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pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. ~ pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. pnamdhGaramond 2Monotype Typography, Inc. ?%O=RxX%fThe Challenges of Scale: Designing Learning Organizations for Instructional Improvement in MathematicsPaul Cobb
Vanderbilt UniversityY&PurposeIllustrate a way of conducting research studies that aim to inform the ongoing improvement of mathematics teaching and learning at scaleZ'History of FailureThe 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[(0Limited Impact of Research on Classroom PracticeSupporting students learning of central mathematical ideas
Instructional materials
Teachers instructional practices
Supporting mathematics teachers development of high-quality instructional practices:<;U<;U\)#Large-Scale ImplementationProjectsFocus is primarily on teacher professional development
Unanticipated obstacles
Conflicts with other district initiatives
Lack of understanding and/or support by school and district administrators&QuQu]*Large-Scale ImplementationNFlying 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 practicesNV?V'
^+ Map Backwards From the ClassroomResearch on high-quality mathematics instruction
Demands on the teacher
Challenges of supporting the development of high-quality instructional practices
School and district support structuresDHQ'HP'1`-$High-Quality Mathematics InstructionKeep one eye on the mathematical horizon and the other on students current understandings, concerns, and interests. (Ball, 1993)$b/Measuring With a Ten Barc0Measuring With a Ten BarEdward: 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]`8````$``)` ` $`$(`(,lfd1Measuring With a Ten BarEdward: 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].l
````Q`)``,e2Measuring 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.X4```>`?`
`f3Measuring With a Ten BarSMeasuring as a sequence of separate units
Measuring as the accumulation of distanceTT(yClassroom DiscourseNot sufficient to show how measured
Also had to explain why measured in a particular way
Measuring organizes distance into unitsZY((((((($7IxEDemands on the TeacherDeep understanding of mathematics
Mathematical knowledge for teaching
Knowledge of how students reasoning develops in particular mathematical domains
Know-in-practice how to pursuing a mathematical agenda by building on students (diverse) contributionsX"$"#1iyF&Improvement in Instructional PracticesStudents 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 activityN'U,X'U,X_>Framing Instructional Improvement at Scale as a Research IssueSeries 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:IiJHw]
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 strategiesnjX7NX6w
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 XX&
!'W,S3X^Data CollectionInstitutional 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.&,1-6S.%,1-6 S$$TVAdd Value to Districts Improvement EffortsFeed back results of analyses to districts
Gap analysis -- how district s plan is actually playing out in schools
Recommend actionable adjustments that might make each district s improvement design more effective
Design experiment at the level of the districtl+Gc/+G
OR
Research Team Paul Cobb Tom Smith
Erin Henrick Kara Jackson
Chuck Munter Sarah Green
John Murphy Karin Katterfeld
Lynsey Gibbons Glenn Colby
Annie Garrison6
n$One District as an Illustrative CaseConjectured support structures
The district s improvement plan
Findings and feedback to the district
Nf$ $$$$e{HConjecture: Teacher Networks$US teachers typically work in isolation
Social support from colleagues in developing demanding instructional practices
Focus of teacher interactions
Classroom instructional practice
Depth of teacher interactions
Mathematical intent of instructional tasks
Student reasoning strategiesbw!Hw!H,'T|I/Conjecture: Key Resources for Teacher Networks 00Time built into the school schedule for collaboration among mathematics teachers
Access to colleagues who have already developed relatively sophisticated instructional practices
Concrete exemplars of high-quality instructional practice &;;a District Plan: Teacher Networks !1-2 mathematics teachers in each school receive additional intensive mathematics professional development
Lead mathematics teachers
Facilitate biweekly or monthly teacher study group meetings&<<>j<b.Findings and Recommendations: Teacher Networks8/
.Quality of professional development for lead teachers high
Does not focus specifically on teaching underserved groups -- English language learners (ELLs)
Additional professional development for lead teachers on:
Teaching language in the context of mathematics -- ELLs`;_:8;_:7H#I r.Findings and Recommendations: Teacher Networks8/
.Collaboration between isolated pairs of mathematics teachers in some schools
Typically low depth
No opportunities for lead teachers to share what they are learning in most schools
Common planning time for mathematics teachers
Additional professional development for lead teachers on:
Process of supporting colleagues learning
Organizing the content of a study group s workMZZZZZMS.:$ $$((po.Findings and Recommendations: Teacher Networks8/
.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>rEBrEBP<8s}JAConjecture: Shared Vision of High Quality Mathematics InstructionInstructional goals -- what students should know and be able to do mathematically
How students' development of these forms of mathematical knowing can be supportedQAConjecture: Shared Vision of High Quality Mathematics InstructionCoordination between district administrative units
Curriculum and Instruction
Leadership
Research and Evaluation
English Language Learners
Special Education:3j3>~KAConjecture: Shared Vision of High Quality Mathematics InstructionOccupational groups: Mathematics teachers, principals, district mathematics specialists, district leadership specialists, &
Differences in:
Responsibilities
Practices
Professional affiliations (and professional identities) &UULConjecture: BrokersParticipate at least peripherally in the activities of two or more groups
Can bridge between differing agendas for mathematics instruction &JBJBd*District Plan: Shared Instructional VisionICurriculum 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 instructiontZZhZ;ZIII:e9Findings and Recommendations: Shared Instructional Vision*:
9UDistrict 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 principalsE \5\d1,d0s9Findings and Recommendations: Shared Instructional Vision*:
9Principals: 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( |Q
t$$Q((P^<(Mt9Findings and Recommendations: Shared Instructional Vision*:
9;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 activitiespKoKAA!M,l3M!Conjecture: Mutual AccountabilitySchool leaders hold mathematics teachers accountable for developing high-quality instructional practices
School leaders are accountable to mathematics teachers (and district leaders) for supporting teachers learningO9Conjecture: 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)F((N(Conjecture: Leadership Content KnowledgePrincipals 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 teachers077}= P(Conjecture: Leadership Content KnowledgeDistributed 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 expertiseF/Rv/Rui$District Plan: Mutual Accountability$bProfessional 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^HZZZH;L<7!Gj3Findings and Recommendations: Mutual Accountability*4
3Most 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~}ZpZ{ZkZ@=+E{k>:j@
u3Findings and Recommendations: Mutual Accountability*4
3Most 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 developmentLgkgkbT?Hv3Findings and Recommendations: Mutual Accountability*4
3+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@Z]Z,1gk3Findings and Recommendations: Mutual Accountability*4
3hGeneric classroom observation form specifies promotion of innovative teaching methods
Redesign observation form to reflect district vision of high-quality mathematics instruction.X TNfq'Summary: Conjectured Support StructuresTeacher networks
Time for collaboration
Access to expertise
Shared instructional vision
Brokers
Mutual accountability
Leadership content knowledge
+ xCurrent and Next StepsFall 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 districtsF-& ;-& &'Research AgendaTest, revise, and modify conjectures about relationships between:
Changes in school and district support structures
Improvement in mathematics teachers instructional practices
Student achievement:BBV.,s<(Research AgendaRefine conjectures:
Identifying additional support structures
Clarifying relationships between support structures
Specifying the conditions under which particular support structures are important b*3R!{Teachers Access to Expertise: Local and External Views of Expertise(F'Local views: Who teachers identify as experts
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cIn context of education, when talk about scale we are referring to the process of taking an instructional innovation that has proved effective in a small number of classrooms and reproducing that success in a large number of classrooms
How to take successful innovations to scale is a pressing problem in math ed. and in other subject matter areas
Collectively, we have learned a great deal in mathematics education over the past 20 years, but we have not learned much about how to up-scale successful instructional innovations\H
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Problematic for a number of reasons, not least of which is limited impact of research on classroom practice
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Evaluation of LSI projects
MSPs, H
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2Folks conducting large-scale implementation projects are well intentioned and work hard
This all-too-common experience is instructive
Research on scale aims to generate knowledge about these structures, about how they might be established as so forth
And how might we identify needed support structures?
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In taking this approach, we assume that the core business of the school is to support students learning of significant disciplinary ideas
This depends crucially on what transpires between teachers and students in classrooms
Map backwards to develop implications for school and district design
Outline of rest of talkBBH
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sSubsequent whole class discussion: Alice and Chris were asked to cut a piece of adding machine tape that signified wooden boards to be used for a smurf house so that it measured 23 cubes long. Alice iterated the smurf bar twice and uttered "10, 20" after each iteration. Then, she placed the smurf bar down once more to find a length of 23, but picked it up, broke off three cubes from the smurf bar and laid the three cubes at the end of the second iteration to indicate a length of 23bP;I[[H
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However, when teacher asks him to repeat to be sure that other students can understand, he reconceptualizes measuring with the ten bar
Unusual/atypical instructional practiceZCH
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Mapping backwards -- support initial emergence and subsequent learning of teacher networks and communities
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Argument for school-based math coaches8:& 1H
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ICollaboration between teachers, and collegiality between teachers and school and district leaders are rarely effective unless they are connected to a shared vision of high quality instruction that gives them meaning and purpose
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A principal who participates in professional development with mathematics teachers might be able to act as a broker between principals and mathematics teachers in the district, thereby facilitating the alignment of perspectives on mathematics teaching and learning across these two groups
Teachers who assume leadership roles in a school or district might also facilitate this form of boundary spanning between groups
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xHSchool leaders -- principals, assistant principals, mathematics coaches
Supporting teachers learning -- working with Ts in their classroom as well as providing PDH
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Principals and district leaders need deep LCK
Overwhelming at elementary level -- different subject matter areas
Impossible at secondary level
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Caveat: Don t hammer teachers/principals
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9Significant proportion of traditionally underserved groups of students -- limited resources
Elmore: Most districts clueless about how to respond to high-stakes accountability
A small minority have reasonably worked out strategies
Districts that have a chance of improving the quality of mathematics instruction
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Cautiously optimistic -- perceived as valuable in the case of four districts
Real test will come in the fall/autumn when we go back to the districts to document what adjustments they have actually made to their improvement plans -- to what extent have they actually act on the basis of our feedback?
Document the consequences of any changes in next round of data collection -- Jan-March
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On-screen ShowVanderbilt UniversityZ96@TimesPapyrusＭＳ ＰゴシックArial GaramondTimes New RomanRed wine ringgThe Challenges of Scale: Designing Learning Organizations for Instructional Improvement in MathematicsPurposeHistory of Failure1Limited Impact of Research on Classroom Practice$Large-Scale Implementation ProjectsLarge-Scale Implementation!Map Backwards From the Classroom%High-Quality Mathematics InstructionMeasuring With a Ten BarMeasuring With a Ten BarMeasuring With a Ten BarMeasuring With a Ten BarMeasuring With a Ten BarClassroom DiscourseDemands on the Teacher'Improvement in Instructional Practices?Framing Instructional Improvement at Scale as a Research IssueResearch PlanResearch PlanData Collection.Add Value to Districts’ Improvement EffortsResearch Team%One District as an Illustrative CaseConjecture: Teacher Networks0Conjecture: Key Resources for Teacher Networks !District Plan: Teacher Networks /Findings and Recommendations: Teacher Networks/Findings and Recommendations: Teacher Networks/Findings and Recommendations: Teacher NetworksBConjecture: Shared Vision of High Quality Mathematics InstructionBConjecture: Shared Vision of High Quality Mathematics InstructionBConjecture: Shared Vision of High Quality Mathematics InstructionConjecture: Brokers+District Plan: Shared Instructional Vision:Findings and Recommendations: Shared Instructional Vision:Findings and Recommendations: Shared Instructional Vision:Findings and Recommendations: Shared Instructional Vision"Conjecture: Mutual Accountability:Conjecture: Leadership Content Knowledge (in Mathematics))Conjecture: Leadership Content Knowledge)Conjecture: Leadership Content Knowledge%District Plan: Mutual Accountability4Findings and Recommendations: Mutual Accountability4Findings and Recommendations: Mutual Accountability4Findings and Recommendations: Mutual Accountability4Findings and Recommendations: Mutual Accountability(Summary: Conjectured Support StructuresCurrent and Next StepsResearch AgendaResearch AgendaHTeachers’ Access to Expertise: Local and External Views of Expertise<Teachers’ Access to Expertise: The Role of the PrincipalPolicy and LearningPolicy ResearchMathematics EducationLearning PolicyPowerPoint PresentationFonts UsedDesign Template
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