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					 Operationalizing the Concept of
 “Fidelity of Implementation” for
NSF-Funded Mathematics Curricula
            Mary Ann Huntley
          University of Delaware
   2005 NSF K-12 Math, Science, & Technology
       Curriculum Developers Conference
               Alexandria, Virginia
                February 28, 2005
                         The Problem
Existing research suggests that the NSF-funded
mathematics curricula are positively impacting students
and teachers (Senk & Thompson, 2003).

However, most impact studies (e.g., Huntley et al., 2000)
fail to adequately address how these curricula are being
implemented.

      AUTHORS
  Teachers Professors   curriculum   Teacher
                                                  ?
                                               curriculum as
                                                               Students


                         materials             implemented
―Two classrooms in which the same [reform
mathematics] curriculum is supposedly being
‗implemented‘ may look very different; the
activities of teacher and students in each room
may be quite dissimilar, with different learning
opportunities available, different mathematical
ideas under consideration, and different
outcomes achieved.‖


                   Kilpatrick (2003, p. 473)
                Overview
Research Paradigms
  • Fidelity Perspective
  • Mutual Adaptation Perspective
  • Curriculum Enactment Perspective

Research Study
  • Purpose & Main Research Question
  • CBAM Theory
       – Overview
       – Innovation Configuration Maps
                Overview
Research Paradigms
  • Fidelity Perspective
  • Mutual Adaptation Perspective
  • Curriculum Enactment Perspective

Research Study
  • Purpose & Main Research Question
  • CBAM Theory
       – Overview
       – Innovation Configuration Maps
Research Paradigms for Studying
   Curriculum Implementation
(Snyder, Bolin, & Zumwalt, 1992)

Fidelity Perspective

Mutual Adaptation Perspective

Curriculum Enactment Perspective
                Overview
Research Paradigms
  • Fidelity Perspective
  • Mutual Adaptation Perspective
  • Curriculum Enactment Perspective

Research Study
  • Purpose & Main Research Question
  • CBAM Theory
       – Overview
       – Innovation Configuration Maps
           Fidelity Perspective
Premise
  New curricula should be implemented the
  way the authors intend.

Research Foci
• Examine deviations of classroom practice
  from original intent of curriculum developers.
• Identify factors that encourage or hinder full
  implementation.
     Fidelity Perspective


Appealing logic, but …

A written curriculum cannot capture
or fully represent teaching.
―Teachers necessarily select from and adapt
materials to suit their own students. This
creates a gap between curriculum developers‘
intentions for students and what actually
happens in lessons. Developers‘ designs thus
turn out to be ingredients in—not determinants
of—the actual curriculum.‖

                  Ball & Cohen (1996, p. 6)
    Curriculum Developers View
  Curricular Adaptation as Desirable
1. Teachers bring their own personal teaching
   philosophies and background experiences to
   their classrooms.

2. Teachers adapt their instruction to the diverse
   needs of their particular students.

3. Authors cannot fully anticipate how particular
   students will engage with the activities in their
   curricular materials.
    Basic Tenet of Effective
    Mathematics Teaching

Teachers know and understand deeply
the mathematics they are teaching and
are able to draw on that knowledge with
flexibility during classroom instruction.
                Overview
Research Paradigms
  • Fidelity Perspective
  • Mutual Adaptation Perspective
  • Curriculum Enactment Perspective

Research Study
  • Purpose & Main Research Question
  • CBAM Theory
       – Overview
       – Innovation Configuration Maps
   Mutual Adaptation Perspective

Premise
   Teachers inevitably modify the curriculum
   during classroom instruction.

Research Focus
   Examine modifications of curriculum
   materials according to specific classroom
   situations.
  Fidelity-Variation Dilemma

―How far may teachers go in their
adaptations without destroying the spirit
and meaning of the curriculum they
implement in their classes?‖

             Ben-Peretz (1990, p. 31)
 Capturing the ‗Spirit‘ of a Curriculum

Conceptualization of Curricula (Bridgham, 1971)
  Trajectories through pedagogic space

Curriculum Envelopes (Ben-Peretz, 1990)
  Boundaries of envelopes – certain general
  characteristics chosen by curriculum developers
      Inside the Envelope    Keep major features of
                             curriculum intact
      Outside the Envelope   Modifying curriculum‘s
                             major features
                Overview
Research Paradigms
  • Fidelity Perspective
  • Mutual Adaptation Perspective
  • Curriculum Enactment Perspective

Research Study
  • Purpose & Main Research Question
  • CBAM Theory
       – Overview
       – Innovation Configuration Maps
 Curriculum Enactment Perspective

Premise
   Curriculum consists of the educational
   experiences jointly created by students
   and teachers.

Research Focus
   Examine how a curriculum takes form
   through the evolving constructions of
   teachers and students.
                Overview
Research Paradigms
  • Fidelity Perspective
  • Mutual Adaptation Perspective
  • Curriculum Enactment Perspective

Research Study
  • Purpose & Main Research Question
  • CBAM Theory
       – Overview
       – Innovation Configuration Maps
         Research Study
 (Spencer Postdoctoral Fellowship)
What does it mean to implement the [xyz
curriculum] as the authors intend?
 • What does it look like?
 • How do you know it when you see it?
 • In what ways does implementation of
   [curriculum 1] differ from implementation
   of [curriculum 2]?
      Purpose of the Study


To examine implementation of two NSF-
funded comprehensive middle-grades
reform mathematics curricula:
     Connected Mathematics (CMP)
     Math Thematics (MT)
     Main Research Question

What does it mean to implement CMP/MT
the way the authors intend? In other words,
what are the essential characteristics and
acceptable adaptations of CMP/MT
implementation?
                Overview
Research Paradigms
  • Fidelity Perspective
  • Mutual Adaptation Perspective
  • Curriculum Enactment Perspective

Research Study
  • Purpose & Main Research Question
  • CBAM Theory
       – Overview
       – Innovation Configuration Maps
 CBAM Theory (Hall & Hord, 2001)
A theory about understanding and facilitating the
change process in organizational and educational
settings.
Premise – an innovation, when used in practice, can
take on many different operational forms
(configurations), with variation along a continuum.


          very close to      distant zone (what is
        what the developer   being done is nearly
           had in mind         unrecognizable)
 Innovation Configuration (IC) Map


A CBAM diagnostic tool to measure an
innovation in practice.

Involves identifying the major components of
an innovation and observable variations of
each component.
 IC Map for Teaching and Learning
Mathematics (Alquist & Hendrickson, 1999)

  Developed to study implementation of
  a new K-12 mathematics program
  developed for DoDDS that is aligned
  with the NCTM Standards (1989).
Component Clusters in the IC Map for
Teaching and Learning Mathematics
 1. Presentation and Facilitation
 2. Engagement with Task/Investigation
 3. Establishing and Maintaining a
    Community of Learners
 4. Focusing on Student Learning
 5. Classroom Resources and Arrangement
 6. Culture of the Classroom
              Organizing Framework
                        Task/             Community of      Classroom
                    Investigation        Learners/Culture    Culture
                       Focus

Teacher Roles &      Presentation,        Establishing &      Physical
Responsibilities      Facilitation,       Maintaining a     Resources &
                   Direct Instruction,      Focus on        Arrangement
                        Making              Learning
                     Connections,
                        Closure

Student Roles &    Engagement with         Focusing on      Culture of the
Responsibilities         Task/              Learning         Classroom
                     Investigation
              Organizing Framework
                        Task/             Community of      Classroom
                    Investigation        Learners/Culture    Culture
                       Focus

Teacher Roles &      Presentation,        Establishing &      Physical
Responsibilities      Facilitation,       Maintaining a     Resources &
                   Direct Instruction,      Focus on        Arrangement
                        Making              Learning
                     Connections,
                        Closure

Student Roles &    Engagement with         Focusing on      Culture of the
Responsibilities         Task/              Learning         Classroom
                     Investigation
Students Engaged in Mathematical Tasks
Throughout the Lesson {engagement, time}


      a                b                c                 d
Most students    Most students    Some students    Few students
are engaged in   are engaged in   are engaged in   are engaged
mathematical     mathematical     mathematical     any of the time.
tasks, most of   tasks, part of   tasks. Many
the time.        the time.        are off task
                                  most of the
                                  time.
              Organizing Framework
                        Task/             Community of      Classroom
                    Investigation        Learners/Culture    Culture
                       Focus

Teacher Roles &      Presentation,        Establishing &      Physical
Responsibilities      Facilitation,       Maintaining a     Resources &
                   Direct Instruction,      Focus on        Arrangement
                        Making              Learning
                     Connections,
                        Closure

Student Roles &    Engagement with         Focusing on      Culture of the
Responsibilities         Task/              Learning         Classroom
                     Investigation
Teacher Poses Mathematical Tasks/Investigations
{poses, frequency, open-ended questions, language}
       a                 b                 c                d                 e
T poses open-      T identifies      T presents the   T structures      T presents/
ended problem,     mathe.            activity with    activity &        explains
highlights         aspects of        little or no     directs sts‘      isolated
mathe. aspects     tasks/invs. &     explanation.     activity. Qs      concept or
& asks sts to      explains how      T uses little    requiring one-    procedure &
det. how to        to figure them    or no mathe.     word answers      assigns
figure them out.   out. T            lang. Some T     are used to       individual sts
Open-ended         directions are    directions are   check for st      work. Qs
Qs are used to     clear. Some       clear. Nearly    understanding.    requiring one-
pose problems,     mathe. lang. is   all Qs require   Isolated use of   word answers
not only at the    used. Some        one-word         mathematical      are used to
beginning but      open-ended        answers.         vocab.            check for st
also throughout    Qs are asked.                                        understanding.
lesson. T uses                                                          Isolated use of
mathe. lang. to                                                         mathe. vocab.
present
tasks/invs.
           Uses of IC Maps

1. Teacher Self Analysis and Reflection

2. Teacher Peer Observation and Coaching

3. Planning for Training and Staff Development
                Overview
Research Paradigms
  • Fidelity Perspective
  • Mutual Adaptation Perspective
  • Curriculum Enactment Perspective

Research Study
  • Purpose & Main Research Question
  • CBAM Theory
       – Overview
       – Innovation Configuration Maps

				
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