Mathematics Teacher
Educators
Working to Assess the Use of
Case-Based
Materials
Breyfogle, Hillman,
Ives, Roth McDuffie, M...
Why Consider Cases? (Mike)
Case discussions share common goals:
• To increase and enrich teachers’ fundamental beliefs
and...
An Example of Purpose: Amy
Background/Context
• Part of work with TEACH MATH (Teachers
Empowered to Advance Change in Math...
The Four Lenses
(Overarching Purpose Across Case Studies)
1. TASK: What makes this a good and/or problematic task?
How cou...
Specific example of a video clip used for these
purposes: "Equalities"
(Thinking Mathematically, Carpenter, Franke, & Levi...
Equalities Example (continued)
How this video clip connects to our purposes
with the lenses:
• Case of bilingual classroom...
Equalities Example (continued)
How this video clip connects to our purposes
with the lenses:
• Case shows a discussion in ...
An Example of Enactment: Mike
Edited clip from a discussion of a case
Context:
• Content-focused methods course - geometry...
Need for Collective Documentation
• Case materials are increasingly available, but
there is little collective or systemati...
Discussion Questions
Small groups discuss the following topics (30 minutes):
• What research questions are we interested i...
Closure
During the last 15 minutes of the session, the subgroups will
share their ideas and the facilitators will collect ...
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Mathematics Teacher Educators Working to Assess the Use of Case-Based Materials

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  • Each lens has other prompts, with a common prompt to focus on: resources and knowledge bases students use (e.g., mathematical, cultural, community, family, linguistic)
     
    Scaffold noticing to prepare for noticing in the real world.
  • (sometimes we just need to explore mathematical relationships - but it can still happen in deep and engaging ways)
  • (and misconceptions) through carefully selected problems that induce cognitive conflict and resolution
  • We have these robust conversations, we have these video examples ... are these videos really worth our time?
  • Is there a question you would like to focus on?
    For what purposes are cases being used by MTEs? 
    How do MTEs choose cases to use? Might there be a particular framework for selecting cases?
    Is the use of cases effective in improving content knowledge and pedagogical content knowledge of teachers? 
     
    Focus on what methods to rigorously study these things.
    How could we go about ...
    What counts as evidence of learning from video cases?
    Does this use of video cases impact teaching practices?
  • Mathematics Teacher Educators Working to Assess the Use of Case-Based Materials

    1. 1. Mathematics Teacher Educators Working to Assess the Use of Case-Based Materials Breyfogle, Hillman, Ives, Roth McDuffie, Moeller, Rigelman & Steele
    2. 2. Why Consider Cases? (Mike) Case discussions share common goals: • To increase and enrich teachers’ fundamental beliefs and understanding about teaching and learning; • To provide opportunities for teachers to become involved in critical discussions of actual teaching situations; and • To encourage teachers to become problem solvers who pose questions, explore multiple perspectives, and examine alternative solutions. - Barnett & Sather, 1992; Shulman & Kepner, 1994
    3. 3. An Example of Purpose: Amy Background/Context • Part of work with TEACH MATH (Teachers Empowered to Advance Change in Mathematics, NSF-funded project), with principal collaborators at 6 universities (Aguirre, Bartell, Drake, Foote, Roth McDuffie & Turner). • Use case study with video clips approximately four times each semester, 1-2 hours per study. • Use Four Lenses as a common tool for case study to focus on "noticing" (Sherin, Jacobs, & Philipp, 2011), as well as purposes mentioned above.
    4. 4. The Four Lenses (Overarching Purpose Across Case Studies) 1. TASK: What makes this a good and/or problematic task? How could it be improved? 2. LEARNING: What specific math understandings and/or confusions are indicated in students’ work, talk, and/or behavior? 3. TEACHING: How does the teacher elicit students’ thinking and respond? (e.g., moves, questions, responses to students’ correct answers/ mistakes/ partial solutions, decisions). 4. POWER & PARTICIPATION: Who participates? Does the classroom culture value and encourage most students to speak, only a few, or only the teacher? Each lens has other prompts, with a common prompt to focus on: resources and knowledge bases students use (e.g., mathematical, cultural, community, family, linguistic)
    5. 5. Specific example of a video clip used for these purposes: "Equalities" (Thinking Mathematically, Carpenter, Franke, & Levi, 2003) • Clip is from a fourth grade bilingual class (English/Spanish) with discussion about the equal sign in 8 + 4 = _ + 5 (Students respond "12" initially) • Teacher uses a variety of open number sentences and true/false number sentences to elicit students’ understandings about the meaning of the equal sign. • Children express problematic conceptions or confusions; teacher poses problems & challenges conceptions/confusions.
    6. 6. Equalities Example (continued) How this video clip connects to our purposes with the lenses: • Case of bilingual classroom with two languages used naturally/ seamlessly connecting to teaching and learning lenses with language as a student resource. • • Case shows a rich/ high level discussion around problems that are not set in a "real context" - connecting to task and learning lenses.
    7. 7. Equalities Example (continued) How this video clip connects to our purposes with the lenses: • Case shows a discussion in which teacher presses, challenges, and extends students thinking - connecting to the teaching lens (questioning types and interaction patterns) and the power & participation lens (authority for knowing, who and how students participate in the discussion)
    8. 8. An Example of Enactment: Mike Edited clip from a discussion of a case Context: • Content-focused methods course - geometry & measurement • Elementary and secondary teachers • Preservice and practicing teachers • The Case of Keith Campbell (Smith, Silver, & Stein, 2005) As you watch, consider: • What do teachers appear to be learning through engagement in the case discussion? • What artifacts might we collect to support our claims about what teachers learned?
    9. 9. Need for Collective Documentation • Case materials are increasingly available, but there is little collective or systematic attention to how case materials are actually used for specific purposes • When case materials are used for specific purposes, there is little documentation about the impact on learning from the use of these case materials
    10. 10. Discussion Questions Small groups discuss the following topics (30 minutes): • What research questions are we interested in pursuing? o What deliberate planning and decision making contributes to strategic use of cases with teachers? o What MTE practices seem to be most effective in implementing cases? o What do we mean when we consider a case "effectively" implemented? o Is the use of cases effective in improving content knowledge and pedagogical content knowledge of teachers? In what ways does using cases contribute to teachers' content knowledge and pedagogical content knowledge? • What methods are best suited to study the proposed research questions? • What data would be helpful to collect across several research sites and what might this research design look like?
    11. 11. Closure During the last 15 minutes of the session, the subgroups will share their ideas and the facilitators will collect them in order to begin an effort to systematically study the use of case-based materials.

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