with whom The Chief Justice joins, concurring in the result in No. 78-610 and dissenting in No. 78-627, post, p. 526.
My views in these cases differ in significant respects from those of the Court, leading me to concur only in the result in the Columbus case, and to dissent from the Court’s judgment in the Dayton case.
It seems to me that the Court of Appeals in both of these cases ignored the crucial role of the federal district courts in school desegregation litigation1 — a role repeatedly emphasized *470by this Court throughout the course of school desegregation controversies, from Brown v. Board of Education, 349 U. S. 294 (Brown II),2 to Dayton Board of Education v. Brinkman, 433 U. S. 406 (Dayton I) ,3 The development of the law concerning school segregation has not reduced the need for sound factfinding by the district courts, nor lessened the appropriateness of deference to their findings of fact. To the contrary, the elimination of the more conspicuous forms of governmen-tally ordained racial segregation over the last 25 years counsels undiminished deference to the factual adjudications of the federal trial judges in cases such as these, uniquely situated as those judges are to appraise the societal forces at work in the communities where they sit.
Whether actions that produce racial separation are intentional within the meaning of Keyes v. School Dist. No. 1, Denver, Colo., 413 U. S. 189; Washington v. Davis, 426 U. S. 229; and Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U. S. 252, is an issue that can present very difficult *471and subtle factual questions. Similarly intricate may be factual inquiries into the breadth of any constitutional violation, and hence of any permissible remedy. See Milliken v. Bradley, 418 U. S. 717 (Milliken I); Dayton I, supra. Those tasks are difficult enough for a trial judge. The coldness and impersonality of a printed record, containing the only evidence available to an appellate court in any case, can hardly make the answers any clearer. I doubt neither the diligence nor fhe perseverance of the judges of the courts of appeals, or of my Brethren, but I suspect that it is impossible for a reviewing court factually to know a case from a 6,600-page printed record as well as the trial judge knew it. In assessing the facts in lawsuits like these, therefore, I think appellate courts should accept even more readily than in most cases the factual findings of the courts of first instance.
My second disagreement with the Court in these cases stems from my belief that the Court has attached far too much importance in each case to the question whether there existed a “dual school system” in 1954. As I understand the Court’s opinions in these cases, if such an officially authorized segregated school system can be found to have existed in 1954, then any current racial separation in the schools will be presumed to have been caused by acts in violation of the Constitution. Even if, as the Court says, this presumption is rebuttable, the burden is on the school board to rebut it. And, when the factual issues are as elusive as these, who bears the burden of proof can easily determine who prevails in the litigation. Speiser v. Randall, 357 U. S. 513, 525-526.
I agree that a school district in violation of the Constitution in 1954 was under a duty to remedy that violation. So was a school district violating the Constitution in 1964, and so is one violating the Constitution today. But this duty does not justify a complete shift of the normal burden of proof.4
*472Presumptions are sometimes justified because in common experience some facts are likely to follow from others. See Ulster County Court v. Allen, 442 U. S. 140; Sandstrom v. Montana, 442 U. S. 510. A constitutional violation in 1954 might be presumed to make the existence of a constitutional violation 20 years later more likely than not in one of two ways. First, because the school board then had an. invidious intent, the continuing existence of that collective state of mind might be presumed in the absence of proof to the contrary. Second, quite apart from the current intent of the school board, an unconstitutionally discriminatory school system in 1954 might be presumed still to have major effects on the contemporary system. Neither of these possibilities seems to me likely enough to support a valid presumption.
Much has changed in 25 years, in the Nation at large and in Dayton and Columbus in particular. Minds have changed with respect to racial relationships. Perhaps more importantly, generations have changed. The prejudices of the school boards of 1954 (and earlier) cannot realistically be assumed to haunt the school boards of today. Similarly, while two full generations of students have progressed from kindergarten through high school, school systems have changed. Dayton and Columbus are both examples of the dramatic growth and change in urban school districts.5 It is unrealistic *473to assume that the hand of 1954 plays any major part in shaping the current school systems in either city. For these reasons, I simply cannot accept the shift in the litigative burden of proof adopted by the Court.
Because of these basic disagreements with the Court’s approach, these two cases look quite different to me from the way they look to the Court. In both cases, there is no doubt that many of the districts’ children are in schools almost solely with members of their own race. These racially distinct areas make up substantial parts of both districts. The question remains, however, whether the plaintiffs showed that this racial separation was the result of intentional systemwide discrimination.
The Dayton case
After further hearings following the remand by this Court in the first Dayton case, the District Court dismissed this lawsuit. It found that the plaintiffs had not proved a discriminatory purpose behind many of the actions challenged. It found further that the plaintiffs had not proved that any significant segregative effect had resulted from those few practices that the school board had previously undertaken with an invalid intent. The Court of Appeals held these findings to be clearly erroneous. I cannot agree.
As to several claimed acts of post-1954 discrimination, the Court of Appeals seems simply to have differed with the trial court’s factual assessments, without offering a reasoned explanation of how the trial court’s finding fell short.6 The *474Court of Appeals may have been correct in its assessment of the facts, but that is not demonstrated by its opinion. I would accept the trial judge’s findings of fact.
Furthermore, the Court of Appeals relied heavily on the proposition that the Dayton School District was a “dual system” in 1954, and today this Court places great stress on the same foundation. In several instances, the Court of Appeals overturned the District Court’s findings of fact because of the trial court’s failure to shift the burden of proof.7 Because I think this shifting of the burden is wholly unjustified, it seems to me a serious mistake to upset the District Court’s findings on any such basis. If one accepts the facts as found by the District Judge, there is almost no basis for finding any constitutional violations after 1954. Nor is there any substantial *475evidence of the continuing impact of pre-1954 discrimination. Only if the defendant school board is saddled with the burdens of proving that it acted out of proper motives after 1954 and that factors other than pre-1954 policies led to racial separation in the district’s schools, could these plaintiffs possibly prevail.
For the reasons I have expressed, I dissent from the opinion and judgment of the Court.
The Columbus case
In contrast, the Court of Appeals did not upset the District Court’s findings of fact in this case. In a long and careful opinion, the District Judge discussed numerous examples of overt racial discrimination continuing into the 1970’s.8 Just *476as I would defer to the findings of fact made by the District Court in the Dayton case, I would accept the trial court’s findings in this case.
The Court of Appeals did rely in part on its finding that the Columbus Board operated a dual school system in 1954, as does this Court. But evidence of recent discriminatory intent, so lacking in the Dayton case, was relatively strong in this case. The particular illustrations recounted by the District Court may not have affected a large portion of the school district, but they demonstrated that the district was not being operated in a racially neutral manner. The District Court found that the Columbus Board had intentionally discriminated against Negro students in some schools, and that there was substantial racial separation throughout the district. The question in my judgment is whether the District Court’s conclusion that there had been a systemwide constitutional violation can be upheld on the basis of those findings, without reference to an affirmative duty stemming from the situation in 1954.
I think the Court’s decision in Keyes v. School Dist. No. 1, Denver, Colo., 413 U. S. 189, provides the answer:
“[W]e hold that a finding of intentionally segregative school board actions in a meaningful portion of a school system, as in this case, creates a presumption that other segregated schooling within the system is not adventitious. It establishes, in other words, a prima facie case *477of unlawful segregative design on the part of school authorities, and shifts to those authorities the burden of proving that other segregated schools within the system are not also the result of intentionally segregative actions.” Id., at 208.
The plaintiffs in the Columbus case, unlike those in the Dayton case, proved what the Court in Keyes defined as a prima facie case.9 The District Court and the Court of Appeals correctly found that the school board did not rebut this presumption. It is on this basis that I agree with the District Court and the Court of Appeals in concluding that the Columbus School District was operated in violation of the Constitution.
The petitioners in the Columbus case also challenge the remedy imposed by the District Court. Just two Terms ago we set out the test for determining the appropriate scope of a remedy in a case such as this:
“If such violations are found, the District Court in the first instance, subject to review by the Court of Appeals, must determine how much incremental segregative effect these violations had on the racial distribution of the . . . school population as presently constituted, when that distribution is compared to what it would have been in the absence of such constitutional violations. The remedy must be designed to redress that difference, and only if there has been a systemwide impact may there be a systemwide remedy.” Dayton I, 433 U. S., at 420.
*478In the context in which the Columbus case has reached us, I cannot say that the remedy imposed by the District Court was impermissible under this test. For the reasons discussed above, the District Court’s conclusion that there was a sys-temwide constitutional violation was soundly based. And because the scope of the remedy is tied to the scope of the violation, a remedy encompassing the entire school district was presumptively appropriate. In litigating the question of remedy, however, I think the defendants in a case such as this should always be permitted to show that certain schools or areas were not affected by the constitutional violation.
The District Court in this case did allow the defendants to show just that. The school board proposed several remedies, but it put forward only one plan that was limited by the allegedly limited effects of the violation. That plan would have remedied racial imbalance only in the schools mentioned in the District Court’s opinion. Another remedy proposed by the school board would have resulted in a rough racial balance in all but 22 “all-white” schools. But the board did not assert that those schools had been unaffected by the violations. Instead, it justified that plan on the ground that it would bring the predominately Negro schools into balance with no need to involve the 22 all-white schools on the periphery of the district. The District Court rejected this plan, finding that it would not offer effective desegregation since it would leave those 22 schools available for “white flight.” The plan ultimately adopted by the District Court used the Negro school population of Columbus as a benchmark, and decreed that all the public schools should be 32% minority, plus or minus 15%.
Although, as the Court stressed in Green v. County School Board, 391 U. S. 430, a remedy is to be judged by its effectiveness, effectiveness alone is not a reason for extending a remedy to all schools in a district. An easily visible correlation between school segregation and residential segregation cannot by *479itself justify the blanket extension of a remedy throughout a district. As Dayton I made clear, unless a school was affected by the violations, it should not be included in the remedy. I suspect the defendants in Columbus might have been able to show that at least some schools in the district were not affected by the proved violations. Schools in the far eastern or northern portions of the district were so far removed from the center of Negro population that the unconstitutional actions of the board may not have affected them at all. But the defendants did not carry the burden necessary to exclude those schools.
The remedy adopted by the District Court used numerical guidelines, but it was not for that reason invalid. As this Court said in Swann v. Charlotte-Mecklenburg Board of Education, 402 U. S. 1:
“Awareness of the racial composition of the whole school system is likely to be a useful starting point in shaping a remedy to correct past constitutional violations. In sum, the very limited use made of mathematical ratios was within the equitable remedial discretion of the District Court.” Id., at 25.
On this record, therefore, I cannot say that the remedy was improper.
For these reasons, I concur in the result in Columbus Board of Education v. Penick, and dissent in Dayton Board of Education v. Brinkman.
Federal Rule Civ. Proe. 52 (a) reflects the general deference that is to be paid to the findings of a district court. “Findings of fact shall not *470be set aside unless clearly erroneous, and due regard shall be given to the opportunity of the trial court to judge of the credibility of the witnesses.” See United States v. United States Gypsum Co., 333 U. S. 364, 394r-395.
"School authorities have the primary responsibility for elucidating, assessing, and solving these problems; courts will have to consider whether the action of school authorities constitutes good faith implementation of the governing constitutional principles. Because of their proximity to local conditions and the possible need for further hearings, the courts which originally heard these cases can best perform this judicial appraisal.” Brown II, 349 U. S., at 299.
“Indeed, the importance of the judicial administration aspects of the case are heightened by the presence of the substantive issues on which it turns. The proper observance of the division of functions between the federal trial courts and the federal appellate courts is important in every case. It is especially important in a case such as this where the District Court for the Southern District of Ohio was not simply asked to render judgment in accordance with the law of Ohio in favor of one private party against another; it was asked by the plaintiffs, students in the public school system of a large city, to restructure the administration of that system.” Dayton I, 433 U. S., at 409-410.
In Keyes v. School Dist. No. 1, Denver, Colo., 413 U. S. 189, the Court did discuss the affirmative duty of a school board to desegregate *472the school district, but limited its discussion to cases “where a dual system was compelled or authorized by statute at the time of our decision in Brown v. Board of Education . . . Id., at 200. It is undisputed that Ohio has forbidden its school boards racially to segregate the public schools since at least' 1888. See Dayton I, 433 U. S., at 410 n. 4; Ohio Rev. Code Ann. § 3313.48 (Supp. 1978); Board of Education v. State, 45 Ohio St. 555, 16 N. E. 373; Clemons v. Board of Education, 228 F. 2d 853, 858.
The Columbus School District grew quickly in the years after 1954. In 1950-1951, the district had 46,352 students. In 1960-1961, over 83,000 students were enrolled. Attendance peaked in 1971-1972 at just over 110,000 students, before sinking to 95,000 at the time of trial. Between *4731950 and 1970, an average of over 100 classrooms a year were added to the district.
Although the Dayton District grew less dramatically, the student population increased from 35,000 in 1950-1951, of whom approximately 6,600 were Negro, to 45,000 at the time of trial, of whom about 22,000 were Negro. Twenty-four new schools were opened in Dayton between 1950 and the time of trial.
For example, the District Court concluded that faculty segregation in *474the Dayton district ceased by 1963. The Court of Appeals reversed, saying:
“In Brinkman I, supra, 503 F. 2d at 697-98, this court found that defendants 'effectively continued in practice the racial assignment of faculty through the 1970-71 school year.’ This finding is supported by substantial evidence on the record. The finding of the district court to the contrary is clearly erroneous.” (Footnotes omitted.) Brinkman v. Gilligan, 583 F. 2d 243, 253 (CA6).
7 Thus, in considering certain optional attendance zones that the District Court found had not been instituted with a discriminatory intent, the Court of Appeals wrote:
“In reaching these clearly erroneous findings of fact, the district court once again failed to recognize the optional zones as a perpetuation, rather than an elimination, of the existing dual system; failed to afford plaintiffs the burden-shifting benefits of their prima facie case; and failed to evaluate the evidence in light of tests for segregative intent enunciated by the Supreme Court, this court and other circuits in decisions cited in this opinion.” Id., at 255.
The Court of Appeals opinion relied upon the same theory in overturning the factual conclusions of the District Court that school construction and site selection had not been undertaken with a discriminatory purpose in Dayton. Thus, it is impossible to separate the conclusions of law made by the Court of Appeals from its rulings that the District Court made clearly erroneous findings of fact.
The two clearest cases of discrimination involved attendance zones. The near-Bexley optional zone operated from the 1959-1960 school year through the 1974-1975 school year. This zone encompassed a small area of Columbus between Alum Creek and the town of Bexley. The area west of the creek was predominately Negro; the area covered by the option was predominately white. Students living in that zone were given the option of being bused entirely through the town of Bexley to “white” Columbus schools on its eastern border. The District Court concluded:
“Nothing presented by the Columbus defendants at trial, at closing arguments, or in their briefs convinces the Court that the Near-Bexley Option was created or maintained for racially neutral reasons. The Court finds that the option was not created and maintained because of overcrowding or geographical barriers.
“. . . Quite frankly, the Near-Bexley Option appears to this Court to be a classic example of a segregative device designed to permit white students to escape attendance at predominately black schools.” 429 F. Supp. 229, 245 (SD Ohio).
The Moler discontiguous zone affected two elementary schools in the southeastern portion of the school district. A majority of the students in the Alum Crest Elementary School were, at all relevant times, Negro. Through 1969, no more than 8.7% of the students at the other school, Moler Elementary, were Negro. The District Court found:
“Between September, 1966 and June, 1968, about 70 students, most of them white, were bused daily past Alum Crest Elementary from the dis-*476contiguous attendance area to Moler Elementary. The then-principal of Alum Crest watched the bus drive past the Alum Crest building on its way to and from Moler. At the time, the Columbus Board of Education was leasing 11 classrooms at Alum Crest to Franklin County. There was enough classroom space at Alum Crest to accommodate the students who were transported to Moler. When the principal inquired of a Columbus school administrator why this situation existed, he was given no reasonable explanation.
“The Court can discern no other explanation than a racial one for the existence of the Moler discontiguous attendance area for the period 1963 through 1969.” Id., at 247.
The Denver School District at the time of the trial in Keyes had 96,000 students, almost exactly the number of students in the Columbus system at the time of this trial. The Park Hill region of Denver had been the scene of the intentional discrimination that the Court believed justified a presumption of systemwide violation. That region contained six elementary schools and one junior high school, educating a small portion of the school district’s students, but a large number of the district’s Negro students.
Wisconsin has implemented a system of subsidized, voluntary, intra- and inter-district majority-to-minority transfers. 1975 Wis. Laws, eh. 220, *489codified at Wis. Stat. § 121.85 (1975). It is too early to determine whether this experiment will attain its objective of encouraging substantial integration. But it is the sort of effort that should be considered by state and local officials and elected bodies. The contrast between the underlying philosophy of the Wisconsin plan and the massive coercion undertaken by the courts below is striking. See Meadows, Open Enrollment and Fiscal Incentives, in School Desegregation, Shadow and Substance 143 (Levin-sohn & Wright eds. 1976).