Journal Article

David Cox describes statstics as being comprised of 'three inter-linked pillars'; the mathematics of probability, the general principles for the design of investigations, and the general principles for analysis and interpretation of investigations. If this is the case, then statstical education must support these inter-linked pillars. There are, however, a number of factors that sometimes prevent it from doing so.

It is common to summarize statistical comparisons by declarations of statistical<br>significance or non-significance. Here we discuss one problem with such declarations,<br>namely that changes in statistical significance are often not themselves statistically<br>significant. By this, we are not merely making the commonplace observation that<br>any particular threshold is arbitrary - for example, only a small change is required to<br>move an estimate from a 5.1% significance level to 4.9%, thus moving it into statistical<br>significance. Rather, we are pointing out that even large changes in significance levels<br>can correspond to small, non-significant changes in the underlying variables.<br>The error we describe is conceptually different from other oft-cited problems - that<br>statistical significance is not the same as practical importance, that dichotomization into<br>significant and non-significant results encourages the dismissal of observed differences<br>in favor of the usually less interesting null hypothesis of no difference, and that any<br>particular threshold for declaring significance is arbitrary. We are troubled by all of<br>these concerns and do not intend to minimize their importance. Rather, our goal is to<br>bring attention to what we have found is an important but much less discussed point.<br>We illustrate with a theoretical example and two applied examples.

It now appears that all traditionally taught college courses are markedly (though unintentionally) biased against many non-traditional students, and, indeed, against most students who have not attended elite preparatory schools. Thus, when we teach merely in traditional ways we probably discriminate strongly on grounds quite different from those we intend (assuming that we intend only effort and merit). Easily accessible changes in how we teach have been shown repeatedly to foster dramatic changes in student performance with no change in standards - in some cases, no students now earn failing grades. Similarly dramatic improvements have been shown in the uniformity of outcomes. For example, the gap between Black performance and the performance of other groups can be entirely eliminated, even in "hard" courses such as calculus.

In this study, we seek a better understanding of how individuals and their daily interactions shape and reshape social structures that constitute a classroom community. Moreover, we provide insight into how discourse and classroom interactions shape the nature of a learning community, as well as which aspects of the classroom culture may be consequential for learning. The participants in this study include two teachers who are implementing a new environmental science program, Global Learning through Observation to Benefit the Environment (GLOBE), and interacting with 54 children in an urban middle school. Both qualitative and quantitative data are analyzed and presented. To gain a better understanding of the inquiry teaching within classroom communities, we compare and contrast the discourse and interactions of the two teachers during three parallel environmental science lessons. The focus of our analysis includes (1) how the community identifies the object or goal of its activity; and (2) how the rights, rules, and roles for members are established and inhabited in interaction. Quantitative analyses of student pre- and posttests suggest greater learning for students in one classroom over the other, providing support for the influence of the classroom community and interactional choices of the teacher on student learning. Implications of the findings from this study are discussed in the context of curricular design, professional development, and educational reform.