I. Introduction

Equity 2000 is a standards-based reform initiative¹ aimed at enhancing mathematics education and achievement among students of color, thereby increasing their likelihood of college enrollment and completion (Pelavin and Kane, 1990). Early lessons on the implementation and outcomes of Equity 2000 have been documented in numerous evaluation reports. For the most part, these reports conclude that in districts where Equity 2000 was piloted, the general math track at the high school level has been virtually eliminated; the number of students who enroll in algebra, geometry, and higher-level mathematics courses has dramatically increased; and districtwide completion rates in Algebra I or higher at the ninth grade have doubled (Everson and Dunham, 1996; Pelavin Research Institute, 1996, 1997). Descriptive case studies on the early years of Equity 2000 implementation in the pilot districts have been produced as well (Richmond, 1996). Together, these reports provide a full picture of the process and outcomes of Equity 2000 during the initiative’s pilot phase, from 1991 to 1996.

The focus of this paper is to describe what has transpired (both during and since the pilot phase) in one Equity 2000 district — Milwaukee Public Schools (MPS) — to support and sustain a key component of Equity 2000: "Districtwide policy change to end [low-level] tracking and raise academic standards for all students, beginning with the requirement that all students complete algebra by the ninth grade and geometry by the tenth grade, and including the reform of the curriculum to reflect standards set by NCTM [National Council of Teachers of Mathematics] and other discipline-based organizations" (The College Board, 1996, p. 1). In particular, the discussion presented in this paper centers on one central issue of the Equity 2000 initiative in MPS: student completion of Algebra I by the end of ninth grade.²

Since launching its Equity 2000 initiative, Milwaukee has tripled the percentage of ninth graders enrolled in Algebra I or higher-level mathematics courses, from 31 percent in 1991 to 99 percent in 1997.³ Over this same period, Algebra I completion rates by the end of ninth grade have more than doubled, increasing from 25 percent to 55 percent.⁴ In fact, more MPS students are now passing Algebra I than had ever attempted to take the course in years before Equity 2000. On the other hand, a consistent pattern over the implementation of this initiative has been that nearly half the MPS ninth graders who enroll in Algebra I (an average of 47 percent) do not pass this course by the end of the school year. These achievement trends indicate the need to understand more about how large, urban school systems can best use standards-based models, such as Equity 2000, to promote mathematics achievement for all students. With this context as a backdrop, the paper addresses three central questions:

• What factors might account for the dramatic increase in the completion rate for ninth graders who enroll in Algebra I or higher?
  
• What issues might account for the 47 percent of ninth-grade students who do not pass Algebra I?
  
• In what ways have these mathematics achievement trends influenced algebra curriculum and instruction in MPS?

Key Themes of the Paper

The following statements highlight the key themes presented and the issues raised in this paper.

In Milwaukee, Algebra I completion has become a universal expectation for all students by the end of ninth grade, and other components of Equity 2000 appear to be institutionalized as well.

• MPS has stuck to its commitment to enroll all ninth-grade students in Algebra I since launching its algebra-for-all mandate in September 1993. The algebra-for-all mandate has been sustained across several changes in the district leadership. MPS educators attribute this staying power to the broad-based involvement of teachers, guidance counselors, and administrators in training for and implementing this policy; to the ongoing support and technical assistance of The College Board; and to the belief that students are willing and able to "rise to the occasion" when presented with the opportunity to learn at high standards. The MPS policy statement on this mandate indicates that the only ninth graders excluded from Algebra I enrollment are students who have already earned algebra credit in middle school and those students whose individual education plans dictate otherwise. Within two years of the mandate, low-level, general math courses such as Applied Math I were eliminated from the high school math curriculum, and after four years, findings show that more MPS students are passing Algebra I by the end of ninth grade than had even attempted to take this course before Equity 2000 was introduced.

• MPS educators credit the Equity 2000 professional development approach as a key factor in fostering implementation of the algebra-for-all mandate. The Equity 2000 professional development model engages a cross-section of education stakeholders including teachers, guidance counselors, and principals. The Equity 2000 professional development consists of summer institutes and follow-up in-service during the school year. MPS estimates that approximately 85 percent of grade 8-10 math teachers in the district participated in some level of Equity 2000 training. Teachers tended to agree with this estimate, while principals reported lower participation rates and cited high staff turnover as an impediment to keeping trained teachers. Lessons from the Milwaukee experience show the value of Equity 2000’s comprehensive professional development delivery model toward building school staff support for the algebra-for-all mandate. Teachers, in particular, felt that by starting Equity 2000 professional development months before the mandate was to take effect, they were better able to understand, prepare for, and adjust to the policy itself and to changes that would result. Although Equity 2000 professional development incorporated issues of content (what we teach), pedagogy (how we teach), and equity (who we teach), comments from MPS educators suggest that the initiative had more impact on attitudes about students’ capabilities and on the pedagogy for delivering instruction than it had on strengthening teachers’ content knowledge. When MPS assumed total responsibility for costs to sustain Equity 2000 professional development in 1996, the intensity of Equity 2000 summer institutes and the frequency of the follow-up in-service were scaled back. However, the district appears to have institutionalized these activities by blending training into existing classroom-based learning experiences and by securing other grant-funded math initiatives. The Milwaukee Urban Systemic Initiative (MUSI), which is funded through a comprehensive five-year grant from the National Science Foundation (NSF), was most notably acknowledged as an invaluable resource for extending and deepening the scope of professional development around mathematics curriculum reform. The proliferation of teacher-to-teacher math networks within the district has also emerged as a key source of professional development by sustaining dialogue around issues supportive of Equity 2000 goals.

• Implementation of the algebra-for-all mandate depended on the willingness and ability of MPS math teachers and guidance counselors to change their practice in innovative ways. The importance of retooling practice was cited repeatedly in interview and focus groups with teachers, guidance counselors, and administrators. This theme was supported by documentation compiled in the MPS Equity 2000 audit reports. From these data sources, we identified that, over the years since Equity 2000 was first launched, Algebra I teachers have increased their use of group work and cooperative learning techniques, real-world application of math concepts, and calculators. Teachers talked not only about the influence that Equity 2000 had on their classroom practice but also about its effect on collegial exchange: more instances of teachers using other teachers as a resource. In addition, guidance services have been expanded as a result of Equity 2000. MPS guidance services now give more attention to introducing students at an earlier age to postsecondary opportunities, to increasing college campus exposure for potential first-generation college-bound students, to encouraging all students to enroll in advanced-level courses, and to working collaboratively with teachers and parents to help students understand the importance of mathematics in securing an array of postsecondary options.

• MPS created a variety of safety net activities to provide academic enrichment and extra support in mathematics; however, MPS educators cite the continuing challenge of motivating students to take advantage of these safety net opportunities. MPS implemented several of the safety net support strategies that were encouraged under the Equity 2000 model. The Saturday Academy program offers enrichment in mathematics and science, college exposure, and parental involvement. The math summer school program, which targets low-performing students, provides a range of academic supports for students in grades 8-12 including Algebra Readiness classes, make-up classes for students who fail Algebra I or Geometry, and (since 1996) classes to prepare for the high school math proficiency examination. School-based academic support is provided through tutoring, algebra support classes, and midyear Algebra I reprogramming courses.⁶ The safety net support structures that MPS has established through its Equity 2000 initiative have the potential to serve a substantial number of students. However, because student participation in many of these safety net activities is optional, teachers report that for various reasons (program location, competing demands with other courses, or lack of motivation) participation is lower than desired. Teachers also pointed out that several MPS high schools had recently adopted block scheduling as a strategy to improve overall student academic performance. Block scheduling provides students more time to learn math (and other subject areas) within the required school curriculum. Both teachers and administrators tended to view block scheduling as an additional safety net (although in some cases, it was reported that block scheduling hampered the school’s ability to offer midyear reprogrammed Algebra I courses). Nonetheless, issues of student motivation and incentives are important to address if the benefits of safety net activities are to outweigh their costs.⁷ If data are not available, the district’s investment in such activities warrants a closer look: For which students, and in what ways, are these safety nets successful in increasing achievement in Algebra I and other measures of high standards in mathematics? Any future research on Equity 2000 should serve to look more closely at this issue.

• MPS has sustained its commitment to the core principles of Equity 2000, absorbing the incremental costs locally now that the pilot phase is over. Eight years after being introduced in Milwaukee, Equity 2000 components appear to have attained a visible and sustained presence within MPS’ overall school improvement priorities. In fact, the Equity 2000 National Office assisted MPS (as well as the other Equity 2000 pilot districts) in the development of an "institutionalization plan" that enabled the district early on to prepare for carrying implementation beyond the initial, five-year Equity 2000 grant. Information collected by MDRC during the 1997-98 school year indicates that costs related to ongoing implementation of the major components of Equity 2000 (that is, professional development, safety nets, parental involvement, college and university partnerships, and data analysis) are funded locally or through other leveraged resources. District institutionalization of Equity 2000 appears to extend beyond the algebra-for-all mandate, professional development, safety net supports, and parental involvement activities. An MPS official pointed out that "in an era of accountability," Equity 2000 emphasis on dissaggregating student data helped to reinforce careful examination of student achievement trends. Because of Equity 2000, Algebra I passing rates are included as a performance measure for annual school accountability reports compiled by the MPS Office of Research and Assessment. Disaggregated trend data on student participation in advanced-placement courses, college entrance examinations, and college enrollment have been compiled annually since 1992. Similarly, MPS partnerships with local institutions of higher education have been strengthened through such initiatives as Equity 2000 and MUSI. In particular, the University of Wisconsin-Milwaukee and Marquette University are central partners in the MPS reform efforts in that they provide a wealth of resources, expertise, and professional growth opportunities focused on mathematics teaching and learning. The ongoing role and eventual legacy of Equity 2000 as expressed by MPS educators reflect a perception that this initiative has played a pivotal role in actualizing high standards, not only in mathematics but across other subject areas as well.

Despite the substantial increase in Algebra I completion within the district, MPS educators are very concerned that nearly half the ninth graders who enroll in Algebra I do not pass by the end of the school year.

• Several barriers to student achievement in mathematics were cited; foremost among these are poor student preparation in math and low student attendance. Teachers (and other respondent groups) indicated that an overwhelming number of ninth graders were not prepared academically to take on the rigors of Algebra I. Teachers reported that they had revised the pace of the Algebra I curriculum — some feel to a "watered-down" state — in order to accommodate the limited amount of material that students could absorb. The perceived lack of student preparation was largely attributed to two factors: the middle school math curriculum and poor content knowledge of middle school math teachers, although some attributed such perceptions about poor student preparation to low teacher expectations or teachers’ inability to engage students in the learning process. There was general consensus, however, that the average daily absentee rate of 25 percent largely contributed to the high number of students who had to repeat Algebra I one or more times. Concern about how to monitor and best serve the needs of "repeater" students emerged as a major issue. It may be worthy of study to identify and review the types of reassignment or instructional strategies that are used with this population to determine how best to raise math achievement among repeaters.

• A second reported impediment to student achievement in Algebra I is large class size and its impact on teachers’ ability to meet the diverse learning needs of a heterogeneous classroom. With the elimination of low-level math courses, the grouping of students based on ability has been greatly reduced in the ninth-grade mathematics curriculum but not totally abolished. A comparative review of the 1994 and 1997 MPS Equity 2000 audit reports showed that high schools have dropped courses such as Chapter I Algebra, but most continue to offer a gifted and talented Algebra I class.⁸ Teachers and guidance counselors report that the majority of ninth-grade students are assigned to "regular" Algebra I classrooms, which thus serve a wide range of students with varying academic skills and capabilities. Teachers admit that they struggle to address the different skill levels and learning styles of their Algebra I students. This challenge is compounded by the reported size of Algebra I classes, which average from 30 to 35 students (largely reflecting a districtwide math teacher shortage). In trying to respond effectively to this challenge, teachers report that they are using such techniques as math manipulatives and cooperative learning. However, to better accommodate the diverse learning needs of students, teachers and administrators advocate the need to provide different Algebra I curriculum options. Sentiment in MPS around the possibility of offering algebra curriculum options may yield opportunities for future research on alternative approaches to ability grouping.

• A third major barrier to student achievement in Algebra I are the limitations on building teacher capacity to implement the algebra-for-all mandate. Despite the high percentage of math teachers who participated in Equity 2000 professional development, it appears that the level and intensity of involvement were not the same for all teachers. Costs for professional development in MPS are very high, limiting the number of participants who can be served at any given training session. Priority for these limited slots was given based not on teaching assignment (that is, teachers who were teaching algebra) but rather on years of teaching experience.⁹ Even with professional development, MPS educators indicate that low teacher expectations, lack of access to needed resources, and resistance to change further served to hinder student achievement in algebra. In regard to teacher expectations, perceived gains in this area were somewhat mixed. While the majority of comments on this issue reflected a perception that the tide of low expectations for all students learning algebra had receded, there were others who thought the belief that "algebra is not for everyone" widely persisted within the teaching ranks. Regarding access to resources and teacher resistance to change, both teachers and administrators felt that Equity 2000 training should be followed up with classroom-based support and monitoring to (1) ensure that instructional resources are available in each school and (2) help teachers practice, develop a comfort level, and feel accountable for implementing new practices that Equity 2000 espouses for working with diverse groups of students. It was noted that the MPS math and science resource teachers (MSRTs) — a core of veteran classroom teachers who were hired in 1996 to serve as resource teachers for the district — represent a step toward addressing these needs.¹⁰

MPS is committed to building on the early accomplishments of Equity 2000 by making additional policy and practice changes to enhance student achievement trends in Algebra I.

• For the first time in over a decade, a district-issued Algebra I curriculum guide for high schools has been developed. Several factors in the district — MUSI, the algebra-for-all mandate, concerns about a watered-down Algebra I curriculum, and the advent of math proficiency standards and assessments — prompted MPS high school principals to request that the district provide a specific algebra curriculum, including scope and sequence. In January 1998, an Algebra Curriculum Committee — comprising math and science resource teachers, middle and high school math teachers, and university faculty — was formed to develop the curriculum guide. The MPS Algebra I Guide: For Heath Algebra I was completed in July 1998, and distribution was accompanied by a series of in-services that provided "how to" information on its use. The guide embraces the shift from topic-driven and teacher-focused instruction to concept-based and student-centered methods, and it includes a framework for what an algebra class should look like. The guide reflects efforts that are being mounted at multiple levels throughout the district to meet the diverse learning needs of students and to better prepare students for the rigors of advanced mathematics courses at the high school level.

• All MPS middle schools are implementing a standards-based middle school math curriculum to develop student proficiency in mathematics. When MPS adopted Equity 2000, the eighth-grade mathematics curriculum was changed to "prepare all students with the mathematics foundation they will need to succeed in high school algebra and geometry" (Talborn, 1991, p. 14). The district adopted the ScottForesman textbook series Exploring Mathematics and UCSMP Transition Mathematics for the eighth-grade mathematics course; sixth- and seventh-grade mathematics courses remained unchanged. Sparked largely by the district’s work through MUSI — and the aforementioned teacher concerns about the lack of student preparation in mathematics — Milwaukee is again in the process of changing the mathematics curriculum at the middle school level through the adoption of the Connected Mathematics Project (CMP), an NSF-supported curriculum which introduces algebraic concepts throughout grades 6-8. By the year 2000, a set of math proficiency assessments for eighth graders (along with other content area proficiency assessments) will serve as a filter to, in effect, end social promotion and ensure that all incoming ninth graders are prepared to take higher-level mathematics courses.¹¹ Strengthening math content knowledge among middle school teachers has been identified as a key priority for effective implementation of the CMP curriculum. The district is providing teacher training in CMP through its Milwaukee Urban Systemic Initiative, and recently the Equity 2000 summer institutes have focused on CMP training for middle school teachers as well.

• Alternative approaches to algebra curriculum sequencing and instruction are being piloted across MPS high schools. At the high school level, many schools are piloting and adopting alternative algebra curriculum programs such as the Pittsburgh Urban Mathematics Program (PUMP) and integrated math curriculum programs such as the Core-Plus Mathematics Project (CPMP) and the Interactive Mathematics Program (IMP). These programs extensively use the instructional techniques of student discussion through word-based problem solving and student group work. Technology is also an integral part of each program. CPMP and IMP differ as well from the "topical learning" found in traditional mathematics courses by providing an integrated approach to problem solving that builds on students’ prior math knowledge to introduce new concepts. These integrated math programs cover the sequence of algebra, geometry, and (in the case of IMP) advanced math over a two- to four-year period. MPS high schools are using these technology-based and integrated curriculum alternatives in addition to the traditional course sequence of Algebra I and more advanced math. It remains to be seen how these curriculum and instructional changes will impact on math achievement and other education outcomes. Some MPS educators worry that the new integrated and technology-based algebra curricula may not provide adequate foundation for students to master algebra and geometry and do well in more advanced mathematics coursework. There is also concern that the integrated math curriculum programs may not align with local accountability assessments. Advocates of the new math curricula, however, believe strongly that students who complete the integrated math programs will develop the same level of skills (or a higher level) as students who successfully complete the traditional route. Certainly, Milwaukee provides fertile ground for putting these issues to the test. A study of the effects of the new curricula would be particularly timely, given that The College Board has developed an end-of-year Algebra I assessment which could serve as the standard tool for evaluating the rigor of all approaches to algebra instruction, including the traditional one-year Algebra I course.

• Equity 2000 appears to have had direct and indirect influences on current efforts in MPS to stay the course for actualizing high standards in mathematics.¹² Clearly, teachers feel that Equity 2000 strongly challenged traditional mind-sets about the capacity of all students to learn algebra and influenced their pedagogical techniques for engaging students in classroom work. However, it was also reported that the Equity 2000 design had fallen short in providing specific programs teachers felt they needed in order to reform the math curricula substantively and better meet students’ diverse needs. Equity 2000 espouses a learning paradigm approach that focuses on how students learn best, whereas the traditional instructional paradigm focuses on content coverage in the classroom. Enabling teachers to make the paradigm shift requires sustained energy, administrative support, time and other resources, and alignment between curriculum and accountability assessments. Through the continued commitment of MPS educators toward high standards and the synergy of curriculum-based initiatives such as Equity 2000, School-to-Work, and MUSI, current efforts to adopt new math curricula programs, to develop curriculum standards and new proficiency assessments, and to provide math resource teachers may result in bridging the gap between learning and instructional paradigms. A clear lesson from the Milwaukee experience is that efforts to reform and align students’ needs, teachers’ practices, the curricula, and methods of assessment require a long-term commitment and multiple sources of support that are linked to a common vision of teaching and learning.

Description of the Paper

Six years after MPS first adopted the Equity 2000 initiative and four years after the district’s algebra-for-all mandate was put into effect, MDRC conducted a preliminary review of implementation issues surrounding a central component of the Equity 2000 initiative in Milwaukee Public Schools (MPS) — student completion of Algebra I by the end of ninth grade. We acknowledge that the goals of Equity 2000 extend beyond this objective and include increased tenth-grade enrollment in Geometry as well as overall enrollment in advanced courses, increased percentages of minority students who take college entrance examinations, and increased minority students’ college enrollment rates. Among Equity 2000 districts, achievement trends in these areas have been well documented in numerous Equity 2000 reports and evaluations.¹³ As such, the focus for the remainder of this paper is as follows:

• Section II provides background on the education policy context and program rationale from which Equity 2000 was created and also presents an overview of the Equity 2000 implementation design.
  
• Section III reports The College Board’s data on ninth-grade student enrollment and passing rates in Algebra I for Milwaukee and describes the steps that were taken in Milwaukee to support implementation of Equity 2000 components and to raise student achievement in Algebra I.
  
• Section IV presents information on the perceptions among MPS educators about challenges they face in getting all students to complete Algebra I by the end of ninth grade.
  
• Section V describes recent efforts within and across MPS middle and high schools to revise the content, delivery, and sequence of algebra instruction to increase student achievement in mathematics.
  
• Section VI provides a closing statement on the perceived legacy of Equity 2000 in Milwaukee Public Schools.

II. Equity 2000: Policy Rationale and Implementation in Milwaukee

Standards reform in education policy has sparked a number of efforts at the national, state, and local levels to articulate exactly what students should know and be able to do in particular content areas at different grade spans along the K-12 curriculum. One content domain that has emerged as the leader in building consensus around standards is mathematics. In 1989, the National Council of Teachers of Mathematics (NCTM) issued its Curriculum and Evaluation Standards for School Mathematics, becoming the first national teacher association to endorse a specific set of curriculum standards.¹⁴ In this groundbreaking document, NCTM suggested that the change from an industrial to an information society called for a revamping of mathematics education in order to adequately prepare all students for life in the twenty-first century. Indeed, NCTM asserted that "women and most minorities" were underrepresented in careers in mathematics, science, and technology and that "the social injustices of past schooling practices can no longer be tolerated" in a society in which mathematics is "a critical filter for employment and full participation" (NCTM, 1989, p. 4). The NCTM standards received widespread support among mathematics educators and also served to influence standards development efforts in other disciplines. The movement toward standards has been manifested in a proliferation of changes in high school graduation requirements, curriculum design and sequencing, and student assessment (Bradley, 1994; Century, 1994; Rothman, 1995).

In the area of mathematics, algebra-for-all has become a rallying cry for high-standards curriculum reform (Chambers, 1994; NCTM, 1993). Based on research findings that support the importance of algebra enrollment as a predictor for academic and vocational success and its designation as a gatekeeper to educational opportunity and lifelong success (NCTM, 1989; Pelavin and Kane, 1990), algebra has been singled out as a vanguard for high standards. This push for algebra is particularly relevant for minorities. Oakes (1990) and others (Equity Coalition, 1992; Southwest Educational Development Laboratory, 1994; Trimble and Sinclair, 1988) have extensively documented the underrepresentation of black and Latino students in higher-level mathematics classes for which algebra and geometry are prerequisites. Thus, the move to high standards as exemplified by Equity 2000 is touted as a viable mechanism to level the mathematics playing field. In the past 10 years, several states and school districts have adopted an algebra-for-all policy, either as a high school graduation requirement or at a targeted grade level, usually ninth grade (Bradley, 1994; Chambers, 1994; Olson, 1994; Silvers, 1995). National mathematics reform initiatives such as Equity 2000 and the Urban Systemic Initiative (funded by the National Science Foundation) helped to fuel this pattern by providing grants to urban districts that promised to make algebra a requirement for all students by the end of ninth grade.

Some in the mathematics community caution, however, that algebra-for-all — absent changes in algebra curriculum design, sequencing, and delivery — is a doomed response to high standards (Chambers, 1994; Steen, 1992). Leading mathematics educator Edward Silvers argues that algebra requirement policies may not be leading to high standards at all but may simply be "mandating mediocrity." In a 1994 Education Week article, then NCTM president Jack Price raised a similar concern that districts may approach an algebra-for-all policy simply by placing all students (at the eighth or ninth grade) in "what we might call a traditional first-year algebra class . . . a course in high school that is currently a filter for higher mathematics" instead of rethinking the learning process of algebraic concepts as "a strand [to be woven] throughout the K-12 curriculum" (Olson, 1994, p. 13). Researchers from the U.S. Department of Education found that in other countries algebra, geometry, and probability are traditionally introduced to students starting in grade 5, while "U.S. students are still stuck in arithmetic, moving onto algebra and other topics only in the 8th or 9th grades, if they do so at all" (LeTendre and Chabran, 1998, p. 8). As a result, the transition from middle school math to high school algebra is difficult. These researchers further conclude that the transition is particularly difficult for minority and poor students, because they are least likely to have had sufficient preparation in the basics of math that would enable them to surmount such a challenge.¹⁵ This is not to say that math educators who raise these concerns do not support the algebra-for-all philosophy. However, cautions issued around such policies may be more in line with the sentiment of Donald Chambers, who in an article entitled "The Right Algebra for All" wrote: "Algebra for all is the right goal at the right time. We just need to get the right algebra" (1994, p. 86).

Equity 2000

The College Board created Equity 2000 in 1990. By increasing the enrollment of students of color in higher-order mathematics courses, Equity 2000 aims, ultimately, to increase their overall academic achievement and college attendance rates. A major goal of this initiative is to close the achievement gap between minority and non-minority and between advantaged and disadvantaged students. Equity 2000 is based on the premise that all students can learn and on research indicating that low-income, minority students — when they master algebra and geometry by the end of tenth grade and have expectations to attend college — tend to enroll in college at about the same rate as their non-minority or more economically advantaged peers (Pelavin and Kane, 1990).

Equity 2000 provides districts with "a process" to foster a high-expectations learning environment for all students by focusing on access to and achievement in Algebra I and Geometry for students who normally would not enroll in these courses. Equity 2000 is a districtwide education reform initiative that seeks to influence systemic changes by eliminating low-level courses in the ninth- and tenth-grade mathematics curriculum, providing ongoing professional development for school staff, developing safety net activities that provide academic enrichment and extra support, increasing parental involvement in student learning, building school-community partnerships, and fostering a high-expectations learning environment through dialogue and examination of student subgroup achievement trends.

In adopting Equity 2000, a participating district’s commitment extends far beyond algebra and geometry enrollment mandates. The district also signs on to provide the capacity-building supports needed to implement the remaining five central components of Equity 2000, which are:

• Professional development for teachers, guidance counselors, and principals — to enhance their professional knowledge and skills and to raise their expectations for students
  
• Safety net academic enrichment programs for students — to increase their motivation and confidence about math
  
• Programs to support parent/family involvement — to help parents and their children understand and get involved in the push for higher standards
  
• Programs linking school districts, colleges and universities, and the local community — to develop and strengthen support of high-standards learning goals
  
• Programs to evaluate Equity 2000 objectives — to help districts and schools effectively examine disaggregated student enrollment and achievement data to enhance school-improvement decision making

Although Equity 2000 supports and encourages teacher practice in alignment with NCTM standards, the initiative does not endorse nor does it suggest adoption of specific mathematics curricula. Rather, Equity 2000 seeks to promote the use of NCTM standards by helping districts to obtain information on best practices through cross-site sharing and other math educator networking activities. These building blocks may (but do not necessarily) lead districts to recognize the need for more comprehensive curricular changes.

Equity 2000 Implementation in Milwaukee

In 1991, Milwaukee Public Schools (MPS) became one of six pilot sites of the Equity 2000 initiative¹⁶ and, in the 1993-94 school year, adopted the policy to enroll all ninth graders in Algebra I. This decision represented one in a continuum of policy adoptions made by MPS during the 1990s to increase academic expectations and achievement for all students.¹⁷ As an Equity 2000 pilot district, MPS received a $1,936,248 five-year grant from The College Board.¹⁸ In accordance with the memorandum of understanding agreed to by the pilot districts, The College Board grant funded the salary of a full-time MPS Equity 2000 coordinator, professional development (including trainers and participant stipends), student safety net activities, travel expenses to Equity 2000 meetings, and other planning activities. Milwaukee was required to leverage some degree of matching funds and in-kind support as well.¹⁹

Along with the grant, MPS received ongoing technical assistance from The College Board.²⁰ Technical assistance provided by The College Board during the pilot phase served to develop and/or strengthen local capacity for (1) establishing professional development delivery systems around high-standards reform in mathematics, (2) providing safety net academic support activities to help students succeed and get parents involved, (3) building partnerships with local institutions of higher education focused on mathematics teaching and learning, (4) compiling and analyzing student achievement data to ensure that all populations of students have access to and are making progress in achieving at high levels, and (5) developing institutionalization plans for reallocating and leveraging local funds to support ongoing implementation of Equity 2000 components. In addition, the Executive Director of the Equity 2000 National Office visited MPS twice a year to provide on-site guidance, observe Equity 2000 activities, and meet with local education policymakers. National technical assistance committees (one for mathematics and one for guidance) were also established to develop guidelines for Equity 2000’s professional development delivery model. Probably the most comprehensive component of the technical assistance effort was provided through the national network support meetings that were hosted by the Equity 2000 National Office, which served to bring representatives from MPS and other pilot districts together to share ideas and learn from leading mathematics education experts. Specialty group network meetings were conducted three or four times a year for Equity 2000 coordinators, math curriculum specialists, guidance directors, and data managers.²¹ District superintendents and school board members attended network meetings twice a year. Principals also attend Equity 2000 network meetings. MPS participants of the Equity 2000 national networks highly regarded these meetings as instrumental in keeping local leaders of the initiative "energized . . . focused . . . [and] informed."

From 1991 to 1997, a full-time MPS Equity 2000 coordinator handled day-to-day management and budget responsibilities for the initiative.²² In August 1997, the coordinator became director of the Milwaukee Urban Systemic Initiative while continuing management responsibility for Equity 2000. (A math teacher is released part time to assist in the coordination of Equity 2000 activities.) Since its inception, a core planning team composed of the Equity 2000 coordinator, math curriculum specialist, and guidance director has met regularly to design and plan Equity 2000 activities. In addition, an "extended leadership group" comprising principals, MPS research staff, and two University of Wisconsin-Milwaukee faculty members meets with the core planning team twice a year to advise the overall project.²³ A math teacher (who serves part time as Equity 2000 coordinator) joined the leadership group in the fall of 1998.

In June 1996, MPS became a demonstration district for Equity 2000.²⁴ Since the fall of 1996, MPS has been the recipient of the five-year demonstration grant of $50,000 annually from The College Board. MPS continues to participate in national network meetings (held twice a year) and has assumed a lead role in providing training and presentations on lessons learned from Equity 2000 implementation to staff from new Equity 2000 adoption sites.²⁵ MPS also hosts visits from and conducts visits to districts interested in adopting Equity 2000 and (where requested) has provided technical assistance to these sites. The Executive Director of the Equity 2000 National Office continues to visit MPS once a year to review progress and provide technical assistance on implementation of the district’s Equity 2000 institutionalization plan.

MDRC’s Preliminary Review of Equity 2000 in Milwaukee

During the 1997-98 school year, MDRC conducted a preliminary review of Equity 2000 implementation in Milwaukee.²⁶ This preliminary review had three purposes:

1. To understand how the implementation of Equity 2000 has evolved over time, including the level of institutionalization achieved for specific components of the initiative
   
2. To gather staff insights on factors that affect student achievement in Algebra I
   
3. To identify alternative approaches that have been adopted by schools since 1991 to help all students achieve at high levels in mathematics

The preliminary review was conducted over a 10-month period, during which time MDRC researchers visited MPS three times (November 1997, May 1998, and July 1998). The following sources provided data and information presented in this paper:

• In-person interviews with MPS central office administrators and teachers involved with the planning, coordination, and evaluation of Equity 2000 activities
  
• Interviews with four high school and two middle school principals
  
• Focus groups with high school math teachers and phone interviews with middle school teachers. (A total of 38 teachers from 11 high schools and two middle schools participated.)
  
• Focus groups with nine guidance counselors, representing five middle schools and four high schools
  
• Phone interviews with staff at The College Board
  
• Collection and review of extant data and reports on Equity 2000 efforts in Milwaukee and nationally

MDRC conducted exploratory research on the evolution of Equity 2000 in Milwaukee and the implementation of the algebra-for-all mandate. Researchers used a reduced interview series to gather information from a select group of individuals who shared the common experience of being integrally involved with the planning and implementation of Equity 2000.²⁷ These individuals participated in in-depth interviews (or focus groups) lasting one or two hours. Where permitted, the focus group conversations were taped and transcribed. After each site visit, interview notes were coded to extract themes which served to inform and direct subsequent field interviews. MDRC also used a variety of independent evaluation data on Equity 2000 in Milwaukee and nationally to supplement the "voices from the field." This analysis process enabled the creation of several propositions about Equity 2000 and factors that support or inhibit the achievement of high standards in mathematics for all students. Unless otherwise indicated, all comments attributed to MPS educators as presented in this paper are based on the interviews and focus groups that were conducted during the preliminary review.

III. Increasing Student Achievement in Mathematics

With this charge, Milwaukee Public Schools became the first Equity 2000 pilot site to put an algebra-for-all policy into effect (Pelavin Research Institute, 1997), thus dramatically increasing the number of students who enroll in and complete Algebra I. The College Board reports that ninth-grade enrollment in Algebra I or higher in MPS tripled (from 31 percent to 99 percent) between 1991 and 1997. For students of color, the increase has been most significant. Among black, Hispanic, and Asian, students enrollment rates increased 75, 78, and 67 percentage points, respectively. The total percentage of MPS students who completed Algebra I or higher-level math courses by the end of the ninth grade has more than doubled since Equity 2000 was launched, increasing from 25 percent to 55 percent between 1991 and 1997. This increase was significant across all ethnic groups, although the achievement gap between minority and non-minority students (with the exception of Asian students) remains significant. When we examine only the data on ninth-grade students enrolled in Algebra I, passing rates actually declined from 1991 to 1997, from 71 percent to 53 percent. It is important to note, however, that the absolute numbers of students taking algebra have increased substantially; thus, such a decline (though by no means acceptable according to MPS standards) might not be unexpected during early implementation years of such initiatives. Nonetheless, a frequently touted outcome of Equity 2000 (both nationally and within MPS) is that the number of students now passing Algebra I is greater than the number of ninth graders who even attempted to take this course in years before the initiative.

This section of the paper highlights other key activities that resulted from Equity 2000 and which sought to increase the levels of Algebra I completion by the end of ninth grade. These activities include (1) professional development to support implementation of the algebra-for-all mandate, (2) retooling of math teachers’ classroom practices, (3) student safety net academic enrichment and support activities, and (4) the expanded role of guidance services in promoting high expectations for all students.

Equity 2000 Professional Development in Milwaukee

Like many reform efforts, successful implementation of Equity 2000 requires schools to adopt new modes of professional practice and interactions among colleagues and with students. In particular, teachers are expected to master new skills, deepen their content knowledge, and change their classroom practices. Research indicates that, in order to meet these new demands, teachers will need "more time to work with colleagues, to critically examine the new standards being proposed, and to revise curriculum [and have] opportunities to develop, master, and reflect on new approaches to working with children" (Corcoran, 1995, p. 1).

Equity 2000 professional development consisted of intensive summer institutes and follow-up in-service during the school year. For teachers and guidance counselors, the institutes began in the summer of 1991, two years before the algebra-for-all mandate was put into effect. For principals, Equity 2000 summer institutes started in 1993. During the pilot phase, Equity 2000 summer institutes for teachers ran for two weeks, eight hours a day. Summer institutes for guidance counselors ran for one week, and those for principals were conducted over two days. There was some overlap in scheduling the institutes in order to bring each participant group (high school and eighth-grade math teachers, guidance counselors, and principals) together for cross-cutting general sessions. The University of Wisconsin-Milwaukee (UWM) was and continues to be a major partner in the design and implementation of the summer institutes. Many of the institute sessions are held on the UWM campus, and UWM faculty served as institute trainers/facilitators early on to develop turnkey trainers among MPS teachers.

The Equity 2000 institutes sought to raise awareness about how adults’ expectations affected students’ views of themselves, their attitudes about school, and their academic performance. These institutes also focused on the gatekeeping role of algebra, the disaggregation of student data, and other equity issues. The guidance institutes, in particular, focused on how to prepare first-generation college-bound students for successful transition into college. Consistent with the Equity 2000 professional development delivery model, teacher institutes regularly incorporated issues of content (what we teach), pedagogy (how we teach), and equity (who we teach). The institutes provided a forum for dialogues about NCTM standards, "Big Ideas" in curriculum content relating to the integration of algebra and geometry, and pedagogical techniques for delivering instruction to diverse learners. During the school year, teachers could sign up for an additional 20 hours of follow-up "rotisserie" workshops that were tailored to address different levels of content knowledge and familiarity with innovative instructional approaches.²⁸ Follow-up in-services were also provided for principals and guidance counselors.

Administrators and teachers were very favorable in assessing Equity 2000’s professional development activities. Teachers reported that Equity 2000 was the first districtwide professional development initiative that focused on math teachers.²⁹

Table 1 presents annual participation counts for Equity 2000 professional development. Teacher participation in Equity 2000 summer institutes has experienced a moderate decline since 1996-97, but that may be expected after the majority of teachers have completed this intensive training and seek only "refresher" follow-up training to maintain or learn about new skills. As a result, we see a higher volume of participation in the follow-up in-service during the later years (although as Table 1 notes teachers may have attended more than one follow-up in-service within a given year). Feedback from MPS teachers as well as documentation from MPS and external evaluation sources indicate that the majority of grade 8-10 math teachers participated in Equity 2000 professional development. During focus groups, teachers estimated that from 60 to 80 percent of math teachers in their building had participated in Equity 2000 professional development through either the summer institute, follow-up in-service, or both. The MPS Equity 2000 coordinator estimated that 85 percent of the targeted math teachers (out of a total of 88 eighth-grade teachers and 195 ninth- and tenth-grade teachers) had participated in Equity 2000 training (Henry, 1993) and that 99 percent of all middle and high school principals and 98 percent of all middle and high school guidance counselors had attended one or more Equity 2000 in-services. MDRC found supporting documentation for these estimates in the teacher survey findings from an independent evaluation conducted by the Pelavin Research Institute (1996), which also concluded that 86 percent of MPS grade 8-10 math teachers and 91 percent of guidance counselors participated in one or more of the Equity 2000 institutes or follow-up in-services (Pelavin Re-search Institute, 1997). On the other hand, MPS high school principals were more likely to estimate that a lower percentage (averaging from 30 to 50 percent) of math teachers in their buildings participated. As reasons for low estimates, principals cited the teachers’ union agreement and high teacher turnover (including the loss of classroom teachers as a result of the creation of MUSI math and science resource teachers).³¹

Over the course of the pilot phase of Equity 2000 and MPS’ transition to a demonstration site, professional development in support of this initiative has evolved in a number of ways. Training costs that once were covered primarily through the Equity 2000 grant are now funded through the reallocation of a variety of federal, state, district, and school funding sources such as the National Science Foundation, Eisenhower, Title I, and Goals 2000 and through the leveraging of foundation grants. In effect, MPS has sustained its commitment to ongoing professional development centered on Equity 2000 goals generally and, in particular, on the algebra-for-all mandate. On the implementation side, teacher training has become more focused on teacher-to-teacher efforts and is classroom-based. For instance, in the early years of Equity 2000, the summer institute trainers were primarily UWM faculty. Today, MPS teachers serve as facilitators, and more training takes place within the classroom setting inasmuch as the summer institute has been partly folded into the MPS math summer school program. Similarly, the follow-up teacher in-services have been blended into the Saturday Academy program.³² As a cost-cutting measure, both the summer institutes and the follow-up in-service have been scaled back in length; the teacher institutes have been shortened from two weeks to one week (and from one week to 2.5 days for guidance counselors), and Equity 2000 follow-up in-services are now conducted four times a year. The target audience for Equity 2000 professional development has also shifted since the pilot phase. In support of MPS’ efforts to increase mathematics achievement at the middle school level, Equity 2000 summer institutes for teachers now target training for sixth- and seventh-grade teachers in math content and implementation of a newly adopted middle school math curriculum;³³ this shift in professional development focuses more on strengthening content knowledge among middle school mathematics teachers. Also, Equity 2000 institutes for principals and follow-up in-services, which focused on middle and high school administrators during the pilot phase, have been expanded since 1997 to include elementary principals as well. Table 2 gives an example of the evolution of the Equity 2000 summer mathematics institutes for teachers. Teachers reported both pros (seeing how things work in the classroom) and cons (missing the intensive, extended training environment of the summer institutes) about changes made in the Equity 2000 professional development delivery model. However, teachers also added that, since the introduction of Equity 2000, there has been an overall increase in the number and types of math teachers’ in-service opportunities within the district.

Most notably mentioned is the Milwaukee Urban Systemic Initiative (MUSI), which was introduced in 1996. MUSI is a five-year, districtwide initiative funded by the National Science Foundation (NSF) that focuses on achievement in mathematics and science by targeting K-12 curriculum reform and teacher professional development. MUSI encompasses an impressive scope of work including the development of curriculum frameworks in mathematics and science (aligned to state standards), development and refinement of the districts’ proficiency assessments, and the investigation and adoption of unified curriculum programs for mathematics and science (MPS, 1997, 1998). With MUSI resources, MPS has greatly extended professional development for math teachers far beyond the scope of training offered through Equity 2000. For example, the MUSI Math/Science Resource Teachers (MSRTs) work in schools on a weekly basis as coaches and facilitators to support teacher implementation of new curricular, skills, and pedagogical approaches. MSRTs are former MPS classroom teachers, many of whom participated actively in the Equity 2000 institutes. During the 1997-98 school year, the 40-member cadre of MSRTs worked in 81 "first-wave" MUSI schools.³⁴ Similar to Equity 2000, a MUSI objective for the high school mathematics curriculum is algebra-for-all. As such, MUSI is supporting teacher training and implementation of innovative algebra and integrated math curriculum programs within MPS high schools.³⁵ An annual MUSI/Equity 2000 in-service session is held for teachers to reinforce the connection between these two initiatives.³⁶

Another NSF-funded activity, the Linked Learning in Mathematics Project (LLMP), also provides tremendous support for teacher training centered on the algebra curriculum and instruction. Created in 1997, LLMP is a collaboration between MPS and Marquette University whose purpose is to help middle and high school teachers implement algebra-for-all by providing training on curriculum-based reforms such as the Connected Mathematics Project (CMP), which has been adopted in all middle schools. A list of other MPS in-service initiatives that have been offered for math teachers is presented in Appendix B.

Also cited as instrumental to the ongoing teacher professional development in support of Equity 2000 goals and mathematics reform, generally, is the establishment and growth of MPS math teacher networks. The first MPS math teacher network (the High School Algebra Study Group) was formed in 1992. Teachers reported that the networking activity expanded their opportunities to come together for support and to share ideas and strategies that were emerging, not only from the summer institutes but also from their own classrooms. These early network participants described their experiences:

Since 1992, other math networks have been established, such as the Middle School Algebra Network, the Geometry Network, the Advanced Math Network, and the Pittsburgh Urban Mathematics Project (PUMP) Network. Network members meet two to three times a month, guided by UWM faculty who work with teachers to give the networks a more formal structure. All but one of the networks are classified as semester or full-year UWM courses through which participating teachers earn undergraduate college credits. Ideas that emerge from the networks are helping to provide classroom tools and to shape policy for the district. For example, early work from the Algebra and Geometry networks produced model exams that were distributed to teachers throughout the district for use in helping to define the content of those courses. Similarly, when the High School Algebra Study Group merged with the Middle School Algebra Network to form the Algebraic Reasoning course in the fall of 1997,³⁷ participants were given responsibility for designing five exemplar performance tasks for the district’s eighth-grade proficiencies. ³⁸ Participation in the network courses is open to any teacher, and an average of 15 to 20 teachers enroll annually in each course. For participating in the networks, teachers receive a stipend paid through federal Eisenhower funds. ³⁹ MUSI resources also serve to support teacher networking activity.

Retooling Teachers’ Classroom Practice

Principals and teachers reported that math classroom instruction had changed to some degree as a result of Equity 2000 professional development. Changes cited include increased use of calculators (including graphing calculators), manipulatives, and technology and less reliance on textbooks. While it was reported that whole-class, lecture-style instruction is still dominant, teachers felt they (and their colleagues) were integrating more student work with calculators and more project- and group-based learning activities as a result of Equity 2000. Principals and teachers also reported that the synergy between Equity 2000 and other district reforms — in particular MUSI and School-to-Work — created a climate of support for teachers to learn about, experiment with, and incorporate alternative approaches to instruction. Teachers, especially, talked not only about changes in classroom practice but also about changes in collegial exchange among teachers. The following comments reflect principals’ and teachers’ responses in this regard:

These statements are supported by the MPS Equity 2000 audit reports, which for high schools were generated annually from 1994 to 1997; middle school audits were conducted for two years starting in 1995.⁴⁰ The audits focused on implementation — specifically, how Equity 2000 strategies for math classroom instruction and guidance were being implemented in schools. In reviewing Equity 2000 high school audit reports conducted in 1994 and 1997, it appears that teaching practices which are encouraged by Equity 2000 have become more prevalent across high school Algebra I classes. Table 3 presents a point-in-time comparison of Equity 2000 audit findings on teaching practices used for Algebra I instruction. ⁴¹ These findings indicate that in 1994 the use of calculators was observed at most schools, and it remains a common technique among Algebra I teachers. The use of group work or cooperative learning was observed in a little more than half the high schools in 1994. By 1997, up to 90 percent of MPS high schools had a majority of Algebra I teachers who reported that they regularly used this teaching technique. Over this same time period, the use of manipulatives and computers in algebra classes appears to have also increased — from being observed in less than half the schools to reported use in all high schools. However, these increases could be considered modest, since use was generally reported to be seldom. ⁴² Probably the most dramatic change in teaching practices for Algebra I has been the integration of real-world applications. During the first year of the algebra-for-all policy, only three high schools were observed using this technique in Algebra I classes; in 1997, algebra teachers in all the high schools reported that they either frequently or regularly integrated real-world applications into their instruction.

Student Safety Net Supports

A key component of Equity 2000 is the provision of student safety net supports. Safety nets both (1) foster students’ motivation and enjoyment for learning mathematics through enrichment programs and (2) provide math tutoring and support or make-up classes for students who need extra help. As reported earlier in this paper, technical assistance provided by the Equity 2000 National Office involved identifying and enabling districts to implement established programs (such as the Saturday Academy) and strategies (like Algebra Readiness classes) for enhancing student academic achievement. In Milwaukee, Equity 2000 safety net activities include city-wide supports and local supports. City-wide supports are centrally coordinated by the district and include such activities as the Saturday Academies (for students and parents), tutoring services through the Math Buddies program, and the math summer school program. Local supports are school-based safety nets such as tutoring services before, during, and after school; algebra support classes; and midyear reprogramming options. Participation data presented in Table 4 show the variety and use of safety nets created through Equity 2000 since the initiative has been in place.

In total, the safety net support structures that MPS has created to enhance students’ mathematics achievement have the potential to serve a substantial amount of students. However, as the information presented below indicates, students’ motivation and incentives to take advantage of such opportunities must be addressed if the benefits of these activities are to outweigh their costs. MDRC was not able to obtain documented information on the impact of safety net support activities — that is, whether students who participated in safety nets actually performed better than a similar group of students who did not. ⁴³ If data are not available, the district’s investment in such activities warrants a closer look: For which students, and in what ways, are these safety nets successful in increasing achievement (especially among students who need the most help) in Algebra I and other measures of high standards in mathematics?