The Challenges of Scale: Designing Learning Organizations for Instructional Improvement in Mathematics Paul Cobb Vanderbilt University

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

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 practices

Large-Scale Implementation Projects Focus is primarily 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 supporting the development of high-quality instructional practices School and district support structures

High-Quality Mathematics 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

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 had to explain why measured in a particular way Measuring organizes 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 Know-in-practice how to pursuing a mathematical agenda by building on students’ (diverse) contributions

Improvement in Instructional Practices Students have to adjust to the teacher Teaching a routine activity Covering instructional objectives + classroom management Teacher adjusts instruction to the students Ongoing assessment of student reasoning Non-routine -- a complex and demanding activity

Framing Instructional Improvement at Scale as a Research Issue Series of conjectures about school and district structures that might 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 financial resources Most districts clueless about how to respond productively to high-stakes accountability A small minority have reasonably worked out strategies

Research Plan Document district plans for improving middle- school mathematics 6-10 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 and resources 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 CobbTom Smith Erin HenrickKara Jackson Chuck MunterSarah Green John MurphyKarin Katterfeld Lynsey GibbonsGlenn Colby Annie Garrison

One District as an Illustrative Case Conjectured support structures The district’s improvement plan Findings and feedback to the district

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 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 sophisticated instructional practices Concrete exemplars of high-quality instructional practice

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

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

Findings and Recommendations: Teacher Networks 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

Findings and Recommendations: Teacher Networks 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

Conjecture: Shared Vision of High Quality Mathematics Instruction Coordination between district administrative units 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 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 Expertise in Curriculum Cabinet Support alignment between Curriculum and Instruction, and Leadership Brokers between district leaders and principals

Findings 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

Findings 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 (in Mathematics) Enables school and district leaders to: Recognize high-quality mathematics instruction Support teachers’ learning directly Organize the conditions for ongoing learning of school and district staff (Stein & Nelson)

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 expertise 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

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

Findings 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., 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

Findings 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

Findings and Recommendations: Mutual Accountability Generic classroom observation form specifies “promotion of innovative teaching methods” Redesign observation form to reflect district vision of high-quality mathematics instruction

Summary: Conjectured Support Structures Teacher networks Time for collaboration Access to expertise Shared instructional vision Brokers Mutual accountability Leadership content knowledge

Current and Next Steps Fall 2009: Document whether districts actually act on the basis of our feedback January-March 2009: Document the consequences of any adjustments May 2009: Second round of feedback to districts

Research Agenda Test, revise, and modify conjectures about relationships between: Changes in school and district support structures Improvement in mathematics teachers’ instructional practices Student achievement

Research Agenda Refine conjectures: Identifying additional support structures Clarifying relationships between support structures Specifying the conditions under which particular support structures are important

Teachers’ Access to Expertise: Local and External Views of Expertise Local views: Who teachers identify as experts Criteria for what counts as instructional expertise External views: Teachers we identified as experts: District views of high-quality mathematics instruction Research literature on mathematics learning and teaching

Teachers’ Access to Expertise: The Role of the Principal Teachers’ access to expertise Teacher networks, mathematics coaches, district math specialists, external expertise Principals’ practices The how of instructional leadership Principals’ knowledge-of-practice Vision of high-quality mathematics instruction (Suppositions about process of teacher learning)

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