This paper comments on the article by Plaut and Booth. Plaut and Booth's first simulation shows that there is essentially perfect discrimination between word and nonwords sharing the same orthographic structure when the simulation is carried out in the way we suggested. We take the view that Plaut and Booth's new simulation work settles little…

The development of conceptual and procedural knowledge about counting was explored for children in kindergarten, Grade 1, and Grade 2 (N = 255). Conceptual knowledge was assessed by asking children to make judgments about three types of counts modeled by an animated frog: standard (correct) left-to-right counts, incorrect counts, and unusual…

Variables that have been coarsely categorized into a small number of ordered categories are often modeled as outcome variables in psychological research. The authors employ a Monte Carlo study to investigate the effects of this coarse categorization of dependent variables on power to detect true effects using three classes of regression models:…

In this study, the precision of subscale score estimates was evaluated when out-of-scale information was incorporated. Procedures that incorporated out-of-scale information and only information within a subscale were compared through a series of simulations. It was revealed that more information (i.e., more precision) was always provided for…

Interrater reliability has thus far not been a common application in phenomenological studies. However, once the suggestion was brought up by a team of supervising professors during the preliminary orals of a phenomenological study, the utilization of this verification tool turned out to be vital to the credibility level of this type of inquiry,…

Nunes and Bryant (Children doing mathematics, Blackwell, Oxford, 1996) proposed that an understanding of the additive composition of number could be a precursor to an understanding of the decimal structure. If this is so, children should achieve an understanding of additive composition before they can handle the decimal structure. The aim of our…

There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean [mu] and variance [sigma][superscript 2], the expected value of the sample variance is [sigma][superscript 2]. The generalization justifies the use of the usual standard error of the sample mean in possibly…

In this paper, we consider some combinatorial and statistical aspects of the popular "Powerball" lottery game. It is not difficult for students in an introductory statistics course to compute the probabilities of winning various prizes, including the "jackpot" in the Powerball game. Assuming a unique jackpot winner, it is not difficult to find the…

Although not perfect, skinfolds (SK), or the measurement of fat under the skin, remains the most popular and practical method available to assess body composition on a large scale (Kuczmarski, Flegal, Campbell, & Johnson, 1994). Even for practitioners who have been using SK for years and are highly proficient at locating the correct anatomical…

This article focuses on the specific skills and abilities of young children in oral counting and enumeration. Responses to an oral counting task and an enumeration task by a sample (n=93) of 3- and 4-year old children attending a range of pre-five establishments in an urban district of northern England are described. The findings, whilst providing…

Given three points in the plane, interest is in the locus of all points for which the sum of the distances to the given points is a prescribed constant. These curves turn out to be sixth degree polynominals in x and y , and thus are complicated. However, it turns out that often there is a point, within the triangle formed by the three given…

This note could find use as enrichment material in a course on the classical geometries; its preliminary results could also be used in an advanced calculus course. It is proved that if a , b and c are positive real numbers such that a[squared] + b[squared] = c[squared] , then cosh ( a ) cosh ( b ) greater than cosh ( c ). The proof of this result…

Given two circles C 1 and C 2 in a plane such that neither one of the two circles is contained in the other, there are either four common tangents when the circles do not intersect at all or the circles have three common tangents when they touch each other externally or only two common tangents when the circles intersect exactly at two points. The…

Multilevel analysis is a useful technique for analyzing longitudinal data. To describe a person's development across time, the quality of the estimates of the random coefficients, which relate time to individual changes in a relevant dependent variable, is of importance. The present study compares three estimators of the random coefficients: the…

This article discusses the use of a problem-based instructional task in an elementary classroom. After estimating the number of blades of grass on a football field, students write letters to explain the results of their research.