Designing Schools to Support
Teachers’ Ongoing Learning
Paul Cobb
Vanderbilt University
Background: US Educational System
• Decentralized education system
• Local control of schooling
• Each US state divided into a number of
independent school districts
• Rural districts with less than 1,000 students
• Urban districts with 100,000 students or more
History of Failure
• The closer that an instructional innovation
gets to what takes place between teachers and
students in classrooms, the less likely it is that
it will implemented and sustained on a large
scale
(Richard Elmore)
Limited Impact of Research on
Classroom Practice
• Supporting students’ learning of central
mathematical ideas
• Instructional materials
• Teachers’ instructional practices
• Supporting mathematics teachers’
development of high-quality instructional
practices
Large-Scale Instructional Improvement
Projects
• Focus is typically on teacher professional
development
• Unanticipated “obstacles”
• Conflicts with other district initiatives
• Lack of understanding and/or support by school
and district administrators
Large-Scale Instructional Improvement
Projects
• Flying blind: Little knowledge of the schools
and districts in which they are working
• Reactive: Plans change in response to unanticipated
obstacles
Large-Scale Instructional Improvement
Projects
• Proactive:
• Document school and district resources and
potential barriers
• Plan for school and district structures, resources,
and relationships that might support teachers’
ongoing improvement of their instructional
practices
Map Backwards From the Classroom
• Research on high-quality mathematics
instruction
• Demands on the teacher
• Challenges of supporting the development of
high-quality instructional practices
• School and district support: structures,
resources, and social relationships
• Institutional setting of mathematics teaching
High-Quality Instruction
• Keep one eye on the mathematical
horizon and the other on students’
current understandings, concerns, and
interests
(Ball, 1993)
Measuring With a Ten Bar
Measuring With a Ten Bar
• Edward: I think it’s 33 [points to where they have
marked 23 with the three cubes] because 10
[iterates the smurf bar once], 20 [iterates the smurf
bar a second time], 21, 22, 23 [counts the first,
second and third cubes within the second iteration]
Measuring With a Ten Bar
• Edward: Ten [iterates the smurf bar once], 20
[iterates the smurf bar again]. I change my mind.
She's right.
• T: What do you mean?
• Edward: This would be 20 [points to the end of
the second iteration].
Measuring With a Ten Bar
• T: What would be 20?
• Edward: This is 20 right here [places one hand at
the beginning of the “plank” and the other at the end
of the second iteration]. This is the 20. Then, if I
move it up just 3 more. There [breaks the bar to
show 3 cubes and places the 3 cubes beyond 20].
That’s 23.
Measuring With a Ten Bar
• Measuring as a sequence of separate
units
• Measuring as the accumulation of
distance
Classroom Discourse
• Not sufficient to show how measured
• Also have to explain why measured
in a particular way
• Measuring organizes distance into
units
Demands on the Teacher
• Teacher adjusts instruction to the students
• Ongoing assessment of students’ reasoning
• Non-routine -- a complex and demanding activity
• Students have to adjust to the teacher
• Covering instructional objectives + classroom
management
• Teaching a routine activity
Demands on the Teacher
• Deep understanding of mathematics
• Mathematical knowledge for teaching
• Knowledge of how students’ reasoning
develops in particular mathematical domains
• Knowing-in-action how to achieve a
mathematical agenda by building on students’
(diverse) solutions
Background: US Educational Policy
• No Child Left Behind Policy
• Standards for mathematics learning
• 50-80 standards per grade common
• Assessments at the end of each school year to
test whether students are achieving these
standards
• Primarily procedural skill at expense of conceptual
understanding
• Yearly student achievement targets in
mathematics for each school
Investigating What it Takes to Improve
Instruction at Scale
• Series of conjectures about school and district
structures, resources, and social, relationships
• Instruments to document the extent to which
those structures, resources, and social
relationships have been established
• Investigate interrelations between:
• Conjectured school and district supports
• Quality of teachers’ instructional practices
• Students’ learning
Investigating What it Takes to Improve
Instruction at Scale
• Four urban districts
• High proportion of students from traditionally
underserved groups of students
• Limited financial resources
• High teacher turn over
• Most schools and districts clueless about how to
respond productively to high-stakes accountability
• A small minority have reasonably worked out strategies
Investigating What it Takes to Improve
Instruction at Scale
• Four annual rounds of yearly data collection
• Document district strategies for improving middleschool mathematics
• Document how those strategies are actually
playing out in schools and classrooms
• First year: Baseline data
• Document change over a three-year period in each
district
Data Collection
• School and district support structures,
resources, and relationships
• Audio-recorded interviews
• On-line surveys
• Quality of teacher professional development
• Video-recordings
• Audio-recordings
Data Collection
• Quality of instructional materials
• Artifact collection
• Quality of teachers’ instructional practices
• Video-recordings of two consecutive
classroom lessons
• Teachers’ mathematical knowledge for
teaching
• Student mathematics achievement data
Analytical Tools
• Extent of teacher networks
• Frequency and depth of teacher interactions
• Visions of high quality mathematics instruction
• Coaches’ practices in supporting teachers’ learning
• Group and classroom settings
• Quality of the curriculum
• Quality of teacher professional development
• Principals’ direct and indirect instructional
leadership practices
Add Value to Districts’ Improvement
Efforts
• Feed back results of analyses to districts
• Gap analysis -- how district’s plan is actually
playing out in schools
• Recommend actionable adjustments that might
make each district’s improvement design
more effective
• Design experiment at the level of the district
Research Team
Paul Cobb
Erin Henrick
Glenn Colby
Lynsey Gibbons
Karin Katterfeld
Rebecca Schmidt
Tom Smith
Kara Jackson
Annie Garrison
Sarah Green
Chuck Munter
Jonee Wilson
Instructional Quality Assessment
Year 1
LMT – Year 1 and 2
LMT – Year 1 and 2
One District as an Illustrative Case
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Conjectured support structures
The district’s improvement plan
Analysis and feedback to the district
Overall findings
Conjecture: Teacher Networks
• US teachers typically work in isolation
• Social support from colleagues in developing
demanding instructional practices
• Focus of teacher interactions
• Classroom instructional practice
Conjecture: Teacher Networks
• Depth of teacher interactions
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How to use instructional materials
Aligning curriculum with state standards
Mathematical intent of instructional tasks
Student reasoning strategies
Conjecture: Key Supports for Teacher
Networks
• Time built into the school schedule for
collaboration among mathematics teachers
• Access to colleagues who have already
developed accomplished instructional
practices
• Concrete exemplars of high-quality instructional
practice
• Rationale for mathematics coaches
District Plan: Teacher Networks
• 1-2 mathematics teachers in each school
receive additional intensive mathematics
professional development
• Lead mathematics teachers
• Facilitate biweekly or monthly teacher study
group meetings
Analysis and Recommendations:
Teacher Networks
• Quality of professional development for lead
teachers high
• Does not focus specifically on teaching
underserved groups -- English language learners
(ELLs)
• Additional professional development for lead
teachers on:
• Teaching language in the context of mathematics
Analysis and Recommendations:
Teacher Networks
• Collaboration between isolated pairs of mathematics
teachers
• Typically low depth
• No opportunities for lead teachers to share what
they are learning in most schools
• Common planning time for mathematics teachers
• Additional professional development for lead
teachers on:
• Process of supporting colleagues’ learning
• Organizing the content of a study group’s work
Analysis and Recommendations:
Teacher Networks
• At least one mathematics teacher in each
school with a sophisticated view of highquality mathematics instruction
• Principals selected teachers for additional
professional development
• District policy: explicit criteria for selecting
lead mathematics teachers
Findings: Teacher Networks
• Online Network Survey
• All mathematics teachers in participating schools
• Measure of potential learning opportunities
for a teacher
• Sum of depth of interaction scores across all of
the teacher’s interactions
Findings: Teacher Networks
Findings: Teacher Networks
• Controlling for size of math department:
Math teachers in Districts B and C participate in
interactions of greater depth than those in
District A
• Scheduled time for teacher collaboration
• Will compare by department and by grade level
• Types of activities in which teachers engage
• Math coaches
• Ties with coach influences depth of interactions
Findings: More Accomplished Others Math Coaches
• District B: School-based math coaches
• District policy: Support learning of all math
teachers
• The extent to which the coach is central in
teacher networks
Findings: More Accomplished Others Math Coaches
• Teachers perceived the coach:
• to be a good mathematics teacher
• able to support them
• Described interactions as useful in improving
their classroom classroom practice
Findings: More Accomplished Others Math Coaches
• Principal able to describe how coach should
support teachers in some detail
• Support all teachers versus weak teachers
• Scheduled time for coach to meet with math
teachers as a group – emphasized the
importance of the meetings
• Co-participated on improving instructional
practice – more likely to seek advice from coach
outside meetings
Findings: More Accomplished Others Math Coaches
• Principal shared responsibility for supporting
teachers’ learning with the coach
• Attended mathematics department meetings
• Observed classroom instruction frequently
• Ongoing discussions about quality of
mathematics instruction and teachers needs
Conjecture: Shared Vision of High
Quality Mathematics Instruction
• Instructional goals -- what students should
know and be able to do mathematically
• How students' development of these forms
of mathematical reasoning can be supported
Conjecture: Shared Vision of High
Quality Mathematics Instruction
• Coordination between district administrative
units
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Curriculum and Instruction
Leadership
Research and Evaluation
English Language Learners
Special Education
Conjecture: Shared Vision of High
Quality Mathematics Instruction
• Occupational groups: Mathematics teachers,
principals, district mathematics specialists,
district leadership specialists, …
• Differences in:
• Responsibilities
• Practices
• Professional affiliations (and professional
identities)
Conjecture: Brokers
• Participate at least peripherally in the
activities of two or more groups
• Can bridge between differing agendas for
mathematics instruction
District Plan: Shared Instructional
Vision
• Curriculum Cabinet -- heads of all district
units + area superintendents
• Professional development in instructional
leadership for all principals
• Not content specific
• Cognitively-demanding tasks
• Maintain the challenge of the tasks as they are enacted
in the classroom
• Compatible with district goals for mathematics
instruction
Analysis and Recommendations: Shared
Instructional Vision
• District leaders: Inconsistent visions + not
specific to mathematics
• Form rather than function views
• Area superintendents participate in
mathematics professional development with
lead teachers
• Support alignment between Curriculum and
Instruction, and Leadership
• Brokers between district leaders and principals
Analysis and Recommendations: Shared
Instructional Vision
• Principals: Not specific to mathematics
• Form rather than function views
• Teachers: At least one mathematics teacher in
each school with a sophisticated view of
high-quality mathematics instruction
• Few formal opportunities for principals to draw
on or learn from expert teachers
Analysis and Recommendations: Shared
Instructional Vision
• Principals share leadership of mathematics
study groups with lead teachers
• Principals gain access to mathematics expertise in
their schools
• Brokers between mathematics teachers and
school/district leaders
• Legitimize work of lead teachers
• Lead teachers can focus on content-specific aspects of
study group activities
Conjecture: Mutual Accountability
• School leaders hold mathematics teachers
accountable for developing high-quality
instructional practices
• School leaders are accountable to
mathematics teachers (and district leaders) for
supporting teachers’ learning
Conjecture: Leadership Content
Knowledge
• Enables school and district leaders to:
• Recognize high-quality mathematics instruction
• Support its development directly
• Organize the conditions for teachers’ ongoing
learning
(Stein & Nelson, 2003)
Conjecture: Leadership Content
Knowledge
• Principals require a relatively deep
understanding of:
• Mathematical knowledge for teaching
• How students learn mathematics
• What is known about how to teach mathematics
effectively
• Teachers-as-learners and effective ways of
teaching teachers
Conjecture: Leadership Content
Knowledge
• Distributed across formal and informal
leaders
• Lead mathematics teachers
• Accomplished teachers as informal instructional
leaders
• Principal instructional leadership involves recognizing
and capitalizing on mathematics teachers’ expertise
District Plan: Mutual Accountability
• Professional development in instructional
leadership for all principals
• In classrooms observing instruction for two
hours each day
• Use developing understanding of (content-free)
high-quality instruction to:
• Assess quality of instruction and give feedback to
teachers
• Organize school-level teacher professional
development
• Develop school improvement plans
Analysis and Recommendations: Mutual
Accountability
• Most principals do not view themselves as
instructional leaders
• Most principals are spending only limited time in
classrooms
• Not aware that district leaders expect them to be in
classrooms
• District leaders need to communicate expectations
for what it means to be an instructional leader
clearly and consistently
• Hold principals accountable for supporting mathematics
teachers in improving their instructional practices
Analysis and Recommendations: Mutual
Accountability
• Most Principals have developed form rather than
function views of high-quality mathematics
instruction
• Feedback to teachers focuses on surface level features of
instruction (e.g., arrange students in groups)
• Most principals are not organizing school-based
professional development for mathematics teachers
• No supports for principals as instructional leaders
beyond professional development
Analysis and Recommendations: Mutual
Accountability
• Principals participate in at least a portion of
mathematics professional development with
lead teachers
• Principals share the leadership of
mathematics study groups
• Area superintendents provide guidance on:
• Providing constructive feedback to teachers
• Organizing school-based professional
development
Analysis and Recommendations: Mutual
Accountability
• Generic classroom observation form
• Promotion of innovative teaching methods
• Redesign observation form to reflect district
vision of high-quality mathematics instruction
Findings: Principal’s Visions of HighQuality Mathematics Instruction
• PD for principal instructional leadership in all
four districts
• Overall improvement from Year 1 to Year 2
• Generally not in conflict with districts’ goals for
instructional improvement
• Form view rather than function view
• Bad news: Communicate expectations for and
press for high-quality instruction
Findings: Principal’s Visions of HighQuality Mathematics Instruction
• Principal PD in District D
• Distinguishing between high- and low-cognitive
demand tasks
• Distinguishing between high- and low-level
enactment of tasks based on:
• Classroom observations
• Student work
• Giving feedback to teachers
• Developing school improvement plans for
mathematics instruction
Findings: Coordination Between
District Administrative Units
• District leaders’ view instructional
improvement as a process of:
• Supporting others’ learning
• Disseminating information about desired
practices and pressing for compliance
• Extent to which mathematics specialists
viewed as a valued resource
Findings: Coordination Between
District Administrative Units
• Relationship between “the line” and technical
assistance departments
• Discourse of:
• High-stakes accountability
• Instructional improvement
• Supporting others’ learning
• Disseminating information and pressing for
compliance
Summary
• Teacher networks
• Time for collaboration
• Access to instructional expertise
• Shared instructional vision
• Brokers
• Mutual accountability
• Leadership content knowledge
Policy and Learning
• Policy
• Local, state, and national policies intentionally
designed to influence teachers’ classroom
practices
• Mathematics education
• Professional development and instructional
materials intentionally designed to influence
teachers’ classroom practices
Policy Research
• The outcomes of specific policies
• The process by which particular policies are
implemented
• No position on what high-quality instruction
looks like
Mathematics Education
• Students’ and teachers’ learning
• Classroom in an institutional vacuum
Learning Policy
• Formulate and refine policies by building on
research on learning and teaching
• Frame instructional improvement as a
problem of organizational learning for
schools and districts