Literature Index

This article presents a critique of the concept of randomness as it occurs in the psychological literature. The first section of our article outlines the significance of a concept of randomness to the process of induction; we need to distinguish random and non-random events in order to perceive lawful regularities and formulate theories concerning events in the world. Next we evaluate the psychological research that has suggested that human concepts of randomness are not normative. We argue that, because the tasks set to experimental subjects are logically problematic, observed biases may be an artifact of the experimental situations and that even if such biases do generalise they may not have pejorative implications for induction in the real world. Thirdly we investigate the statistical methodology utilised in tests for randomness and find it riddled with paradox. In a fourth section we find various branches of scientific endeavour that are stymied by the problems posed by randomness. Finally we briefly mention the social significance of randomness and conclude by arguing that such a fundamental concept merits and requires more serious considerations.

The Statistics Anxiety Rating Scale has 51 items, each scored on a 5-point rating scale to measure statistics anxiety with six subscales, Worth of Statistics, Interpretation Anxiety, Test and Class Anxiety, Computational Self-concept, Fear of Asking for Help, and Fear of Statistics Teachers. Psychometric properties included analyses of construct and concurrent validities an internal consistency and test-retest reliability. 221 college students (74% women; M age=28 yr.) in elementary statistics courses at several southwestern state universities participated. The findings are consistent with previous reports and indicate adequate concurrent validity, internal consistency, and split-half reliability, but for construct validity confirmatory factor analysis yielded marginal support.

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.

This article discusses a game called push-penny that can be used to develop students' intuitive feelings for the consequences of randomness.