Practices Worthy of Attention
Local Innovations in Strengthening Secondary Mathematics
Pamela L. Paek
a publication of
The Charles A. Dana Center
at The University of Texas at Austin
About The University of Texas at Austin Charles A. Dana Center
The Charles A. Dana Center (www.utdanacenter.org) supports educators, education leaders,
policymakers, and communities in strengthening education. As a research unit of The University of
Texas at Austin’s College of Natural Sciences, the Dana Center maintains a special emphasis on
mathematics and science education. The Dana Center’s mission is to strengthen the mathematics and
science preparation and achievement of all students. We do this through supporting alignment of all
key mathematics and science education components, prekindergarten–16: mathematics and science
standards, accountability systems, assessments, and teacher preparation.
For more information about the Dana Center and its programs, see our homepage at
www.utdanacenter.org. For additional resources to strengthen your mathematics program, see our Mathematics
TEKS Toolkit at www.mathtekstoolkit.org and our web catalog at www.utdanacenter.org/catalog. For
information and online signup for our additional professional development offerings for leaders and teachers,
mathematics educators, and science educators, see our professional development site at
www.utdanacenter.org/pd/index.php.
Any opinions, findings, conclusions, or recommendations expressed in this material are those of the
author(s) and do not necessarily reflect the views of The University of Texas at Austin.
The University of Texas at Austin
The Charles A. Dana Center
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Austin, Texas
78722-2348
www.utdanacenter.org
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April 2008 release.
Acknowledgments
Unless otherwise noted, individuals listed here are affiliated with the Charles A. Dana Center.
Project Team
Editorial and Production Team
Pamela L. Paek, research associate (project lead)
Amy Dolejs, editor and designer
Christine Bailie, graduate research assistant
Melissa Campos-Hernandez, copyeditor
Susan Hudson Hull, program director,
mathematics and national initiatives
Rachel Jenkins, copyeditor
Sarah Searcy, copyeditor
Uri Treisman, executive director
External Reviewers
Rachel Curtis, Education Program Advisor, The
Aspen Institute
Michael Roach, Assistant Director of Curriculum
& Instruction, Indiana Department of Education
Kaye Forgione, Senior Associate in Mathematics,
Achieve
Linda Rosen, President, Education and
Management Innovations, Inc.
Guershon Harel, Professor of Mathematics,
University of California, San Diego
Paul Ruiz, Senior Advisor, The Education Trust
Beryl Jackson, Mathematics Teacher, Howard
University Middle School of Mathematics and
Science
Maggie Myers, Lecturer, Department of
Computer Sciences, University of Texas at Austin
Laura McGiffert Slover, Vice President, Content
and Policy Research, Achieve
Terry Vendlinski, Senior Researcher, National
Center for Research on Evaluation, Standards,
and Student Testing (CRESST)
Special Appreciation
We thank the Bill and Melinda Gates Foundation for their generosity and support for this work.
Specifically, we’d like to thank Melissa Chabrán, Education Policy and Research Officer at the Gates
Foundation, for her insights, feedback, and support throughout the project.
Our Thanks
We acknowledge with gratitude the generosity of the many district and school administrators,
teachers, researchers, and other educators who granted us permission and gave us information to
include their practices in this project. We would especially like to thank the following people for their
time and effort in developing the 22 profiles.
Chris Bishof, Principal, Eastside College
Preparatory School
Cathy Martin, Director of Mathematics, Denver
Public Schools
Catherine Boyce, Secondary Mathematics Staff,
Portland Public Schools
Laurie Mathis, Program Director, Charles A.
Dana Center, University of Texas at Austin
Eugenia Brelias, Mathematics Department Chair,
Evanston Township High School
Eric McDowell, Mathematics Curriculum
Developer, Bellevue School District
Margaret Calvert, Secondary Mathematics Staff,
Portland Public Schools
Lucy Michal, Mathematics Instructor, El Paso
Community College
Linda Chaput, founder and chief executive officer
of Agile Mind, Inc.
Suzanna Navarro, Executive Director, El Paso
Collaborative for Academic Excellence
Laura Cooper, Assistant Superintendent –
Curriculum and Instruction, Evanston Township
High School
Kris O’Clair, Intervention Coordinator, Denver
Public Schools
Linda Curtis-Bey, Director Department of
Mathematics & Science New York City
Department of Education
Benjamin Daley, Chief Academic Officer, High
Tech High
David Foster, Program Director, Silicon Valley
Mathematics Initiative
Dennis Futty, Senior Coordinator, Research &
Planning, Norfolk Public Schools
Michael Grote, Director of Staff Development,
Columbus Public Schools
Jennifer Husbands, Director of the High Tech
High HTH Graduate School of Education
Edward Joyce, Senior Program Director
Secondary Mathematics, Boston Public Schools
Timothy Kanold, Former Director of
Mathematics and Superintendent of Adlai E.
Stevenson High School District 125
Bill Kimball, Director of Assessment and Data
Management, Lamoille South Supervisory Union
Jim Lynn, Visiting Director, Office of High
School Development, University of Illinois at
Chicago
Jennifer Pagani-Hines, Chief Program Officer,
YES College Preparatory Schools
Cheryl Rectanus, Secondary Mathematics Staff,
Portland Public Schools
Regeta Slaughter, Lecturer, Department of Math
Statistics and Computer Science, University of
Illinois at Chicago
Doug Sovde, Principal, Chinook Middle School,
Bellevue School District
Bob Stanton, Assistant Superintendent, Lamoille
South Supervisory Union
Marnie Thompson, Consultant in Educational
Research and Educational Change
Laurel Vorachek, Director of Testing and
Assessment, Anchorage School District
Denise Walston, Senior CoordinatorMathematics, Norfolk Public Schools
Caroline Wylie, Research Scientist, Educational
Testing Service
Dion Yahoudy, Director of Resource
Development, Bellevue School District
Jan Zuber, Assistant Superintendent, Bellevue
School District
Practices Worthy of Attention
Executive Summary
The Dana Center works to improve the effectiveness of district and school reform efforts,
particularly in urban districts and schools. One vehicle for this work is the Urban Mathematics
Leadership Network, which currently includes 20 major urban districts. The Dana Center and
Achieve launched UMLN in 2004 to rapidly disseminate news of promising practices in
mathematics education to urban districts. The practitioners who participate in UMLN wanted
to identify practices currently in use that show promise of improving secondary mathematics
teaching and learning and that specifically address district-level concerns and needs,
including:
•
Helping all students succeed in Algebra;
•
Ensuring that upper-level high school courses provide preparation for and a smooth
transition to higher education and the work force;
•
Developing methods to address the mathematics needs of special populations;
•
Identifying model instructional programs; and
•
Strengthening teacher capacity and growing the supply of teachers.
The Dana Center conducted a national search, led by the author, for practices in urban schools
and districts that show promise—on the basis of early evidence and observation—of
increasing student learning in secondary mathematics, especially for students traditionally
challenged in this area. We call such practices “practices worthy of attention” (PWOA). The
PWOA work has three overarching goals:
1. Better understand existing initiatives, innovations, and programs that are being used to
improve secondary mathematics teaching and learning around the country and mark these
for further scientific inquiry.
2. Identify common themes in these practices that can be used to strengthen student
achievement in urban systems across the country.
3. Support practitioners of these practices by providing research support that can help them
more rigorously evaluate how well their practices are working and use that information to
strengthen their methods of operation.
This summary report describes our work to date on identifying and describing promising
initiatives, innovations, and programs in urban schools and districts. As all readers will
acknowledge, there is continual innovation in education. One of our goals with Practices
Worthy of Attention was to document what is really happening in the field to strengthen
secondary mathematics around the country. The practices we highlight may be common, but
the specific structures and strategies used to implement them are worthy of attention. As we
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Executive Summary
examined the schools, districts, and programs in this study, we found innovation in two
categories:
•
their approaches to raising student achievement and improving student learning in
mathematics, and
•
their approaches to increasing teacher capacity.
This summary report briefly describes the innovative aspects of practices that fell into those
categories. The categories are more fully described, with examples from each practice, in two
cross-case analyses. Each practice is also described at length in an individual practice profile.
The cross-case analyses and practice profiles are available on the Dana Center website at
www.utdanacenter.org/pwoa.
Historical Background for This Work
Recent federal and state education policies call for a substantial increase in the breadth and
depth of mathematical knowledge that students must acquire in order to graduate from high
school. For example, a growing number of states that once required knowledge only of middle
school–level mathematics for high school graduation have, over the past five to seven years,
begun to require that all students demonstrate mastery, via an exit examination, of Algebra I
and Geometry content (Center on Education Policy, 2006). To give students opportunities to
take higher-level mathematics courses in high school, which will better prepare them for
mathematics they may use in their postsecondary lives, many states and districts have policies
encouraging students to take Algebra I in the eighth grade. These policies have had an effect:
The National Assessment of Educational Progress (NAEP) shows that in 2000, only 27% of
eighth-grade students nationwide took Algebra I, whereas by 2005, 42% of eighth-graders
nationwide took Algebra I (Mathews, 2007).
Outside of policy requirements, improving student access to and achievement in mathematics
is important because students’ performance in middle school and high school math correlates
with their overall academic success in high school and beyond. The National Educational
Longitudinal Study (NELS) indicates that students who take rigorous high school
mathematics courses are much more likely to go to college than are those who do not take
those courses (U.S. Department of Education, 2002). Research suggests that specific math
courses, like Algebra I, serve as gatekeepers to more advanced mathematics courses and can
affect mathematics enrollment and achievement in high school, which in turn affects
enrollment in college and completion of a four-year degree (Adelman, 2006; Ma, 2001). The
NELS study shows that 83% of students taking Algebra I and Geometry go to college within
two years of graduating from high school, whereas only 36% of those who do not take these
courses enroll in college. Therefore, understanding the factors that contribute to improved
student learning in Algebra I and a successful transition to Geometry is a critical first step
toward increasing the postsecondary opportunities available to students.
Unfortunately, few school districts in the nation have the capacity to help their students meet
these rigorous mathematics requirements. National- and state-level reports document that,
especially in urban areas, there is a critical shortage in the supply of appropriately trained and
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Practices Worthy of Attention
Executive Summary
certified mathematics teachers as well as a high rate of attrition among those teachers
(National Science Board, 2006). Many secondary mathematics teachers lack deep knowledge
of the mathematics content they are expected to teach (Barth & Haycock, 2004; Massell,
1998). In fact, Ingersoll (1999) found that a third of all secondary school teachers of
mathematics nationwide had neither a major nor a minor in mathematics. Moreover, research
shows inconsistencies in instruction across classrooms within the same district and even
within the same school. Teachers interpret the same instructional ideas in various ways
(Marzano, 2003; Stigler & Hiebert, 1998, 1999) and accordingly make independent decisions
about whether and how to ignore, adapt, or adopt policymakers’ recommendations for
instruction (Spillane, Reiser, & Reimer, 2002).
In urban districts faced with these and other difficult issues—including heavy turnover among
administrators, administrators who do not understand what is needed to support a high level of
mathematics learning, and low expectations for student performance from both teachers and
administrators—mathematics instruction has proven very difficult to improve (Bamburg,
1994; Beck-Winchatz & Barge, 2003; Tauber, 1997). As a result, all too often, students in
urban school districts are not given adequate opportunity to enroll and succeed in challenging
mathematics in their secondary years (National Science Board, 2006).
In addition, for most of its history, the U.S. educational system has had in place a large
number and wide range of uncoordinated and sometimes conflicting mandates for
administrators and teachers. Recent policies, enacted at the federal, state, and local levels, are
intended to align policy- and program-level mandates to create a coherent reform package.
Because these reforms often aim to transform both content and instruction, they require
significant changes in teachers’ practices and the development as well as implementation of
an administrative infrastructure to support such changes (Cohen & Hill, 2001).
To address these problems and meet governmental reform mandates, schools and districts are
expending enormous quantities of resources in an effort to improve their secondary
mathematics programs and deliver a consistent and rigorous curriculum that is aligned with
state standards and assessments and that prepares students for success in college and entry
into high-quality workplaces. Many of these reform strategies are structured to increase the
coherence of educational policies, programs, and practices (Fuhrman, 2001).
The cost of these reform efforts can be high. In fact, recent studies estimate that districts
spend anywhere from $200 to $300 per student per year on the direct costs of teacher
professional development alone, and this may well be an underestimate, since the budgeting
and tracking of these expenditures is confounded by the fact that multiple, sometimes obscure
budget lines may account for professional development (Council for Education Policy
Research and Improvement, 2005; Killeen, Monk, & Plecki, 2002; Neville & Robinson,
2004).
Despite these substantial investments, evidence suggest that the effectiveness of district and
school reform efforts varies greatly—a fact that has become increasingly clear in the Dana
Center’s work with large urban districts nationwide. Fullan (1991) summed up this mismatch
between investment and outcomes: “Nothing has promised so much and has been so
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Executive Summary
frustratingly wasteful as the thousands of workshops and conferences that led to no significant
change in practice when teachers returned to their classrooms” (p. 315).
The PWOA project was inspired by these challenges that schools and districts face and by the
need for education systems to invest resources wisely. Thus began the work of identifying
practices in secondary mathematics education that may merit further attention, greater
investment, and wider dissemination.
Defining Practices Worthy of Attention
Research on PWOA work differs from other work describing “best practices” or “promising
practices” in that PWOA starts from where schools and districts presently are, focusing on
work and ideas currently in progress. Starting with practices that have not yet been identified
as “best” or “promising” through specific national criteria, such as those of the What Works
Clearinghouse or the National Center for Educational Accountability, means that there is
often little or no documentation of how a practice is being implemented, and scarce evidence
of the practice’s impact or effectiveness. Therefore, the first step in researching a practice was
spending time with the practitioners in each school or district to discover the theory of action
behind the practice and to document the implementation of the practice and the evidence of its
effectiveness so far. This step not only provides a historical record of activities, but also
honors the work, giving practitioners a chance to see their ideas and efforts documented in a
way that shows a picture of the work to date. This step also provides a starting point for
researchers to continue to work with practitioners to better measure the effects of the practices
on secondary mathematics teaching and learning.
Developing methods to accurately and comprehensively measure and assess the impacts of
these practices on mathematics teaching and learning helps fulfill a current need of urban
districts and schools. In the Dana Center’s work with urban districts and schools around the
country, we hear a great deal of discussion about using data collected from evaluations and
assessments of teaching practices to inform instructional practice and programmatic decision
making, but we see very few districts that have an infrastructure that allows for the collection,
analysis, and strategic use of such data. Ironically, just as policymakers and district leaders are
looking to raise the evidentiary standard for adopting a school improvement practice, the size
of district offices—including that of their research and evaluation staff—is being greatly
curtailed, or staff is being diverted to deal with the reporting exigencies related to No Child
Left Behind. Many urban districts thus don’t have the staff and financial resources to clearly
determine what data are needed by each person in the system and how such data can be used.
Most importantly, these districts haven’t yet worked out how to translate the knowledge
gained from the data into effective decision making at each level of the education system.
Understanding Existing Initiatives and Programs
Each school and district we studied had a different perspective and a unique set of practices in
place to improve secondary mathematics achievement. The goal of studying each district,
school, and program was not always to discover innovations in how practitioners dealt with
similar issues, but rather to document what practitioners were doing to strengthen secondary
Charles A. Dana Center at the University of Texas at Austin
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Practices Worthy of Attention
Executive Summary
mathematics education. Thus, although the practice highlighted may be commonplace, the
specific structures and strategies being employed by the school or district to implement it are
worthy of attention.
We interviewed staff in over 30 schools and districts. On the basis of our findings, we
narrowed our focus to 22 sites. For each site, we wrote an individual profile that includes a
description of the practice, its goals, the need it serves, the research behind it (if the site
identified any), and any evidence the school or district is using for measuring gains in student
learning.
Five thematic categories emerged from this field of research.
•
Secondary mathematics/Algebra I focus. The focus on secondary mathematics differs
across sites. Some practices focus on helping struggling students by providing an
opportunity for students to learn academic and self-efficacy skills, in addition to algebraic
foundations, in the summer prior to their first year in high school. Other practices use
double-period specialized courses that intensify efforts to reinforce concepts and provide
catch-up opportunities for those students behind schedule, thus allowing them to complete
the mathematics courses required for high school graduation and/or college admission.
Still other practices require all eighth-grade students to pass Algebra I before entering the
ninth grade. Some schools and districts in this category realigned their K–7 mathematics
curricula to prepare students for mastery of Algebra I in eighth grade.
•
Special population cross-training and collaboration. Some practices focus on
increasing teacher capacity for serving groups of students with special needs, such as
students with limited English proficiency and students in special education. These
practices are designed to help teachers learn how to provide high-quality mathematics
rather than watered-down content or dramatically slowed-down instruction for such
subpopulations. The practices facilitate good teaching by focusing on the types of
instructional tasks that teachers can use to differentiate instruction to meet the diverse
needs of students, encourage the use of academic vocabulary, and provide various entry
points for students to learn the mathematical concepts. These practices also provide
teachers with feedback on specific ways that some students may struggle as a result of
language acquisition issues or cognitive impairment.
•
District leadership with mathematics focus. In some districts, practices operate at the
level of district reform and focus first on changing the perceptions of administrators and
teachers about students’ learning abilities. In these cases, the practices encompass
professional development specific to mathematics to reinforce the idea that all students
have the capacity to learn, while also engaging teachers in professional learning
communities or as teacher leaders. Administrators support and assist teachers further by
finding convenient times (e.g., common planning periods) for teachers to meet with each
other and work specifically on substantive teaching and learning issues in mathematics,
and by offering release time for teachers to visit each other’s classrooms.
•
Assessment. Many practices have a component that focuses on assessment—formative
assessments, benchmark assessments, interim assessments, large-scale assessments, item
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Executive Summary
analyses comparing results of different assessments, and/or the development and
implementation of local assessment systems. These practices are based on the belief that
assessment can serve as a vehicle for driving, revising, and supporting instruction.
Professional development in these practices first helps teachers learn how to use data from
these different types and levels of assessment to evaluate student knowledge, and then
helps teachers use that information to improve their teaching of different mathematics
concepts.
•
Charter schools or small schools. Charter or small schools are usually formed in
response to dissatisfaction with how larger public schools are functioning. The practices
of the schools in this study yield high success rates for first-generation college-bound
students (typically economically disadvantaged students and racial/ethnic minorities).
Methodology
Initial Selection of Programs, Schools, and Districts
The first step was to interview administrators and teachers at schools and districts across the
U.S. that embody diverse educational systems but that all primarily serve students classified
as economically disadvantaged and/or as racial and ethnic minorities. We contacted our
known networks of mathematics leaders and teachers to help us develop an initial pool of
possible practices worthy of attention. Achieve, the Dana Center, and the lead researcher, who
was aware of some practices due to her previous work, suggested a number of practices that
might be worthy of further examination. In addition, the lead researcher took advantage of a
June 2006 UMLN meeting to interview representatives from all UMLN member districts.
Protocol for Initial Interviews
At the June 2006 UMLN meeting, we used a four-question protocol to interview mathematics
administrators from UMLN districts. Interviews took about 15–20 minutes each. The
interview protocol included a definition of what constitutes a practice worthy of attention,
which was read to the district administrators being interviewed:
A practice worthy of attention (PWOA) is a practice being used in your district that
shows promise of improving mathematics education within your district and across
districts. The PWOA we are looking for are specifically looking at the grade range of
middle school through college (e.g., the middle school to high school transition in
math or the high school to college transition in math). A PWOA is an example of how
you have solved problems or challenges your district faced, ideally with tools that
measure the effects of change.
The project lead had developed several categories for practices worthy of attention on the
basis of key issues that had emerged repeatedly in the Dana Center’s work with urban
districts. Interviewees were asked to identify potential practices worthy of attention according
to these categories. The categories were academic youth development, equity issues, math
leadership development, algebra readiness, formative/benchmark assessments, the K–16
continuum, coaching, high school mathematics requirements, special education, concept- and
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Practices Worthy of Attention
Executive Summary
skills-bound tests, literacy issues, teacher induction, students with limited English proficiency,
managed curriculum, and technology uses. Administrators were also provided an “other”
category if they wished to identify a practice that did not fall into one of the specific
categories.
The first interview question asked the administrators which practices they would nominate for
their district; the interviewer and interviewee then discussed and agreed on which category or
categories the practices belonged to. The interviewees were asked to summarize the practices,
and this information was documented along with the category assignment. The second
question concerned what types of documentation of the practice existed (e.g., training
protocols, documents describing upcoming trainings, documents describing school or district
initiatives) and what evidence was used to show the effectiveness of the practice (e.g.,
school/district evaluations of students and/or teachers, third-party evaluator reports,
improvement in test scores). The final two questions were logistical. One concerned finding a
time to visit the district when the interviewer would be able to talk informally with a large
number of teachers and either observe the practice in action or attend a professional
development meeting, and the other asked for the name of the best contact person for the
PWOA project.
Dana Center staff reviewed the interviews with UMLN district staff, looking for practices that
most closely met the definition of practices worthy of attention. Eight practices were chosen
for further investigation via follow-up phone interviews. The follow-up phone interviews with
UMLN district staff were somewhat unstructured but had two main goals: (1) to get more
details about the nominated practice, including documentation or evidence of effectiveness
available to date, and (2) to schedule a site visit and work out whom the researcher could
interview onsite. Each phone interview took about an hour and was scheduled in advance via
email. Interviewees knew ahead of time the interview’s two main goals and thus had their
calendars and information about the practice on hand for the call.
For non-UMLN schools and districts, most initial interviews were conducted by phone. In a
handful of cases, the lead researcher was able learn about the practices when they presented
their work at a conference. The protocol for the phone interviews was a combination of the
two protocols already discussed (the interviews conducted at the June 2006 UMLN meeting
and the follow-up phone interviews).
In the end, 30 programs, schools, and districts were initially contacted. Eight were not
followed up with a site visit, either because the practice did not fit the goals of the project or
because the site did not respond to requests for a visit.
Site Visits and Profiles of the Practices
The lead researcher visited most of the 22 sites to develop a fuller picture of how the practices
were actually being implemented and evaluated. During most of these visits, the lead
researcher attended a professional development workshop centered on the practice being
studied; this allowed her to get more detailed information about the practice by witnessing
how schools and districts were explaining and teaching it. The visits also included time for the
lead researcher to talk further with the person interviewed on the phone. On site, the lead
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Executive Summary
researcher had ready access to any materials related to the practice that she could bring back
to the Dana Center for further study. The lead researcher also had informal, face-to-face
conversations with other staff members to learn what they thought about the practices. For a
few sites, an actual site visit was not feasible, but enough information about the sites’
practices was available for the researcher to write a profile, with feedback from the district or
program to ensure that the profile correctly reflected the practice.
For each of the final 22 practices, we wrote a profile that provides demographic information
about the student population that the practice serves, describes how the practice was
developed and implemented, and presents any evidence that the program, school, or district
has collected to demonstrate the practice’s effectiveness. These profiles can be found on the
Dana Center’s website at www.utdanacenter.org/pwoa.
Examining the Profiles
The original intent of this project was to identify the top ten practices worthy of attention. To
help us do this work, we convened a national advisory committee comprising district
mathematics staff, current and former secondary mathematics teachers, education
policymakers, college mathematics professors, state-level mathematics representatives, and
district mathematics specialists. The advisory committee met to discuss the pool of practices
and develop a method for rating them in terms of the rigor of their curricular and academic
goals, the depth and breadth of their associated professional development, and early evidence
of their effects on meeting academic goals.
The advisory committee meeting included three primary activities: (1) learning about the
project and getting an overview of the different practices, (2) reviewing draft criteria for
rating the practices, and (3) finalizing the criteria to be used for rating the practices.
Committee members were asked to think about what makes one practice more worthy than
another, how to develop criteria for ranking the practices given the different sources, types,
and amounts of data about them, and what other types of information were needed to rank the
practices.
Committee members were also asked to consider the animating ideas behind the practices in
order to identify those that had innovative ideas and approaches for improving learning and
closing the achievement gap in secondary mathematics. Committee members were asked to
evaluate which of the practices were generally applicable—that is, not geared only to specific
frameworks or types of students—and thus could be scalable and usable across various sites.
The committee members provided specific feedback about the types of data they thought
should be collected and analyzed to evaluate the practices, and they made preliminary
recommendations, on the basis of their own research and practical experience, about how the
schools and districts could improve their practices.
During their development of the criteria for rating each profile, committee members created a
set of screening questions to decide whether a practice was worthy of attention or whether it
should be eliminated from the pool before time was spent rating it. They devised the
following three yes-or-no screening questions to determine whether a practice was worthy of
being rated: (1) Does the documentation indicate that the practice is indeed a discernible
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Executive Summary
practice? (2) Does the practice respond to a well-defined student/school/district need? (3) Is
the goal of this practice worthy? (i.e., does it attend to the mathematical integrity of the
curriculum or pay attention to the needs of students?) Or, do you see this practice as meeting
its stated goal? If a rater answered no to any of these questions, then the practice would not be
rated. Although a few advisory committee members felt that a small number of practices
didn’t meet the screening requirements, no practice was screened out by more than one
reviewer. Therefore, all 22 practices were included for rating by the committee.
Although the committee members rated each profile, it was their feedback, along with their
ratings, that helped change the project’s next step from choosing the top ten practices worthy
of attention to doing cross-case analyses. The committee members felt that the widely varying
grain sizes of the practices made it impossible to fairly choose a top ten. They suggested that
instead we do a cross-case analysis of the profiles in three main categories: curricular and
academic goals, professional development, and evidence of effectiveness.
The cross-case analysis was carried out on the basis of the committee’s recommendation, and
different profiles were highlighted in themes from those three categories. This analysis
became very complex, again because of the varying grain sizes of the practices. In addition,
although this analysis drew out the innovations in the profiles, the innovations were buried in
commonplace practices. As such, the cross-case analysis was reworked to highlight the
innovations yet still stay true to the goal of the project and the criteria established by the
advisory committee. The result was two cross-case analyses that discuss the innovative ways
schools and districts approach the challenges of raising student achievement and building
teacher capacity.
Results
As we examined the schools, districts, and programs in this study, we found innovation in two
categories:
•
their approaches to raising student achievement and improving student learning in
mathematics, and
•
their approaches to increasing teacher capacity.
Practices that exemplify these categories are described in two separate cross-case analyses,
with snapshots of each practice. The cross-case analyses are briefly described below, and the
full analyses are available on the Dana Center website at www.utdanacenter.org/pwoa.
Raising Student Achievement Through Academic Intensification
All of the schools, districts, and programs profiled in this study have increased their
expectations for student achievement, but some of them focused particularly on academic
intensification strategies to help students meet the higher expectations. These strategies fall
into two broad categories: (1) raising standards and expecting higher levels of achievement
for all students, which means an intensification of what students are required to do, and (2)
providing targeted and intense support to help students achieve at a higher level. The types of
Charles A. Dana Center at the University of Texas at Austin
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Practices Worthy of Attention
Executive Summary
practices that emerged in support of academic intensification include: building summer bridge
programs, requiring and supporting more rigorous mathematics courses, and providing intense
and ongoing support throughout the school day.
Raising student achievement through academic intensification requires changes in the
attitudes and practices of administrators, teachers, and students. In summer bridge programs,
students learn about the value of academic effort and build peer and teacher relationships that
will support them throughout high school. Success in these programs necessitates firm belief
on the part of teachers that their students really can succeed in high school mathematics and
that collegial student peer groups can be a strong support for that success; when the teachers
in these programs believe and demonstrate these ideas, they have a greater chance of
convincing students to engage wholeheartedly in their own education.
Similarly, requiring rigorous courses of all students demands a change in how districts and
schools think about student ability. In the practices focused on raising student achievement,
districts and schools are getting students into rigorous mathematics courses earlier and
providing much more support for both students and teachers. Intense, embedded daily
supports, for example, constantly reiterate the idea that mathematics is important and that,
with hard work and a strong network of teacher and peer support, all students can take and
pass rigorous mathematics courses.
Building Teacher Capacity
All of the schools, districts, and programs profiled in this study have increased their
expectations for what teachers should do, but some of them have focused intense attention on
improving teacher practices. The practices designed to build teacher capacity provide
opportunities for teachers to expand their current practices through focused interaction with
other teachers and through accessing resources with individual support. The practices require
support from administrators if the traditional ways teachers have interacted are to be
overcome. As teachers are asked to support students with various experiences and
backgrounds, districts and schools are asked to support teachers the same way instead of
providing all teachers the same training and expecting all of them to perform the same way.
Three main approaches emerged from our observations: redefining mathematics teacher roles
and responsibilities, making instruction public, and having new, customizable tools for
teaching.
With broadened roles and responsibilities, teachers redefine how they think of teaching and
what they can contribute. They learn that they can gain expertise for successfully working
with subpopulations of students in need of their help, be part of a development team for
building common assessments at the district level, or participate as leaders in the district for
promoting change in mathematics. When instruction is public, teachers learn about the power
of collaboration for improving their practice and lose the fear of observers in the classroom.
With structured observation protocols and regular opportunities for feedback, teachers forget
about working in isolation and focus more on the ways they can work together on student
achievement. Finally, with new tools and customized support, teachers can access the
individual training and feedback they need to make good practices part of their daily
instruction.
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Practices Worthy of Attention
Executive Summary
Discussion and Next Steps
Schools, districts, teachers, and administrators often adopt or continue educational practices
without having a meaningful understanding of the theory behind these practices, which results
in poor implementation of good ideas or abandonment of practices when an administrator
leaves the school or district. Similarly, most schools, districts, teachers, and administrators do
not have clear evidence of whether the practices are really helping to improve their students’
achievement. Our work on Practices Worthy of Attention is beginning to shed light on what
needs to be done by researchers and practitioners together to uncover meaningful information
about practices, gauge their success, and determine how to adapt and incorporate successful
practices into secondary mathematics programs nationwide.
Many articles and books about closing or eliminating the mathematics achievement gap have
focused on broad approaches and general ideas without specifying how these ideas can be
translated into practice. Although these approaches and ideas capture the essence of
successful strategies, the vocabulary used to describe them can be interpreted in different
ways. A district can often accurately claim that it is using professional development and
learning communities to improve its mathematics pedagogy, but how the district defines
“professional development” and “learning communities” is crucial in determining how these
ideas are implemented and, ultimately, how successful they are.
To successfully tackle the challenges faced by all educators and leaders in improving
mathematics teaching and learning, researchers must spend more time in schools and districts,
observing and analyzing how the broad approaches and big ideas are actually codified,
implemented, and assessed within and across districts. The Practices Worthy of Attention
work is a first step toward creating a nationwide group of practitioners who can share specific
strategies with and learn from one another, thus opening doors across districts, much as
classrooms have been opened within schools. By taking the time to observe and evaluate
actual practices, we can find out directly how research is interpreted and implemented and
therefore advise mathematics leaders and teachers in ways that directly affect their work.
The next phase of this work is to partner Dana Center researchers with schools and districts to
raise the standards of evidence by which we measure the effectiveness of these practices. This
will allow for the fulfillment of a key purpose of this work: not only to identify common
themes in these practices that can be used to strengthen teachers’ practices and student
achievement in urban systems across the country, but also to determine the effects of districts’
initiatives for improving teacher practices and, in turn, the effects of those practices on
students’ secondary mathematics progress and achievement. The PWOA work is a first step
toward creating a community of inquiry among researchers and urban schools and districts to
explore existing initiatives and programs that are being used to improve secondary
mathematics teaching and learning around the country.
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