Transcript The BIFOCAL Project

Moving Beyond Implementation:
Challenges and Possibilities
NCSM
April 24 - 26, 2006
Edward A. Silver, Valerie Mills, Lawrence Clark,
Geraldine Devine, Hala Ghousseini
1
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
2
A Common Dilemma
School District USA, introduced a problembased, 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?
3
QuickTime™ and a
decompressor
are needed to see this picture.
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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 emerge

 How
to manage multiple solutions
 How to reach all students in the classroom
5
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.
8
Processes Associated With
Implementation of Standards-based
Mathematics Curricula
Level IV: Refinement & Building Local Capacity
Level III: Implementation
PLATEAU
Level II: Selection & Adoption
Level I: Awareness
(St. John, Heenan, Houghton, & Tambe, 2001)
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The Role of the BIFOCAL Project
Level IV: Refinement & Building Local Capacity
Level III: Implementation
PLATEAU
BIFOCAL
Level II: Selection & Adoption
Level I: Awareness
(St. John, Heenan, Houghton, & Tambe, 2001)
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The Goals of the BIFOCAL Project

Understand the
implementation plateau

Assist teachers and
schools
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The BIFOCAL Project
Beyond Implementation:
Focus on Challenge and Learning
Project Team
Edward Silver, Valerie Mills, Alison Castro, Charalambos
Charalambous, Lawrence Clark, Gerri Devine, Hala
Ghousseini, Melissa Gilbert, Dana Gosen, Jenny Sealy,
Beatriz Font Strawhun, & Gabriel Stylianides
12
The BIFOCAL Project
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 History

Year One
teacher leaders (experienced CMP users)
10 full-day sessions
 12


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
15
BIFOCAL: Background in a Nutshell

Supporting Frameworks/Perspectives :
 “Practice-based” approach (Ball, Smith)
 Mathematical Task Framework (QUASAR)
 Case Analysis & Discussion
 Lesson Study
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BIFOCAL: Practice-Based Approach
Professional development experiences
 situated in authentic teaching practice
 allow 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 Framework
Tasks as
they appear
in curricular
materials
Tasks as
set up by
teachers
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 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

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
time for student thinking
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BIFOCAL: Background in a Nutshell


Motivation: “Implementation plateau”
phenomenon
Supporting Frameworks/Perspectives :
 “Practice-based” approach (Ball, Smith)
 Mathematical Task Framework (QUASAR
project)
 Case Analysis & Discussion
 Lesson Study
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A Typical Year One
BIFOCAL 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
Development Synergy
Case-Based
Professional
Development
Modified
Lesson Study
Curriculum-Based
Professional
Development
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Blending CAD and MLS as the
Professional Development Evolves
Modified Lesson
Study (3)
Instructional
Issues XYZ
Case Analysis and
Discussion (3)
Case Analysis and
Discussion (2)
Instructional
Issues XY
Modified Lesson
Study (2)
Modified Lesson
Study (1)
Case Analysis and
Discussion(1)
Instructional
Issue X
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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
28
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
January 2006
March 2004
November 2003
October 2003
May 2003
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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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Learning In Transition: October 2003
Giselle: I noticed right off the bat that he [Randy Harris] asked
a 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 questions 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.
Facilitator: So what would you do?
Giselle: […] Bring the other students in. I would want to involve
another student and another idea. How quickly? I don’t know. But
I know I would want the kids interacting more.
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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.

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.

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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,
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.
34
Still Learning: January 2006


Giselle helps another teacher realize the
idea of using assessment for learning .
“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” .
35
QuickTime™ and a
H.263 decompressor
are needed to see this picture.
36
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.
37
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
38
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
39
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?
40
Thanks for being such an attentive
audience…
Contact Information:
[email protected]
Valerie Mills
[email protected]
Edward Silver
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