The purpose of this paper is to delineate some insights into the concept of multisets along with a couple of combinatorial results related to multisets. The paper indicates that a general formula needs to be worked out for determining the cardinality of the "Set" (whose elements may be multisets but do not repeat) of all multisubsets of a finite…

In this note, using the theory of Pell equation, the authors discuss the integrity of certain series involving generalized Fibonacci and Lucas numbers.

The problem of estimating the cross-product of two mean vectors in three-dimensional Euclidian space is considered. Two "natural" estimators are developed, both of which turn out to be biased. A third, unbiased estimator, resulting from a jackknife procedure, is also investigated. It is shown that, under normality, the latter is best among all the…

This book includes two main sections: a discussion of problem solving and a section on computation with whole numbers. A primary theme of the text is that problem solving sets the stage for meaning and conceptual development with respect to numbers. The section on problem solving includes numerous problem-solving activities that have a dual…

Users of logistic regression models often need to describe the overall predictive strength, or effect size, of the model's predictors. Analogs of R[superscript 2] have been developed, but none of these measures are interpretable on the same scale as effects of individual predictors. Furthermore, R[superscript 2] analogs are not invariant to the…

This article introduces a bootstrap generalization to the Modified Parallel Analysis (MPA) method of test dimensionality assessment using factor analysis. This methodology, based on the use of Marginal Maximum Likelihood nonlinear factor analysis, provides for the calculation of a test statistic based on a parametric bootstrap using the MPA…

This study examined the effects of prior knowledge, learner preference for control, and type of control (learner or program) on the achievement of middle-school students in a computer-based instructional program on adding and subtracting integers. Students were blocked by preference-for-control scores and randomly assigned to either a…

Cluster randomized trials (CRTs) have been widely used in field experiments treating a cluster of individuals as the unit of randomization. This study focused particularly on situations where CRTs are accompanied by a common complication, namely, treatment noncompliance or, more generally, intervention nonadherence. In CRTs, compliance may be…

Passive and active visuospatial working memory (VSWM) were investigated in relation to maths performance. The mental rotation task was employed as a measure of active VSWM whereas passive VSWM was investigated using a modified Corsi Blocks task and a matrix pattern task. The Raven Progressive Matrices Test measured fluid intelligence. A total of…

To address the confusion resulting from difficulties with proportional reasoning among preservice physical science students, a cube-assembly activity was used to bring a sense of concreteness to abstract ideas. The activity took students from the concrete step of assembling cubes of various sizes and directly measuring their properties to slightly…

The first part of this two-part paper [see EJ787497] described the development of a new freshman business mathematics (FBM) course at our college. In this paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modelling, to realistic business problems. These memos have…

We use administrative data on a sample of births between 1978 and 1985 to investigate the short-, medium-, and long-term consequences of poor infant health. Our findings offer several advances to the existing literature on the effects of early infant health on subsequent health, education, and labor force attachment. First, we use a large sample…

Despite numerous empirical studies, there is surprisingly little agreement about whether the Social Security earnings test affects male labor supply. In this paper, we provide a comprehensive analysis of the labor supply effects of the earnings test using longitudinal administrative earnings data and more commonly used survey data. We find that…

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third…

The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the…