This study extends the debate concerning the mathematical skills deficit of bioscience undergraduates towards a deeper understanding of their mathematics learning, since only through the latter can appropriate and effective explicit teaching be implemented. Three hundred and twenty-six first-year bioscience undergraduates, from three pre- and four…

This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…

This article reports on a comprehensive literature review and meta-analysis of 68 experiments on teaching mathematics to individuals with significant cognitive disabilities. Most of the studies in the review addressed numbers and computation or measurement. Within the computation studies identified, most focused on counting, calculation, or number…

In psychometrics, it is often the case that one encounters data that may not be considered random but selected in a systematic way according to some explanatory variable. In this article, maximum likelihood estimation is considered when data are supposed to arise from a bivariate normal distribution that is truncated in an extreme way. Two methods…

The fuzzy perspective in statistical analysis is first illustrated with reference to the "Informational Paradigm" allowing us to deal with different types of uncertainties related to the various informational ingredients (data, model, assumptions). The fuzzy empirical data are then introduced, referring to "J" LR fuzzy variables as observed on "I"…

This article reviews the arguments for reporting effect size estimates as part of the statistical results in empirical studies. Following this review, formulas are presented for the calculation of major mean-difference and association-based effect size measures for t tests, one-way ANOVA, zero order correlation, simple regression, multiple…

This study investigated the development of children's knowledge of many-to-one counting. Four-year-olds ("n" = 51) either participated in a training or in a control group. The training taught children how to allot "Y" physically not present items to each of "X" objects and how to count these items in the process. It…

M. Pena, L. L. Bonatti, M. Nespor, and J. Mehler (see record 2002-06215-001) argued that humans compute nonadjacent statistical relations among syllables in a continuous artificial speech stream to extract words, but they use other computations to determine the structural properties of words. Instead, when participants are familiarized with a…

L. L. Bonatti, M. Pena, M. Nespor, and J. Mehler (see record 2006-06642-010) argued that P. Perruchet, M. D. Tyler, N. Galland, and R. Peereman (see record 2004-21166-008) confused the notions of segmentation and generalization by ignoring the evidence for generalization in M. Pena, L. L. Bonatti, M. Nespor, and J. Mehler (see record…

Computational precision is sometimes given short shrift in a first programming course. Treating this topic requires discussing integer and floating-point number representations and inaccuracies that may result from their use. An example of a moderately simple programming problem from elementary statistics was examined. It forced students to…

A linear combination of a set of measures is often sought as an overall score summarizing subject performance. The weights in this composite can be selected to maximize its reliability or to maximize its validity, and the optimal choice of weights is in general not the same for these two optimality criteria. We explore several relationships…

A method for generating sums of series based on simple differential operators is presented, together with a number of worked examples with interesting properties.

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.

Advocates of the ''continuity hypothesis'' have argued that innate non-verbal counting principles guide the acquisition of the verbal count list (Gelman & Gallistel, 1978). Some studies have supported this hypothesis, but others have suggested that the counting principles must be constructed anew by each child. Defenders of the continuity…