Discusses the meaning of information in terms of Shannon's mathematical theory of communication and the concept of uncertainty. The uncertainty associated with the transmission of the signal is argued to have more significance for information science than the uncertainty associated with the selection of a message from a set of possible messages.…

The asymptotic posterior normality of latent variable distributions is established under very general and appropriate hypotheses, providing a probabilistic basis for assessing ability estimation/prediction accuracy in the long test case, as well as a first step in making the Dutch Identity conjecture rigorous. (SLD)

Utilizes problems from children's literature to guide mathematics lessons on probability. (ASK)

Presents an extended hands-on project for eighth-grade mathematics classrooms in which students are to determine the probability that a local creek would flood. (ASK)

The notion that non-human animals are capable of episodic memory is highly controversial. Here, we review recent behavioral work from our laboratory showing that the fundamental features of episodic memory can be observed in rats and that, as in humans, this capacity relies on the hippocampus. We also discuss electrophysiological evidence, from…

Young infants are very sensitive to feature distribution information in the environment. However, existing work suggests that they do not make use of correlation information to form certain perceptual categories until at least 7 months of age. We suggest that the failure to use correlation information is a by-product of familiarization procedures…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

The effect of different combinations of item response theory (IRT) item parameters (item difficulty, item discrimination, and the guessing probability) on the reliability and construct validity (correlation with the latent trait being measured) of pretest, posttest, and gain scores was analytically examined using the 3-parameter logistic (3PL)…

This article describes four hands-on activities that can be used to develop probabilistic and statistical thinking in the middle grades. (Contains 3 figures and 1 table.)

This article describes how a group of fifth-grade mathematics students measured irregularly shaped objects using geometric probability theory. After learning how to apply a ratio procedure to find the areas of familiar shapes, students extended the strategy for use with irregularly shaped objects, in this case, leaves. (Contains 2 tables and 8…

This article illustrates how teachers can use the Harry Potter book series to teach linear modeling and probability to their students. (Contains 2 tables and 4 figures.)

Previous research has shown that--due to the extensive attention spent to proportional reasoning in mathematics education--many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the "illusion of linearity". For example, in…

In this study, the authors used multivariate statistical analysis to examine the impact of cost on the likelihood that a person will both enroll in and complete a Master of Business Administration (MBA) program. They considered both the "explicit" cost of paying tuition and the "implicit" cost, or opportunity cost, of earnings foregone while in…

To assess item dimensionality, the following two approaches are described and compared: hierarchical generalized linear model (HGLM) and multidimensional item response theory (MIRT) model. Two generating models are used to simulate dichotomous responses to a 17-item test: the unidimensional and compensatory two-dimensional (C2D) models. For C2D…

Computerized adaptive tests (CATs) are individualized tests that, from a measurement point of view, are optimal for each individual, possibly under some practical conditions. In the present study, it is shown that maximum information item selection in CATs using an item bank that is calibrated with the one- or the two-parameter logistic model…