Source: Journal of Mathematics Teacher Education, Volume 18, Issue 1, February 2015, p. 27-51.
(Reviewed by the Portal Team)
This article draws on Lampert’s three-pronged model of teaching practice (Lampert, 2001) to explore the possible
contributions of elementary classroom teachers to the learning-to-teach-mathematics experiences of preservice teachers (PSTs). The authors focus on a third-space context in which mentor teachers (MTs), PSTs, and university teacher educators collaborated to plan and analyze task-based problem-solving interviews of children.
The three-pronged model of teaching practice
Lampert’s model describes teaching as simultaneously managing three different relationships:
• the relationship with elementary children, which includes learning about children’s personal, family, community, and academic histories.
• the relationship with mathematical content including subject-specific knowledge such as familiarity with the school curriculum and content standards, and awareness of strategies for teaching specific content;
• the relationship between the child and mathematical content, which includes ensuring that children are learning the content by designing, monitoring, scaffolding, and enhancing children’s engagement with important mathematical ideas.
This study was part of a larger research initiative, which focused on the design of a third-space model for preparing elementary mathematics and science teachers.
The participants in this study were 11 preservice teachers who worked with 25 mentor teachers (MTs) at two elementary (K-5) schools over a three-semester period.
The participants watched videos of task-based interviews and talked about the interviewers’ moves for eliciting and clarifying children’s thinking.
At the end of the morning, the authors paired PSTs with MTs to plan the specific tasks they would use when interviewing children and to predict children’s strategies.
Data included all whole-group interactions (including the discussions before and after the interviews, but not the actual interviews of children) during two joint sessions were videotaped, resulting in approximately 9 h of video data, which was transcribed for the analysis.
Using a variation of Lampert’s three-pronged model of teaching practice, the authors analyzed three categories of MT contributions to a third-space activity involving the task-based interview.
Specifically, MTs demonstrated how understanding of children’s relationships to mathematics could be enhanced by connecting children’s activity to classroom contexts.
And MTs demonstrated how teachers constantly learn about their practice by considering what unfolds in practice, in this case what unfolded in the practice of the interview.
Each of these contributions potentially enhanced the learning-to-teach context by bringing teacher framings to the conversation and demonstrating ways in which teachers can draw upon the particulars of the classroom context to assess and develop the connections between children and mathematical ideas.
Leveraging MT contributions
This analysis suggests ways in which university teacher educators might enhance the development of methods/field third spaces by anticipating and preparing to leverage MT contributions.
As the university teacher educator gains a vision for potential MT contributions, she can showcase and label MT talk, making connections between the methods and field TCM triangles.
Furthermore, as university teacher educators focus on and label the unique contributions MTs make to the learning-to-teach context, MTs may be empowered to see their own knowledge as valuable and important for PST learning, perhaps creating a more equal footing in conversations around teacher preparation.
In addition, as university teacher educators highlight connections between MTs’ ideas and experiences and the theories and frameworks from methods, MTs and PSTs may see how the university-based knowledge is applicable to the elementary classroom, opening the door for valuable third-space conversations among PSTs, MTs, and university teacher educators.
This analysis also points the way toward the attributes of tasks, activities, and probes that might be particularly useful in eliciting rich third-space contributions from MTs.
As PSTs, MTs, and university teacher educators sought to make sense of children’s moves (the child–mathematics relationship in the TCM triangle), the MTs’ talk provided explanations, contextual detail, and critiques of MT practices, generating potentially rich opportunities for PST (and university teacher educator) learning about many aspects of the TCM triangle.
Increasing the complexity of work for university teacher educators
While the authors noticed many benefits for PSTs of working together with MTs on the interview task, MTs contributions also added complexity to the work of the university teacher educator. First, including the MTs in a methods activity meant that there were many people with ideas, questions, and insights to share.
A second challenge arising from the presence of the MTs was the increased complexity of messages about teaching.
While the university teacher educator structured events to foreground certain ideas about the task-based interview, the MTs (at the invitation of the university teacher educator) included other ideas and concerns.
Also, in some instances, MT contributions offered insights about the classroom context that could enrich the analyses of children’s mathematical understanding.
More and more, university teacher educators have embraced collaborative work with MTs, seeking to craft a variety of third spaces in order to lessen the methods/field gap and enhance the learning of PSTs.
This study provides some pieces that have been missing from this effort: a framework for making sense of what university teacher educators and MTs contribute to this third space and specific analysis regarding MT contributions to third spaces.
As a consequence, the authors can begin to see how university teacher educators and MTs each bring important emphases to moments of learning to teach and how university teacher educators might shift their methods TCM triangle to better leverage contributions from MTs.