CELEBREZZE, Circuit Judge.
These appeals present the merits of a school desegregation suit brought against the Kalamazoo Board of Education, its Members, and its Superintendent, and against the Michigan State Board of Education and its Superintendent.1 The District Court’s Order grants permanent injunctive relief in the form of a desegregation plan adopted by the Kalamazoo Board of Education on May 7, 1971, but revoked on July 6, 1971. The injunction requires the State and local defendants to refrain from further segregative actions and inactions. The District Court assessed the costs of the proceedings against Appellants, but left the question of attorney fees for subsequent resolution.
The State and local defendants filed appeals, which have been consolidated in this proceeding. The issues are essentially three; whether the District Judge should have recused himself, whether the District Court’s standard of liability was incorrect, and whether the District Court’s findings were clearly erroneous.
[180]*180Recusal
Appellants moved, pursuant to 28 U.S.C. § 144 (1968),2 that the District Judge, Noel P. Fox, recuse himself because of his personal bias or prejudice in the case. The affidavit which accompanied the recusal motion contained numerous allegations about the propriety of certain rulings of the District Judge. Finding that the allegations failed to establish the personal bias or prejudice required to sustain a recusal motion, the District Court denied the motion.
Appellants’ affidavit included allegations that the District Judge held “an unshakable conviction” that there is no distinction between de facto and de jure segregation for constitutional purposes; that the relief granted was biased in favor of the black plaintiffs and prejudicial to poor whites; that personal bias for the plaintiffs was demonstrated by the manner in which the parties were characterized and the treatment accorded the parties, counsel, and witnesses; that an irrelevant and erroneous finding was made with regard to certain advice given by the defendants’ attorney; that a Motion for Protective Order filed by plaintiffs was given improper treatment; and that there was undue delay in holding the trial on the merits of the case. All these allegations relate to, and are sought to be supported by, proceedings in and rulings by the District Court.
Treating the facts alleged in the affidavit as true and looking only to the sufficiency of those facts in considering the recusal motion, Berger v. United States, 255 U.S. 22, 41 S.Ct. 230, 65 L.Ed. 481 (1921), we find that the allegations do not suffice to support a claim of personal bias or prejudice on the part of the District Judge. As we have stated previously:
The bias or prejudice which will disqualify a judge must be “personal” bias or prejudice as distinguished from a judicial one.
It is not sufficient if the alleged bias or prejudice arises out of the judge’s background and associations rather than his appraisal of the complaining party personally.
Nor is it sufficient that the alleged bias or prejudice arises from the judge’s view of the law, which may have been expressed by him in some prior case.
A judge is not disqualified merely because he believes in upholding the law, even though he says so with vehemence.
Adverse rulings during the course of the proceedings are not by themselves sufficient to establish bias and prejudice. Knapp v. Kinsey, 232 F.2d 458, 466 (6th Cir. 1956).
See United States v. Amick, 439 F.2d 351, 369 (7th Cir. 1971); Plaquemines Parish School Board v. United States, 415 F.2d 817, 824-825 (5th Cir. 1969); Tynan v. United States, 126 U.S.App.D.C. 206, 376 F.2d 761, 764-765 (1967). We affirm the District Court’s denial of the recusal motion.
Standard of Liability
Appellants challenge the standard of liability applied by the District Court, asserting that the District Court held them responsible for remedying de facto segregation and ignored the requirement that de jure segregation be shown as a predicate to a desegregation order.
We agree with Appellants that no remedy may be ordered when no consti[181]*181tutional violation has occurred. The federal courts are not free to intrude on the legitimate prerogatives of elected school officials. But the federal courts are guardians of constitutional rights and will protect minorities and majorities alike when they are deprived of the equal protection of the laws, despite an inevitable intrusion into decisions left to public officials in the absence of a constitutional violation. Given a constitutional violation, a remedy is not only proper but necessary. Brown v. Board of Education, 347 U.S. 483, 74 S.Ct. 686, 90 L.Ed. 873 (1954), 349 U.S. 294, 75 S.Ct. 753, 99 L.Ed. 1083 (1955); Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971).
We need not confront the question whether de facto segregation in a public school district establishes a constitutional violation of the Equal Protection Clause.3 The District Court explicitly adopted a test dependent on purposeful segregation by public school officials:
For the purposes of this case, the court assumes that the plaintiffs must establish that the defendants are guilty of de jure segregation of the Kalamazoo public schools.
[T]he major legal elements and conditioning factors of the constitutional tort of de jure segregation [footnote omitted] are reasonably clear. Under the Keyes theorem, in addition to showing that segregated schools exist, plaintiffs should establish (1) that the state to a significant degree caused or maintained these segregated conditions, and (2) that the state intentionally, i. e., purposefully, created or maintained them.
Under Keyes, in an intentional case, to be guilty of a constitutional violation, the state and local authorities must have in fact caused or maintained the segregated conditions which are complained of. Under this theory, it is a complete defense that the state and local authorities have not at all caused or maintained these conditions. Similarly, the state will not be held legally responsible if it has only occasionally committed segregative acts and these acts are of trivial importance and bear no significant relation to the modern situation.
Rather, the standard must be that the state and local agencies to a substantial degree contributed to the creation or maintenance of segregated schooling in Kalamazoo. .
Under Keyes, defendants must not only have caused the schools to be segregated, but must have intentionally caused them to be segregated.
Of course, in order to make its ultimate determination on the issue of intention, the court must fully consider the evidence and arguments presented by all the parties, including the claim by the Kalamazoo school board that it was resolutely applying a racially neutral neighborhood school policy. . . .
It is established that where an appropriate factual showing has been made, including a showing that an existing segregated situation is to a significant extent the natural probable, and actual result of the actions and inactions of the state and local agencies, the plaintiffs have laid an eviden-tiary foundation for the conclusion that the results, segregated schools, were intended to be reached by these authorities. 368 F.Supp. 143, 157, 159, 161, 162.
We find this to be a correct formulation of the de jure test, flowing directly from our holdings in Bradley v. Milliken, [182]*182484 F.2d 215, 222, 241-242 (6th Cir. 1973) (en banc), rev’d on other grounds, 418 U.S. 717, 94 S.Ct. 3112, 41 L.Ed.2d 1069 (July 25, 1974), and Davis v. School District of Pontiac, 443 F.2d 573 (6th Cir. 1971), aff’g 309 F.Supp. 734, 744 (E.D.Mich.1970), cert. denied, 404 U.S. 913, 92 S.Ct. 233, 30 L.Ed.2d 186 (1971), cited with approval in Keyes v. School District No. 1, 413 U.S. 189, 210, 93 S.Ct. 2686, 37 L.Ed.2d 1043 (1973). See also Brinkman v. Gilligan, 503 F.2d 684 (6th Cir. 1974); United States v. Board of School Commissioners, 474 F.2d 81 (7th Cir. 1973), aff’g 332 F.Supp. 655 (S.D.Ind.1971), cert. denied, 413 U.S. 920, 93 S.Ct. 3066, 37 L.Ed.2d 1041 (1973). Although our conclusion regarding a cross-district remedy was reversed by the Supreme Court in Milliken v. Bradley, the Supreme Court unanimously affirmed our determination that de jure segregation had been proven within the City of Detroit, on the basis of the same standard used by the District Court in this case.4
A finding of de jure segregation requires a showing of three elements: (1) action or inaction by public officials (2) with a segregative purpose (3) which actually results in increased or continued segregation in the public schools.5 A presumption of segregative purpose arises when plaintiffs establish that the natural, probable, and foreseeable result of public officials’ action or inaction was an increase or perpetuation of public school segregation. The presumption becomes proof unless defendants affirmatively establish that their action or inaction was a consistent and resolute application of racially neutral policies. Keyes v. School District No. 1, supra; Bradley v. Milliken, supra; Davis v. School District of Pontiac, supra; Kelly v. Guinn, 456 F.2d 100 (9th Cir. 1972), cert. denied, 413 U.S. 919, 93 S.Ct. 3048, 37 L.Ed.2d 1041 (1973); Branche v. Board of Education, 204 F.Supp. 150 (E.D.N.Y.1962); People v. San Diego Unified School District, 19 Cal.App.3d 252, 96 Cal.Rptr. 658 (Ct.App.1971); Johnson v. San Francisco Unified School District, 339 F.Supp. 1315, 1318 (N.D.Cal.1971), app. for stay denied, Guey Heung Lee v. Johnson, 404 U.S. 1215, 92 S.Ct. 14, 30 L.Ed.2d 19 (1971).6
Findings of Fact
We turn to Appellants’ objections to the District Court’s factual findings. Our function on review is'limited to ascertaining whether the District Court’s application of its legal standard to the facts before it was clearly erroneous. Goss v. Board of Education of Knoxville, 482 F.2d 1044, 1047 (6th Cir. 1973), cert. denied, 414 U.S. 1171, 94 S.Ct. 933, 39 L.Ed.2d 120 (1974); Northcross v. Board of Education of Memphis, 489 F.2d 15, 17 (6th Cir. 1973), cert. denied, 416 U.S. 962, 94 S.Ct. 1982, 40 L.Ed.2d 313 1974). Appellants challenge many individual findings of the District Court, but the theme of the local Appellants is that the Kalamazoo Board of Education has always followed a neighborhood school policy and has never intentionally furthered segregation, and the basic argument of the State Appellants is that there is no evidence at all that they contributed to segregation in the Kalamazoo public schools.
When constitutional rights are involved, the issue is seldom whether public officials have acted with evil motives or whether they have consciously plotted with bigotry in their hearts to deprive [183]*183citizens of the equal protection of the laws. Rather, under the test for de jure segregation, the question is whether a purposeful pattern of segregation has manifested itself over time, despite the fact that individual official actions, considered alone, may not have been taken for segregative purposes and may not have been in themselves constitutionally invalid. Davis v. School District of Pontiac, 443 F.2d 573, 576 (6th Cir.), cert. denied, 404 U.S. 913, 92 S.Ct. 233, 30 L.Ed.2d 186 (1971). Benevolence of motive does not excuse segregative acts. As the Supreme Court stated in Wright v. Council of City of Emporia, 407 U.S. 451, 461, 92 S.Ct. 2196, 2203, 33 L.Ed.2d 51 (1972), “The ‘dominant purpose’ test finds no precedent in our decisions. . The existence of a permissible purpose cannot sustain an action that has an impermissible effect.”
The findings of the District Court are explicit, detailed and extensive, and need not be repeated herein. See 368 F.Supp. 143 (W.D.Mich.1973). We shall consider the overall situation in the Kalamazoo schools and three specific areas of school policy in determining whether the District Court’s conclusions are clearly erroneous.
By stipulation it is admitted that much of the Kalamazoo public school system is racially segregated. The District Court found that of 29 elementary schools, with a total Black student percentage enrollment of 16.1%, 92.3% of the Black elementary students attended 5 schools, no Black pupils attended 6, and 14 schools had fewer than five Black students. Of five junior high schools, with a total Black enrollment of 14.7%, the Black student population of two amounted to only 1.7% of each school’s enrollment, while the Black enrollment at the other three amounted to 26.2%, 24.6%, and 13.9%, respectively. Of two senior high schools, the student body of one was 1.6% Black while the Black student enrollment at the other was 19.7% of the school’s population. Thus, while some Kalamazoo schools reflect the racial mix in Kalamazoo generally, some schools are identifiably “White” and others are identifiably “Black.”
Racial segregation in the Kalamazoo schools was found to be directly tied to educational inequality between the races. The District Court found, “Black students have fallen as many as four grades behind their White counterparts by the time they leave school. Furthermore, the Citizens’ Committee on Integration . reported in 1969 that identifiably Black schools ranked at the bottom of the system in terms of academic achievement.” 368 F.Supp. at 155. Upon a thorough review of the evidence, we cannot find fault with the conclusions that the Kalamazoo public schools are racially segregated and that students in identifiably Black schools suffer educationally and psychologically from the segregated conditions.
Appellants do not attack these conclusions as vigorously as they deny that they have intentionally furthered school segregation. We need not consider each particular attack on the District Court’s findings to conclude that the finding of purposeful segregation by public action and inaction not only is not clearly erroneous but is fully supported by the record. This conclusion is apparent from a review of three areas of school policy.
First, the District 'Court found that the local Appellants had used attendance zone policies to further and perpetuate racial segregation. The District Court flatly rejected Appellants’ argument that the Kalamazoo Board had administered a “neighborhood school policy” in a racially neutral fashion. “It is apparent that Kalamazoo elementary schools were not situated and boundaries were not drawn in a fashion which regularly placed students in the schools closest to their homes.” 368 F.Supp. at 165. The Board made one elementary school more than twice as large as the smallest school, rather than disperse students attending the large school to schools closer to their homes. While attendance zones were often altered in overwhelmingly White areas of the city, the “rigidification of the boundaries of schools attend[184]*184ed by the majority of Black students had the predictable and actual effect of cementing Black students into special areas and particular schools within those areas, and of preserving many other areas and schools for Whites.” 368 F.Supp. at 166. Optional attendance zones were used to assure eventual racial segregation in areas of the city with changing residential patterns.
An example of purposeful segregation through attendance zone policies concerns Harding Elementary School, which was closed in 1960. Half of Harding’s parent population which was 15.7% Black had their children reassigned to Edison School. The other half which was less than 2% Black had their children reassigned to an optional attendance zone. The Board then located a portable building at a nearby predominantly White school, despite available space at Edison, which had a substantial number of Black students. This combination of actions had the predictable and actual effect of eventually designating Edison as a “Black” school. As the District Court found, “The Kalamazoo Board was purposely confining Black elementary children in the south central portion of the city to Edison school.” 368 F.Supp. at 167.
Such use of attendance zone policies provides the basis for a finding of de jure segregation. Bradley v. Milliken, 484 F.2d 215, 221-236 (6th Cir. 1973) (en banc), rev’d on other grounds, 418 U.S. 717, 94 S.Ct. 3112, 41 L.Ed.2d 1069 (July 25, 1974); Davis v. School District of Pontiac, 443 F.2d 573, 576 (6th Cir.), cert. denied, 404 U.S. 913, 92 S.Ct. 233, 30 L.Ed.2d 186 (1971); United States v. Board of School Commissioners of Indianapolis, 474 F.2d 81, 85-86 (7th Cir.), cert. denied, 413 U.S. 920, 93 S.Ct. 3066, 37 L.Ed.2d 1041 (1973). We find that the attendance zoning policy of the Kalamazoo Board did not follow a racially neutral “neighborhood school policy” but encouraged and perpetuated segregation in the public schools.
Second, the Kalamazoo Board’s policies on school construction and siting perpetuated and increased racial segregation, according to the District Court. North-glade elementary school, for example, was “racially identifiable” as a Black school when it opened in 1959. 368 F.Supp. at 170. Opening the school with its attendance boundaries, in combination with other actions and inactions of the Board, resulted in the “foreseeable and actual effect” of “containpng] the future growth of [the] Black elementary [school] student population on the north side in three schools,” which by 1969 had become 53.8%, 87.2%, and 95.6% Black. The District Court found a policy of encouraging all-White schools in the northwestern part of the city by construction and school attendance policies. 368 F.Supp. at 170-171. Furthermore, the Board’s involvement in the Arcadia project, a new housing development, amounted to substantial assistance in creating a virtually all-White community and elementary school. 368 F.Supp. at 173 — 174. In so doing, the Board did not merely establish a school in an area which had become racially segregated through the operation of purely private forces, but actually involved itself in creating a segregated community and a segregated school. In addition, the Board added “permanent and portable classrooms to White schools [in cases where] there was a significant amount of space available in racially identifiably Black schools [with] the obviously foreseeable and actual effect of perpetuating the segregated conditions which prevailed” from 1961 to 1970 and beyond. 368 F.Supp. at 173.
In these and other instances, which we find supported by evidence in the record, the Board’s school construction and siting policies furthered and solidified Kalamazoo public school segregation. As the District Court stated, its findings “at least parallel and probably exceed the observation of the Sixth Circuit Court of Appeals, affirming the District Court’s finding of state responsibility for school segregation in Pontiac, Michigan ‘that school location and attendance boundary line decisions, for the past 15 years, more often than not tended to [185]*185perpetuate segregation.’ Davis, 443 F.2d at 576.” 368 F.Supp. at 172. See also Bradley, 484 F.2d at 236-238.
A third substantial factor in the creation and perpetuation of a dual school system in Kalamazoo was faculty staffing policy, which the Supreme Court has cited as “among the most important indi-cia of a segregated system.” Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 18, 91 S.Ct. 1267, 1277, 28 L.Ed.2d 554 (1971).7 The District Court found “that the deliberate assignment of teachers on a racial basis exacerbated the detrimental effects of state-imposed segregation, and was itself a significant segregative act.” 368 F.Supp. at 178. Of the Black elementary staff in the Kalamazoo public schools in 1970, 80% were concentrated in the four elementary schools which contained 80% of the Black elementary pupils (out of 29 elementary schools in the system). Similar patterns existed for junior high and high school levels, albeit with less dramatic intensity. The Board seems to admit the disproportionate assignment of Black staff to “Black” schools, but argues that the rationale for such assignment by race was educational — to provide Black students with suitable role models and to decrease the tensions between teacher and pupil in the classroom.
The propriety of assigning Black staff to primarily Black schools, in the absence of a dual school system, is not in question here, except as it relates to the question whether a dual school system existed because of official actions contributing to the creation and perpetuation of a segregated school system. The inevitable result of assigning 80% of the system’s Black elementary staff to schools with predominantly Black student bodies was to increase the identifia-bility of those schools as “Black.” Whatever the wisdom and legality of placing more Black staff in schools with greater Black student populations, considered by itself, the disproportionate staff assignment by race clearly supports the District Court’s conclusion that school board policies and actions served to create and strengthen the racial identifiability of certain schools as “Black” and thereby to further and perpetuate a dual school system in Kalamazoo. See Swann, 402 U.S. at 18, 91 S.Ct. 1267; Kelly v. Guinn, 456 F.2d 100, 107 (9th Cir. 1972); Davis v. School District of Pontiac, 443 F.2d 573, 576 (6th Cir. 1971).
The District Court cited other factors of relevance to its overall finding, including the provision of inferior buildings to schools with a large Black population,8 the conscious neglect of many opportunities for decreasing racial segregation in the system,9 and the “paucity of Black administrators and teachers” in the system.10
Finally, the District Court cited the action which immediately precipitated this suit as the “most concrete uncontro-vertible predicate for the grant of equitable relief which Plaintiffs seek” — the July 6, 1971 resolution which revoked the May 7, 1971 plan which the Board had adopted to desegregate the school system. This revocation,11 in light of the [186]*186prior cumulative constitutional violation by the school authorities, is further evidence of the Board’s racially segregative purpose. As the District Court stated, “This action literally transformed an integrated system (albeit a very new one) into a racially segregated system.” 368 F.Supp. at 199.
We need not consider the revocation of the May 7 desegregation plan on its own to conclude that it supports the District Court’s overall conclusion that the Kalamazoo public schools are de jure racially segregated. See Keyes v. School District No. 1, 413 U.S. 189, 93 S.Ct. 2686, 37 L.Ed.2d 1043 (1973); Brinkman v. Gilligan, 503 F.2d 684 (6th Cir. 1974).
We affirm the District Court’s finding that the Kalamazoo Board of Education, its members and its superintendent have substantially contributed to the segregated conditions that make the Kalamazoo schools a dual system, effectively classifying students on the basis of race and denying Black children the equal protection of the laws.
A final consideration is the liability of the State Appellants for the de jure segregation of the Kalamazoo schools. The District Court found:
In sum, the Superintendent had general supervisory authority over public education in Michigan between 1954, the date of the Brown decision, and the adoption of the new Constitution. The State Board of Education and the Superintendent as its chief executive officer have shared this constitutional power between 1963 and the present. During this entire period, the Superintendent and the Board were aware of racial segregation in Michigan public schools through complaints to this effect and then through their own statistical data. Still, the Superintendent and the State Board have persistently failed to act in a meaningful way to ameliorate the situation.
These facts compel the conclusion that the State of Michigan, through the State defendants in this case, has intentionally sanctioned the segregation of schools by local boards, and has made a substantial contribution to the creation and maintenance of segregated public schools in Kalamazoo and elsewhere. While the court notes that the Michigan Attorney General issued an opinion in 1970 that the State Board did not have the jurisdiction to hear appeals and review decisions of boards of education on attendance zones, the court finds that too many genuine opportunities for action have existed since Brown in 1954 for the segregation evidenced by the census statistics to be fully excused by pleas of racial neutrality and merely adventitious segregation.
The State Board’s persistent failure to implement the Joint Policy Statement of 1966 has been effective notice to local school districts throughout Michigan of a policy of non-supervision in the area of desegregation. These school boards were able to conclude that they could take actions for perpetuating Black schools without the interposition of the State Board and the State Superintendent. This non-action exacerbated the segregated conditions in many school systems in the State of Michigan, diminished the likelihood of voluntary desegregation, and permitted or perhaps encouraged the kind of counterproductive action exhibited in Kalamazoo on July 6, 1971, 368 F.Supp. at 190.
Upon a thorough review of the briefs and record, we find the District Court’s conclusion as to the State Appellants to be supported by substantial evidence in the record.
The substantial control of Michigan state officials over local schools operations has been stated previously by this Court and need not be repeated herein. See Bradley v. Milliken, 484 F.2d 215, 238-241 (6th Cir. 1973) (en banc), rev’d on other grounds, 418 U.S. 717, 94 S.Ct. 3112, 41 L.Ed.2d 1069 [187]*187(July 25, 1974). Given de jure segregation in the Kalamazoo schools, substantially contributed to by local school officials, the State Board of Education and Superintendent may properly be held jointly responsible for segregated conditions in the Kalamazoo schools, in view of their consistent inaction in preventing increased segregation or remedying existing segregation in the Kalamazoo schools and their consistent funding of school construction projects, support for operating fund requests, and other assistance provided to Kalamazoo officials. The failure to take the many available measures against Kalamazoo officials for their segregative actions renders the State Board and Superintendent responsible for de jure segregation in the Kalamazoo schools and subjects them to the reasonable commands of the District Court’s desegregation order. See United States v. State of Texas (Texas Education Agency), 321 F.Supp. 1043 (E.D.Tex.1970), 330 F.Supp. 235, aff’d with mod., 447 F.2d 441 (5th Cir.), stay denied, 404 U.S. 1206, 92 S.Ct. 8, 30 L.Ed.2d 10 (Black, J.), cert. denied, 404 U.S. 1016, 92 S.Ct. 675, 30 L.Ed.2d 663 (1971).
Finding no reversible error in the proceedings below or in the order issued therefrom, yve affirm the decision of the District Court.