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Abstract Generalizing or making claims that extend beyond particular situations is a central mathematical practice and a focus of classroom mathematics instruction. This study examines how aspects of generality are produced through the situated activities of a group of middle school mathematics students working on an 8-week population-modeling project. The project involved creating and analyzing mathematical models of population growth. Two classroom episodes are presented that focus on students' activities across curricular tasks in which they discuss the category of sensible models of population growth and describe a pattern of guppy population growth in a natural environment. Participation frameworks introduced in the context of the episodes describe how students compare situations to determine if they belong to the same general category and predict and justify the behavior of modeled phenomena. The analysis suggests that mathematical generalizing is the outcome of processes distributed across students, tasks, embodied activity, and modeling tools.
A. Susan Jurow (Mon,) studied this question.