This study examined numerosity comparison in 3-year-old children. Predictions derived from the analog numerical model and the object-file model were contrasted by testing the effects of size and ratio between numerosities to be compared. Different perceptual controls were also introduced to evaluate the hypothesis that comparison by preschoolers…

In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals.

The purpose of this study was to empirically evaluate the impact of loglinear presmoothing accuracy on equating bias and variability across chained and post-stratification equating methods, kernel and percentile-rank continuization methods, and sample sizes. The results of evaluating presmoothing on equating accuracy generally agreed with those of…

This book is about playing with mathematics, teaching: (1) How to multiply and divide large numbers mentally; (2) Making addition and subtraction easy; (3) Tricks for understanding fractions and decimals; and (4) How to quickly check answers for each calculation. Described as a foolproof way to do multiplication, division, factoring estimating,…

This paper presents a model for guiding undergraduates to success in computational science. A set of integrated, interdisciplinary training and research activities is outlined for use as a vehicle to increase and produce graduates with research experiences in computational and mathematical sciences. The model is responsive to the development of…

Two groups of 10 male rats were trained to nose poke for food pellets at four alternatives that provided differing rates of pellet delivery on aperiodic schedules. After a fixed number of pellets had been delivered, 5, 10 or 20 in different conditions of the experiment, a 10-s blackout occurred, and the locations of the differing rates of pellet…

We present a fun activity that can be used to introduce students to error analysis: the M&M game. Students are told to estimate the number of individual candies plus uncertainty in a bag of M&M's. The winner is the group whose estimate brackets the actual number with the smallest uncertainty. The exercise produces enthusiastic discussions and…

One of my goals as an instructor is to teach students critical thinking skills. This paper presents an example of a student-led discussion of heat conduction at the first-year level. Heat loss from a human head is calculated using conduction and radiation models. The results of these plausible (but wrong) models of heat transfer contradict what…

The sexual abuse of children has received a tremendous amount of attention in recent years. Accordingly, both the criminal justice and mental health systems deal with child molesters. Since much of the public concerns revolve around the potential dangerousness of any given child molester, practitioners are frequently responsible for making…

A method is outlined for evaluating the reliability and criterion validity of weighted scales based on sets of unidimensional measures. The approach is developed within the framework of latent variable modeling methodology and is useful for point and interval estimation of these measurement quality coefficients in counseling and education…

Sixty-four adults participated in a study examining the accuracy of metacognitive judgments during 28 hr of sleep deprivation (SD) and continuous cognitive work. Three tasks were studied (perceptual comparison, general knowledge, and mental addition), collectively spanning a range of cognitive abilities and levels of susceptibility to SD.…

The author considers a latent trait model for the response time on a (set of) pure speed test(s), the multiplicative gamma model (MGM), which is based on the assumption that the test response times are approximately gamma distributed, with known index parameters and scale parameters depending on subject ability and test difficulty parameters. Like…

Properties of the Spearman correction for attenuation were investigated using Monte Carlo methods, under conditions where correlations between error scores exist as a population parameter and also where correlated errors arise by chance in random sampling. Equations allowing for all possible dependence among true and error scores on two tests at…

The growth curve model has been a useful tool for the analysis of repeated measures data. However, it is designed for an aggregate-sample analysis based on the assumption that the entire sample of respondents are from a single homogenous population. Thus, this method may not be suitable when heterogeneous subgroups exist in the population with…

Background: Based on standard social benefit registers, the prevalence of intellectual disability (ID) in Finland is estimated to be 0.6%, while epidemiological surveys yield 1.1%. Combining several registers, our aim was to find a more reliable estimate of the prevalence of ID, especially among children and adolescents. This is important when…