The PDK audit began with a review of the methodology the audit team planned to follow in preparing their report. We generally found the methodologies to be reasonable. We did, however, identify several weaknesses in the implementation of this methodology. For example, PDK did not appear to follow their own system with regards to interviews. The interviews performed were not a part of a randomised design and there appears to have been no effort made to get a representative cross-section of opinions from teachers, let alone parents. Moreover, the conclusions drawn from the statements are often arbitrary and baseless. The PDK report represents an unscientific and unprofessional use of interview material.

An even more glaring flaw is that the audit misrepresents a central result in a key research paper on grouping (Slavin, 1990) and fails to provides a balanced description of the diversity of views among leading researchers about the impact of ability grouping. Nor does the audit does not make any attempt to empirically back their assertions about a causal linkage between ability grouping and the achievement gap with any data from the county.

This section’s focus is on what we believe to be the most important findings and our views on these findings.

This finding is most appropriately broken down into its two components.

First, we as a group agree with the statement that the system goal of ‘Success for Every Student’ is not being met by the county school system. We as a group are strongly supportive of the county school system’s long-standing attempts to narrow the achievement gap. We believe that with the renewed energy focused on this issue the school system can materially contribute to reducing this gap.

The persistence of the gap from the 60’s to present has greatly reduced the number of people who think that they know how to eliminate racial differences in test performance. These gaps exist at every level—school district, county, state, and national—and earlier attempts to bridge the gap have not had as much effect as optimists thought. For example, nationally, starting with the passage of the Elementary and Secondary Education Act of 1965, after $118 billion in expenditures the goal of reducing the student achievement gap has not been met. It is important to acknowledge the magnitude of the challenge and the time and resources that will be needed to see any change in this area.

Second, the audit states that tracking and ability grouping limit the achievement of under performing ethnic groups. In the academic literature, there is a diversity of views on the effects of various forms of ability grouping on the general population of students. Tom Loveless, director of the Brown Center on Education Policy at the Brookings Institution, wrote a scathing op-ed in the October 22 issue of the Washington Post pointing out that the PDK audit:

After a careful review of the relevant literature, in contrast to the findings of the audit, we find that:

• There is a preponderance of evidence that ability grouping combined with an accelerated curriculum provides strong benefits for highly able students.
• While there is a diversity of views in the educational field, there are many high quality research papers that say ability grouping is effective for all ability groups.
• The results from the only citation on grouping in the audit report, Slavin 1990, are misinterpreted.

As observed in a recent book on the racial test score gap, eliminating demanding classes—an implication of the PDK audit’s findings—seems ridiculous. We should be trying to get more minority and lower economic status children to take these classes rather than eliminate them. Any proposal for reducing the achievement gap that seems likely to lower high ability children’s achievement is likely to break the political consensus for such goals.

The audit exhibits a very singular perspective on the effects of tracking and grouping. In our view, educational researchers have not yet identified all the factors important to determining the outcomes of grouping schemes, and so the broad recommendations of academics in this area should be viewed as suggestive, but inadequate as a foundation for decision making. Until education research can provide reliable and reproducible results, there will be high degree of uncertainty around the actual outcomes of implemented programs. This suggests that the county should be cautious in changing programs or strategies without sufficient testing and subsequent monitoring to determine if the expected results are obtained for MCPS students.

The audit details a clear achievement gap in the MCPS school system and observes that ability grouping in mathematics is practised by the school system. However, no evidence linking ability grouping as the causal factor creating the achievement gap is provided in the audit report.

Moreover, the idea that students will have access to the same instruction in a class with students of widely varying abilities is unrealistic. Teachers will soon realize which students are highly able to grasp material and will be forced to differentiate instruction among students in the same classroom in order to challenge students according to their ability.  A teacher cannot effectively teach students in the same classroom whose disparate ability causes them to proceed at such varying rates.  With only 45 minutes in a class period, a teacher who wishes to give equal time to both groups would only have 22.5 minutes to review homework from each group as well as teach new material.  The reality is that heterogeneous ability grouping is most likely to decrease the quality of instruction because teachers have less time to spend instructing students in each group. The "gifted/talented," "skills" and "regular" students will not have access to 45 minutes of challenging instruction.  Rather, all groups suffer because the teacher is burdened with effectively teaching two or three different classes within the same class.

It is interesting that Loveless, in his criticism of the PDK audit, offers an example of a California school with mainly African American and Hispanic students from low income families that attained outstanding achievement by practising the very opposite of the PDK recommendations. In contrast, the PDK audit offered no examples of school systems that have ended the achievement gap through their recommendations.

We agree that there are substantial gaps in the level of success experienced by various student groups. The audit provides an abundance of data to prove that there is a substantial gap in the level of achievement by Hispanic and African American students in the county school system. However, the achievement gaps shown for the county are consistent with those observed nationally and are unlikely to be the result of the structure and implementation of the MCPS mathematics curriculum.

The achievement gap in test scores appears before children enter kindergarten and it persists into adulthood. Research on the achievement gap has identified many factors such as parental schooling, income differences, parenting strategies, and grandparents’ education and income as major factors in determining school achievement. Schools can have little impact on a child’s socio-economic family background, yet these seem to be the major determinants of the achievement gap.

African American and Hispanic students scores tend to be centered about one standard deviation below that of non-Hispanic white and Asian students. Measured by percentile, in reading skills the black-white gap hardly changes between 1^st and 12^th grade; in math it widens a little. On an individual level, half of the achievement gap can be explained by differences in their first grade scores. Such findings have persuaded some social scientists that schools do not contribute much to the achievement gap. If this gap is not caused primarily by inequities in the school system, attempts to eliminate inequities through the structure and implementation of curriculum will be ineffective in closing this gap.

Although they have not caused the achievement gap, nonetheless, schools should make every reasonable effort to try to close the gap. A careful and unbiased review of the literature seems to suggest that the best way for schools to proceed is to try to make sure students get the most effective instruction at the level that they need. Ability grouping, perhaps with lower class sizes for lower ability groups, is one way to provide more effective instruction to partially offset the impacts of family background. Other important strategies are to screen out low performing teachers prior to hiring and to identify low performing teachers and provide them with effective intervention to improve their effectiveness. ‘Compensatory’ spending on primarily African American and Hispanic schools could be valuable, at least if the money were used to cut class sizes and implement policies that can be shown to be effective. Yet, realistically, the extent to which the school system can be expected to end the achievement gap is limited.

If we want equal outcomes, we need to narrow the skill gap before children enter schools. There are two ways of improving 3&4 year olds: change pre-school experience and change home experience. Changing preschool is less important but easier than changing homes. For example, Stephen Barnett’s review of research on preschool effects strongly suggests that cognitively oriented preschool programs can improve African American children’s achievement scores. The MCPS’s new priority for early childhood intervention prior to kindergarten is an important step towards meeting this need.

Parenting practices have more impact than preschool practices. Indeed, changing the way parents deal with their children may be the single most important thing we can do to improve children’s cognitive skills. But getting parents to change their habits is even harder than getting teachers to change. In this vein, we applaud efforts such as those by the NAACP Parents Council and the MCPS’s outreach efforts, to help all parents understand what they can do to develop their children’s abilities at young ages.

When the auditors make statements such as "To further diminish academic opportunities for some minority groups, the district has a three-track system for student placement in mathematics" the auditors expose the limitations of their knowledge. The MCPS system needs a high quality analysis of schools to identify those strategies that are the most effective for improving the academic performance for all the counties students. This audit report does little more than reiterate the ideology of one group of educational researchers.

We agree with the auditors that there is wide variation in the offerings and instructional practices across schools in the system. We also agree that there is insufficient evidence as to the efficacy of the various instructional offerings.

We do not agree with the auditor’s view that equal access across all schools to such programs is necessary for an effective school system. An alternative to imposing uniformity of offerings across schools is instead to focus on the outcomes and hold the individual schools accountable for the performance of their schools. We believe that schools that have the latitude to tailor their offerings and practices to meet the needs of their students will better serve the county. For example, we believe that the targeting of additional resources for the K-2 grades to schools with the greatest needs is a prudent policy by the schools system.

The auditors were critical of the written curriculum guide because:

While accurate, it is unclear that the first two criticisms will have a material impact on the quality of student learning or the effectiveness of teaching. The last criticism has been the subject of a substantial quantity of public discourse. For example, Prof. R. James Milgram’s (Stanford University) letter to the editor in the Montgomery Journal, October 16^th, 2000 that concludes that ‘implementing these recommendations would be impossible, waste valuable time and seriously derail MCPS’s goal of improving mathematics achievement for all students…. school system wasted its money on this audit.’ Prof. W. Stephen Wilson (Johns Hopkins University) concludes that ‘there is no way of interpreting this section that makes any sense…it doesn’t make any sense if you know what you are talking about mathematically.’

Critics of the report point to discussion of fundamental theorems in the audit report as evidence that the auditors lack a basic understanding of mathematics, and as a result the validity of their entire analysis is suspect.

The PDK takes it as a given that the MCPS math curriculum should be closely aligned to NCTM standards, which are highly controversial, and that its assessment system should be aligned to the MSPAPs, which have also become the subject of recent controversy. There is no solid research connecting either the NCTM standards or the instructional practices promoted by the MSDE through the MSPAP to higher mathematical achievement. Although at face value alignment has obvious advantages, simply aligning the curriculum for the sake of alignment, without evaluating the standards to which we are aligning it, would be irresponsible. We believe that the MCPS should look beyond the Maryland Content Standards and should also align the curriculum with exemplary state standards, such as the California math standards and well as the best international standards, such as Singapore math.

The MCPS perform an impressive 1 to 1.6 standard deviations above national norms. This is especially impressive because it is likely to understate the performance of the school system and helps explain why in this population 30% of the 2^nd grade children can be classified as gifted and talented. As pointed out by the audit, the school system has not focused its instruction to ‘teach to the test,’ and so MCPS children will tend to score lower than other jurisdictions. In contrast, Maryland as a state scores below national norms.

A consequence of scoring in this range is that MCPS may need to look beyond state standards and so the appropriate materials and tests may be different for MCPS than for other school systems in the state.

It should be kept in mind that the role of state testing is especially key for identifying low performing school systems. Aligning testing to the curriculum will remove a common excuse given by schools identified as low performing.

We concur that the school system’s performance in their use of data could be improved. We think that recent reports of shortcomings in the evaluation of reduced class ratios and in implementing uniform testing standards in some subject areas raises questions about the available evaluation skills in the MCPS school administration.

For example, not all schools in MCPS exhibit equal success in helping below grade level students progress to on grade level, and on grade level students progress to above grade level. Using existing testing results to identify the most effective schools and their programs could assist in identifying the most productive strategies for academic excellence.

It would be interesting to explore the reasons for larger differences between scores for the African American population in different schools and to search for a way to explain the reasons for wide differences in average SAT scores—for example, why are the average scores for African Americans at Seneca and BCC high schools low (416, and 456, respectively) relative to the scores at Richard Montgomery and Whitman (534 and 537 respectively) as reported in Table 2.34 of the audit report.

Alternatively, it would be interesting to examine the practices of schools that exhibited especially large racial achievement gaps. For example, Bethesda Elementary has an especially large achievement gap, yet it has historically not practised ability grouping.

In cases where there are limited resources, the question of what is fair is a complex one, and should be subject to an open public discourse. There has been strong political support for an unequal allocation of resources to programs for very young students to help bridge the achievement gap. School systems should avoid formulas that would reward ineffective schools with more resources but should not further punish the kids at those schools by removing resources. Any reallocation of resources should be based on a full and accurate analysis of the current allocation system and accompanied by oversight and accountability to ensure that the extra funds are put to effective use.

The information in Exhibit 13.1 does not give a balanced indication of expenditures per student as a function of SES/Racial gap. Since Title 1 funds and grant monies play an important budgetary role any evidence of differentials on expenditures should include these sources of funding.

This report identifies findings to support and tactical goals to achieve the recommendations of the MCCPTA Ad Hoc Committee on Math Audit.

A survey designed to solicit broad based parent opinion on the math program was developed by an Ad Hoc Committee of interested parents in response to the MCPS Math Audit. The survey was distributed to all local PTAs through the Montgomery County Council of Parent Teacher Associations. Local PTAs were asked to distribute the survey to parents in their school. Parents were directed to mail or fax in their responses to the MCCPTA office. Several schools collected parent surveys and delivered them to the MCCPTA office. Below are the findings of the survey responses. Appendix A contains details on the survey responses.

• More than 2,000 parents took the time to fill in and return the parent survey and most parents wrote in additional comments. This response is much greater than any other parent survey and reflects the fact that many parents have opinions about the content, pace, and instructional methods used to teach math to their children.
• Responses came from every corner of Montgomery County. At one school the survey was translated into Spanish.
• Among parents who responded to the survey, 83 percent report that their child is currently grouped with others of similar ability for math instruction. Furthermore, 96 percent of parents who responded prefer to have their children grouped with students of similar abilities for math instruction.
• Most parents who answered the survey (73 percent) believe that their child is being taught math at an appropriate level. However, 28 percent of parents believe their child would benefit from more advanced math instruction, while 4 percent believe their child would benefit from less advanced math instruction.
• Approximately 70 percent of all parents who responded report that they help their children with their math homework.
• Overall, about 21 percent of parents who responded provide non-school based support to their children in the area of math instruction. This includes both private tutoring and additional parent support.

Appendix A