The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has…

A simple, direct condition is formulated for determining the mode(s) of a probability mass function. This condition is then applied to the Poisson and hypergeometric mass functions.

Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…

For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

This note describes a procedure for estimating the range restriction component used in correcting correlations for unreliability and range restriction when an estimate of the reliability of a predictor is not readily available for the unrestricted sample. This procedure is illustrated with a few examples. (Contains 1 table.)

This paper introduces the language associated with a polygon microworld called Polygon R&D, which has the mathematical crispness of Logo and has the discreteness and simplicity of a Turing machine. In this microworld, polygons serve two purposes: as agents (similar to the turtles in Logo), and as data (landmarks in the plane). Programming the…

Using computer simulation, the authors assessed the accuracy of J. E. Hunter, F. L. Schmidt, and H. Le's (2006) procedure for correcting for indirect range restriction, the most common type of range restriction, in comparison with the conventional practice of applying the Thorndike Case II correction for direct range restriction. Hunter et…

This article provides technical descriptions of five fixed parameter calibration (FPC) methods, which were based on marginal maximum likelihood estimation via the EM algorithm, and evaluates them through simulation. The five FPC methods described are distinguished from each other by how many times they update the prior ability distribution and by…

Results from nine experiments were analyzed to evaluate the relationship between relative problem completion rates (RPCR) and judgments of time involving mathematics assignments. For each experiment, control assignments contained only target mathematics computation or word problems. Matched experimental assignments contained similar target…

The Financial Accounting Standards Board (FASB) has recently issued Statement of Financial Accounting Standards No. 141 (Revised 2007) Business Combinations. The object of this Statement is to improve the relevance, representational faithfulness, and comparability of reported information about a business combination and its effects. This Statement…

The purpose of this research was to study effects of teaching activities using team learning with different and non-different major subjects on innovative knowledge creation of undergraduate students. The subjects were 14 undergraduate students registered in Technology Activities course (2726311), faculty of Education, Chulalongkorn University.…

The present study compared item and ability invariance as well as model-data fit between the one-parameter (1PL) and three-parameter (3PL) Item Response Theory (IRT) models utilizing real data across five grades; second through sixth as well as simulated data at second, fourth and sixth grade. At each grade, the 1PL and 3PL IRT models were run…

The purpose of this study was to develop general outcome measures (GOM) in mathematics so that teachers could focus their instruction on needed prerequisite skills. We describe in detail, the manner in which content-related evidence was established and then present a number of statistical analyses conducted to evaluate the technical adequacy of…

BRT Math Screening Measures focus on students' mathematics performance in grade-level standards for students in grades 1-8. A total of 24 test forms are available with three test forms per grade corresponding to fall, winter, and spring testing periods. Each form contains computation problems and application problems. BRT Math Screening Measures…

In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of…