Resumen de Valuing Informal Arguments and Empirical Investigations during Collective Argumentation
Considerable literature has documented both the pros and cons of students' use of empirical evidence during proving activities. This article presents an analysis of a classroom episode involving in-service middle school, high school, and college teachers that demonstrates that learners need not be steered away from empirical investigations during collective argumentation. The analysis demonstrates that empirical investigations and subsequent informal reasoning during collective argumentation can provide opportunities for the instructor to introduce important mathematical tools and conceptions, and opportunities to discuss various levels and types of arguments and their individual importance to mathematical thinking, all the while progressing toward formal proof. Implications for the training and professional development of those who prepare students for college mathematics and those who teach college mathematics are discussed.
