Timothy Boerst Pamela Moss Merrie Blunk DIAS Project University of Michigan

1
Timothy BoerstPamela MossMerrie BlunkDIAS
ProjectUniversity of Michigan
Unpacking Core Teaching Practices in Elementary
Mathematics to Support Teacher Learning and
Assessment

• National Science Foundation
• Discovery Research K-12 PI Meeting
• Washington, DC November 9, 2009

2
Session Overview

• Conception of assessment guiding DIAS
• High leverage mathematics teaching practices and
  leading a discussion
• Naming and describing the work of leading a
  discussion in mathematics
• Drawing on analytical language to discuss an
  example of novice discussion leading
• Concluding ideas

3
DIAS Project Goals

• To develop an assessment system for use in
  elementary mathematics teacher education that
• focuses on teaching practice grounded in
  professional and disciplinary knowledge as it
  develops over time
• addresses multiple purposes of a broad array of
  stakeholders working in different contexts and
• creates the foundation for programmatic coherence
  and professional development across time and
  institutional contexts.

4
DIAS Research Team

• Pamela Moss, Deborah Loewenberg Ball, Timothy
  Boerst, Annemarie Palincsar, with Hyman Bass.
  Merrie Blunk, Monica Candal, Michaela ONeill,
  Laurie Sleep Meri Tenney-Muirhead,
• University of Michigan, School of Education
• Mark Wilson, with Amy Dray, Xiaoting Huang,
• Heeju Jang,
• University of California, Berkeley
• Berkeley Evaluation and Assessment Research
  Center (BEAR)

5
Multiple Stakeholders Purposes

• In the preparation of teachers, assessment is
  needed by multiple stakeholders for multiple
  purposes, from admissions through the first years
  of teaching, for example
• To support student teachers in self assessment
• To support instructorsin school and university
  contextsin providing clinical feedback, or
  deciding what to do next in planning and
  enacting instruction, or making consequential
  decisions about readiness to teach
• To support program leaders and instructors in
  improving the curriculum, evaluating the quality
  of preparation student teachers receive, tracking
  group progress over time
• To support outside stakeholders in decisions
  requiring information about the quality of the
  program or its graduates

6
(No Transcript)
7
Mixed Methods Assessment System

• Different purposes require different
  configurations of evidence of student teachers
  learning and the factors that shape it
• Different purposes requires different methods to
  support
• routine interaction about teaching practice
• clinical and deliberative judgment of multi-media
  records of teaching practice
• program-level evaluations involving aggregation,
  comparison, and modeling of learning trajectories
  across time and contexts
• And yet, in order for the system to be coherent
  across these purposes, a common infrastructure is
  needed
• Key Sources Moss, Haniford,
  Girard, 2006 Moss, Pullin, Gee, Haertel, and
  Young 2008 Wilson, 2005, 2009

8
A Common Infrastructure Across Purposes

• Identify high leverage practices whose aspects
  can be (a) articulated, unpacked, studied, and
  rehearsed and (b) reintegrated in more holistic
  acts of teaching
• Articulate a palette of shared language for
  guiding and analyzing each high leverage practice
  that points to its essential components and
  describes increasing levels of sophistication
• Design examples of scaffolded sets of learning
  and assessment activities, staged over time, that
  support engagement in increasingly complex
  routine of teaching and provide multi-media
  records of teaching practice
• Articulate features of the context that shape
  practice so that these features can be (a) taken
  into account in analyzing the practice and (b)
  orchestrated in order to support learning in the
  setting
• Develop exemplars that provide analyses of cases
  of teaching practice in terms of the shared
  language for that teaching practice.
• Key sources Ball, Sleep, Boerst, and Ball,
  2009 Grossman et al, 2009 Grossman and
  MacDonald, 2008 Lampert, 2001 Moss, 2009
  

9
Decomposing practice

• Temporarily decompose1 teaching into smaller
  practices whose aspects
• can be articulated, unpacked, studied, and
  rehearsed
• can be reintegrated in more holistic acts of
  teaching
• Identify practices that are high-leverage2 in
  the work of teaching

1(Grossman Shahan, 2005) 2(Ball, Sleep,
Boerst, Bass, 2009)
10
High Leverage Mathematics Teaching Practice

• Occur frequently in mathematics teaching
• Support work that is central to mathematics
• Help to improve the learning and achievement of
  all students
• Apply across different approaches to teaching
  mathematics

(Cohen, Raudenbush, and Ball, 2003 Lampert, 2001)
11
High Leverage Mathematics Teaching Practice in
Teacher Education

• Can be articulated and taught
• Is accessible to novice teachers
• Is able to be practiced by beginners in their
  field-based settings

12
High Leverage Mathematics Teaching Practice in
the DIAS Project

• In-lesson assessment
• Planning lesson sequences
• Explaining mathematical ideas
• Leading a whole class discussion (our focus for
  this session)
• Discussions are
• viewed a primary mechanism for promoting
  conceptual understanding of mathematics
  (Michaels, OConnor, Resnick, 2008),
• a means of supporting students in learning
  disciplinary specific ways in which language is
  crafted (Yackel Cobb, 1996),
• foundational to the use of a growing number of
  curriculum materials (TERC, 1998), and
• an area in which there is an increasing amount of
  work being done to name and describe teaching
  practice (e.g. Lampert, 2001 Chapin et al.,
  2009 Smith et al., 2009)

13
Some Challenges of Supporting the Learning of
Discussion Leading Practices

• Naming and describing components of an integrated
  teaching practice
• Naming and describing a practice that may have
  areas that are unique to mathematics and others
  are are relevant across subject matters
• Embodying the multidimensional qualities practice
  (pedagogy that is mathematical and sensitive to
  students)
• Specifying practice in ways that apply to
  variations of teaching
• Deploying language in ways that an array of users
  can draw on as they support the learning of
  teaching

14
Naming Areas of Whole Group Discussion Leading
Practice

• Areas include
• Initiating, taking up, and coordinating
  participation
• Making contributions
• Recording and representing mathematics
• Planning for and appraising a discussion

(Cohen, Raudenbush, and Ball, 2003 Lampert, 2001)
15
Explore the Mathematical Qualities of Discussion
Leading Practices

• The focus
• Area Initiating, taking up, and coordinating
  participation
• Aspect Eliciting- an oral prompt to encourage a
  contribution about a new point
• (not following up responses, coordinating
  participation, or encouraging attention to the
  contributions of others)
• The example
• Lesson 8 in a fourth grade unit on Big numbers,
  estimation, and computation
• 30 Caucasian and Asian students
• Week 3 of student teaching (had recently
  completed the 1 required math methods course)
• We join just after the students had successfully
  been reading numbers and naming particular place
  values within those numbers
• The purpose of the discussion segment we will
  watch is to jointly consider the relative value
  of places in a number

16
Explore the Mathematical Qualities of Discussion
Leading Practices

• 3. The draft tool
• Four levels of sophistication, with 4 being the
  highest in the table, attending to
• the intended mathematics,
• extending the mathematics,
• substance expected in response, and
• indications that students understand the prompt
• Dedicated space to record evidence relevant to
  different levels of the work that may be observed
• The use (the same)
• To provide feedback to this novice about her
  eliciting of student contributions. Use
  descriptions from the tool and examples from the
  video to answer the question
• What would you suggest that she work on next?

17
Focus Questions for Discussion

• What feedback would you give the novice teacher
  about eliciting student contributions during this
  discussion? Try drawing on language from the
  tool and examples from the video.
• In what ways did/didnt the descriptions of
  eliciting in the tool support you in attending to
  the mathematics of this work?

18
Explore the Mathematical Qualities of Discussion
Leading Practices

• The focus
• Area Making contributions
• Aspect Offering mathematical information-
  Sharing mathematics (e.g. notation, explanations,
  models, language, etc) that has not yet been
  mentioned in the discussion
• (not summarizing, presenting new connections, or
  explicating practices and norms )
• The example (the same as before)
• 3. The draft tool
• Four levels of sophistication attending to
  purpose, clarity, accuracy, accessibility,
  timing, mode of communication, and potential and
  use to advance the mathematics of the discussion
• Dedicated space to record evidence relevant to
  different levels of the work that may be observed
• The use (the same)
• To provide feedback to this novice about her
  offering of mathematical information. What would
  you suggest that she work on next? Try drawing
  on language from the tool and examples from the
  video.

19
Focus Questions for Discussion

• What feedback would you give the novice teacher
  about offering information during this
  discussion? Try drawing on language from the
  tool and examples from the video.
• In what ways did/didnt the descriptions of
  offering information in the tool support you in
  attending to the mathematics of this work?

20
Conclusion DIAS Responses to Challenges of
Supporting the Learning of High Leverage
Practices

• Naming and describing components of an integrated
  teaching practice
• Articulate areas of practice that correspond with
  work flows and sequences in records of practice,
  literature, and in descriptions of practice by
  expert practitioners
• Articulate aspects that capture a finer grain
  size of teaching work that correspond with each
  area
• Naming and describing a practice that may have
  areas that are unique to mathematics and others
  are are relevant across subject matters
• Include practices that are relevant to the
  leading of mathematics and be sensitive to those
  that may be central or unique to mathematics
  discussions
• Embodying the multidimensional qualities practice
• Embed attention to mathematics and students in
  descriptions of degrees of sophistication

21
Conclusion DIAS Responses to Challenges of
Supporting the Learning of High Leverage
Practices

• Deploying language in ways that are usable in
  different contexts
• Try out language against an array of mathematics
  discussions (topics, experience, contexts,
  curricula)
• Construct an array of tools from the palette of
  language available in a comprehensive source
  document
• Deploying language in ways that an array of users
  can draw on as they support the learning of
  teaching
• Support the learning of, and learn from, field
  instructors, cooperating teachers, and methods
  instructors