Teacher quality and curriculum are discussed in subsections C through E below. The adequacy of school facilities and classrooms is discussed in subsections F through G. The adequacy of "instrumentalities of learning" is discussed in subsection H below. Educational outputs are discussed in subsection I below. Relevant educational inputs and outputs must be examined over multiple years. The evidence at trial demonstrates the obvious proposition that education is cumulative. Primary and secondary school students acquire mastery of subjects by building on an expanding base of knowledge. A student's result on a sixth grade reading examination reflects her experience in grades one through five, and not merely of what she has learned in sixth grade. C . M e a s u r e s o f Te a c h e r Q u a l i t y The evidence demonstrates the validity of the intuitive conclusion that quality of teaching has a direct effect on student outcomes. This finding is confirmed by SED studies, by the empirical studies of plaintiffs' experts, and by the observations of numerous BOE district superintendents who testified at trial. Even defendants' experts agreed that quality teaching plays a role in effective education, though they differed with plaintiffs on the extent of that role and the correct measures of teacher quality. There are several probative measures of teacher quality, including the number of uncertified teachers teaching in New [187 [187 Misc.2d Misc.2d 25] 25] York City public schools, teachers' scores on certification exams, and the quality of teachers' undergraduate education. By each of these measures, the quality of New York City's public school teachers—in the aggregate—is inadequate. The court hastens to add that there are many excellent and dedicated teachers employed in New York City public schools— many of whom foster learning under extremely adverse conditions. It is not hyperbolic to describe some New York City public school teachers as heroes. However, there are too many ill-trained and inexperienced teachers to meet the difficult challenges presented in the New York City public schools. 1 . C e r t i fic at i o n As part of its effort to ensure that qualified teachers are employed in the State's public schools, the State created a system of certification. New York City has an overlapping system of license requirements for teachers. Under the current system in effect until 2003, the State has two categories of certification and a third category for uncertified teachers called temporary license. 16 In 2003 the Regents will impose more rigorous certification standards. It is possible for an uncertified teacher to be an effective pedagogue. However, the evidence at trial demonstrates that lack of certification is generally an indicator that a teacher falls below minimal adequacy. The court also finds that the converse is not true. Numerous BOE personnel, including district supervisors, testified that certification standing alone is no guarantee of teacher quality. The court finds this testimony to be credible. For the last decade, approximately 10% to 14% of New York City's public school teachers have lacked certification in any given school year. The specific percentage of uncertified teachers [187 [187 Misc.2d Misc.2d 26] 26] listed as employed in a given district at a specific time is dependent upon which persons are counted as teachers, the definition of certification used, and the time in the school year that certification is assessed. Although figures from various sources differ slightly, they demonstrate that there is a high percentage of uncertified teachers working in New York City's public schools. Plaintiffs' expert Hamilton Langford, a professor of economics and public policy at the State University of New York at Albany, defined as uncertified any teacher who does not teach a single course in a subject area for which he is certified. (Such individuals may be certified in another subject.) Dr. Langford's research demonstrates that in the 1997-1998 school year, the last year for which data were available, 13.7% of New York City's public school teachers were not certified in any subject they taught, as compared with only 3.3% in the rest of the State. Using a slightly different standard, SED issued a report that found that in 1997-1998 17% of New York City's public school teachers taught more than 20% of their time in a subject in which they lacked State certification, compared with a Statewide average (which includes New York City) of 9%. 17 Statistics from BOE demonstrate that the percentage of uncertified teachers has fluctuated between 11.4% and 13.3% between the 1991-1992 and 1999-2000 school years. 18 The highest percentage of uncertified teachers in New York City high schools tends to be in math and sciences. BOE records show that as of October 1, 1999, 476 uncertified teachers taught high school biology, 152 taught high school chemistry, and 435 taught high school mathematics. Using the conservative assumptions that each teacher instructs five classes a day of 25 students each (most high school classes are larger), and that these uncertified teachers were not replaced by certified ones, last year 59,500 students were taught high school biology by an uncertified teacher, 19,000 students were taught high school chemistry by an uncertified teacher, and 54,375 students were taught high school mathematics by an uncertified teacher. Defendants contend that these shortages are in subjects in which there is a nationwide shortage of teachers. However, in [187 [187 Misc.2d Misc.2d 27] 27] New York State, localities other than New York City experience nowhere near the shortages seen in the City. Uncertified teachers tend to be concentrated in New York City's lowest-performing schools. Such schools often present the most difficult working conditions, such as poor physical plants, large class sizes, and locations in high-crime neighborhoods. To some degree, this concentration of uncertified teachers in low-performing schools is enabled by the teachers' collective bargaining agreement with BOE. With some restrictions, experienced teachers are able to transfer out of such schools pursuant to a contract provision that gives senior teachers priority in filling vacant positions in other schools. It is understandable that many, though not all, experienced teachers faced with the poor working conditions of many lowperforming schools would take the opportunity to transfer to schools in safer neighborhoods with better working conditions. This phenomenon is