1. The BEAR Center Timothy Boerst Pamela Moss Merrie Blunk DIAS Project University of Michigan National Science Foundation Discovery Research K-12 PI Meeting Washington, DC November 9, 2009 Unpacking Core Teaching Practices in Elementary Mathematics to Support Teacher Learning and Assessment

2. The BEAR Center 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. The BEAR Center 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. The BEAR Center 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, Berkeley Berkeley Evaluation and Assessment Research Center (BEAR)

5. The BEAR Center 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

6. The BEAR Center

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. The BEAR Center 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. The BEAR Center Decomposing practice Temporarily decompose 1 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)

10. The BEAR Center High Leverage Mathematics Teaching Practice (Cohen, Raudenbush, and Ball, 2003; Lampert, 2001) 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

11. The BEAR Center 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 teacher teacher educator

12. The BEAR Center 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)

13. The BEAR Center 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. The BEAR Center Naming Areas of Whole Group Discussion Leading Practice (Cohen, Raudenbush, and Ball, 2003; Lampert, 2001) Areas include: Initiating, taking up, and coordinating participation Making contributions Recording and representing mathematics Planning for and appraising a discussion

15. The BEAR Center Explore the Mathematical Qualities of Discussion Leading Practices 1.The focus o Area: Initiating, taking up, and coordinating participation o 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 example o Lesson 8 in a fourth grade unit on “Big numbers, estimation, and computation” o 30 Caucasian and Asian students o 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 numbers o The purpose of the discussion segment we will watch is to jointly consider the relative value of places in a number

16. The BEAR Center 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?

17. The BEAR Center 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?

18. The BEAR Center Explore the Mathematical Qualities of Discussion Leading Practices 1.The focus o Area: Making contributions o 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.

19. The BEAR Center 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?

20. The BEAR Center Conclusion: DIAS Responses to Challenges of Supporting the Learning of High Leverage Practices Naming and describing components of an integrated teaching practice o 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 matters o 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 o Embed attention to mathematics and students in descriptions of degrees of sophistication

21. The BEAR Center Conclusion: DIAS Responses to Challenges of Supporting the Learning of High Leverage Practices Deploying language in ways that are usable in different contexts o 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 teaching o Support the learning of, and learn from, field instructors, cooperating teachers, and methods instructors