This experiment aimed to expand previous findings on the development of mental number representation. We tested the hypothesis that children's familiarity with numbers is directly reflected by the shape of their mental number line. This mental number line was expected to be linear as long as numbers lay within the range of numbers children were…

The strength of a rat's eating reflex correlates with hunger level when strength is measured by the response frequency that precedes eating (B. F. Skinner, 1932a, 1932b). On the basis of this finding, Skinner argued response frequency could index reflex strength. Subsequent work documented difficulties with this notion because responding was…

This paper describes some computer-based activities to bring the study of charged particle optics to undergraduate students, to be performed as a part of a one-semester accelerator-based experimental course. The computational simulations were carried out using the commercially available SIMION program. The performance parameters, such as the focal…

Given the commonness of pets in communities throughout the United States, Canada, and Australia, among other countries, pet stewardship should be a natural topic of study for the integration of science, mathematics, and technology. Therefore, the term "stewardship" will be examined by applying observation and research to shape our…

The aim of this study was to investigate the strategies used by third graders in solving the 81 elementary subtractions that are the inverses of the one-digit additions with addends from 1 to 9 recently studied by Barrouillet and Lepine. Although the pattern of relationship between individual differences in working memory, on the one hand, and…

Bioinformatics is a relatively new interdisciplinary field that integrates computer science, mathematics, biology, and information technology to manage, analyze, and understand biological, biochemical and biophysical information. We present our experience in teaching an interdisciplinary course, Introduction to Bioinformatics, which was developed…

There are large differences across countries in instructional time in public schooling institutions. For example, among European countries such as Belgium, France and Greece, pupils aged 15 have an average of over a thousand hours per year of total compulsory classroom instruction while in England, Luxembourg and Sweden the average is only 750…

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…

This study examined the impact of teachers' characteristics and self-reported practices on students' Algebra achievement while controlling for students' characteristics. This study is based on the secondary analysis of data collected from a nationally representative sample of 9 th grade students and their mathematics teachers during…

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…