
833 F.Supp. 214 (1993)
UNITED STATES of America, Plaintiff,
and
Yonkers Branch, NAACP, et al., Plaintiffs-Intervenors,
v.
CITY OF YONKERS, Yonkers Community Development Agency, Yonkers Board of Education, Defendants,
and
U.S. Department of Housing and Urban Development, Samuel Pierce, Secretary, Added-Defendants,
and
The State of New York; Mario Cuomo, as Governor of the State of New York; the Board of Regents of the State of New York; Martin C. Barell, R. Carlos Carballada, Adelaide L. Sanford, Willard A. Genrich, Emlyn I. Griffith, Jorge L. Battista, *215 Lora Bradley Chodos, Louise P. Matteoni, Edward Meyer, Floyd S. Linton, Salvadore Sclafini, Mimi Levin Lieber, Shirley C. Brown, Norma Gluck, Thomas Frey and James McCabe, Sr., in their official capacities as members of the State Board of Regents; the Department of Education of the State of New York; Thomas Sobol, as Commissioner of Education of the State of New York; and the Urban Development Corporation of the State of New York and Vincent Tese, as Director of the Urban Development Corporation, Added-Defendants.
No. 80 Civ. 6761 (LBS).
United States District Court, S.D. New York.
August 30, 1993.
*216 Sandra Lynn Beber, U.S. Dept. of Justice, Civ. Rights Div., Washington, DC.
Michael H. Sussman, Goshen, NY, for plaintiff-intervenor NAACP.
Marion R. Buchbinder, Dept. of Law of the State of N.Y., New York City (Stephen Jacoby, of counsel), for New York State defendants.
Hogan & Hartson, Washington, DC (Steven J. Routh, of counsel), and Anderson Banks Moore Curran & Hollis, Mt. Kisco, NY (Lawrence W. Thomas, of counsel), for Yonkers Bd. of Educ. of the City of Yonkers.
Raymond P. Fitzpatrick, Jr., Johnston, Barton, Proctor, Swedlaw & Naff, Birmingham, AL (David P. Whiteside, of counsel), for City of Yonkers.

OPINION
SAND, District Judge.
As a result of good faith and zealous implementation by the Yonkers Board of Education ("YBE") and its staff of this Court's initial School Remedy Order of May 13, 1986 (Educational Improvement Plan ("EIP") I), the racial separation of students in the Yonkers Public Schools, which had existed for decades, ended. As the YBE correctly states, "Within less than a year of the issuance of EIP I, the Yonkers Board achieved desegregation of enrollments among the schools; something that many other school districts have taken years or even decades to accomplish." YBE, Post-Trial Brief, p. 2. This achievement was brought about by instituting a voluntary magnet school program, including procedures for school selection by parents, busing and other similar measures. The transition took place in a relatively smooth and peaceful manner, without the disturbances and disruption which plagued desegregating school districts elsewhere in this country. What makes this accomplishment even more remarkable is that it took place despite the fact that during the years in question, Yonkers was engaged in a bitter and divisive effort to thwart this Court's orders to remedy, to some degree, the racial discrimination with respect to housing which has existed in Yonkers for well over 40 years.
The YBE, joined in this proceeding by plaintiff-intervenors, the Yonkers Branch, National Association for the Advancement of Colored People ("NAACP"), takes the position that the placement of majority and minority students and staff in the same school buildings in numbers proximate to their incidence in the general school population, so that schools are no longer racially identifiable, is but the first step to achieving a truly unitary school system. Such a unitary school system is in place only when students, regardless of race, have similar educational opportunities and experiences.
The YBE and NAACP contend that vestiges of segregation remain in the Yonkers Public School system which, although capable of being remedied or eradicated, are not being adequately addressed. As a consequence, it is urged that the Yonkers Public School system (sometimes "YPS") continues to discriminate against blacks and hispanics and that dissatisfaction with the existing system, on the part of both minority and majority parents, threatens to negate or diminish the accomplishments thus far achieved.
*217 The YBE and NAACP further assert that the failure to address adequately these vestiges of segregation results, not from a lack of commitment on the part of the Superintendent of Schools or his staff, but from a lack of funds. The YBE has promulgated a detailed and extensive program (EIP II) in which it sets forth the steps which it believes should be appropriately taken to eradicate vestiges of segregation. Believing that City resources were inadequate to meet the perceived needs[1] and that the State of New York shared a liability with the City for the presence of these vestiges of segregation, the YBE instituted these proceedings against the State which had not heretofore been a party to this protracted litigation. The YBE, joined by the NAACP, seeks to impose upon the State a fiscal responsibility, shared with the City, to fund EIP II.

Scope of Issue
In prior proceedings, the State has moved to dismiss, and sought summary judgment on a number of grounds, including sovereign immunity, statute of limitations and laches. These motions have been denied. See United States v. YBE, 893 F.2d 498 (2d Cir.1990) (appeal dismissed).
The YBE had alleged the existence of seven vestiges of segregation:
(1) the level of minority achievement; (2) the self-esteem and attitudes of students toward education and the educational process; (3) the relationships between majority and minority students; (4) the attitudes and effectiveness of teachers and administrators in educating majority and minority students in integrated schools and classrooms; (5) the continuing need for adjustments in curriculum and programs to facilitate quality education in integrated environments under the existing desegregation remedy; (6) the continued disparities in the quality of school facilities and resources; and (7) community perceptions concerning the Yonkers schools and the quality of education under the current desegregation plan.
The position taken by the City of Yonkers in these proceedings has been somewhat blurred. The City in the first instance denies that vestiges of segregation exist in the Yonkers Public Schools, but if such vestiges exist, the City alternatively argues (as federal procedure permits it to do), that the State, not the City, should pay the costs of their eradication.
In our Opinion of July 10, 1992, denying the motions of the Added State and UDC Defendants ("State Defendants")[2] we concluded that we could not, despite the YBE and State defendants' proffer of conflicting expert testimony, "definitively determine on this motion whether such vestiges remain in the Yonkers school system".
"Further," we wrote, "we believe that this is a sufficiently discrete issue from the questions of State related causation, liability, and relative responsibility to make bifurcation of this issue feasible". Opinion, July 10, 1992.
Accordingly we advised: "the Court will proceed to determine, after a trial on the merits, the question whether inadequately addressed vestiges of segregation remain in the Yonkers school system. This question has three components: (1) what vestiges, if any, exist; (2) what steps are presently being taken to address such vestiges, if any are found to exist; (3) the adequacy of (2) and availability of more effective measures. All other issues will be deferred for later consideration."
The Court also stated that "we put all parties on notice that if vestiges of segregation are found to exist and to be inadequately addressed, the Court will consider what action is appropriate and will not be limited to the relief sought by the YBE and NAACP against the State. If no vestiges exist, this litigation against the State will, of course, be dismissed."
*218 The scope of this initial phase of these proceedings was further clarified in a telephone conference with counsel for all parties held on May 25, 1993. The City in its Post-Trial brief, p. 2, correctly summarizes the conclusion reached at that conference as follows: "Thus, the issues presently before the Court do not include an evaluation of any specific, proposed additional remedy, or an assessment of how any such remedies might be funded. The issues instead are limited to the question of whether vestiges of prior segregation continue to exist in the Yonkers school system and the extent to which such vestiges are presently being addressed."
The Court, having heard twelve days of testimony, shall now proceed to address the specific questions set forth in our July 10, 1992 opinion.

What is a Vestige of Segregation?
The YBE asserts that the testimony adduced at the hearing proves: "numerous related discriminatory conditions or vestiges of prior de jure segregation and inequalities that continue to exist in the Yonkers Public Schools, including the following:
(1) Within many schools in Yonkers, there remains racial and ethnic segregation of students among various levels of courses, programs, classes, and in-class groupings, which affects the quality and type of education provided to children of different racial and ethnic groups;
(2) The implementation of EIP I has not addressed or alleviated many of the conditions of inequality that were fostered by the racially dual system of education in Yonkers, such as racially disparate attitudes and expectations of teachers and administrators; teaching methods that support effective instruction primarily for middle or upper middle class white students in homogeneous classrooms; curriculum that is neither multicultural nor aligned to the goals and objectives of the desegregating school system; and a lack of adequate services for students with limited English proficiency, and other pupil personnel services, that are particularly important to the effective education of minority children;
(3) The implementation of EIP I itself has given rise to a number of problems that must be addressed to ensure effective education in a desegregated setting, such as the increased difficulty of obtaining parental involvement in schools that, by necessity, no longer serve populations drawn exclusively from surrounding, segregated neighborhoods;
(4) Although EIP I has been successful to date in maintaining desegregated school enrollments, its ability to support continued voluntary desegregative movement of students within Yonkers and its ability to attract enough middle class and non-minority students to provide for meaningful desegregation in the future will be seriously undermined unless the magnet school programs are fully implemented and the overall quality of education in the system is improved; and
(5) There continue to exist extremely high levels of as yet unremedied residential segregation in Yonkers, which require the Yonkers Board not only to maintain EIP I but also to offset to the extent practicable the negative effects that flow from the fact that a substantial portion of minority students in Yonkers live in highly segregated, publicly assisted or other housing in the Southwest quadrant of the City.
YBE Post-Trial brief pp. 3-4. Before addressing the question whether "vestiges of segregation" exist in the Yonkers Public Schools, one must of course begin with some working definition of that term.
Although the Supreme Court has not explicitly stated what the term "vestige" encompasses, the line of cases beginning with Brown v. Board of Education of Topeka, 347 U.S. 483, 74 S.Ct. 686, 98 L.Ed. 873 (1954) and continuing through the recent decision of Freeman v. Pitts, ___ U.S. ___, 112 S.Ct. 1430, 118 L.Ed.2d 108 (1992) suggests the following definition. A vestige of segregation is a policy or practice which is traceable to *219 the prior de jure system of segregation and which continues to have discriminatory effects. A vestige is not the lingering effect or consequence of segregation, such as poor relations between majority and minority students, but such an effect or consequence may be evidence that a vestige of segregation exists. The duty of the courts and the school boards is to eliminate vestiges of past discrimination "to the extent practicable." Board of Education of Oklahoma City v. Dowell, 498 U.S. 237, 111 S.Ct. 630, 112 L.Ed.2d 715 (1991). Any remaining segregative or discriminatory aspects of the school system must be eliminated "root and branch" Green v. County Board of New Kent County, 391 U.S. 430, 438, 88 S.Ct. 1689, 1694, 20 L.Ed.2d 716 (1968).
In United States v. Fordice, ___ U.S. ___, ___, 112 S.Ct. 2727, 2735-36, 120 L.Ed.2d 575 (1992), the Supreme Court elaborated on the concept of a vestige of segregation in the context of desegregating state-run institutions of higher learning. The Court explained:
Our decisions establish that a State does not discharge its constitutional obligations until it eradicates policies and practices traceable to its prior de jure dual system that continue to foster segregation ... [the task is to examine] a wide range of factors to determine whether the State has perpetuated its formerly de jure segregation in any facet of its institutional system ... If policies traceable to the de jure system are still in force and have discriminatory effects, those policies too must be reformed to the extent practicable and consistent with sound educational policies.
In Freeman, the Court emphasized the relationship that must exist between an alleged vestige and the original constitutional violation. The Court stated,
The vestiges of segregation that are the concern of the law in a school case may be subtle and intangible but nonetheless they must be so real that they have a causal link to the de jure violation being remedied.
___ U.S. at ___, 112 S.Ct. at 1448.
There is no exclusive list of factors which a district court may examine to determine if there are vestiges of segregation. However, the courts have accepted the "Green factors," named after the decision in Green v. County School Board, 391 U.S. 430, 435, 88 S.Ct. 1689, 1693, 20 L.Ed.2d 716 (1967) as a starting point. In Green, the Court suggested that vestiges of segregation can extend "not just to the composition of student bodies ... but to every facet of school operations-faculty, staff, transportation, extra-curricular activities and facilities."
In Keyes v. School District No. 1, Denver, Colorado, 413 U.S. 189, 196, 93 S.Ct. 2686, 2691, 37 L.Ed.2d 548 (1973), the Court identified "community and administration attitudes toward the school" as elements of segregation. In Freeman, the Court approved the district court's consideration of differences in the quality of education afforded to the students, as measured by the achievements of minority students, as an acceptable inquiry into the existence of vestiges.
Justice Marshall, in dissent in Dowell, provided a more philosophical approach to defining "vestige," which, although not as useful in directly identifying an instance of a vestige, is helpful in focusing the inquiry. He wrote, at 498 U.S. 260-61, 111 S.Ct. 644:
Although the Court has never explicitly defined what constitutes a "vestige" of State enforced segregation, the function that this concept has performed in our jurisprudence suggests that it extends to any condition that is likely to convey the message of inferiority implicit in a policy of segregation.
The line between a "vestige" of segregation and ongoing discriminatory conduct is not clearly drawn. It may well be that the difference between a "vestige" and a current discrimination may relate solely to the historical fact that prior discrimination has been found to exist, or the vigor with which school administrators, intentionally or not, have addressed or condoned discriminatory conditions. As the State asserts in its Post-Trial Brief, p. 6:
"Of course, regardless of whether a school district has been found liable for de jure segregation, it may nonetheless be engaged in current discriminatory conduct *220 which deprives minority students of their constitutional rights. Such conduct is not a "vestige" of a past condition; it is an ongoing constitutional wrong which may be judicially addressed."
Although the distinction between on-going discriminatory conduct and a "vestige" may be of significance with regard to other questions relevant to State liability and remedy, if minority students attending Yonkers Public Schools suffer a constitutional injury, the label affixed to the cause of such injury is of no moment in determining in this phase of the case whether some corrective action is needed.

Burden of Proof
The YBE cites in its Post-Trial Brief, p. 17, language in Fordice to the effect that once State officials have been shown to have contributed to unconstitutional segregation, "the burden of proof falls on the State, and not on the aggrieved plaintiffs, to establish that it has dismantled its prior de jure segregated system." ___ U.S. at ___, 112 S.Ct. at 2741; accord id. at ___, 112 S.Ct. at 2743-44. (O'Connor J., concurring). Thus the YBE asserts, that when it returns to court, as it has, to seek additional desegregation relief, the burden of proof rests on the defendants to show that any current segregation or discriminatory conditions are not in fact causally related to the prior dual system.
We note, however, that although fully applicable to the City, which was a party to the liability and remedy phases of this case, the extent to which these observations are pertinent to the State, newly joined to this litigation, is more problematic. Further, our primary inquiry at this phase is to determine whether discriminatory conditions exist in the Yonkers public schools. Questions of causation have been deferred.

Achievement Levels
Although as noted supra at pp. 217, 218, the YBE has cited numerous examples of alleged vestiges, some of these may be thought of as "lingering effects" of segregation rather than as a continuing discriminatory condition. The phenomenon principally relied upon by the YBE and NAACP at trial, and which this Court deems to be of paramount importance, is the disparity which exists between majority and minority students with regard to achievement levels on standard reading and math tests. After all, the primary function of a school system is to teach, and if evidence discloses that children are not learning at acceptable levels, all else pales in significance.
We begin our analysis with two basic premises. The first, that all children can learn and no children should fail, is not disputed. Indeed, it is the guiding principle propounded by the New York State Education Department. A New Compact for Learning, Improving Public Elementary, Middle and Secondary Education Results in the 1990's, July 15, 1991, passim.
The second basic premise is that one looks to achievement results on standardized tests to determine whether equality of educational opportunity has been achieved. The City challenges this second premise on two grounds.
First, the City asserts (Post-Trial Brief, pp. 5-6) that "the constitutional test is whether students have equal access, not whether such equality of access produces consistently equal outcomes". In other words, the City advances the proposition that, so long as majority and minority students are exposed to equal educational opportunities, the constitutional obligation is discharged even if the teaching techniques and curriculum are unsuited to the special needs of some students. But if the schools do not adequately address the needs of some of their students, it is difficult to understand how those students can be said to have had an equal educational opportunity. If, for example, all students were taught in a foreign language, which only some students understood, the educational experience of both groups of students could hardly be described as being equal.
The State does not join the City in advancing this claim. Indeed, reference to A New Compact for Learning is again relevant. The Second principle of the Compact reads:
Our mission is not to keep school  it is to see that children learn. The energies of *221 all participants should be focused on achieving the desired outcomes. Accountability does not end with following established rules and procedures; its essence is found in results.

(Emphasis added.)
The fourth principle of the Compact reads:
Every child in New York State is entitled to the resources necessary to provide the sound, basic education which that State Constitution requires. The requirement is not equality input, but equity of outcome.

(Emphasis added.)
The concept that the State's standard is not equality of input but equity of outcome is repeatedly stressed in the Compact. See, e.g., p. 5.
Our point is not that some State criterion is allegedly being violated by the YPS. Rather the point is that it is accepted doctrine among educators that one looks to results to measure equity of educational opportunity.
The City also asserts that the decision made by Superintendent Donald Batista to use the Metropolitan Achievement Test ("MAT") skews the results because the tests are themselves racially biased and that other tests were available, and that many of these achievement tests were available in languages other than English. City Post-Trial Brief, p. 9.
We reject the suggestion that the Superintendent deliberately selected a test which would lower the levels of the achievement realized in the Yonkers Public Schools. Such a scenario is simply too Machiavellian to be attributed to this conscientious and dedicated educator. Nor do we believe it is improper or unfair to use the MAT. Although the MAT may indeed reflect a cultural bias and require a degree of proficiency in English, it is a useful measure of academic achievement and is an accepted measure of how our society determines educational levels.
Which brings us to the critical question whether it is in fact the case that minority students (black and hispanic) lag behind majority students (for these purposes, white and Asian students) in reading and math as measured by those test results. We find that they do, and that to a statistically significant extent, race is a factor with regard to levels of academic achievement in the Yonkers Public Schools.
As plaintiffs have amply demonstrated, the raw data discloses that minority students score appreciably below majority students in their reading and math scores. More significantly, the multiple regression analysis performed by the YBE's expert, Dr. Jamills Braddock (Appendix A hereto) demonstrates that race is a statistically significant factor in accounting for this disparity even after factoring out other possible causes such as placement in special education, limited English proficiency, receiving free or reduced lunches (used as a proxy for socio-economic status), prior test scores, and attendance at schools heavily impacted with students receiving free or reduced lunches.
A considerable portion of the defendants' argument at trial and in their post-trial briefs is devoted to an attack on Dr. Braddock's methodology. But even if the Court were to disregard Dr. Braddock's analysis in its entirety and rely solely on the analysis of the State's own expert, Dr. David Rindskopf (Appendix B), the conclusion that race is a statistically significant factor with regard to math and reading achievement levels would remain unchanged.
When Dr. Rindskopf addressed the question "whether there were race differences in test performance after taking into account other possible reasons for race differences other than what might be going on in school" (Tr. 1992), the answer was in the affirmative up to the stage in the analysis when an adjustment was made based on residence in the same southwestern Yonkers census tract. But we find unpersuasive the reasons advanced for this selective use of residence in a southwestern Yonkers census tract as a relevant factor. (Dr. Braddock had utilized attendance at a school having a large percentage of students receiving free lunches to adjust for neighborhood and other environmental and socio-economic factors.)
Unquestionably both the YBE's and the State's statistical analyses suffer from a lack of adequate base data as the City's expert *222 witness, Dr. David Steinberg, has testified. However, on balance, we find that the YBE has sustained its burden of proving that race is a significantly significant factor in the gap which exists, and appears to be widening, between minority and majority achievement levels measured by math and reading MAT results. Although the YBE describes achievement results as a vestige, we regard such results to be the consequence of conditions which are themselves more properly regarded as the vestiges.
A myriad of other factors (birth weight, educational and occupational background of parents, parental interest and involvement, single parents status, proficiency in English, mobility and other socio-economic factors) undoubtedly impact greatly on a child's readiness to learn. However, if we begin as all parties do with the premise that all children can learn and recognize that school occupies as much as it does of a child's life, the YBE's burden of showing that these achievement disparities result from vestiges of segregation is not a heavy one.[3]

Causes of Disparities in Achievement
The YBE's evidence concerning the probable causes of disparate achievement levels is largely anecdotal but it comes from educators intimately involved in the Yonkers Public School system. They assert that there are two significant respects in which the Yonkers school system is inadequately addressing the needs of minority students. The first relates to what is being taught, (i.e., the curriculum) and more importantly, the techniques of teaching being utilized, often by teachers inadequately trained in dealing with multi-culture classes and who have reduced expectations of what minority students can achieve. The second respect in which there is an alleged failure adequately to address the needs of the school system as it is in transition from a dual to a unitary system relates to available facilities and equipment.
It does not require much expertise to appreciate that different approaches may be appropriate in teaching a larger class of students from diverse backgrounds than in teaching a more homogeneous group. Nor is it surprising to hear educators urge that there is a need for a curriculum which is more meaningful to minority students that the classic majority-oriented curriculum. Moreover, it has been well recognized that students are highly responsive to the expectation of their teachers. Too often anticipation of a low achievement level becomes a self-fulfilling prophesy.
The YBE asserts that it lacks funds to train teachers adequately, revise curriculum, fully utilize the many programs which have been developed by such institutions as Johns Hopkins, employ sorely needed social workers and guidance counsellors, and otherwise address the educational needs of all of the Yonkers students.
It urges that the failure to meet these needs are reflected not only in MAT test results but also in disproportionate referral of minority students to special education classes, suspensions, retentions, and dropouts. It proposes in great detail in EIP II how it would seek to address these matters were it fiscally able to do so.

Facilities
As noted, plaintiffs urge that there are inadequate facilities to enable full implementation of EIP I and to eradicate vestiges of segregation from the YPS. Although plaintiffs had originally characterized the lack of adequate facilities as itself being a vestige, the claim now advanced is that lack of adequate facilities impedes implementation of desegregation. Tr. pp. 189-90. This shift in position is well advised since it is clear that *223 there is little or no correlation between the adequacy of a particular school facility and its prior racial identification.
The YBE has prepared an extensive facilities study, "The Ingraham Report," which, though not put forth as a master plan, lays out an extensive (and expensive) long range program of facility renovation and construction.
All parties agree that the population trends in Yonkers will call for the construction of at least one new elementary school in Yonkers. It is also clear that many schools in Yonkers are old, decrepit, and suffer from years of deferred maintenance occasioned by lack of funds. What is disputed is the extent to which facility improvement is needed for purposes of desegregation.
The YBE urges that the critical factor in implementing EIP I is a voluntary magnet program. This magnet program must have sufficient appeal so that it encourages majority students to remain in the YPS and encourages both majority and minority students to attend schools other than neighborhood schools. The YBE urges that no matter how appealing the content of a magnet school program may be, if it is housed in an inadequate facility, parents as well as students are likely to look elsewhere. Ample testimony has been presented to satisfy the Court, and we find that existing facilities are inadequate to implement fully EIP I, let alone implement EIP II.
We cite but one example. Surely the advent of desegregation has resulted in a greater need for the services of social workers and guidance counsellors. Ironically despite this greater need, the ratio of such support staff to students has decreased. Where once there was a social worker assigned to each school building, this is no longer the case. Moreover, social workers devote much of their time to preparation of case histories for special ed. referrals rather than student counselling. All of this is of course relevant to the first portion of our vestige analysis. But the testimony also supports the finding that some schools are so overcrowded that office space does not exist to provide a suitable place for social workers and guidance counsellors to meet with the students.
We find that eradication of vestiges of segregation in the YPS will require improvement of facilities and furnishing additional equipment (e.g., computers) and supplies, the exact extent of which is beyond the scope of this phase of these proceedings.

The Defenses Asserted
Defendants urge that the experience of the YPS, including lower minority achievement test scores and other circumstances such as disproportionate suspension rates, retentions and drop-outs, is not peculiar to the YPS but reflects national trends. Studies with respect to achievement scores support the claim that the problem is not limited to Yonkers but affects other urban desegregating schools as well. But the widespread nature of the problem of adequately addressing the needs of minority children does not provide an excuse for inaction. Rather the data gathered and techniques (e.g., cooperative learning[4]) developed in other communities and universities, provide a resource and opportunity to improve the manner in which the problem may be addressed in Yonkers.
Defendants further urge that the failure to implement adequately teacher training to address the needs of heterogeneous classes is not a function of lack of funds but results instead from teacher intransigence.
First, teacher training is in fact costly. Such training must take place either during regular class hours (incurring the costs of a substitute teacher to cover the class to which the trainee was regularly assigned) or must be conducted after hours (incurring overtime costs). We find that lack of funds, not disinterest, has inhibited the extent of teacher training in Yonkers.
Defendants advance the further claim that under the "Academic Freedom" clause of the collective bargaining agreement,[5] a teacher *224 may resist all efforts to introduce innovative teaching techniques, such as cooperative learning, into that teacher's classroom without being subject to discipline or sanction.
We believe this contention to be more theoretical than real. For the most part teachers enter the profession out of a desire to teach to students who learn. The Academic Freedom clause (Appendix C) appears to relate to content rather than methodology (e.g., the right to teach evolution). While there may be one or two teachers so set in their ways as to be unable or unwilling to master new teaching techniques, we accept the testimony of the YBE witnesses that the number of such teachers would be so negligible as not to have a significant impact on the YPS.
Further, defendants urge that EIP II is essentially designed to improve Yonkers public education overall rather than to address specifically areas relating to segregation. The State urges that "a remedy for unconstitutional conditions in schools is impermissible if it is addressed to a general improvement in the quality of the local school system." Arthur v. Nyquist, 712 F.2d 809 (2d Cir.1983), cert. denied, 466 U.S. 936, 104 S.Ct. 1907, 80 L.Ed.2d 456 (1984). While this may be true, it is equally the case that an effort to eradicate vestiges of segregation cannot be faulted because majority students may benefit as well.
We find that vestiges of segregation exist in the YPS and that the YBE seeks to address those vestiges. A Court should not decline to invoke a desegregation remedy simply because it improves education for both minority and non-minority students. See Jenkins v. State of Missouri, 855 F.2d 1295, 1303 (8th Cir.1988), cert. denied on relevant question, 490 U.S. 1034, 109 S.Ct. 1930, 104 L.Ed.2d 402 (1989); accord Arthur v. Nyquist, 712 F.2d 809, 813 (2d Cir.1983), cert. denied, 466 U.S. 936, 104 S.Ct. 1907, 80 L.Ed.2d 456 (1984).
The State argues that since so many students entered the YPS after EIP I was implemented and since they were never therefore subjected to a segregated school system, any shortcomings in their educational experience cannot be attributable to segregation. The argument is entirely circular. If all vestiges of segregation were eradicated prior to a student's entry into the YPS, obviously such a student would have suffered no injury because of past history. If however, vestiges of segregation continue in the YPS, a newcomer is nevertheless subject to the adverse effects of such segregation which continue to impact on the educational experience of that student.
Finally, and of greater concern, is the claim that EIP I has been entirely successful and the circumstances upon which the YBE now relies are entirely the result of demographic changes in Yonkers over which the YBE has no control.
In 1985 the YPS had a total student population of 18,945, of which 10,070 (53.2%) were white (including Asians), and 8,875 (46.8%) were black and hispanic. In 1985, the black and hispanic students were at almost equal levels (4,563 black; 4,290 hispanic). (Ex. 31). For the 1992 school year, the total student population was 20,246, of which 7,080 (35.0%) were white, and 13,166 (65%) were black and hispanic. (Ex. 3A). In 1992 the minority student population consisted of 5,750 black and 7,416 hispanic students. (Ex. 31).
Thus two trends are apparent. There has been a diminution in the number of white students attending the YPS and a large influx of hispanics.[6]
The influx of hispanic students has no doubt placed great strains on the YPS. This results not only from the sheer numbers but the fact that many of the recent entries come with little or no English proficiency and little schooling in their native lands. It also appears that the recent wave of hispanic immigrants comes from various countries in Central America and are themselves a less cohesive group than the earlier hispanic immigrants who came primarily from Puerto Rico and Santo Domingo.
*225 But these demographic changes do not explain or condone the failure to eradicate vestiges of segregation. This is not a case where white flight skews the minority/majority balance in the public schools. A school board takes its student body as it finds it, and although the influx of new hispanic children with special educational needs doubtless adds considerably to the YBE's burdens, it does not change the basic nature of its task. Nor has it diminished the YBE's commitment to eradicate vestiges of segregation given the means to do so.

Conclusion
Although the limited scope of this phase of the proceedings (see pages 217-218 supra) does not encompass an overall consideration of fiscal matters, it is appropriate to note, placing these issues in context, that Yonkers has had a long history of funding its school system less generously than its more affluent Westchester neighbors. (The median income for a Yonkers family of four according to the 1990 census was $44,000, compared to $55,000 for the County as a whole).
Because Yonkers has offered lower starting salaries than other Westchester communities or nearby New York City, has endured repeated budget crises, and perhaps because of the political and social turmoil which has been a part of Yonkers life for so long, teacher recruitment has not been easy.
According to Assistant Superintendent Joseph Michael Guerney, Yonkers spends less per capita for education than any other community in Westchester and would continue to do so even if the entire burden of funding EIP II were placed upon the City. (Tr. 1632, 1633).
Operating in this fiscal context and in a city which has in the past resisted housing desegregation efforts with astonishing tenacity, the YBE's task of integrating its long segregated school system is indeed a formidable one. We find that the YBE, its former Superintendent, Dr. Joan Raymond, and her successor, Dr. Donald Batista, and their staffs, addressed this task with enthusiasm and a sincere desire to make EIP I succeed. This case is markedly different from the many cases in which further relief is sought by class representative because the managers of the City's school system have been either passive or half-hearted in their efforts to desegregate.
We are satisfied that Dr. Batista's evaluation of the problems confronting the YBE in its efforts to eradicate vestiges of segregation is an accurate one. We find that although minority students in Yonkers attend school in the same buildings as majority students, they are undergoing different educational experiences. Proof of this lies, we believe, in the data shown with respect to achievement scores, suspensions, retentions and drop-outs rates.
We therefore answer the questions posed in our July 10, 1992 Opinion as follows:
(1) We find that vestiges of segregation remain in the Yonkers Public School system.
(2) We find that many steps are being taken to address these vestiges including teacher training programs, utilization of innovative teaching techniques devised and tested elsewhere, efforts to increase parental involvement, development of magnet school programs, and similar efforts.
(3) We find that the steps being taken in (2) above are inadequate to eradicate vestiges of segregation "root and branch" and must be expanded and implemented in a manner which of necessity will entail the expenditure of additional funds. Not only must teaching techniques and curriculum be reexamined and redesigned to meet these needs, but the physical condition of the YPS must be restored and enhanced if a desegregation program which relies primarily on voluntary selection of magnet schools is to retain its accomplishments to date and attain its ultimate goal of a truly unitary school system.
We emphasize that we have answered these three questions only and have not addressed any questions relating to the State's liability for the existence of these conditions nor any question relating to the relative responsibility of the City and State. These further questions will be addressed at the next stage of these proceedings.
The parties are to confer and advise the Court in writing by Oct. 4, 1993 when they will be ready to proceed to trial on the remaining questions.
SO ORDERED.


*226 APPENDIX A


                                 TABLE 1-A
         Effects of Student Race-Ethnicity on 1990 (90-91 School Year)
                Metropolitan Achievement Test Scores (Reading)
         With Controls for Student Background, Prior Achievement Tests,
                            and School Characteristics
                                                                       (Add)
                                                                      Student
                                   Unadjusted                       Background[1]
---------------------------------------------------------------------------------------------------
Grade                          B                t                 B                 t
---------------------------------------------------------------------------------------------------
FIRST (N = 991)
---------------------------------------------------------------------------------------------------
African American           - 30.988          10.20[***]          - 27.446           8.93[***]
---------------------------------------------------------------------------------------------------
Latino                     - 34.132          11.87[***]          - 15.934           4.93[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .111                                     .194
---------------------------------------------------------------------------------------------------
SECOND (N = 1018)
---------------------------------------------------------------------------------------------------
African American           - 31.324          10.51[***]          - 26.469           9.20[***]
---------------------------------------------------------------------------------------------------
Latino                     - 40.454          14.21[***]          - 15.535           5.09[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .130                                     .266
---------------------------------------------------------------------------------------------------
THIRD (N = 885)
---------------------------------------------------------------------------------------------------
African American           - 36.138          12.52[***]          - 31.079          11.37[***]
---------------------------------------------------------------------------------------------------
Latino                     - 40.618          14.39[***]          - 14.083           4.78[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .154                                     .325
---------------------------------------------------------------------------------------------------
FOURTH (N = 851)
---------------------------------------------------------------------------------------------------
African American           - 32.925          10.62[***]          - 27.322           9.44[***]
---------------------------------------------------------------------------------------------------
Latino                     - 42.488          14.93[***]          - 13.891           4.64[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .154                                     .338
---------------------------------------------------------------------------------------------------
FIFTH (N = 749)
---------------------------------------------------------------------------------------------------
African American           - 26.357          9.39[***]           - 21.816         8.47[***]
---------------------------------------------------------------------------------------------------
Latino                     - 34.184          12.52[***]          - 10.599         3.83[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .121                                     .314
---------------------------------------------------------------------------------------------------
SIXTH (N = 757)
---------------------------------------------------------------------------------------------------
African American           - 24.075           7.64[***]          - 18.693           6.23[***]
---------------------------------------------------------------------------------------------------
Latino                     - 34.458          11.15[***]          - 12.889           4.08[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .099                                     .246
---------------------------------------------------------------------------------------------------
SEVENTH (N = 644)
---------------------------------------------------------------------------------------------------
African American           - 28.237           8.47[***]         - 22.452             7.44[**]
---------------------------------------------------------------------------------------------------



*227
Latino                     - 40.429            12.75[***]      - 20.536             6.74[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .122                                     .309
---------------------------------------------------------------------------------------------------
EIGHTH (N = 644)
---------------------------------------------------------------------------------------------------
African American           - 24.542             7.45[***]      - 19.020             6.22[***]
---------------------------------------------------------------------------------------------------
Latino                     - 34.120            10.46[***]      - 18.634             5.92[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .095                                     .254
---------------------------------------------------------------------------------------------------
NINTH (N = 594)
---------------------------------------------------------------------------------------------------
African American           - 32.173             8.28[***]      - 25.747             7.25[***]
---------------------------------------------------------------------------------------------------
Latino                     - 44.145            11.62[***]      - 22.786             6.11[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .121                                     .299
---------------------------------------------------------------------------------------------------
                                      (Add)                                (Add)
                                    Prior Test                             School
                                     Scores[2]                      Characteristics[3]
---------------------------------------------------------------------------------------------------
Grade                         B                   t                    B                  t
---------------------------------------------------------------------------------------------------
FIRST (N = 991)
---------------------------------------------------------------------------------------------------
African American           - 19.908            5.76[***]        - 18.774            5.42[***]
---------------------------------------------------------------------------------------------------
Latino                     - 12.101            3.39[***]        - 12.358            3.49[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                           .272                                   .285
---------------------------------------------------------------------------------------------------
SECOND (N = 1018)
---------------------------------------------------------------------------------------------------
African American           - 16.854            5.27[***]        - 17.701            5.47[***]
---------------------------------------------------------------------------------------------------
Latino                     -  9.789            2.93[**]         - 10.050            3.01[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                           .391                                   .394
---------------------------------------------------------------------------------------------------
THIRD (N = 885)
---------------------------------------------------------------------------------------------------
African American           - 23.496            7.54[***]        - 24.746            7.95[**]
---------------------------------------------------------------------------------------------------
Latino                     -  9.537            2.87[**]         -  9.619            2.91[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                           .444                                   .453
---------------------------------------------------------------------------------------------------
FOURTH (N = 851)
---------------------------------------------------------------------------------------------------
African American           - 13.428            4.62[***]        - 13.108            4.48[***]
---------------------------------------------------------------------------------------------------
Latino                     -  3.984            1.84                -  3.798            1.28
---------------------------------------------------------------------------------------------------
  Adjusted R2                           .586                                   .587
---------------------------------------------------------------------------------------------------
FIFTH (N = 749)
---------------------------------------------------------------------------------------------------
African American           -  9.586            3.59[***]        - 10.992            4.05[***]
---------------------------------------------------------------------------------------------------
Latino                     -  1.363             .47                -  1.759             .61
---------------------------------------------------------------------------------------------------
  Adjusted R2                           .553                                   .567
---------------------------------------------------------------------------------------------------
SIXTH (N = 757)
---------------------------------------------------------------------------------------------------
African American           -  7.142            2.14[*]          -  7.826            2.33[*]
---------------------------------------------------------------------------------------------------



*228
Latino                       - 1.888              .54           - 1.943                 .55
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .433                                     .434
---------------------------------------------------------------------------------------------------
SEVENTH (N = 644)
---------------------------------------------------------------------------------------------------
African American             - 7.543            2.18[*]       -10.569               3.12[**]
---------------------------------------------------------------------------------------------------
Latino                       - 5.952            1.71[@]      - 7.704               2.27[*]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .535                                    .562
---------------------------------------------------------------------------------------------------
EIGHTH (N = 644)
---------------------------------------------------------------------------------------------------
African American             - 3.615            1.05            - 5.713                1.69[@]
---------------------------------------------------------------------------------------------------
Latino                       - 7.554            2.14[*]      - 8.652                2.50[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                          .473                                    .501
---------------------------------------------------------------------------------------------------
NINTH (N = 594)
---------------------------------------------------------------------------------------------------
African American             - 5.164            1.62            - 5.253                1.68[@]
---------------------------------------------------------------------------------------------------
Latino                       - 5.147            1.51            - 4.001                1.20
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .705                                      .715
---------------------------------------------------------------------------------------------------



                                    TABLE 1-B
            Effects of Student Race-Ethnicity on 1990 (90-91 School Year)
                 Metropolitan Achievement Test Scores (Mathematics)
            With Controls for Student Background, Prior Achievement Tests,
                              and School Characteristics
                                                                            (Add)
                                                                           Student
                                    Unadjusted                          Background[1]
---------------------------------------------------------------------------------------------------
Grade                           B              t                    B                t
---------------------------------------------------------------------------------------------------
FIRST (N = 987)
---------------------------------------------------------------------------------------------------
African American             - 30.206       10.04[***]        - 26.824             8.65[**]
---------------------------------------------------------------------------------------------------
Latino                       - 25.122        8.83[***]        -  9.551             2.93[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .082                                    .136
---------------------------------------------------------------------------------------------------
SECOND (N = 1021)
---------------------------------------------------------------------------------------------------
African American             - 26.836        9.35[***]        - 23.589              8.12[***]
---------------------------------------------------------------------------------------------------
Latino                       - 25.500        9.30[***]        -  8.602              2.79[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .074                                     .142
---------------------------------------------------------------------------------------------------



*229
THIRD (N = 885)
---------------------------------------------------------------------------------------------------
African American            - 28.577          11.78[***]       - 24.146            10.00[***]
---------------------------------------------------------------------------------------------------
Latino                      - 25.701          10.84[***]       -  8.655             8.33[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .113                                   .218
---------------------------------------------------------------------------------------------------
FOURTH (N = 858)
---------------------------------------------------------------------------------------------------
African American            - 31.201          10.87[***]       - 26.441             9.30[***]
---------------------------------------------------------------------------------------------------
Latino                      - 31.717          12.03[***]       - 11.292             3.84[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .121                                    .227
---------------------------------------------------------------------------------------------------
FIFTH (N = 761)
---------------------------------------------------------------------------------------------------
African American            - 26.658           9.85[***]       - 28.604             8.85[***]
---------------------------------------------------------------------------------------------------
Latino                      - 22.879           8.69[***]       -  7.869             2.75[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .085                                    .179
---------------------------------------------------------------------------------------------------
SIXTH (N = 766)
---------------------------------------------------------------------------------------------------
African American            - 26.188           8.66[***]       - 21.117             7.01[***]
---------------------------------------------------------------------------------------------------
Latino                      - 26.849           9.05[***]       - 12.283             3.87[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .081                                     .158
---------------------------------------------------------------------------------------------------
SEVENTH (N = 648)
---------------------------------------------------------------------------------------------------
African American            - 27.236           9.81[***]       - 23.005             8.71[***]
---------------------------------------------------------------------------------------------------
Latino                      - 29.717          11.26[***]       - 17.094             6.41[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .110                                     .224
---------------------------------------------------------------------------------------------------
EIGHTH (N = 631)
---------------------------------------------------------------------------------------------------
African American            - 25.525           9.07[***]       - 21.267             7.82[***]
---------------------------------------------------------------------------------------------------
Latino                      - 24.476           8.77[***]       - 14.307             5.11[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .089                                     .189
---------------------------------------------------------------------------------------------------
NINTH (N = 581)
---------------------------------------------------------------------------------------------------
African American            - 36.488          11.62[***]       - 30.271            10.08[***]
---------------------------------------------------------------------------------------------------
Latino                      - 34.041          11.09[***]       - 22.818             7.25[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .147                                     .257
---------------------------------------------------------------------------------------------------



*230
                        TABLE 1-B
Effects of Student Race-Ethnicity on 1990 (90-91 School Year)
     Metropolitan Achievement Test Scores (Mathematics)
With Controls for Student Background, Prior Achievement Tests,
                    and School Characteristics
                                  (Add)                           (Add)
                                 Prior Test                       School
                                  Scores[2]                     Characteristics[3]
---------------------------------------------------------------------------------------------------
Grade                          B               t               B               t
---------------------------------------------------------------------------------------------------
FIRST (N = 987)
---------------------------------------------------------------------------------------------------
African American            - 11.425            3.58[***]        -  9.754           3.06[**]
---------------------------------------------------------------------------------------------------
Latino                      -  4.735            1.46                -  4.809           1.49
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .368                                     .381
---------------------------------------------------------------------------------------------------
SECOND (N = 1021)
---------------------------------------------------------------------------------------------------
African American            - 10.709        3.63[***]            - 10.411           3.49[***]
---------------------------------------------------------------------------------------------------
Latino                      -  3.132        1.02                    -  2.892            .94
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .400                                     .404
---------------------------------------------------------------------------------------------------
THIRD (N= 885)
---------------------------------------------------------------------------------------------------
African American            - 12.778        4.85[***]            - 13.023           4.89[***]
---------------------------------------------------------------------------------------------------
Latino                      -  2.680         .96                    -  2.812           1.01
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .426                                     .425
---------------------------------------------------------------------------------------------------
FOURTH (N = 858)
---------------------------------------------------------------------------------------------------
African American            - 14.411        5.11[***]           - 14.321            5.06[***]
---------------------------------------------------------------------------------------------------
Latino                      -  7.785        2.71[**]            -  7.844            2.73[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                           .516                                   .515
---------------------------------------------------------------------------------------------------
FIFTH (N = 761)
---------------------------------------------------------------------------------------------------
African American            -  9.417        3.38[***]           -  9.413            3.35[***]
---------------------------------------------------------------------------------------------------
Latino                      -  1.587         .54                   -  1.609             .54
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .481                                  .479
---------------------------------------------------------------------------------------------------
SIXTH (N = 766)
---------------------------------------------------------------------------------------------------
African American            -  9.991        3.08[**]            -  9.863             3.03[**]
---------------------------------------------------------------------------------------------------
Latino                      -  3.953        1.17                   -  3.931             1.16
---------------------------------------------------------------------------------------------------
  Adjusted R2                          .397                                    .396
---------------------------------------------------------------------------------------------------
SEVENTH (N = 648)
---------------------------------------------------------------------------------------------------
African American            - 11.810        3.65[***]        - 14.148               4.43[***]
---------------------------------------------------------------------------------------------------
Latino                      -  6.148        1.89[@]          -  7.457               2.33[*]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .408                                     .432
---------------------------------------------------------------------------------------------------
EIGHTH (N = 631)
---------------------------------------------------------------------------------------------------
African American            - 12.146        3.56[***]        - 14.766               4.52[***]
---------------------------------------------------------------------------------------------------
Latino                      -  7.768        2.22[*]          -  9.321               2.78[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .294                                     .358
---------------------------------------------------------------------------------------------------
NINTH (N = 581)
---------------------------------------------------------------------------------------------------



*231
African American          - 16.355        4.98[***]         - 16.296                5.15[***]
---------------------------------------------------------------------------------------------------
Latino                    -  3.933        1.12                 -  5.433                1.61
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .536                                     .569
---------------------------------------------------------------------------------------------------



                                 TABLE 2-A
        Effects of Student Race-Ethnicity on 1991 (91-92 School Year)
              Metropolitan Achievement Test Scores (Reading),
        With Controls for Student Background, Prior Achievement Tests,
                           and School Characteristics
                                                                       (Add)
                                                                      Student
                                 Unadjusted                         Background[1]
---------------------------------------------------------------------------------------------------
Grade                        B               t                    B                      t
---------------------------------------------------------------------------------------------------
FIRST (N = 1181)
---------------------------------------------------------------------------------------------------
African American          - 31.561       10.24[***]         - 24.181                7.69[***]
---------------------------------------------------------------------------------------------------
Latino                    - 33.395       11.64[***]         - 13.617                4.34[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .099                                      .197
---------------------------------------------------------------------------------------------------
SECOND (N = 858)
---------------------------------------------------------------------------------------------------
African American          - 29.778        9.28[***]         - 22.100                6.89[***]
---------------------------------------------------------------------------------------------------
Latino                    - 39.075       12.85[***]         - 15.993                4.85[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .111                                     .238
---------------------------------------------------------------------------------------------------
THIRD (N = 916)
---------------------------------------------------------------------------------------------------
African American          - 25.022        8.79[***]         - 21.565                7.74[***]
---------------------------------------------------------------------------------------------------
Latino                    - 34.463       12.88[***]         - 11.236                3.84[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                         .105                                     .233
---------------------------------------------------------------------------------------------------
FOURTH (N = 815)
---------------------------------------------------------------------------------------------------
African American          - 29.257       10.28[***]         - 26.403                9.81[**]
---------------------------------------------------------------------------------------------------
Latino                    - 37.507       13.52[***]         - 11.439                3.95[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                          .121                                     .294
---------------------------------------------------------------------------------------------------
FIFTH (N = 806)
---------------------------------------------------------------------------------------------------
African American          - 30.082       11.00[***]         - 25.247                9.70[***]
---------------------------------------------------------------------------------------------------



*232
---------------------------------------------------------------------------------------------------
Latino                  - 32.528            13.00[***]      -  9.954             3.71[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .125                               .269
---------------------------------------------------------------------------------------------------
SIXTH (N = 712)
---------------------------------------------------------------------------------------------------
African American        - 26.534             8.75[***]      - 23.147             8.18[***]
---------------------------------------------------------------------------------------------------
Latino                  - 35.736            12.29[***]      - 14.463             4.77[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .108                               .253
---------------------------------------------------------------------------------------------------
SEVENTH (N = 745)
---------------------------------------------------------------------------------------------------
African American        - 26.407             8.58[***]      - 24.709             8.65[***]
---------------------------------------------------------------------------------------------------
Latino                  - 41.354            13.99[***]      - 20.843             6.89[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .132                               .274
---------------------------------------------------------------------------------------------------
EIGHTH (N = 587)
---------------------------------------------------------------------------------------------------
African American        - 26.223             7.57[***]      - 24.299             7.49[***]
---------------------------------------------------------------------------------------------------
Latino                  - 35.713            10.77[***]      - 17.925             5.34[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .093                            .217
---------------------------------------------------------------------------------------------------
NINTH (N = 577)
---------------------------------------------------------------------------------------------------
African American        - 24.950             6.49[***]      - 20.783             5.91[***]
---------------------------------------------------------------------------------------------------
Latino                  - 39.280            10.79[***]      - 15.860             4.47[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .096                               .282
---------------------------------------------------------------------------------------------------
                                       TABLE 2-A
            Effects of Student Race-Ethnicity on 1991 (91-92 School Year)
                    Metropolitan Achievement Test Scores (Reading),
             With Controls for Student Background, Prior Achievement Tests,
                                 and School Characteristics
                                  (Add)                              (Add)
                                Prior Test                           School
                                   Scores[2]                       Characteristics[3]
---------------------------------------------------------------------------------------------------
Grade                     B                     t            B                    t
---------------------------------------------------------------------------------------------------
FIRST (N = 1181)
---------------------------------------------------------------------------------------------------
African American        - 17.062             5.26[***]      - 18.274             5.72[***]
---------------------------------------------------------------------------------------------------
Latino                  - 11.385             3.56[***]      - 12.822             4.10[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                       .311                               .343
---------------------------------------------------------------------------------------------------
SECOND (N = 858)
---------------------------------------------------------------------------------------------------
African American        - 13.026             3.33[***]      - 14.507             3.69[***]
---------------------------------------------------------------------------------------------------
Latino                  - 11.541             2.92[***]      - 12.380             3.15[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                       .330                               .341
---------------------------------------------------------------------------------------------------
THIRD (N = 916)
---------------------------------------------------------------------------------------------------
African American        - 12.616             3.85[***]      - 12.572             3.84[***]
---------------------------------------------------------------------------------------------------



*233
Latino               - 8.535      2.53[**]      - 8.928         2.68[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                 .360                       .374
---------------------------------------------------------------------------------------------------
FOURTH (N = 815)
---------------------------------------------------------------------------------------------------
African American     -12.997      4.09[***]     -14.337         4.50[***]
---------------------------------------------------------------------------------------------------
Latino               - 5.334      1.60             - 5.304         1.60
---------------------------------------------------------------------------------------------------
  Adjusted R2                 .472                       .479
---------------------------------------------------------------------------------------------------
FIFTH (N = 806)
---------------------------------------------------------------------------------------------------
African American     -13.705      4.78[***]     -14.613         5.08[***]
---------------------------------------------------------------------------------------------------
Latino               - 2.825       .97             - 3.412         1.17
---------------------------------------------------------------------------------------------------
  Adjusted R2                 .504                       .508
---------------------------------------------------------------------------------------------------
SIXTH (N = 712)
---------------------------------------------------------------------------------------------------
African American     - 7.682      2.29[*]        - 9.739           2.96[**]
---------------------------------------------------------------------------------------------------
Latino               - 1.641       .46              - 1.855            .54
---------------------------------------------------------------------------------------------------
  Adjusted R2                 .468                       .492
---------------------------------------------------------------------------------------------------
SEVENTH (N = 745)
---------------------------------------------------------------------------------------------------
African American     -10.699      3.26[***]     -11.651            3.66[***]
---------------------------------------------------------------------------------------------------
Latino               - 6.259      1.80[@]       - 7.104            2.11[*]
---------------------------------------------------------------------------------------------------
  Adjusted R2                 .482                       .512
---------------------------------------------------------------------------------------------------
EIGHTH (N = 587)
---------------------------------------------------------------------------------------------------
African American     - 5.933      1.46             - 6.706              1.70[@]
---------------------------------------------------------------------------------------------------
Latino               - 1.615       .39             - 2.747               .68
---------------------------------------------------------------------------------------------------
   Adjusted R2                .440                       .477
---------------------------------------------------------------------------------------------------
NINTH (N = 577)
---------------------------------------------------------------------------------------------------
African American     - 7.574      2.03[*]        - 8.250             2.24[*]
---------------------------------------------------------------------------------------------------
Latino                 4.059      1.06                4.046             1.07
---------------------------------------------------------------------------------------------------
  Adjusted R2                 .589                       .603
---------------------------------------------------------------------------------------------------



*234
                                       TABLE 2-B
             Effects of Student Race-Ethnicity on 1991 (91-92 School Year)
                    Metropolitan Achievement Test Scores (Mathematics),
             With Controls for Student Background, Prior Achievement Tests,
                                  and School Characteristics
                                                                     (Add)
                                                                    Student
                                Unadjusted                      Background[1]
---------------------------------------------------------------------------------------------------
Grade                     B                     t            B                    t
---------------------------------------------------------------------------------------------------
FIRST (N = 1174)
---------------------------------------------------------------------------------------------------
African American        - 24.425             8.19[***]      - 19.449             6.20[***]
---------------------------------------------------------------------------------------------------
Latino                  - 23.384             8.43[***]      -  9.053             2.90[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                       .058                               .111
---------------------------------------------------------------------------------------------------
SECOND (N = 853)
---------------------------------------------------------------------------------------------------
African American        - 28.343             9.45[***]      - 22.084             7.09[**]
---------------------------------------------------------------------------------------------------
Latino                  - 30.272            10.65[***]      - 13.676             4.27[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                       .087                               .156
---------------------------------------------------------------------------------------------------
THIRD (N = 917)
---------------------------------------------------------------------------------------------------
African American        - 21.710             9.05[***]      - 18.153             7.50[***]
---------------------------------------------------------------------------------------------------
Latino                  - 23.138            10.27[***]      -  7.613             2.99[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .079                               .160
---------------------------------------------------------------------------------------------------
FOURTH (N = 819)
---------------------------------------------------------------------------------------------------
African American        - 26.192             9.91[***]      - 23.305             8.88[***]
---------------------------------------------------------------------------------------------------
Latino                  - 30.253            11.74[***]      - 12.350             4.37[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .098                               .200
---------------------------------------------------------------------------------------------------
FIFTH (N = 813)
---------------------------------------------------------------------------------------------------
African American        - 31.065            11.81[***]      - 27.988            10.59[***]
---------------------------------------------------------------------------------------------------
Latino                  - 24.495            10.17[***]      - 11.047             4.08[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .107                               .169
---------------------------------------------------------------------------------------------------
SIXTH (N = 721)
---------------------------------------------------------------------------------------------------
African American        - 27.996             9.67[***]      - 24.868             8.74[***]
---------------------------------------------------------------------------------------------------
Latino                  - 21.531             7.76[***]      - 10.813             3.55[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .097                               .138
---------------------------------------------------------------------------------------------------
SEVENTH (N = 757)
---------------------------------------------------------------------------------------------------
African American        - 25.482             9.68[***]      - 22.797             4.52[***]
---------------------------------------------------------------------------------------------------
Latino                  - 27.765            10.95[***]      - 15.644             5.82[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .097                               .187
---------------------------------------------------------------------------------------------------
EIGHTH (N = 589)
---------------------------------------------------------------------------------------------------
African American        - 29.619             9.68[***]      - 27.386             9.31[***]
---------------------------------------------------------------------------------------------------
Latino                  - 29.710            10.14[***]      - 17.274             5.68[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .098                               .180
---------------------------------------------------------------------------------------------------
NINTH (N = 571)
---------------------------------------------------------------------------------------------------
African American        - 29.533            10.01[***]      - 25.408       8.89[***]
---------------------------------------------------------------------------------------------------
Latino                  - 28.576            10.23[***]      - 16.073             5.57[***]
---------------------------------------------------------------------------------------------------
  Adjusted R2                        .112                               .210
---------------------------------------------------------------------------------------------------



*235
                                   TABLE 2-B
           Effects of Student Race-Ethnicity on 1991 (91-92 School Year)
                Metropolitan Achievement Test Scores (Mathematics),
           With Controls for Student Background, Prior Achievement Tests,
                               and School Characteristics
                                (Add)                        (Add)
                              Prior Test                     School
                               Scores[2]                  Characteristics[3]
---------------------------------------------------------------------------------------------------
Grade                  B                 t            B                 t
---------------------------------------------------------------------------------------------------
FIRST (N = 1174)
---------------------------------------------------------------------------------------------------
African American    - 7.805            2.59[**]      - 8.031            2.63[**]
---------------------------------------------------------------------------------------------------
Latino              - 7.510            2.52[**]      - 8.084            2.73[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                  .338                           .346
---------------------------------------------------------------------------------------------------
SECOND (N = 853)
---------------------------------------------------------------------------------------------------
African American    - 6.800            1.95[*]       - 7.975            2.26[*]
---------------------------------------------------------------------------------------------------
Latino              - 9.237            2.65[**]     - 9.613            2.76[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                  .390                           .392
---------------------------------------------------------------------------------------------------
THIRD (N = 917)
---------------------------------------------------------------------------------------------------
African American    - 8.721            3.24[***]     - 7.822            2.88[**]
---------------------------------------------------------------------------------------------------
Latino              - 6.364            2.30[*]       - 6.469            2.34[*]
---------------------------------------------------------------------------------------------------
  Adjusted R2                  .370                          .372
---------------------------------------------------------------------------------------------------
FOURTH (N = 819)
---------------------------------------------------------------------------------------------------
African American    - 8.651            2.87[**]     - 9.046            2.87[**]
---------------------------------------------------------------------------------------------------
Latino              - 5.220            1.65[@]      - 5.234            1.65[@]
---------------------------------------------------------------------------------------------------
  Adjusted R2                  .438                           .438
---------------------------------------------------------------------------------------------------
FIFTH (N = 813)
---------------------------------------------------------------------------------------------------
African American    -17.578            6.27[***]    -17.316            6.16[***]
---------------------------------------------------------------------------------------------------
Latino              - 9.031            3.17[**]     - 8.92             3.13[**]
---------------------------------------------------------------------------------------------------
  Adjusted R2                  .465                           .418
---------------------------------------------------------------------------------------------------
SIXTH (N = 721)
---------------------------------------------------------------------------------------------------
African American    - 7.995            2.44[*]      - 8.656            2.60[**]
---------------------------------------------------------------------------------------------------
Latino                1.859             .54               1.62             .47
---------------------------------------------------------------------------------------------------
  Adjusted R2                  .417                           .418
---------------------------------------------------------------------------------------------------
SEVENTH (N = 757)
---------------------------------------------------------------------------------------------------
African American    -12.272            4.30[***]     -12.898           4.69[***]
---------------------------------------------------------------------------------------------------
Latino              - 6.926            2.31[*]       - 7.16             2.48[*]
---------------------------------------------------------------------------------------------------
  Adjusted R2                  .427                           .470
---------------------------------------------------------------------------------------------------
EIGHTH (N = 589)
---------------------------------------------------------------------------------------------------
African American    -14.089            3.75[***]     -14.779           4.15[***]
---------------------------------------------------------------------------------------------------
Latino              - 9.541            2.51[**]     - 9.699            2.70[**]
---------------------------------------------------------------------------------------------------



*236
  Adjusted R2                    .377                           .445
---------------------------------------------------------------------------------------------------
NINTH (N=571)
---------------------------------------------------------------------------------------------------
African American    -12.607              3.72[***]     - 14.068           4.31[***]
---------------------------------------------------------------------------------------------------
Latino              -  .671               .19             -  1.357            .41
---------------------------------------------------------------------------------------------------
  Adjusted R2                    .451                           .492
---------------------------------------------------------------------------------------------------



                                      TABLE 3
          Summary of Significant Student Race-Ethnicity Effects on MAT Scores
                                     SUBJECT(S)
GRADE          READING                                         MATHEMATICS
---------------------------------------------------------------------------------------------------
                               1990-91         1991-92                            1990-91    1991-92
FIRST      African American    (- 19)          (- 18)         African American     (- 10)    (- 8)
           Latino              (- 12)          (- 13)         Latino                         (- 8)
SECOND     African American    (- 18)          (- 15)         African American     (- 10)    (- 8)
           Latino              (- 10)          (- 12)         Latino                         (- 10)
THIRD      African American    (- 25)          (-13)          African American     (- 13)    (- 8)
           Latino              (- 9)           (- 9)
FOURTH     African American    (- 13)          (- 14)         African American     (- 14)    (- 9)
                                                              Latino               (- 8)     (- 5)*
FIFTH      African American    (- 11)          (- 15)         African American      (- 9)    (- 17)
                                                              Latino                         (- 9)
SIXTH      African American    (- 8)           (- 10)         African American     (- 10)    (- 9)
SEVENTH    African American    (- 11)          (- 12)         African American     (- 14)    (- 13)
           Latino              (- 8)           (- 7)          Latino                (- 7)    (- 7)
EIGHTH     African American    (- 6)*     (- 7)*    African American     (- 15)    (- 15)
           Latino              (- 9)                          Latino                (- 9)    (- 10)
NINTH      African American    (- 5)*     (- 8)          African American     (- 16)    (- 14)
---------------------------------------------------------------------------------------------------
NOTE: Numbers (unstandardized beta's) in parentheses represent significant difference's from white
students' MAT scores at or beyond the .05 level, unless denoted by an asterisk which indicates difference
from white students' MAT scores at the .10 level.



*237 APPENDIX B


                                    TABLE 3 (1991)
               SUMMARY OF STATISTICALLY SIGNIFICANT RACE DIFFERENCES
                         CONTROLLING FOR VARIOUS VARIABLES
               NO CONTROLS   CONTROL FOR:      CONTROL FOR:       CONTROL FOR:      CONTROL FOR:
                             SPECED, LEP       SPECED, LEP        SPECED, LEP       SPECED, LEP
                                               LUNCH = (F, R)     LUNCH ≠ (F, R)    LUNCH = (F, R)
                                                                                   CENSUS TRACT
                   BW  BH  HW    BW  BH  HW       BW  BH  HW         BW  BH  HW        BW  BH  HW
GRADE = 1, 2
 READING           W    B   W     W   H   W       W    H   .         W    .   W         .   .   .
 MATH              W    .   W     W   H   W       W    H   .         W    .   W         .    H   .
 LANGUAGE          W    B   W     W   .   W       W    H   .         W    .   W         .    .   .
 TOTAL             W    .   W     W   H   W       W    H   .         W    .   W         .    .   .
GRADE = 3-4
 READING           W    B   W     W   H   W       W   H   W          W   .    W         .    H    .
 MATH              W    .   W     W   H   W       W   H   W          W   .    W         .    .    .
 LANGUAGE          W    .   W     W   H   W       W   H   .          W   .    W         .    H    .
 TOTAL             W    .   W     W   H   W       W   H   .          W   .    W         .    H    .
GRADE = 5-6
 READING           W    B   W     W   .   W       W   .   W          W   .    W     .    .   .
 MATH              W    .   W     W   H   W       W   H   .          W   .    W     .    .   .
 LANGUAGE          W    B   W     W   .   W       W   H   W          W   .    W     .    .   .
 TOTAL             W    .   W     W   .   W       W   H   W          W   .    W     .    .   .
GRADE = 7-9
 READING           W    B   W     W   .   W       W   .   W          W   .    W     .    .   .
 MATH              W    .   W     W   .   W       W   .   W          W   .    W     .    .   .
 LANGUAGE          W    B   W     W   .   W       W   .   W          W   .    W     .    .   .
 TOTAL             W    B   W     W   .   W       W   .   W          W   .    W     .    .   .
---------------------------------------------------------------------------------------------------
Notes: B = BLACK; H = HISPANIC; W = WHITE.
       BW = The B W comparison
       BH = The B H comparison
       HW = The H W comparison
       A significant difference is represented by the label for the higher scoring group. A dot represents a non-significant difference.


APPENDIX C

ACADEMIC FREEDOM
The nature of American Democracy demands that citizens be able to listen to all sides of a controversial issue, sort out the facts, and arrive at independent conclusions. Students in school, therefore, have a right to be exposed to issues which are within their intellectual grasp and are under current debate in society. This right imposes certain obligations upon the teachers and the administration.
The Board will attempt to employ qualified teachers, to supply them with the necessary teaching materials and to maintain an atmosphere of academic freedom in the schools.
The teachers, individually, will be responsible for determining when and how to deal with controversial issues according to the maturity and abilities of their students and in accordance with current Board policies and will be responsible for the evaluation of their student's work.
The administration shall be available to assist teachers when in doubt as to the appropriateness of certain controversial issues. It shall further have the responsibility of approval of any and all speakers brought into the schools to present a viewpoint to students.
The Board and the Federation agree that the community and the students have the right to expect that controversial issues will be presented in a fair and unbiased nature and the parties agree that they will take reasonable steps to assure this.
NOTES
[1]  Yonkers is one of the four largest cities in New York State in which the School Board lacks the ability to raise funds through taxation but is dependent entirely on an allocation of funds from the general City budget.
[***]  For convenience, we refer to all defendants as the "State" for purposes of this stage of the proceedings.
[***]  In our liability opinion, we noted that unlike attendance zone changes or school openings "whose numerical and racial impact can be fairly readily evaluated" (624 F.Supp. 1438, n. 110), academic performance is influenced by factors over which the Board has no control, such as "socio-economic factors." We went on to state, "In the absence of concrete and similarly persuasive evidence demonstrating the accuracy and statistically meaningful nature of the purported correlation between achievement tests scores and the conduct of Yonkers school officials, we are unwilling to conclude on the basis of minority students' lower achievement test scores that such students have been denied the educational opportunities afforded other students in the district." We now find that such "concrete" and persuasive evidence has been presented.
[***]  Cooperative Learning is a teaching technique in which students are clustered to work jointly in solving a problem or in some other learning exercise.
[**]  Agreement between the Board of Education of the City of Yonkers, New York and the Yonkers Federation of Teachers, A.F.T. The full text of this provision is set forth in Appendix C hereto.
[***]  As to the diminution in white students, a study commissioned by the YBE in 1988, prepared by Christine H. Rossell of Boston University, attributed this demographic change to factors other than the traditional white flight from a desegregating school system. Analysis of Enrollment Trends, December 29, 1988; YBE Ex. 31.
[**]  Student Background characteristics include controls for age, sex, LEP status and SES (free lunch status).
[***]  Prior Test Scores are represented by student's first grade or earliest available MAT/MRT scores.
[***]  School Characteristics include controls for schools size (total enrollment) and poverty concentration (percent of students on free-reduced price lunch).
[***]   denotes p [***]   denotes p [***]   denotes p [**]   denotes p [***]  Student Background characteristics include controls for age, sex, LEP status, and SES (free lunch status).
[***]  Prior Test Scores are represented by student's first grade or earliest available MAT/MRT scores.
[***]  School Characteristics include controls for schools size (total enrollment) and poverty concentration (percent of students on free-reduced price lunch).
[***]   denotes p [***]   denotes p [***]   denotes p [***]   denotes p [***]  Student Background characteristics include controls for age, sex, LEP status, and SES (free lunch status).
[***]  Prior Test Scores are represented by student's first grade or earliest available MAT/MRT scores.
[***]  School Characteristics include controls for school size (total enrollment) and poverty concentration (percent of students on free-reduced price lunch).
[***]   denotes p [***]   denotes p [***]   denotes p [***]   denotes p [***]  Student Background characteristics include controls for age, sex, LEP status, and SES (free lunch status).
[***]  Prior Test Scores are represented by student's first grade or earliest available MAT/MRT scores.
[***]  School Characteristics include controls for school size (total enrollment) and poverty concentration (percent of students on free-reduced price lunch).
[***]     denotes p [***]     denotes p [***]    denotes p [***]   denotes p 
