Quality Teaching in One San Diego Classroom: Scaffolding Student Mathematical Narratives

• In Event: Culturally Specific Perspectives on Quality Mathematics Teaching

Abstract

This study examined the practice of a San Diego teacher, noteworthy because of the technical mathematical fluency with which her 8th grade students reflected on their learning of mathematics in post-lesson video-stimulated interviews. We investigated the strategies used by the teacher to assist the students in making connections between their classroom activities and the conceptual content and mathematical practices that were the focus of that activity.

Our analysis suggested that it was the teacher’s management of the transitions from one type of instructional activity to another that facilitated the students’ constructed connection between mathematical concepts and classroom activities. We identify transitions as the moments when the teacher actively seeks to re-direct students’ attention to engagement with a new task. The lesson transcript was used to categorize teacher attempts at connecting one task to another, both organizationally and conceptually.

While the transitions in this classroom were not always efficient, student engagement levels were high. This conflicts with existing literature (eg Brophy, 1988) reporting that student engagement rates require that transitions between academic activities are brief and orderly. Relatedly, Stevenson and Stigler (1992) found that more time was spent in transition between instructional activities in American classrooms than in either Japan or China. In fact, this San Diego teacher seized every opportunity to create a teaching moment. As a consequence, what might appear to be a lengthy transition became an academic activity in its own right.

Our analysis identified ten different categories of dialogue present in the moments identified as instructional transitions. These categories orchestrated both organizational and cognitive connection from one type of task to another. The transitions were integrated so well that the students appeared to engage with the sequence of tasks as a seamless progression. Revisiting the student post-lesson interview data that originally motivated our more focused analysis suggests a connection between the teacher’s orchestrated coherence of classroom discourse and the coherence of the student-constructed mathematical narratives that constitute a major learning outcome of that teacher’s practice.

This integration of conceptual and pedagogical coherence offers a new perspective on quality teaching practice by shifting emphasis from connecting instructional task types with testable student performances to a more subtle and sophisticated reading of classroom outcomes in which students are seen as developing their own coherent mathematical narratives, facilitated by the teacher’s management of the transitions between instructional activities. The integration of diverse mathematical terms into student reconstructive accounts of lesson content is consistent with this hypothesis. The highly discursive nature of this strategy suggests a cultural specificity reflective of its origins in a pedagogical tradition that affords much greater opportunity for student interactive speech than is typical of the other classrooms described in this symposium.

References
Brophy, J. (1988). Research linking teacher behavior to student achievement: Potential implications for instruction of charter 1 students. Educational Psychologist, 23(3), 235-286.

Stevenson, H. W., & Stigler, J. W. (1992). The learning gap: Why our schools are failing and what we can learn from Japanese and Chinese education. New York: Simon & Schuster.

Authors

• David J. Clarke, University of Melbourne

• Carmel Mesiti, University of Melbourne