Purposeful Statistical Investigation Merged with K-6 Content: Variability, Learning and Teacher Knowledge Use in Teaching

Pfannkuch (1997) contends that variation is a critical issue throughout the statistical inquiry process, from posing a question to drawing conclusions. This is particularly true for K-6 teachers when they attempt to use the process of statistical investigation as a means of teaching and learning across the spectrum of the K-6 curricula. In this context statistical concepts and ideas are taught and learned in conjunction with the important content area ideas and concepts. For a K-6 teacher, this means that the investigation must not only be planned in advance, but also aimed at being responsive to students. The potential for surprise questions, unanticipated responses and unintended outcomes is high, and teachers need to "think on their feet" statistically and react immediately in ways that accomplish content objectives, as well as convey correct statistical principles and reasoning. The intellectual demands in this context are no different than in other instances where teachers are trying to teach for understanding (i.e., Cohen, McLaughlin, &amp; Talbert, 1993; Ma, 1999).<br>In this line of research, we explore the role variability plays in this form of teaching and learning. Simultaneously, we analyze what teachers need to know about variability and be able to do with variability in data so that purposeful investigations into topics of the curriculum can be successful in teaching both statistical concepts and process and the important ideas associated with content. We work from a situative perspective (Greeno, 1997) and analyze the degree to which the statistical knowledge needed for teaching appears to have been learned for understanding (Hiebert &amp; Carpenter, 1992) and leads to generative understanding (Franke, Carpenter, Levi &amp; Fennema, 2001). The findings of this study point toward the situated nature of knowledge about variability needed for and used in teaching and leads to significant implications for the growth of teachers' statistical knowledge.