ABSTRACT
Early investigators in a topic of study often take for granted that the phenomenon of interest is straightforward to identify and characterize. Differing conceptualizations of the field usually come into focus only after some of the initial work has been done and people are in a position to survey the landmarks of the field and note the points of disagreement. This may be our current state of progress in research on variation and uncertainty, which has been widely investigated both by psychologists (e.g., Kahneman, Solvic, & Tversky, 1982; Konold, 1989; Nisbett, Krantz, Jepson, & Kunda, 1983; Nisbett & Ross, 1980) and by educators (Mokros & Russell, 1995; Pollatsek, Lima, & Well, 1981; Strauss & Bichler, 1988). Psychological studies typically concern whether and how participants’ informal ways of thinking are consistent with strategies prescribed by a canonical view of concepts like probability, chance, and sample size. Similarly, educational studies tend to focus on how participants learn or think about certain statistics, such as the entailments of the mean of a sample. In this chapter, we describe a somewhat different approach to statistical reasoning, one that emphasizes data modeling (Lehrer & Romberg, 1996). As we describe, a data modeling approach
focuses on how statistical reasoning is recruited as a way of investigating genuine questions about the world. Data modeling is, in fact, what professionals actually do when they reason statistically (Wild & Pfannkuch, 1999), and moreover, it is central to a wide variety of enterprises, including engineering, politics, medicine, and natural science.
