We show that human observers strongly underestimate a linear or circular trajectory that a luminous spot follows in the dark. At slow speeds, observers are relatively accurate, but, as the speed increases, the size of the path is progressively underestimated, by up to 35%. The underestimation imposes little memory load and does not require…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This third installment of "Explorations in Statistics" investigates confidence intervals. A confidence interval is a range that we expect, with some level of confidence, to include the true value of a population parameter…

A question we posed in a recent final examination has uncovered a fundamental difficulty for students in understanding destructive interference. The problem stated that glass of index n[subscript 3] was coated with a thin film of a substance with index n[subscript 2]. The question then asked the student to calculate (a) the minimum coating…

A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

Seven independent groups estimated the location of North American cities using both spatial and numeric response modes and a variety of perceptual and memory supports. These supports included having location markers for each city color coded by nation and identified by name, giving participants the opportunity to see and update all their estimates…

In the Basic Local Independence Model (BLIM) of Doignon and Falmagne ("Knowledge Spaces," Springer, Berlin, 1999), the probabilistic relationship between the latent knowledge states and the observable response patterns is established by the introduction of a pair of parameters for each of the problems: a lucky guess probability and a careless…

A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of…

The purpose of this study was to extend the literature regarding elementary teachers' beliefs about mathematics instruction to include special education teachers by surveying special education and general education teachers' mathematics teaching efficacy. In addition, the researchers' surveyed teachers' mathematics skills. The participants (n =…

A "Framework for K-12 Science Education" identified eight practices as "essential elements of the K-12 science and engineering curriculum" (NRC 2012, p. 49). Most of the practices, such as Developing and Using Models, Planning and Carrying Out Investigations, and Analyzing and Interpreting Data, are well known among science…

Number sense is critical to the development of higher order mathematic abilities. However, some children have difficulty acquiring these fundamental skills and the knowledge base of effective interventions/remediation is relatively limited. Based on emerging neuro-scientific research which has identified the association between finger…

The purpose of this study was to provide preliminary evidence of the criterion-related validity of curriculum-based measurement (CBM) for reading, mathematics, and written expression with postsecondary students with intellectual and developmental disabilities (ID). The participants included 41 postsecondary students with ID enrolled in a 2-year…

Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

When first introduced to the analysis of algorithms, students are taught how to assess the best and worst cases, whereas the mean and amortized costs are considered advanced topics, usually saved for graduates. When presenting the latter, aggregate analysis is explained first because it is the most intuitive kind of amortized analysis, often…

Estimation of parameters of random effects models from samples collected via complex multistage designs is considered. One way to reduce estimation bias due to unequal probabilities of selection is to incorporate sampling weights. Many researchers have been proposed various weighting methods (Korn, & Graubard, 2003; Pfeffermann, Skinner,…