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Timothy BoerstPamela MossMerrie Blunk

DIAS ProjectUniversity of Michigan

National Science FoundationDiscovery Research K-12 PI MeetingWashington, DC • November 9, 2009

Unpacking Core Teaching Practices in Elementary Mathematics to Support

Teacher Learning and Assessment

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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

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DIAS Project GoalsTo 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.

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DIAS Research Team

Pamela Moss, Deborah Loewenberg Ball, Timothy Boerst, & Annemarie Palincsar, with Hyman Bass. Merrie Blunk, Monica Candal, Michaela O’Neill, Laurie Sleep & Meri Tenney-Muirhead, University of Michigan, School of Education

Mark Wilson, with Amy Dray, Xiaoting Huang, & Heeju Jang, University of California, BerkeleyBerkeley Evaluation and Assessment Research Center (BEAR)

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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 instructors—in school and university

contexts—in 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

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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

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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

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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-leverage”2 in the work of teaching

1(Grossman & Shahan, 2005); 2(Ball, Sleep, Boerst, & Bass, 2009)

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High Leverage Mathematics Teaching Practice

(Cohen, Raudenbush, and Ball, 2003; Lampert, 2001)

environments

teachers

students

students

content

• 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

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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

environments

teachers

students

students

contentenvironments

teachers

students

students

contentteacher

teacher

teacher educator

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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, O’Connor, & 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)

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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

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Naming Areas of Whole Group Discussion Leading Practice

(Cohen, Raudenbush, and Ball, 2003; Lampert, 2001)

environments

teachers

students

students

content

Areas include:• Initiating, taking up, and

coordinating participation• Making contributions• Recording and representing

mathematics• Planning for and appraising a

discussion

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Explore the Mathematical Qualities of Discussion Leading Practices

1. The focuso Area: Initiating, taking up, and coordinating participationo 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)

2. The exampleo Lesson 8 in a fourth grade unit on “Big numbers, estimation, and

computation”o 30 Caucasian and Asian studentso Week 3 of student teaching (had recently completed the 1 required math

methods course)o We join just after the students had successfully been reading numbers and

naming particular place values within those numberso The purpose of the discussion segment we will watch is to jointly consider

the relative value of places in a number

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Explore the Mathematical Qualities of Discussion Leading Practices

3. The draft tool o 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

o Dedicated space to record evidence relevant to different levels of the work that may be observed

4. The use (the same)

o 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?

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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/didn’t the descriptions of eliciting in the tool support you in attending to the mathematics of this work?

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Explore the Mathematical Qualities of Discussion Leading Practices

1. The focuso Area: Making contributionso 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 )

2. The example (the same as before)

3. The draft tool o 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

o Dedicated space to record evidence relevant to different levels of the work that may be observed

4. The use (the same)o 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.

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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/didn’t the descriptions of offering information in the tool support you in attending to the mathematics of this work?

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Conclusion: DIAS Responses to Challenges of Supporting the Learning of High Leverage

Practices • Naming and describing components of an integrated teaching

practiceo Articulate areas of practice that correspond with work flows and

sequences in records of practice, literature, and in descriptions of practice by expert practitioners

o 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 matterso 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 practiceo Embed attention to mathematics and students in descriptions of

degrees of sophistication

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Conclusion: DIAS Responses to Challenges of Supporting the Learning of High Leverage

Practices • Deploying language in ways that are usable in different

contextso Try out language against an array of mathematics discussions

(topics, experience, contexts, curricula)o 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 teachingo Support the learning of, and learn from, field instructors,

cooperating teachers, and methods instructors