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Moving Beyond Implementation: Challenges and Possibilities
NCSM April 24 - 26, 2006
Edward A. Silver, Valerie Mills, Lawrence Clark,
Geraldine Devine, Hala Ghousseini
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Today’s Session: An Overview Today’s Session: An Overview
The Implementation Plateau
The BIFOCAL Project
Background
The Mathematics Task Framework & Levels of Cognitive Demand
Design Principles and Structural Features
Instructional Issues Addressed in BIFOCAL
The Case of Giselle
Questions and Discussion
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A Common Dilemma
School District USA, introduced a problem-based, reform-oriented mathematics instructional program in the middle
grades (i.e., CMP) about four years ago . Student achievement increased steadily
for three years, but appears to be leveling off. Why? What can be done to support
teachers and sustain growth?
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Comments on Video Clip
Teachers discuss case in relation to their classroom experiences implementing a problem-based curricula
Issues of curriculum materials are not the focus
Issues of instructional refinement emergeHow to manage multiple solutionsHow to reach all students in the classroom
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Implementation Plateau Characterized by teachers who participated in
curriculum centered professional development during the implementation of a standards-based mathematics program
Teachers are familiar and confident using new program features such as: new lesson format designs, Student tasks that require eliciting and evaluating student’s
written mathematical explanations, and Investigations that utilize various grouping structures in the
classroom Teachers are generally committed to their own use of
the new materials
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Implementation Plateau
After the first year, student achievement on various standardized measures typically improves steadily for three to five years, then growth appears to level off.
Teachers feel generally confident, but …not fully competent and unable to articulate the problem
Vulnerable time for districts as concerns reemerge
District’s resources no longer available
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Implementation Plateau
The curriculum implementation plateau is a stage when teaching and learning appear
to bog down; there is a need to refine instructional practices established during implementation, to continue building local
capacity, and to maintain growth in student performance through sustained, long-term teacher engagement and the provision of a
space for guided reflection on the instructional issues they currently face.
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Processes Associated With Implementation of Standards-based
Mathematics Curricula
Level I: Awareness
Level II: Selection & Adoption
Level IV: Refinement & Building Local Capacity
Level III: Implementation
(St. John, Heenan, Houghton, & Tambe, 2001)
PLATEAU
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The Role of the BIFOCAL Project
Level I: Awareness
Level II: Selection & Adoption
Level IV: Refinement & Building Local Capacity
Level III: Implementation
(St. John, Heenan, Houghton, & Tambe, 2001)
PLATEAU
BIFOCAL
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The Goals of the BIFOCAL Project
Understand the implementation plateau
Assist teachers and schools
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The BIFOCAL ProjectBeyond Implementation:
Focus on Challenge and Learning
Project TeamEdward Silver, Valerie Mills, Alison Castro,
Charalambos Charalambous, Lawrence Clark, Gerri Devine, Hala Ghousseini, Melissa Gilbert,
Dana Gosen, Jenny Sealy, Beatriz Font Strawhun, & Gabriel Stylianides
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The BIFOCAL The BIFOCAL ProjectProject
The following organizations provide funding for various aspects of BIFOCAL:
• The National Science Foundation (via CPTM)
• The University of Michigan
• The Mathematics Education Endowment Fund
• The Oakland Intermediate School District
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BIFOCAL: Project HistoryBIFOCAL: Project History Year One
12 teacher leaders (experienced CMP users) 10 full-day sessions
Year Two 12 teacher leaders and 48 teachers (Ele., MS, HS) 6 full-day sessions 6 school-based sessions lead by teacher leaders
Year Three Similar design to Year Two Focus on assessment for learning
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Teaching with Challenging Mathematics Tasks
Teachers must decide “what aspects of a task to highlight, how to organize and orchestrate the work of the students, what questions to ask to challenge those with varied levels of expertise, and how to support students without taking over the process of thinking for them and thus eliminating the challenge.” NCTM, 2000,
p.19
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BIFOCAL: Background in a NutshellBIFOCAL: Background in a Nutshell
Supporting Frameworks/Perspectives : “Practice-based” approach (Ball,
Smith)Mathematical Task Framework
(QUASAR)Case Analysis & DiscussionLesson Study
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BIFOCAL: BIFOCAL: Practice-Based Practice-Based ApproachApproach Professional development experiences
situated in authentic teaching practiceallow the everyday of teaching to
become the object of on-going investigation and inquiry
Build around professional learning tasks (Smith, 2000; Ball & Cohen,
1999)
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The Mathematical Task The Mathematical Task FrameworkFramework
Tasks as set up by teachers
Tasks as they appear in curricular materials
Tasks as enacted by teacher and students Student
learning
Stein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000)
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MTF - The Bottom LineMTF - The Bottom Line
Tasks are important, but teachers also matter!
Teacher actions and reactions … influence the nature and extent of
student engagement with challenging tasks,
affect students’ opportunities to learn from and through task engagement.
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Some MTF-Related Challenges Facing All Teachers of
Mathematics Resisting the persistent urge to tell and to direct;
allowing time for student thinking
Knowing when/how to ask questions and to provide information to support rather than replace student thinking
Helping students accept the challenge of solving worthwhile problems and sustaining their engagement at a high level
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BIFOCAL: Background in a NutshellBIFOCAL: Background in a Nutshell
Motivation: “Implementation plateau” phenomenon
Supporting Frameworks/Perspectives : “Practice-based” approach (Ball, Smith)Mathematical Task Framework (QUASAR
project)Case Analysis & DiscussionCase Analysis & DiscussionLesson StudyLesson Study
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A Typical Year One A Typical Year One BIFOCAL SessionBIFOCAL Session
Case Analysis and Discussion (CAD) Solve mathematical task Read, analyze/discuss teaching cases (text,
video, student work samples)
Modified Lesson Study (MLS) Discuss lesson enactment from previous session Select target lesson Use structured set of questions to guide
collaborative planning
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Feb 2004
Marie Hanson Case: The Candy Jar Task“What mathematical goals might a teacher
using this task have for students?” “What kinds of thinking/reasoning might we
anticipate students using with this task?” “What student misconceptions or errors might
we anticipate with this task?”
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Feb 2004 Marie Hanson Case
What inferences might you draw about these students understanding or misunderstanding? (cite line numbers to support your conclusions)
What did Marie do to assess student understanding or misunderstanding? (cite line numbers to support your conclusions)
Identify Marie’s instructional decisions in this segment and:
indicate how these moves either helped to maintain or undermine the demand of the tasks
speculate on the rationale Marie may have used to inform her use of multiple student solution approaches and its relationship to the mathematical goal of the lesson
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Feb 2004 Modified Lesson Study - Adapted TTLP Selecting and Setting up a Mathematical Task
What are your math goals for the lesson? What are all the ways the task can be solved? How will you introduce students to the activity so as not to
reduce the demands of the task? Supporting Students’ Exploration of the Task
As students are working independently or in small groups Sharing and Discussion the Task
Which solution paths do you want to have shared during the class discussion in order to accomplish the goals for the lesson?
What will you see or hear that lets you know that students in the class understand the mathematical ideas or problem-solving strategies that are being shared?
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A Mathematics Professional A Mathematics Professional Development SynergyDevelopment Synergy
ModifiedLesson Study
Case-Based Professional Development
Curriculum-BasedProfessional Development
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Blending CAD and MLS as the Blending CAD and MLS as the Professional Development Professional Development
EvolvesEvolves
Modified Lesson Study
(1)
Case Analysis and
Discussion(1)
Case Analysis and Discussion
(2)Modified
Lesson Study (2)
Case Analysis and Discussion
(3)
Modified Lesson Study
(3)
Instructional Issue X
Instructional Issues XY
Instructional Issues XYZ
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Instructional Issues Available for Refinement at the Implementation
Plateau Identifying mathematical goals, short-term and long -termConsidering multiple solution strategies Scaffolding student thinking in ways that support the cognitive demands of the mathematics task Assessing student understanding of mathematical ideas Deciding how to support students without taking over the process of thinking for them and thus eliminating the challenge of the task Anticipating student misconceptions
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The Case Of Giselle Background information Openness in voicing concerns and
sharing dilemmas
Tracing her learning trajectory with respect to: Questioning techniques-supporting student work
without doing the thinking for them Sharing multiple solutions
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The Case Of Giselle
May 2003
October 2003
November 2003
March 2004
January 2006
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May 2003
The kids [in David’s class] were talking with each other. There were a couple of instances where he was not even doing the questioning. They were excited to ask the questions. The first thing I thought about was “Wow, they are really confident!” I don’t get enough of that in my room. I am usually the questioner.
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GiselleGiselle: […] Bring the other students in. I would want to involve another student and another idea.involve another student and another idea. How quickly? I don’t know. But I know I would want the kids interacting I would want the kids interacting moremore.
Learning In Transition: October
2003 GiselleGiselle: I noticed right off the bat that he [Randy Harris] asked a lot of questionsa lot of questions. [...] I didn’t think it was as appropriate there. He was trying to get her up to where he thought she should be. This is something I would do. If my students are not all there I do ask a lot of I do ask a lot of questionsquestions and I don’t think that is always the right thing to do […]His question was far too specific and [the student] wasn’t doing any higher level thinking… He walks her through what it should have been step by step […] She gives all the right answers, but she wouldn’t have gotten there without the questions.FacilitatorFacilitator: So what would you do?
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I am really concerned about their cognitive development. Are they really getting anything out of it as they should be? Or am I just holding their hand and walking them one on one? You know what I mean? I wanted them to be successful, so I came to find to sacrifice something. It’s a little bit of cognitive demand, definitely. Cause I wanted them to be motivated.
Learning In Transition: November 2003
At first you are reminding them […] “pull out from previous stages”, “look for something that would help you”, “how can you draw the lines”, “how can you make a triangle”, all that. But eventually they need to do that independently. You know, you are not always going to be in their hip pocket. They have to know what they are looking for.
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I would look at what they were doing and what they were not getting at all and I would ask them things that would generate relationships, like what is the relationship between the height of the tallest man and this tree.
Learning in Transition: March 2004
You can prepare questions beforehand but you have to look at what the kids are doing and it changes. […]I got them to get with a partner and compare statements, and see if there were errors before we got together and shared. In terms of questions, I really ended up coming up with them as we worked through,
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Still Learning: January 2006
Giselle helps another teacher realize Giselle helps another teacher realize the idea of using assessmentthe idea of using assessment forfor learninglearning .
“Instead of just telling the kids what they did wrong and then showing them the right way to do it, we wanted them to brainstorm together on what was wrong in that approach” .
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QuickTime™ and aH.263 decompressor
are needed to see this picture.
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Implementation Plateau
The curriculum implementation plateau is a stage when teaching and learning appear to bog down; there is a need to refine instructional practices established during implementation, to continue
building local capacity, and to maintain growth in student performance through sustained, long-
term teacher engagement and the provision of a space for guided reflection on the
instructional issues they currently face.
38
Instructional Issues Available for Refinement at the Implementation
Plateau Identifying mathematical goals, short-term and long -term Considering multiple solution strategies Scaffolding student thinking in ways that support the cognitive demands of the mathematics task Assessing student understanding of mathematical ideas Deciding how to support students without taking over the process of thinking for them and thus eliminating the challenge of the task Anticipating student misconceptions
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Teaching with Challenging Mathematics Tasks
Teachers must decide “what aspects of a task to highlight, how to organize and orchestrate the work of the students, what questions to ask to challenge those with varied levels of expertise, and how to support students without taking over the process of thinking for them and thus eliminating the challenge.” NCTM, 2000, p.19
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Instructional Issues Available for Refinement at the Implementation
Plateau As you talk with and observe teachers who are poised on the implementation plateau, what aspects of practice do you believe teachers would value an opportunity to explore?
What feels challenging about professional development at this stage of implementation?
What feels compelling about professional development at this stage of implementation?
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Thanks for being such an attentive audience…
Contact Information:valerie.mills@oakland
.k12.mi.usValerie Mills
[email protected] Silver