In this article, an alternative multiplication method for rhotrices is proposed. The method establishes some relationships between rhotrices and matrices. This article has discussed a modified multiplication method for rhotrices. The method has a direct relationship with matrix multiplication, and so rhotrices under this multiplication procedure…

3 experiments were conducted to assess young (5-7 years) children's ability to judge the relative amount that a character would receive if sharing a material with 1 friend (halves) or 2 friends (thirds). Materials included items that appeared in 3 forms: continuous, discrete, and composite. In the first 2 experiments, performance was best with…

In this article, we define the inversion vector of a permutation of the integers 1, 2,..., n. We set up a particular kind of permutation, called a partial random permutation. The sum of the elements of the inversion vector of such a permutation is a random variable of interest.

The origins of this paper lay in making beds by putting pieces of plywood on a frame: If beds need to be 4 feet 6 inches by 6 feet 3 inches, and plywood comes in 4-foot by 8-foot sheets, how should one cut the plywood to minimize waste (and have stable beds)? The problem is of course generalized.

A simple modification substantially simplifies the use of the gradient projection (GP) rotation algorithms of Jennrich (2001, 2002). These algorithms require subroutines to compute the value and gradient of any specific rotation criterion of interest. The gradient can be difficult to derive and program. It is shown that using numerical gradients…

In this note, we give a method for finding the inverse of a three by three magic square matrix without using the usual methods for finding the inverse of a matrix. Also we give a method for finding the inverse of a three by three magic square matrix whose entries are also matrices. By using these ideas, we can construct large matrices whose…

The DA-T Gibbs sampler is proposed by Maris and Maris (2002) as a Bayesian estimation method for a wide variety of "Item Response Theory (IRT) models". The present paper provides an expository account of the DA-T Gibbs sampler for the 2PL model. However, the scope is not limited to the 2PL model. It is demonstrated how the DA-T Gibbs…

Methods for calculating confidence intervals for the mean are reviewed for the case where the data come from a log-normal distribution. In a simulation study it is found that a variation of the method suggested by Cox works well in practice. An approach based on Generalized confidence intervals also works well. A comparison of our results with…

The data illustrate outliers that are not mistakes and not observations that are unusually high or low. The reasons for them are all interesting historically. They illustrate that "outliers" need not be errors but may instead be particularly interesting cases. The data also illustrate that different data displays may differ in their ability to…

Hadamard's two integral inequalities are generalized and the quadrature formulae associated with them are demonstrated.

This note considers continuous functions f on an interval [a, b] and develops sufficient conditions to answer the question, for what points c in the interval is there a rectangle with height f(c) and some width beta-alpha that has a signed area equal to [integral of] beta over alpha f(x)dx?

In this article the authors demonstrate two instances where the jackknife can be used to enhance hierarchical linear model (HLM) analyses. The jackknife was used to improve the HLM estimates of composite measures by jackknifing over items. The first study examined fixed-effects and variance component estimation. The jackknife appeared to reduce…

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph.

This Technical Report is designed to provide technical detail to support the analysis and findings presented in the "Head Start Impact Study Final Report" (U.S. Department of Health and Human Services, January 2010). Chapter 1 provides an overview of the Head Start Impact Study and its findings. Chapter 2 provides technical information on the…

This study implemented a three-stage problem-based estimation instruction scenario and combined it with mobile technology to provide elementary teachers with an effective e-tool for observing student estimation and leading effective class or group discussions on the selection and assessment of appropriate strategies for solving daily estimation…