This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

Ways of using calculators to presents the concept and methodology of concurrent processing are discussed. Several problems that could be used to compare sequential versus concurrent processing are presented. (MK)

Presented is a derivation for the matrix representation of an arbitrary boost, a Lorentz transformation without rotation, suitable for undergraduate students with modest backgrounds in mathematics and relativity. The derivation uses standard vector and matrix techniques along with the well-known form for a special Lorentz transformation. (BT)

In this article the authors develop a model that employs a factor analysis structure at Level 2 of a two-level hierarchical linear model (HLM). The model (HLM2F) imposes a structure on a deficient rank Level 2 covariance matrix [tau], and facilitates estimation of a relatively large [tau] matrix. Maximum likelihood estimators are derived via the…

This paper presents the development of the fusion model skills diagnosis system (fusion model system), which can help integrate standardized testing into the learning process with both skills-level examinee parameters for modeling examinee skill mastery and skills-level item parameters, giving information about the diagnostic power of the test.…

The relationships among types of errors observed during probability problem solving were studied. Subjects were 50 graduate students in an introductory probability and statistics course. Errors were classified as text comprehension, conceptual, procedural, and arithmetic. Canonical correlation analysis was conducted on the frequencies of specific…

Described is an approach to computational matrix algebra that takes advantage of a high quality, low cost microcomputer software package. The examples and applications discussed focus on matrix multiplication. (Author/CW)

Three experiments involving 138 college students investigated why one type of graphic organizer (a matrix) may communicate interconcept relations better than an outline or text. Results suggest that a matrix is more computationally efficient than either outline or text, allowing the easier computation of relationships. (SLD)

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing…

Three methods of synthesizing correlations for meta-analytic structural equation modeling (SEM) under different degrees and mechanisms of missingness were compared for the estimation of correlation and SEM parameters and goodness-of-fit indices by using Monte Carlo simulation techniques. A revised generalized least squares (GLS) method for…

This paper proposes a methodology to calculate both the difficulty of the basic problems and the difficulty of solving a problem. The method to calculate the difficulty of problem is according to the process of constructing a problem, including Concept Selection, Unknown Designation, and Proposition Construction. Some necessary measures observed…

Researchers studying monitoring accuracy currently use two different indexes to estimate accuracy: relative accuracy and absolute accuracy. The authors compared the distributional properties of two measures of monitoring accuracy using Monte Carlo procedures that fit within these categories. They manipulated the accuracy of judgments (i.e., chance…

This issue of the journal contains abstracts and critiques of 11 research reports. Three of the reports concern problem solving; the remainder pertain to the following topics: the impact of secondary schooling and secondary mathematics on student mathematical behavior; figural matrices; computer-video instruction in mathematics; equivalent…

The Second International Conference on Educational Data Mining (EDM2009) was held at the University of Cordoba, Spain, on July 1-3, 2009. EDM brings together researchers from computer science, education, psychology, psychometrics, and statistics to analyze large data sets to answer educational research questions. The increase in instrumented…