The processes and procedures used by expert mental calculators are identified from a literature review. Experts are characterized by knowledge of a variety of methods, ability to recall numerical equivalents, and ability to remember the numbers involved in various stages of calculations. (MNS)

Begins with a definition of mental computation and then provides an overview of its evolution during the twentieth century. Significant benefits from teaching mental computation are highlighted, along with a framework and guidelines for instructing elementary school students. A parallel discussion is also provided for computational estimation. (RH)

The exceptionality of the skills of calendrical savants and the role of practice were investigated. Experiment 1 compared four autistic calendrical savants to Professor Conway, a distinguished mathematician with calendrical skills. Professor Conway answered questions over a greater range of years but some savants knew more calendrical…

This is a powerful critique of two decades of educational reform in New Zealand, from an educator who was deeply involved. It is also a provocative call for action. Bali Haque has been both a secondary school principal required to implement reform and a senior public servant in the New Zealand Qualifications Authority (NZQA) tasked with pushing…

An estimation tool for symmetric univariate nonlinear regression is presented. The method is based on introducing a nontrivial set of affine coordinates for diffeomorphisms of the real line. The main ingredient making the computations possible is the Connes-Moscovici Hopf algebra of these affine coordinates.

The relationship between stratified alpha (alpha-sub(s)) and the reliability of a test composed of interrelated nonhomogeneous items is examined. It is mathematically demonstrated that when there is congeneric equivalence within the strata or subtests, the difference between the coefficients is a function of the variances of the loadings within…

This research focused on confidence intervals (CIs) for 10 measures of monotonic association between ordinal variables. Standard errors (SEs) were also reviewed because more than 1 formula was available per index. For 5 indices, an element of the formula used to compute an SE is given that is apparently new. CIs computed with different SEs were…

Three experiments examined the effects of target-distractor (T-D) similarity and old age on the efficiency of searching for single targets and enumerating multiple targets. Experiment 1 showed that increasing T-D similarity selectively reduced the efficiency of enumerating small (less than 4) numerosities (subitizing) but had little effect on…

The emergence of modern humans with their extraordinary cognitive capacities is ascribed to a novel type of cognitive computational process (sustained non-routine multi-level operations) required for abstract projectuality, held to be the common denominator of the cognitive capacities specific to modern humans. A brain operation (latching) that…

Charles Dodgson (Lewis Carroll) discovered a "curious" method for computing determinants. It is an iterative process that uses determinants of 2 x 2 submatrices of a matrix to obtain a smaller matrix. When the process ends, the result is the determinant of the original matrix. This article discusses both the algorithm and what may have led Dodgson…

Do preschool children appreciate numerical value as an abstract property of a set of objects? We tested the influence of stimulus features such as size, shape, and color on preschool children's developing nonverbal numerical abilities. Children between 3 and 5 years of age were tested on their ability to estimate number when the sizes, shapes, and…

Vision was for a long time considered to be essential in the elaboration of the semantic numerical representation. However, early visual deprivation does not seem to preclude the development of a spatial continuum oriented from left to right to represent numbers (J. Castronovo & X. Seron, 2007; D. Szucs & V. Csepe, 2005). The authors investigated…

We applied overlapping waves theory and microgenetic methods to examine how children improve their estimation proficiency, and in particular how they shift from reliance on immature to mature representations of numerical magnitude. We also tested the theoretical prediction that feedback on problems on which the discrepancy between two…

In this article, the author presents a six by six array in which individuals can obtain 182 in total even if they use a different set of numbers. The author then explain why this is possible. The author uses the k-translation of a sequence for this equation. (Contains 8 figures, 2 tables and 6 footnotes.)

A concrete example is used to illustrate maximum likelihood estimation of a structural equation model with two unknown parameters. The fitting function is found for the example, as are the vector of first-order partial derivatives, the matrix of second-order partial derivatives, and the estimates obtained from each iteration of the Newton-Raphson…