board of Education has been the law of the land since 1954, the Justice Department still has 177 open desegregation cases. Almost half are in just two states, Alabama and Mississippi.

The "Magnolia State" has a painful history with desegregation. A deadly riot broke out in 1962 when James Meredith tried to become the first black student enrolled at Ole Miss.

Margaret Swartzfager's kids go to Cleveland High while Edward Duvall's go to East Side High.

"If the parents would step aside and let the kids feel their way through it, the kids are going to deal with it a lot better than the parents will," Swartzfager said.

"So where do you go from here?" Miller asked.

"These kids, whether you're black or white, are going to be our leaders for tomorrow, and we need to invest in them. ... It can work if we want it to," Duvall said.

The school district says it believes the ruling will limit the choices of parents and students and will look at all options for appeal. The judge last week gave both sides 21 days to come up with a timeline for the latest integration plan.