1. Mathematics Teacher
Educators
Working to Assess the Use of
Case-Based
Materials
Breyfogle, Hillman,
Ives, Roth McDuffie, Moeller,
Rigelman
& Steele

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. 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. 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. 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. 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. 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. 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. 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. 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. 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.