Paul Cobb Vanderbilt University ICME 11, Monterrey, Mexico, July 2008

The Challenges of Scale: Designing Learning Organizations for Instructional Improvement in

Mathematics

Paul CobbVanderbilt University

ICME 11, Monterrey, Mexico, July 2008

Purpose

• Illustrate a way of conducting research studies that aim to inform the ongoing improvement of mathematics teaching and learning at scale

Background: US Educational System

• Decentralized education system• Long history of 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 more than 100,000

students

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

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 practice

Large-Scale ImplementationProjects

• Focus is almost exclusively on teacher professional development

• Unanticipated “obstacles”• Conflicts with other district

initiatives• Lack of understanding and/or support

by school and district administrators

Large-Scale Implementation

• Flying blind: Little knowledge of the schools and districts in which they are working• Reactive: Plans changed in response to

unanticipated obstacles

• Proactive: Anticipate school and district structures that might support mathematics teachers’ ongoing improvement of their instructional practices

Map Backwards From the Classroom

• Research on high-quality mathematics instruction

• Demands on the teacher• Challenges of developing high-quality

instructional practices

• School and district support structures

The Swing of the Pendulum

• Student-centered approaches• Celebrate students’ discoveries and

methods as ends in themselves

• Teacher-centered approaches• Focus on conveying mathematical

ideas to students

Transcending This Forced Choice

• Keep one eye on the mathematical horizon and the other on students’ current understandings, concerns, and interests (Ball, 1993)

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]


• 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].


• 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 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 structures distance into units

Demands on the Teacher

• Deep understanding of mathematics• Mathematical knowledge for teaching

• Knowledge of how students’ reasoning develops in particular mathematical domains

• Skill in pursuing a mathematical agenda by building on students’ contributions

Improvement in Instructional Practices

• Students have to adjust to the teacher• Teaching routine• Covering instructional objectives +

classroom management

• Teacher adjusts instruction to the students• Ongoing assessment of student reasoning• Non-routine -- complex and demanding

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 for each school in mathematics

Framing Instructional Improvement at Scale as a

Research Issue• Series of conjectures about school

and district structures that support teachers’ ongoing learning

• Instruments to document the institutional setting of mathematics teaching• Extent to which the conjectured

support structures have been established

Research Plan

• Four urban districts• High proportion of students from

traditionally underserved groups of students

• Limited resources

• Most districts clueless about how to respond to high-stakes accountability• A small minority have reasonably

worked out strategies

Research Plan

• Document district plans for improving middle-school mathematics

• Six middle schools - 30 teachers• Four rounds of yearly data

collection• First year: Baseline data• Document change over a three-year

period in each district

Data Collection

• Institutional setting of mathematics teaching• Audio-recorded interviews and surveys

• Quality of teacher professional development• Video-recordings

• 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

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 Tom Smith

Erin Henrick Kara JacksonChuck Munter Sarah

GreenJohn Murphy Karin

KatterfeldLynsey Gibbons Glenn

Colby

One District as an Illustrative Case

• Conjectured support structures

• The district’s improvement plan

• Findings and feedback to the district

Conjecture: Teacher Networks

• US math teachers typically work in isolation

• Social support from colleagues in developing demanding instructional practices• Focus of teacher interactions

• Classroom instructional practice

• Depth of teacher interactions• Mathematical intent of instructional tasks• Student reasoning strategies

Conjecture: Key Resources for Teacher Networks

• Time built into the school schedule for collaboration among mathematics teachers

• Access to colleagues who have already developed relatively accomplished instructional practices• Concrete exemplars of high-quality

instructional practice

District Plan: Teacher Networks

• 1-2 mathematics teachers in each school receive intensive mathematics professional development

• Lead mathematics teachers • Facilitate biweekly or monthly

teacher study group meetings

Findings 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 -- ELLs


• Collaboration between isolated pairs of mathematics teachers in some schools• 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


• At least one mathematics teacher in each school with a sophisticated view of high-quality mathematics instruction• Principals selected teachers for

additional professional development

• District policy: criteria for selecting lead mathematics teachers

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 knowing can be supported


• Coordination between district administrative units• Curriculum and Instruction• Leadership• Research and Evaluation• English Language Learners• Special Education


• 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 • Vision of high quality instruction -- not

content specific• Intellectually-demanding tasks• Maintain the challenge of the tasks as they

are enacted in the classroom• Compatible with district goals for mathematics

instruction

Findings 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• Broker between district leaders and

principals• Support alignment between

Curriculum and Instruction, and Leadership


• 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 teacher expertise


• Principals share leadership of mathematics study groups with leader teachers• Principals gain access to mathematics

expertise in their schools• Broker 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 for supporting teachers’ learning

Conjecture: Leadership Content Knowledge

• Enables school and district leaders to:• Recognize high-quality mathematics

instruction • Support its development• Organize the conditions for

continuous learning of school and district staff(Stein & Nelson)


• Principals require a relatively deep understanding of:• Mathematical knowledge for teaching • What is known about how to teach

mathematics effectively• How students learn mathematics • Teachers-as-learners and effective

ways of teaching teachers


• Distributed across formal and informal leaders• Lead mathematics teachers• Accomplished teachers as informal

instructional leaders

District Plan: Mutual Accountability

• Professional development in instructional leadership for all principals• Spend two hours in classrooms each day• Use developing understanding of

(content-free) high-quality instruction to:• Assess and communicate about instruction• Organize school-level teacher professional

development• Develop school improvement plans

Findings and Recommendations: Mutual Accountability

• Most principals do not view themselves as instructional leaders

• Most principals are spending only limited time in classrooms• Inconsistent messages from district leaders --

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


• 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., arranging 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


• Area superintendents provide guidance on:• Providing constructive feedback to

teachers• Organizing school-based professional

development• Principals participate in at least a

portion of mathematics professional development with lead teachers

• Principals share the leadership of mathematics study groups


• Generic classroom observation form specifies “promotion of innovative teaching methods”

• Redesign observation form to reflect district vision of high-quality mathematics instruction

Summary

• Teacher networks• Time for collaboration• Access to expertise

• Shared instructional vision• Brokers

• Mutual accountability• Leadership content knowledge

Next Steps

• Fall/autumn 2008:• Document district plan• To what extent have they actually

acted on the basis of our feedback?

• January-March 2009:• Document the consequences of

any changes

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

Documents

Paul Cobb Vanderbilt University ICME 11, Monterrey, Mexico, July 2008