Optimizing Mathematics Achievement Through
Centrally Coordinated Instructional Reform
Patricia F. Campbell
Center for Mathematics Education
Department of Curriculum and Instruction
University of Maryland
College Park, MD 20742-1175
patc@umd.edu
Address presented at Optimizing Mathematics Achievement for All Students, the First Annual
Research Symposium of the Maryland Institute for Minority Achievement and Urban Education,
College Park, MD, September 23-24, 2004.
Some of the work reported herein was developed through the support of a grant from the
National Science Foundation under the project title, “Mathematics: Application and Reasoning
Skills” (Grant No. ESI 95-54186). Any opinions, findings, and conclusions or recommendations
expressed herein are those of the author and do not necessarily reflect the views of the National
Science Foundation.
Steven Kramer completed the statistical analyses reported herein, under the auspices of the NSF
grant referenced above. The author is grateful for his assistance and contributions. The
Baltimore elementary mathematics reform effort was conceived and guided by Andrea Bowden,
was coordinated in the Baltimore City Public School System (BCPSS) by Melva Greene, and
benefited from the efforts of Grace Benigno, Duane Cooper, Donnette Dais, Thomas Rowan,
Felice Shore, Marilyn Strutchens, Anne Wallace, and the BCPSS’s Instructional Support
Teachers for Mathematics. The author acknowledges the input and backing of each of these
individuals.
The author developed the six BCPSS Elementary Mathematics Curriculum guides referenced in
this manuscript, incorporating the input and review of BCPSS personnel.
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2
Optimizing Mathematics Achievement Through Centrally Coordinated Instructional Reform
“The harsh reality is that our educational system produces starkly
uneven outcomes. Although some students develop mathematical
proficiency in school, most do not. And those who do not have
disproportionately been children of poverty, students of color,
English-language learners, and, until recently, girls.”
(RAND Mathematics Study Panel, 2003, p. 10)
May 2004 marked the passage of 50 years since the landmark Supreme Court decision
Brown vs. Board of Education of Topeka, Kansas. While access to public schooling is
essentially established in the United States, equity of access to quality public education, the
promise of the Brown vs. Board of Education ruling, is not. While federal educational policy
espouses a commitment to reducing the achievement gap through the No Child Left Behind Act
of 2001 (NCLB), currently the primary positive impact of NCLB has been

raising the general public’s recognition that federal legislation may influence educational
decisions at the state and district level and

documenting schools’ disaggregated student achievement data in mathematics and
reading across demographic groupings defined by race and ethnicity, poverty, Englishlanguage proficiency, and special education status.
Public documentation of disaggregated student achievement data may be interpreted as a positive
force because it has pushed schools and districts that were satisfied with their aggregated
achievement levels to openly acknowledge achievement gaps, a first step in marshalling the
collaborative resolve necessary to seek solutions, to implement reform, and to stop
systematically under-educating students. Unfortunately, in the past, public knowledge of
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achievement gaps in national or state data disaggregated by race and ethnicity, English-language
status, or urban-suburban-rural school district location has not led to widespread change
supporting the education of marginalized students. The challenge implicit in the Brown ruling
and explicit in the title of NCLB is not for the citizenry simply to acknowledge the existence of
achievement gaps, but for public education to change in such a way that it yields equity in the
distribution of educational outcomes, regardless of students’ demographic characteristics and
geographic locale. This will not happen unless and until the instructional program in each school
in every district supports quality teaching and learning.
NCLB has focused attention on student achievement in reading and mathematics as
measured by standards-based assessments that are standardized within states. While educational
standards are a component of strong instructional programs, as are standardized measures of
student achievement, these elements alone will not yield increased student achievement. Indeed,
“teachers and students, and features of their environment, are the active agents of instruction”
(Cohen, Raudenbush, & Ball, 2003, p. 134). This paper proposes that equity in the distribution
of educational outcomes demands change in the reality of instructional practice experienced and
defined by these agents. For mathematics learning, this means addressing each component of the
curriculum-professional development-instruction-assessment-policy network that constitutes an
instructional program for mathematics within a school and a school district. The first section of
this paper defines and offers a rationale for this perspective referencing background material
addressing educational reform, while the second section of the paper offers a characterization of
the possible effects of this perspective by examining a district-wide reform initiative for
elementary mathematics that was based on this model. Finally, the paper concludes with a
discussion of implications.
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There are many factors both inside and outside of the classroom that influence teaching
and learning in the reality of public schooling. Not the least of these are school conditions (e.g.,
Carroll, Fulton, Abercrombie, & Yoon, 2004; Snipes, Doolittle & Herlihy, 2002), school-familycommunity connections (Boethel, 2003), and constraining social forces (e.g., Knitzer, 2002).
While this paper addresses implications for student achievement in mathematics through a lens
focused on curriculum and instruction, it acknowledges the influence and complexity of factors
that are not considered in this presentation, including the economic, social, and cultural aspects
of learning and schooling.
Educational Reform
Systemic Reform
Historically, individual schools and school districts have adopted numerous school
improvement projects or programs, often simultaneously. Frequently these efforts were
fragmented and inconsistent, possibly even conflicting with other school practices or with state
and district policies that were concurrently in effect. In 1991, Smith and O’Day called for a
“systemic” vision of educational reform that coordinated policy with governance in order to meet
bold goals for student learning and achievement. State curriculum frameworks were to define a
vision for improved curriculum and instruction across all schools, drawing on a broad
participatory process to garner input. Schools were to have flexibility in framing and applying
strategies for meeting these higher expectations, along with the resources to meet this
responsibility. State education policies were to be aligned so teacher licensure, textbook and
resource adoption, state assessments, and funding formulas reinforced and sustained local efforts.
In theory, systemic reform had a laudable purpose: “to upgrade significantly the quality
of the curriculum and instruction delivered to all children” (O’Day & Smith, 1993, p. 251).
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Recognizing that pedagogical expertise and material resources are not equally accessible in all
schools, systemic reform, as defined by Smith and O’Day, did not simply rely on the efforts of
individual restructured schools, because there was little confidence that schools of poverty had
the knowledge or capacity to improve. Rather, their vision of systemic reform relied on “the
reinforcing effect of the alignment of the parts of the system and of enhanced professional
conversation around a shared set of content goals” (O’Day & Smith, 1993, p. 269). But these
authors challenged that even more was possible through systemic reform, noting:
Common content and alignment of key components of the system provide a basis for
identifying the necessary core of appropriate resources and practices and for determining
whether they are of sufficient quality for providing all students the opportunity to learn
the challenging material of the curriculum frameworks. (O’Day & Smith, 1993, p. 275)
In other words, they conjectured that if systemic reform was implemented, evaluation of the
quantity and quality of resources and practices such as curriculum materials, professional
development, and instructional approach could inform school improvement and expose
inequities in students’ opportunity to learn. Further, quantification of the quality and availability
of resources and of the quality and nature of implemented practices would permit examination of
the relationship between these variables and student achievement.
Has the promise of systemic reform as a mechanism for educational opportunity
materialized? In practice, to a substantial degree, state curriculum frameworks are aligned with
standardized assessments, although the cost and availability of standardized assessments have
frequently been the driving forces shaping curriculum content rather than curriculum content and
processes defining aligned assessments. But the remaining components of systemic reform are
not uniformly evident, particularly in schools and districts that enroll many low-income students
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and students of color. While NCLB has raised the stakes for schools, teachers, and students, this
increased responsibility to meet state and federal expectations has not been met with increased
resources (e.g., Carey, 2002), even though, theoretically, sufficient resources are a feature of
systemic reform and of NCLB. However, because NCLB has pushed states to specify content
goals and to specify standardized measures for evaluating expected achievement, it is now
possible to model relationships between student achievement and resources.
Recent formulations have established that the fiscal resources required to achieve student
performance standards in reading and mathematics will vary across schools. Schools with
substantial numbers of low-income or limited-English-speaking students may require over twice
as much funding per student to achieve an average student performance level as compared to
schools enrolling students who traditionally have met these performance standards. Further, this
funding increase must be maintained over time (Commission on Education Finance, Equity and
Excellence, 2002; Reschovsky & Imazeki, 2003). Unless funding for instructional reform at the
state and federal level extends beyond curriculum standards and assessments and helps districts
meet the actual cost of supporting students’ attainment of those standards—including
instructional materials and resources, teacher preparation and licensure, professional
development, and local capacity building—the promise of systemic reform as a mechanism for
addressing achievement gaps is severely limited. But funding alone is not enough.
The implication of systemic reform’s reliance on the “reinforcing effect” of alignment
and “enhanced professional conversation” (O’Day & Smith, 1993) is that funding must be
allocated in ways that support teachers’ capacity for and students’ engagement in significant
instructional reform. Otherwise, educational and political leaders may find themselves in the
unacceptable and illegitimate position of holding students and teachers accountable for meeting
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high standards that their preparation and resources cannot address.
Instructional Program Coherence
Instruction is ultimately delivered in classrooms within schools. The impact of wholeschool reform programs and state policies on instructional practice can vary widely from school
to school. Noting this, Newmann, Smith, Allensworth, and Bryk (2001) coined the term
“instructional program coherence” to signify the degree to which a school implemented “a set of
interrelated programs for students and staff that are guided by a common framework for
curriculum, instruction, assessment, and learning climate and that are pursued over a sustained
period” (p. 297). In elementary schools, a common instructional framework includes not only a
specification of curriculum objectives across subjects, but also curricular resources, specified
instructional strategies, and student assessments that are coordinated within and between grade
levels, with all teachers at each grade level supporting each other’s implementation of the
framework. At the secondary level, instructional program coherence may be more important
within a given subject (such as mathematics) and between courses in that subject (such as
Algebra I and II), with teachers of a given course supporting each other’s implementation.
In order to maintain focus, instructional program coherence also calls for alignment of the
content and approaches within school-sponsored auxiliary efforts with the framework. For
example, the approaches taken or discussed in efforts such as student support programs or parent
engagement sessions should be aligned with the in-school academic program. Administrators of
schools with instructional program coherence use expertise in executing the framework as their
standard for recruiting, hiring, and evaluating teachers. Professional development is sustained,
consistently addressing aspects of the framework; school-based resource allocation eliminates
competing approaches and advances school-wide implementation of a specified perception of
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curriculum and instruction. A key to instructional program coherence is coordination of
instruction because “it requires extensive, continuing communication among teachers, mutual
assistance, and working together to improve instruction according to the framework” (Newmann
et al., 2001, p. 312). As defined by Newmann and his colleagues, instructional program
coherence does not address educational policy beyond a local school, although these authors
admit that federal, state, or district policy could advance, destabilize, or be extraneous to
instructional program coherence. Thus, systemic reform initiatives may or may not impact
instructional program coherence.
Initial evidence collected at 11 predominantly minority elementary schools in Chicago
indicated that elementary schools with substantial instructional program coherence, as measured
along a continuum from low to high coherence, also had significantly increased gains in student
achievement on standardized tests of reading and mathematics over a 4-year period, roughly
equivalent to two additional months of schooling per year. This study also noted a significant
negative relationship between instructional program coherence and school size, the percentage of
low-income students, and the percentage of non-White students (Newmann et al., 2001). In this
sample, schools with high levels of instructional program coherence also had strong principals
who promoted collaboration and focused resources on a few school improvement goals over 3 or
more years. However, instructional program coherence does not guarantee professional
community or shared in-school responsibility for student learning nor does it presume academic
potency, as a narrowly focused and regimented instructional program could have high coherence,
as could a professionally rich program marked by academically challenging instruction.
What are the implications of instructional program coherence for student achievement?
First, coordination across curriculum content, instructional approach, professional development,
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instructional materials, and assessment is important. For mathematics achievement, this is
critical because today’s learning goal is for students to develop a deep, broad, and connected
understanding of mathematics that integrates “conceptual understanding, procedural fluency,
strategic competence, adaptive reasoning, and [a] productive disposition”1 (Kilpatrick, Swafford
& Findell, 2001, p. 11). This cannot occur unless instruction supports the learning of this logical
and increasingly complex content over time, from one grade or course to the next, along a
coherent learning trajectory (Simon, 1995). Although, theoretically, instructional program
coherence could pertain to any curriculum, if students are to develop mathematical
understanding of demanding content, then the academic integrity of the educational program
being implemented is crucial. Further, teachers will need to know more mathematics and to reconceptualize their perspective of what it means to learn and teach mathematics for
understanding to all students, not just to some students. This not only means that professional
development addressing mathematical content and pedagogy is needed, but also that professional
development must connect with practice, build communication between teachers, provide for
collaboration, and be sustained over time. Aligned assessments and instructional materials need
to be available and stable so that they promote curriculum implementation and clarify further for
teachers exactly what is expected in terms of mathematical learning by all students. Finally,
teachers and administrators need time to learn, to ask questions, and to develop expertise.
Instructional Program Coherence and Equity
There are indicators that instructional program coherence may not be sufficient to yield
equity in the distribution of educational outcomes. In the Newmann et al. (2001) study, even
though all 11 schools were participating in a 5-year initiative to support whole-school reform,2
there was a significant negative relationship between instructional program coherence and school
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size, the percentage of low-income students, and the percentage of non-White students. That is,
despite the presence of funding for whole-school reform through a variety of “selected”
approaches, instructional program coherence did not necessarily emerge. And, it was less likely
to emerge in larger schools and in schools with a greater proportion of low-income and/or
minority students. This means that school-by-school reform may not be sufficient to generate
equity in student achievement as schools with greater numbers of previously marginalized
students may in fact be the very schools that are less able to define and implement coherent
change, much less maintain and sustain improvement. For mathematics achievement, the
probability of success through individual school improvement efforts is even less likely as many
local schools simply do not have “organizational capacity” for mathematics reform (Newmann,
King, & Rigdon, 1997; O’Day & Smith, 1993; Price & Ball, 1997).
For urban centers, there is another concern with relying on school-defined reform.
Student and teacher mobility in urban centers is high. If urban schools have differing
instructional programs that address and sequence mathematics content uniquely, the curriculum
and instructional approach experienced by transient students will be fragmented and possibly
inadequate, limiting their achievement. As teachers of mathematics move between schools in an
urban district, they may find themselves experiencing professional frustration that may even lead
to resignation, as they are expected to learn to teach in yet another program that does not
complement their prior approach. It is very difficult to sustain reform and to support academic
achievement without continuity of staffing (Carroll, Fulton, Abercrombie, & Yoon, 2004).
This is not to say that a common framework for curriculum, instruction, assessment, and
professional development is not important, it is, and the delivery of any instructional program
ultimately occurs in individual schools and classrooms. Indeed, educational reform is enhanced
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if teachers collaborate within a school. However, as noted by Fullan (2001), while
it is possible for an individual school to become highly collaborative despite the district it
is in, … it is not likely that it will stay collaborative. If the district does not foster
professional learning communities by design, it undermines them by default. (p. 165;
emphasis in original)
It is the school district that must reconcile state standards for instruction as well as state and
federal expectations for student achievement with local context and community pressures. As
such, districts matter not only because they might guide, support, or inhibit their schools’ efforts
toward reform, but also because effective district engagement is critical for maintaining
successful reform (Elmore & Burney, 1999; McLaughlin & Talbert, 2003; Spillane &
Thompson, 1997). If mathematics reform is to support student achievement for all learners, then
it needs to be instituted and coordinated centrally at the district level, accessing input across a
broad spectrum of participants, and then it needs to be carried out locally.
Fostering Local Implementation of Mathematics
Reform Through Central Coordination
So how might one conceptualize a centrally coordinated mathematics reform effort that
would foster school-based implementation of a coherent curriculum addressing rich
mathematical content in order to yield equity in increased student achievement? Borrowing from
the definition of school-level instructional program coherence (Newmann et al., 2001), centrally
coordinated reform would need to incorporate curriculum standards with the expectation that
instructional approaches, instructional materials, and assessments would be aligned and
consistently implemented to support student achievement of mathematics content and process
objectives. But, as suggested by systemic reform’s perspective of the role of curriculum
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standards, a district’s mathematics curriculum framework should not be so specified that it would
eliminate teachers’ professional judgment as to how to teach their students. Yet, it should
characterize “good teaching of worthwhile mathematics” (Porter, 1989, p. 354). A district’s
framework should not require a fixed sequence of pre-planned lessons nor demand the rigidity of
specific textbook pages each day. But it should organize grade-level mathematics content and
process objectives into units of instruction, characterizing instructional focus, suggesting pacing
guidelines, and referencing aligned, available commercial resources. It may also reference state
standards.
If purchased in sufficient quantities, district adoption of aligned commercial textbooks,
appropriate technology, and manipulative materials would not only make instructional resources
available to all classrooms, it could also communicate to teachers that mathematics instruction
and achievement as delineated by the curriculum framework are important and expected. The
integration of a curriculum framework and instructional resources with district-wide and schoolbased professional development could further disseminate the message and the spirit of a reform
initiative while providing teachers opportunities to learn that are grounded in schooling (Cohen
& Hill, 2000; Spillane, Diamond, & Jita, 2003).
To foster local implementation, not only would it be necessary for professional
development to enhance teachers’ understanding of mathematics content and to focus on
teachers’ and administrators’ understanding of and perspectives on mathematics curriculum,
pedagogy, and assessment, the professional development would also have to address how to
situate this reform in each school’s social, economic, and geographic context. Because
professional development would need to be relevant to practice and to establish a knowledge
base for instructional decisions, it may need to be both district wide and school based. To meet
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the challenge of school-based professional development, some schools may decide to identify
exemplary teachers for release from instructional responsibilities to serve as on-site mathematics
specialists, team leaders, or department chairs. Typically these individuals are expected to
provide instructional support and to foster teachers’ professional growth within schools while
encouraging a “stronger sense of agency and collective efficacy” (Strahan, 2003, p. 142).
Newmann et al.’s (2001) definition of instructional program coherence included schoolbased administrative dimensions such as stability of assessments, allocation of funding,
provision of professional development, scheduling of time, and evaluation of teachers. But a
centrally coordinated mathematics reform effort would also demand central office engagement
with issues of curriculum and instruction. District-level administrators could support the extent
and impact of instructional improvement by coordinating access to internal and external
expertise, organizing the development of a common, district-wide curriculum framework for
mathematics, coordinating the design and delivery of sustained professional development to
support implementation of that framework, developing and enhancing mechanisms for on-site
professional support, and participating in the development of standardized assessments. District
policy would advance instructional reform if it established standards for both teachers and
administrators for participation in professional development addressing mathematics curriculum
and instruction, defined expectations for on-site professional support, set expectations for
grading, established criteria for recruiting, hiring, and mentoring teachers that emphasized
commitment to instructional improvement, included framework implementation in definitions of
instructional accountability, used the framework to establish student accountability goals, and
allocated district resources to support instructional improvement.
Figure 1 presents a conceptual model depicting how a curriculum framework,
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Student
Achievement
District-wide
Student
Assessments*
Administrative
Support*
Instruction
District
Curriculum Framework*



Objectives Aligned with
State Assessments
Instructional Model
Units of Instruction
School-based
Professional
Development*
Instructional
Materials*
District-wide
Professional
Development*
* Development, content, and/or implications for use influenced by district-level policy
Direction of influence in development or use
------ Alignment
Figure 1: Conceptual model for district-wide instructional reform
School
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instructional materials, professional development, and administrative support may impact
instruction as evidenced by improved student achievement. This model presumes that the
content and credibility of professional development is influenced by the availability and content
of instructional materials as well as by a district’s curriculum framework; similarly it presumes
that teachers’ use of commercial instructional materials and the district’s curriculum is
influenced by professional development. Adopted commercial instructional materials must align
with the objectives in the curriculum framework. District-wide student assessments must be
aligned with the curriculum and are presumed to influence instruction. But underlying this
model is the assumption that professional development is key, because teachers are “relatively
autonomous professionals” (McLaughlin, 1987) and unless there is a change in the way that
teachers teach, there will be no improvement in student achievement.
Elementary Mathematics Reform in an Urban District
From 1996-2002, the Baltimore City Public School System (BCPSS) engaged in a
district-driven systemic reform effort addressing K-5 mathematics that eventually was made
available to 87% of the public elementary schools in Baltimore. As such, it offers insight into
how an urban district defined a targeted reform effort and how the differing components of this
reform did or did not work together to impact student achievement in mathematics.
Background
In 1995, BCPSS operated under a school-based management plan where funds were
distributed directly to local schools from the Baltimore City Council through a dollar-per-pupil
allocation. While there was a nominal district-wide mathematics curriculum, schools had
complete autonomy. Although Maryland had developed a standards-based assessment system
termed the Maryland School Performance Assessment Program (MSPAP), BCPSS had not
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adapted. A 1995 needs assessment revealed that although the Maryland State Department of
Education had released mathematics objectives for the MSPAP in 1990, the BCPSS elementary
mathematics curriculum was not in alignment in terms of either content or instructional
approach. There were no system-wide assessments for elementary mathematics.
The last district-wide purchase of elementary mathematics textbooks in the BCPSS had
occurred in 1987. Under site-based management, textbook purchases constituted local,
discretionary expenditures. Many elementary schools simply had no commercial mathematics
textbooks, and most schools had no manipulative materials in 1995. Across those elementary
schools that had purchased mathematics textbooks independently, there was no uniformity.
There was no district-wide professional development for K-5 mathematics in 1995-96.
While there were 121 elementary schools in BCPSS, professional development addressing
elementary mathematics was only available to teachers from 17 schools through a 7-day summer
institute supported by the Baltimore Urban Systemic Initiative and Title II (Eisenhower) funds
and through classroom demonstration visits as offered by three visiting teachers.
Elementary mathematics achievement as measured by the MSPAP and the
Comprehensive Tests of Basic Skills Version 4 (CTBS/4; CTB/McGraw-Hill) was quite low,
and, by 1996, 28 elementary schools had been named as eligible for State reconstitution,
requiring submission of annual plans for school improvement as well as oversight from the
Maryland State Department of Education.
To address the need for elementary mathematics reform, a working collaboration was
forged between the Baltimore Urban Systemic Initiative, BCPSS, and the University of
Maryland. BCPSS and the University of Maryland successfully sought additional funding from
the National Science Foundation to address K-5 mathematics in Baltimore and then coupled
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these funds with revenue from the Baltimore Urban Systemic Initiative, Title II grants, Title I
allocations, City-State Partnership authorizations, local schools’ discretionary sources, and
University of Maryland cost sharing. The City-State partnership was a federal court-mandated
plan that brought increased State funding to BCPSS for 5 years and established a new schooldistrict management partnership, effectively ending autonomous school-based management.
The elementary mathematics reform effort in BCPSS was instituted and coordinated
centrally, but carried out locally. Leaders of the centralized initiative believed that while local
school personnel did not know how to improve, it was not because they lacked the will to
improve. Elementary teachers and administrators across Baltimore knew something had to
change, and they were willing to consider change, but only if they believed the proposed
mechanisms for reform were credible.
Components of the Reform (1996-2002)
Over time, the BCPSS elementary mathematics initiative incorporated a number of
interrelated components: curriculum development aligned with Maryland’s high stakes
objectives, a revised instructional model, purchase of instructional materials, professional
development, student assessment, and increased school-based instructional and administrative
support. While BCPSS directors and officers, primarily in the Division of Curriculum and
Instruction, met periodically with leaders of the elementary mathematics initiative, including the
supervisor of science and mathematics and the elementary mathematics coordinator, to discuss
issues related to elementary mathematics in BCPSS, district policy decisions regarding the
elementary mathematics program were ultimately the responsibility of centralized leadership in
BCPSS, not the reform effort.
Curriculum Guides. One of the major components of the reform effort in BCPSS was the
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development of grade-specific, elementary mathematics curriculum guides. Too often the
“conventional wisdom” is that curriculum in high poverty schools should follow a fixed
sequence of lessons, emphasizing practice and moving from basic to more advanced skills.
While this approach was adopted via a Direct Instruction program in 13% of the elementary
schools in BCPSS, the BCPSS curriculum guides developed in 1997 offered a different
approach, addressing the content and process objectives3 of the MSPAP as well as computational
proficiency. Each grade-specific curriculum guide presented a K-5, developmental sequencing
of big ideas and instructional objectives for each mathematical topic and process, as well as
grade-specific units of instruction, noting placement and duration as well as clustering and
ordering of the grade-level process and content objectives. The units of instruction also offered
sample instructional tasks that served to clarify the instructional goals of each unit. Revised
guides issued in 2000-01 re-ordered some of the units of instruction while modifying each of the
units to reference MSPAP objectives as well as page numbers from the adopted textbooks. The
revised guides also included a glossary defining mathematical terms and vocabulary.
Instructional Model. The instructional approach outlined in the curriculum guides and put
forward in the professional development portrayed students and teachers working together to
“make sense” of mathematics. Based on a number of principles in the National Council of
Teachers of Mathematics’ Professional standards for teaching mathematics (1991), teachers
were encouraged to shift their instruction from a show-and-tell or demonstrate-and-practice
model to an approach that emphasized asking questions and questioning answers. Lesson
planning for this instructional approach included preparation of specific questions to serve one of
three different purposes that would occur over the course of a lesson: guiding analysis of the
mathematical task, problem or abstraction under discussion; fostering or challenging student
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understandings of the mathematics content; and drawing attention to the mathematics implied by,
or probing the reasoning underlying, student solutions.
Instructional Materials. Due to financial constraints, no commercial materials were
referenced or purchased to support implementation of the initial curriculum guides when they
were distributed to schools in 1997. However, City-State partnership funds supported the
district-wide purchase of elementary mathematics textbooks4 and manipulative materials for
schools in 1999; the curriculum guides were the content standard applied during the review of
commercial textbook materials.
Professional Development. As noted by Cahnmann and Remillard (2002), professional
development in an urban center faces a dual challenge. Not only is it necessary for professional
development to enhance teachers’ and administrators’ understanding of mathematics content and
pedagogy, it is also necessary for professional development to address how to situate this reform
in urban schooling. For this reason, the organizational model for professional development in
the BCPSS elementary mathematics effort was both district wide and school based. Districtwide professional development included quarterly Saturday workshops, after-school workshops,
summer institutes, centrally located professional release workshops, and graduate courses.
School-based professional development consisted of grade-level planning meetings, professional
interactions between Instructional Support Teachers (ISTs) and individual teachers, and scripted
half-day workshops on professional release days. ISTs were exemplary elementary teachers
from within BCPSS who were released from classroom duties and assigned to one or two
schools for a period of 1 to 5 years in order to coordinate grade-level planning meetings and to
support individual teachers' efforts to interpret reform and to define and implement change in
practice. Initially identified through an annual district-wide application and interview process,
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ISTs were to facilitate implementation of the curriculum, to identify and unravel needs, to
provide instructionally focused leadership for improvement, and to foster a community of
practice. They also served as the instructional staff for most district-wide professional
development in BCPSS. ISTs met for their own professional enhancement with personnel from
the BCPSS Office of Sciences and Mathematics and from the University of Maryland; these
sessions provided a venue for sharing and learning as well as fostering a sense of ownership and
collective responsibility for shaping continued reform.
Student Assessments. Once the commercial instructional materials and revised curriculum
guides were in place, administrators across the BCPSS immediately began asking for aligned
district-developed assessments to provide information about the status of the elementary
mathematics program within schools and to respond to State expectations for standardized
accountability in reconstitution-eligible schools. In order to generate time, assessments from
McGraw-Hill’s Math in My World were administered in 1999-2000. These assessments were not
always aligned with instructional practice, were rarely aligned with the Investigations materials,
and did not measure some of the expectations in the curriculum guides. Subsequently, the
district developed unit assessments aligned with the curriculum. Containing both short answer
and constructed response items, these required assessments measured both short-term and
cumulative learning.
Policy. A number of policy directives addressing curriculum, professional development,
instructional materials, and assessment influenced the course and sustainability of the elementary
mathematics reform effort in BCPSS.
The court-ordered mandate forming the City-State Partnership required the distribution of
standards-based curricula to all teachers by the beginning of the 1997-98 school year. This
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21
meant elementary schools had to select either the Direct Instruction elementary mathematics
program or the elementary mathematics curriculum developed for the BCPSS reform effort.
While 108 schools5 selected the new BCPSS curriculum guides, the reform effort was not
prepared to provide professional development for this many teachers nor could it provide ISTs
for this many schools. At this time, only 51 schools had an assigned released teacher serving the
IST role for mathematics. In the 57 schools that did not have access to either professional
development or on-site support, the reform curriculum may have been perceived merely as a
detailed policy document.
The City-State partnership funds purchased reading and language arts materials in 1998,
and the 1998-99 school year was designated as the “Year of Reading.” In keeping with this
focus, the Chief Academic Officer limited the expansion of the elementary mathematics ISTs to
one additional school and ordered that no cross-site professional development addressing
mathematics instruction could be delivered during 1998-99, including quarterly Saturday
workshops, after-school workshops, and the graduate mathematics education course. The
professional development program generating new ISTs ceased to exist.
The purchase of the commercial textbooks in the summer 1999 ushered in the “Year of
Math.” BCPSS policy “strongly encouraged” all elementary mathematics teachers to attend one
of the five summer institutes offered in 1999, and 1,631 teachers from 102 schools did so. A
new Chief Academic Officer then reassigned the responsibility for appointing and supervising all
school-based personnel to principals, simultaneously requiring all reconstitution-eligible
elementary schools to include two full-time, IST-type positions in their school improvement
plans, one for mathematics and one for reading/language arts. Between the policy requiring fulltime IST positions in reconstitution-eligible schools, increased school interest in mathematics
Instructional Reform
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reform as generated by the summer institutes and the new textbooks, and the absence of
programmatic efforts to develop ISTs in the prior year, there was a shortage of mathematics ISTs
in 1999-2000. Qualified ISTs could only fill the positions in 55 schools. Because of the IST
shortage, because funding allocations for new ISTs were not permanent BCPSS lines (being
dependent on state reconstitution resources), and because the new policy on school-based
personnel meant that there was now no common district standard for ISTs, 14 principals
appointed already-released teachers in their buildings to provide on-site support for mathematics.
Unfortunately, district policy did not require these new leaders to participate in the reestablished, but somewhat limited, IST-enhancement opportunities. At the same time, 37
elementary schools still had no school-based support for mathematics instruction. However,
BCPSS re-instituted district-wide professional development for elementary mathematics, along
with a policy stating that every teacher of elementary mathematics was expected to attend 100
hours of professional development. Teachers responded, and attendance at district-wide
professional development sessions during 1999-2001 was high.
There were three other BCPSS policy initiatives that influenced the elementary
mathematics reform effort. At the start of the 1999-2000 school year, BCPSS instituted a policy
allowing students to take their new elementary mathematics textbooks home; this permitted
teachers to assign homework. At the same time, however, one area administrator established a
policy requiring 3 hours of reading instruction during the first 3 hours of each school day. This
policy not only impacted the timing of mathematics instruction, it also limited the availability of
time each day wherein ISTs could work with teachers and/or in classrooms to influence
mathematics instruction, while conveying an underlying message that mathematics instruction
was not important in that administrative area. This underlying message was somewhat lessened
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when a subsequent BCPSS policy linked student promotion, criteria for report-card grades, and
summer school identification with the district-wide unit assessments for mathematics. This
positively influenced implementation of the standards-based curriculum and its instructional
approach, while encouraging principals to attend to their schools’ mathematics program.
In 2001, yet another Chief Academic Officer proposed that each elementary principal
appoint two full-time release teachers, one to serve as a reading coach and one to serve as a
mathematics coach. This policy, as implemented in 2001-03, did establish nominal on-site
support for mathematics in every elementary school, and many former ISTs were re-titled as
coaches. However, this unfunded policy did not provide a mechanism for enhancing “newly
anointed” coaches.
The BCPSS central administration was re-organized in the summer 2002, eliminating all
content offices, including the Office of Sciences and Mathematics; all curriculum content
supervisors in BCPSS either retired or were reassigned to other responsibilities. Supervision of
curriculum and instruction, including sponsorship of any cross-site professional development for
either mathematics teachers or coaches, was shifted to regional administrative areas.
Impact of the Reform
At the start of the elementary mathematics reform effort in 1996, BCPSS enrolled 53,610
students in the elementary grades; the system was 85.6% Black/African American, 12.9% White,
0.6% Asian/Asian American or Pacific Islanders, 0.5% Hispanic/Latino, and 0.4% American
Indian/Alaskan natives (87.1% minority). Over the 6-year course of the effort, the elementary
student population in BCPSS declined by about 4,000 students; the percentage of Black/African
American students increased slightly (to 87%) while the percentage of White students declined
(to 11.5%) and the percentage of other race/ethnicity groupings remained constant. Throughout,
Instructional Reform
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only about 1% of the enrolled elementary students had limited English proficiency while the
percentage of elementary students accessing free or reduced lunch increased (from 69% to 74%).
This elementary mathematics initiative involved over 3,300 teachers in district-wide
professional development during 1996-2001 (see Table 1). Many teachers also benefited from
on-site professional development as offered by ISTs, but these data were not recorded. In 200102, there were 3,710 elementary teachers employed in schools using the BCPSS elementary
mathematics curriculum guides; 509 (13.7%) of these teachers were not listed as faculty in
Table 1
BCPSS Teachers Participating in Elementary Mathematics Professional
Developmenta With 2001-02 Employment Statusb
Hours of
Professional
Development
a
Teachers Participating
During 1996-2001
Participating Teachers
Percent of Participating
Remaining in
Teachers Remaining in
2001-2002
2001-2002
1-9
923
486
52.8
10-29
336
218
64.9
30-59
487
285
58.5
60-84
745
422
56.6
85-99
186
144
77.4
≥ 100
678
535
78.9
Total
3,355
2,090
63.0
These data include only district-wide professional development, not site-based professional
development.
b
Only teachers who attended professional development and who were employed at a school
using the BCPSS elementary mathematics curriculum for at least one grade are included in this
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table.
BCPSS at the start of the prior school year. Although all elementary teachers do not teach
mathematics, almost two-thirds of the veteran teachers (2,080 out of 3,201) had engaged in some
portion of the district-wide professional development sessions over the previous 5 years, as had
10 teachers hired mid-year in 2000-01.
A critical indicator of impact is student achievement, as assessed by standardized
measures. Two very different standardized assessments were consistently administered in
BCPSS over 1997-2001, characterizing student learning over a diverse span of mathematical
content. First, there was census administration of the CTBS/4 in May 1998 and 1999 and of the
CTBS/5 in March 2000 and 2001. In order to permit longitudinal analysis of these data across
Grades 1-5, CTB/McGraw-Hill provided equated scores over these measures. The term
TerraNova is used in this paper to describe these student achievement scores. Second, the
MSPAP was an integrated performance assessment annually administered each May in grades 3
and 5 that applied matrix sampling to yield a measure of a school’s level of achievement. For
this analysis, these MSPAP data were regrouped to reflect teacher participation in professional
development.
Considering the structure of the reform initiative, three questions may be posed.
1. Did district-wide factors other than professional development influence student
achievement in mathematics?
2. What was the effect of district-wide professional development, curriculum standards, and
aligned instructional materials on student achievement in mathematics?
3. Was there an additional impact on student achievement attributable to ISTs?
Influence of Factors Other Than Professional Development. To determine if factors other
than professional development influenced student scores on the TerraNova, the mean NCE
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TerraNova mathematics composite scores and the mean NCE MSPAP mathematics scores of
students whose teachers never attended any of the cross-site professional development sessions
were determined. As noted in Figure 2, as measured by TerraNova mean NCE scores, there was
a slight insignificant change in student mathematics achievement between 1997-98 and 1998-99.
But, between 1998-99 and 2000-01, there was a steady and substantial increase at each grade.
As shown in Figure 3, as measured by the MSPAP mean NCE scores, there was an insignificant
change in students’ mathematics achievement between 1997-98 and 1998-99. However,
between 1998-99 and 2000-01, there was a slight increase in the MSPAP mean NCE scores at
each grade, with this growth being somewhat more pronounced at third grade. Thus, factors
other than district-wide professional development had a positive influence on student
achievement in elementary mathematics in the BCPSS over 1999-2001. In particular, possible
60
Mean NCE Math
50
Grade 1
40
Grade 2
30
Grade 3
Grade 4
20
Grade 5
10
0
1998
1999
Year
2000
2001
Figure 2: Mean TerraNova NCE Total Mathematics scores of students whose teachers did not
attend professional development
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27
60
Mean NCE Math
50
40
Grade 3
30
Grade 5
20
10
0
1998
1999
2000
2001
Year
Figure 3: Mean growth in MSPAP NCE Total Mathematics scores of students whose teachers
did not attend professional development
influences include the placement of textbook resources aligned with the curriculum guide in
schools as of the fall 1999 and the introduction of common unit assessments, as well as policy
directives assigning ISTs and setting criteria for student promotion and grading.
Quantifying professional development. Because there was great variety in the forms of
professional development accessed by BCPSS teachers during this reform effort, the sessions
were qualitatively characterized as one of three types of professional development offerings:
Targeted Professional Development, Generic Professional Development, and the graduate
mathematics education course. Targeted Professional Development encompassed workshops or
institutes that integrated mathematics content with pedagogy, focused on identified objectives in
the BCPSS mathematics curriculum guides, were organized by grade level, and were taught by
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either an IST or a partner from the University of Maryland. Each of these characteristics held for
the professional development offerings that were termed Targeted. All remaining mathematics
education workshops and institutes were termed Generic. These included offerings such as minicourses enhancing teachers’ personal knowledge of mathematics, half-day workshops promoting
pedagogical approaches without reference to specific mathematics curriculum objectives, or allday conferences sponsored by the Maryland Council of Teachers of Mathematics.
Because a teacher could only complete the graduate mathematics education course once,
this independent variable was assigned a 0/1 metric. However, among teachers who attended the
other professional development offerings, there were large variations in attendance patterns. It
was necessary to define a measure that characterized a teacher’s engagement in the Targeted and
in the Generic professional development sessions in a given year as well as the distribution of
that teacher’s engagement in that type of professional development over time. This measure also
had to be independent of teacher effect. In order to do this, this analysis computed two metrics
(termed “Delta”). One Delta metric reflected a teacher’s attendance at sessions coded as Generic
Professional Development; the other Delta metric reflected a teacher’s attendance at sessions
coded as Targeted Professional Development. For a type of professional development, either
Targeted or Generic, Delta was defined as the difference between a cumulative measure of
professional development attendance that a teacher earned as of a given year and the arithmetic
average of that teacher’s annual cumulative measures over the number of years that the teacher
was employed in BCPSS. These measures of professional development attendance also had
criteria for a minimum threshold of attendance; teachers did not receive “credit for attendance” at
an institute or workshop if they attended less than 85% of the offering.
The analysis of the impact of professional development, within the context of aligned
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curriculum standards and instructional materials, was completed using a Cross-classified
Multilevel Model that reflected the four hierarchical levels of student, classroom, teacher, and
school, as well as within-classroom and within-teacher variance. This analysis examined the
relationship between student achievement as measured by students’ mathematics scale scores on
the TerraNova and the MSPAP with their teachers’ engagement in each of the three types of
professional development, estimating the value-added effect of professional development per
change in the Delta metrics or per completion of the graduate course.
Effect of professional development, curriculum standards, and aligned instructional
materials. The statistical analysis revealed that both the graduate mathematics education course
and the Targeted Professional Development had a statistically significant positive effect on
student achievement as measured by the TerraNova, while the Generic Professional
Development had a statistically significant negative effect. None of these forms of professional
development significantly influenced student performance on the MSPAP under a p < .05
criterion, although the Targeted Professional Development did meet a p < .10 standard (p =
.057), indicating a positive trend that was not statistically significant.
The analysis indicated that, on average, students of teachers who completed the graduate
mathematics education course had a 10.03 point improvement (p = .035) in their mathematics
scale scores on the TerraNova. Further, students’ scale scores on the TerraNova improved by
1.14 points for each point gain in Targeted Delta values earned by their teachers over time (p =
.002). What does that mean? Suppose a teacher was placed at a school in BCPSS without an
IST during 1997-98; as a result this teacher was not eligible to attend any BCPSS-sponsored,
district-wide professional development for mathematics in 1997-98. Suppose this teacher then
transferred to a school with an IST in the following year and attended the following Targeted
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Professional Development sessions: three Saturday workshops in 1998-99; the summer institute
and one Saturday workshop in 1999-2000; three Saturday workshops in 2000-01. This teacher’s
Targeted Delta values increase by 3 points each year. The statistical model predicted that the
value-added effect of this teacher’s attendance at Target Professional Development on his or her
students’ mathematics scale scores on the TerraNova will be another 3.42 points each year (i.e.,
a 3.42 point improvement in their scale scores in 1998-99; a 6.84 point improvement in 19992000; and a 10.26 point improvement in 2000-01). Further, the TerraNova scale score increases
associated with Targeted Professional Development are in addition to the scale score
improvement attributed to those other factors in BCPSS that were simultaneously positively
influencing student achievement in mathematics.
The significant negative relationship noted for the Generic Professional Development is
interesting. The statistical model predicted a mathematics scale score loss of 2.51 points on the
TerraNova for each Generic Delta point gain (p = .0003). Cohen and Hill (2000) reported that
professional development that did not directly address the content and pedagogy of the intended
curriculum for elementary mathematics had no discernable effect on student achievement, but
they did not find a significant negative impact. It may be that generic professional development
interferes with completion of the curriculum, negatively impacts instructional expectations, or
interrupts the coherence of the intended curriculum trajectory. Further investigation is necessary
to understand the implications of this result.
Effect of ISTs. All schools did not have ISTs to provide on-site support for mathematics
instruction and curriculum implementation. Further, as influenced in part by BCPSS policy,
there was high variability in the identification, expectations, and expertise of these released
teachers, and schools did not consistently employ them. Therefore, analysis of the influence of
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released teachers on student achievement in mathematics had to control for three factors: a
school’s tradition of mathematics achievement; the number of years that a school had a released
teacher for mathematics; and the released teacher’s expertise as an instructional support for
mathematics instruction.
To adjust for a school’s tradition of achievement, 1996 MSPAP mathematics scores were
used as a control variable. To monitor tenure, a variable indicating the numbers of years that a
school had a released teacher for mathematics was noted. Finally, the released teachers were
rated in terms of their understanding of both mathematics content and the intended pedagogical
reform and as well as their effectiveness in working with teachers. Based on these ratings, 18
“top ISTs” were identified.
Because years of “top IST” access was factor in this analysis, the student achievement
data that were of interest were the mathematics scale scores from the spring 2001 administrations
of the TerraNova and the MSPAP, when it was possible for a school to have had on-site support
for mathematics for as long as 4 years. There were 43 schools with a release teacher for
mathematics in 2000-01 who was not a “top IST.” There were 11 schools who had a “top IST”
in 2000-01, but persons with this level of expertise had only been assigned to school for 1 or 2
years (2 schools and 9 schools respectively). There were no schools that employed a “top IST”
for exactly 3 years, so this length of tenure was not included in the analysis. There were 7
schools that had a “top IST” assigned for 4 consistent years ending in 2000-01. Finally, in 36
schools, there was no release teacher for mathematics in 2000-01.
A comparison of student achievement in 2000-01 revealed no significant difference
mathematics scale scores from either the TerraNova or the MSPAP between schools that had a
release teacher for mathematics who was not top rated, schools that did not have even this
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support, and schools that had a top-rated IST for only 1 or 2 years. Released teachers to support
instruction in mathematics only had a significant effect on a school’s mathematics student
achievement, and then only as measured on the TerraNova, when highly knowledgeable ISTs
were assigned to provide support for teachers in that school for 4 years. The statistical model
predicted that knowledgeable ISTs brought a value-added effect of an improvement of 9.89
mathematics scale score points (p = .009) on the TerraNova, an increase beyond that attributable
to teachers’ engagement in Targeted Professional Development, the graduate mathematics
education course, and other factors in BCPSS supporting mathematics achievement. Additional
analyses confirmed that this significant effect on student achievement was due to schools’ access
to a top IST for 4 years, not to some unknown but unique features within those schools.
Implications
The implication that may be drawn from the analysis of the Baltimore data is that a
centrally coordinated mathematics reform effort in a predominantly minority urban district
marked by poverty can foster school-based implementation of an aligned curriculum framework
addressing rich mathematical content in order to yield increased student achievement. The “parts
of the system” in Baltimore’s elementary mathematics reform effort included a coherent
curriculum defining challenging yet balanced content, an explicit instructional model, aligned
instructional materials and resources, continuing targeted professional development, aligned
assessments, and district policies that encouraged school implementation. Targeted professional
development in this initiative integrated mathematics content and pedagogy, was focused on
BCPSS mathematical expectations, addressed the implications of those expectations for
instructional decisions, and emphasized the BCPSS instructional model. This form of
professional development positively influenced student achievement when it was consistently
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attended by teachers, targeted the responsibilities of the teachers, and was delivered by personnel
knowledgeable of mathematics content and pedagogy and familiar with the demands of teaching
in the BCPSS. The integrated components of the systemic effort as defined in Baltimore had a
significant, positive, value-added impact on student achievement in mathematics that was not
evident when components of the reform effort were isolated (inconsistent on-site support;
instructional support evidencing minimal expertise in mathematics content and/or pedagogy;
sporadic attendance at professional development; curriculum standards and
textbook/instructional resources without professional development; professional development
addressing mathematics content or pedagogy that is not connected to the curriculum). The
implication of the Baltimore initiative addressing elementary mathematics is that school-based
instructional support teachers who have a strong understanding of both mathematics content and
the standards-based curriculum and pedagogy and who are skilled teacher leaders/professional
developers can yield an additional increased positive influence on mathematics student
achievement, but only if classroom teachers have support teachers of this caliber in their schools
for several consecutive years.
The reform effort in Baltimore overlapped with many of the components of Newmann et
al.’s (2001) perspective of instructional program coherence. This coherence was most evident to
teachers within the pacing and clustering features of the BCPSS mathematics curriculum guides.
Not only did the curriculum guides clarify goals and set high expectations, they also presumed
that teachers would make decisions as to how to meet these goals in their classrooms.
Professional development was necessary because it increased teachers’ understanding of their
students’ mathematical thinking as well as teachers’ own knowledge of mathematical content
and pedagogy, but it was effective only when it connected these understandings to the
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34
curriculum, instructional model, and textbook resources and when it addressed implications for
implementation in the reality of BCPSS schools.
District involvement was critical in this reform effort, not only because it relied on the
adoption and promotion of a common instructional framework, but also because of simultaneous
school reform efforts instituted by BCPSS. In particular, City-State Partnership funds allowed
the purchase of commercial textbooks and instructional resources in 1999 and, in many schools,
State or district resources funded on-site support positions for mathematics. The development of
standards-based assessments occurred because elementary school principals and area-based
administrators called for them. In addition, all of the former piecemeal improvement efforts
addressing elementary mathematics in the participating elementary schools were stopped; no
new acquisitions were permitted unless they advanced the instructional framework. This central
administration resolve was critical not only for district-wide acceptance of the initiative’s
standing in the BCPSS, but eventually for the effort’s success. While schools varied in how or
whether they supported the reform effort’s vision of mathematics teaching and learning,
competing or diffuse approaches to mathematics instruction were not being introduced. This
coherence could not have evolved without the support and understanding of the BCPSS
administrators and policy makers. Further, both the funding base and the BCPSS administration
permitted mathematics educators within the central office, ISTs, and teachers time to learn. As a
result, not only was there continuity, but there was also opportunity for sustained professional
improvement.
Although the centrally coordinated reform effort as exemplified in Baltimore only
addressed elementary mathematics curriculum and instruction, there is no reason to believe that
the principles underlying this approach could not be applied to mathematics reform within the
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middle school or high school. Indeed, the importance of having district efforts support the
development of a coherent curriculum framework addressing a trajectory over the entire span of
kindergarten through 12th-grade mathematics would seem to be critical.
The scope of this paper has not addressed the role of the local principal in instructional
reform, although as noted by Newmann et al. (2001) and others, school-based leadership is
critical in a reform effort. Principals define on-site policy, determine where to invest
discretionary resources, foster or hinder staff collaboration and efficacy, and influence parentcommunity involvement. Indeed, anecdotal evidence drawn from the reform effort in Baltimore
emphasized the critical role of the principal while at the same time establishing that, in a districtwide initiative, re-assignment of the principalship need not short circuit on-site reform.
While the federal and City-State funding that helped support the elementary mathematics
reform effort in Baltimore ended with the close of the 2001-02 school year, thus far student
achievement in elementary mathematics in BCPSS has continued to improve (see Figure 4). Yet,
central administration re-organization and severe funding shortfalls in BCPSS have left the
elementary mathematics program splintered, relying on the perspective of regional officers and
school-based leaders. Unfortunately, the central, district-level coordination that catalyzed and
sustained the elementary mathematics reform effort, in spite of multiple, high-level
administrative changes in personnel, is no longer evident in BCPSS. District-wide Targeted
Professional Development offerings are no longer in place. Further, state-level redefinition of
the timing for administration of the standardized assessments responding to NCLB has opened
the door for schools to uniquely define the pacing and clustering of mathematics objectives in the
curriculum, a challenge that BCPSS is now addressing.
It is not sufficient to simply rely on local schools to effect the change needed to meet the
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70
Median National Percentiles
60
50
1998
1999
2000
2001
2002
2003
40
30
20
10
0
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Figure 4: BCPSS median national percentiles of TerraNova Total Mathematics scores
national challenge of the achievement gap. The implication of the elementary mathematics
initiative in Baltimore is that reform yielding equity in the distribution of student achievement
will require sustained district leadership that focuses on a challenging curriculum framework
with an aligned instructional model, that supports and monitors school-based implementation,
and that inhibits interference from this single-minded emphasis on instructional reform, yet
honestly and openly reflects on current status to define mid-course corrections while remaining
cognizant of the implications of state policies. Spillane and Thompson (1997) suggested that for
a district to develop the capacity for change, the leaders who take responsibility for instructional
reform in a district must be committed to the premise that the reform is important not simply
because of a mandate for improvement, but because, when implemented, the reform will result in
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37
individual students and teachers engaging with the subject matter during instruction in a more
exciting, challenging, and productive manner. They also declared that local reformers need to
have a disposition to continue to learn about improving instruction and fostering reform,
recognizing that there will always be much more to learn. This occurred in Baltimore where
local leaders and outside experts developed a shared commitment that matured into a mutual
obligation to support and learn from each other in order to advance the reform initiative so that
teachers and students could “do better.” That is the real key to unlocking and sustaining the
promise of instructional reform, as we already know much about how to address the achievement
gap in mathematics. The question is: Do we have the resolve to put what we know into practice
and to keep working together to learn and do more?
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Notes
1
As defined by Kilpatrick, Swafford and Findell (2001), mathematical proficiency is
composed of five interdependent strands:
 conceptual understanding—comprehension of mathematical concepts, operations, and
relations
 procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently,
and appropriately
 strategic competence—ability to formulate, represent, and solve mathematical
problems
 adaptive reasoning—capacity for logical thought, reflection, explanation, and
justification
 productive disposition—habitual inclination to see mathematics as sensible, useful,
and worthwhile, coupled with a belief in diligence and one’s own efficacy. (p. 5)
2
All 11 schools in the instructional program coherence study were participating in the
Chicago Annenberg Challenge, a large-scale initiative providing funding for improved student
achievement through whole-school reform addressing: “school and teacher isolation, school size
and personalism, and time for learning and improvement” (Newmann et al., 2001, p. 302).
3
The Maryland Mathematics Content Standards spanned geometry, measurement,
probability, number, arithmetic operations, statistics, and algebraic reasoning. Students were
also expected to apply mathematics in other disciplines, to connect mathematical concepts, and
to communicate both a description and a justification of their problem solving approaches orally
and in writing. State performance assessment tasks specified whether they were to be completed
individually or in a cooperative group setting, but all written submission of responses were
Instructional Reform
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constructed individually.
4
Each of the schools implementing the BCPSS elementary mathematics curriculum
received student and teacher's editions and manipulative materials for McGraw-Hill's Math in
My World as well as Investigations in Number, Data, and Space from Scott Foresman Addison
Wesley.
5
In 1996-97, there were 121 regular schools in the BCPSS enrolling students attending all
or part of grades K-5. At the start of the 1997-98 school year, 13 schools joined the Direct
Instruction initiative, leaving 108 schools associated with this reform program. In 1998-99, one
of the participating schools was closed as part of urban renewal and another school adopted the
Direct Instruction program, leaving 106 schools. In 2000-01, 97 schools were participating as 6
schools were closed due to declining enrollment and 3 schools were reconstituted and assigned to
a private contractor.
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40
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