1、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,T
2、he 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 I
3、nstructional 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 L
4、ack 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 structur
5、es 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 distric
6、t 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,Measuring With a Ten Bar,Edward: I think its 33 points to where they have marked 23 with
7、 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. Shes
8、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 mov
9、e it up just 3 more. There breaks the bar to show 3 cubes and places the 3 cubes beyond 20. Thats 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
10、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
11、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 c
12、omplex 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 conjectur
13、ed 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 reaso
14、nably 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
15、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 m
16、athematical knowledge for teaching Student mathematics achievement data,Add Value to Districts Improvement Efforts,Feed back results of analyses to districts Gap analysis - how districts plan is actually playing out in schools Recommend actionable adjustments that might make each districts improveme
17、nt design more effective Design experiment at the level of the district,Research Team,Paul Cobb Tom SmithErin Henrick Kara JacksonChuck Munter Sarah GreenJohn Murphy Karin KatterfeldLynsey Gibbons Glenn Colby Annie Garrison,One District as an Illustrative Case,Conjectured support structures The dist
18、ricts 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 interaction
19、s 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 C
20、oncrete 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 Recomm
21、endations: 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,Findin
22、gs 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 developme
23、nt for lead teachers on: Process of supporting colleagues learning Organizing the content of a study groups 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 teache
24、rs 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 m
25、athematical 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 Qualit
26、y 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
27、 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 con
28、tent 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 mathemat
29、ics 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 Recommenda
30、tions: 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 expe
31、rt 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 t
32、eachers 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 leader
33、s) 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 & Ne
34、lson),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: L
35、eadership 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 Acco
36、untability,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
37、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 t
38、hat 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 Reco
39、mmendations: 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 profess
40、ional 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
41、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
42、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,Cu
43、rrent 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: Chan
44、ges 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 partic
45、ular 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 in
46、struction 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 Princi
47、pals 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 an
48、d 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,
