study takes steps towards building that knowledge by analyzing a teacher and class that regularly
worked collaboratively to extend their mathematical understandings.
Methods and Data Sources
Data for this study was collected during the 2000-2001 school year. The focal case was Ms.
Nelson’s ninth-grade pre-algebra class comprising twenty students. Ms. Nelson was a highly
experienced (Nationally Board certified and a recipient of the Presidential Science and Math
Award for Teaching) and consistently organized collaborative inquiry activities that attended to
the development of students’ conceptual understanding regardless of course of class
composition. This was validated by a researcher team for the Stanford Mathematics Teaching
and Learning Study (Principal Investigator, Dr. Jo Boaler; see also Boaler & Staples, 2003). The
sampling strategy then was purposive (Yin, 1994) and the case was chosen to offer insight into
teacher practices that support mathematically intensive collaborative learning environments.
The research was conducted from an interpretivist paradigm, drawing upon ethnographic
methods described by Eisenhart (1988). Data collection included videotapes and observations of
lessons (105 hours); interviews with students (19); teacher interviews (4); and video viewing
sessions with the teacher (7). In addition Ms. Nelson and I had frequent conversations after
lessons. Data analysis followed principles of grounded theory (Strauss & Corbin, 1990). From
the process of coding field notes and video content logs patterns were identified. This process
included codifying particular teaching strategies that seemed to support students’ participation in
mathematical collaborative activities. A refined set of codes was applied to ten transcribed
videotapes of whole-class collaborative activities. In addition, videos of sequential lessons were
analyzed to trace the development of mathematical ideas over time. Finally, analyses were
refined and validated by reviewing videotapes and my analyses with Ms. Nelson. She confirmed
that the results presented an accurate portrayal of her practice, both the description of the practice
and how it functioned to support students’ participation and learning in the classroom.
Results
Results indicated that Ms. Nelson guided the development of the mathematical ideas during
whole-class discussion by simultaneously centralizing students’ ideas and thinking, pursuing
high-level task implementation, and attending to mathematics (here, algebra) as a body of
knowledge and set of practices that students were learning. I discuss each of these three
commitments and examine particular pedagogical strategies that Ms. Nelson used to guide
development of the mathematics during collaborative discussions.
Centralizing students’ thinking
At the heart of the class’s collaborative discussions was students’ thinking. Ms. Nelson
regularly used students’ ideas as the basis of the class’s exploration of a problem or concept. She
constantly elicited students’ ideas, asked for explanations, and had them present their solutions at
the board. These strategies are familiar ways to bring students’ ideas to the fore.
Ms. Nelson went beyond this however. She recognized that for a student’s idea to be used as
the starting point for the class’s explorations, other students needed to comprehend and consider
the idea in order to have an opportunity to learn from the subsequent discussion. Towards this
end, Ms. Nelson employed a variety of strategies. For example, she frequently asked students to
repeat their ideas and record them on the board. She also restated them verbatim herself. Indeed,
it was rare to have a student’s idea only stated once. Ms. Nelson also asked questions that helped
Convention