Orchestrating Whole Group Discourse to Mediate Mathematical Meaning

The most common pattern of classroom discourse follows a three-part exchange of teacher initiation, student response, and teacher evaluation or follow-up (IRE/IRF) (Cazden, 2001). Although sometimes described as encouraging illusory understanding (Lemke, 1990), triadic exchanges can mediate meaning (Nassaji & Wells, 2000). This paper focuses on one case from a study of discursive practices of seven middle grades teachers identified for their expertise in mathematics instruction. The central result of the study was the development of a model to explain how teachers use discourse to mediate mathematical meaning in whole group instruction. Drawing on the model for analysis, thick descriptions of one teacher’s skillful orchestration of triadic exchanges that enhance student understanding of mathematics are presented.

Sentencing Guidelines, Judicial Discretion, And Social Values

This paper studies the institutional structure of criminal sentencing, focusing on the interaction between legislatures, which set sentencing ranges ex ante, and judges, who choose actual sentences from within those ranges ex post. The key question concerns the optimal degree of judicial discretion, given the sequential nature of the process and the possibly divergent interests of legislatures and judges regarding the social function of criminal punishment. The enactment of sentencing reform in the 1970s and 80s provides both a context for the model and an opportunity to evaluate its conclusions.