In this article, the author takes up the special trinomial (1 + x + x[squared])[superscript n] and shows that the coefficients of its expansion are entries of a Pascal-like triangle. He also shows how to calculate these entries recursively and explicitly. This article could be used in the classroom for enrichment. (Contains 1 table.)

Enthalpy changes corresponding to the gas phase heats of dissociation of 12 organic halides were calculated using two semiempirical methods, the Hartree-Fock method, and two DFT methods. These calculated values were compared to experimental values where possible. All five methods agreed generally with the expected empirically known trends in the…

Deaf and hearing college students' mean reaction times (RTs) were compared on a mental calculation task in which they had to verify the accuracy of solutions to addition and multiplication problems. The deaf students were divided into higher and lower readers. Higher deaf readers and hearing students had similar RTs and accuracy on addition…

The emergence of powerful mathematical computing environments, the growing availability of correspondingly powerful (multi-processor) computers and the pervasive presence of the Internet allow for mathematicians, students and teachers, to proceed heuristically and "quasi-inductively." We may increasingly use symbolic and numeric computation,…

We introduce a multidimensional item response theory (IRT) model for binary data based on a proximity response mechanism. Under the model, a respondent at the mode of the item response function (IRF) endorses the item with probability one. The mode of the IRF is the ideal point, or in the multidimensional case, an ideal hyperplane. The model…

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…

The psychological literature currently emphasizes reporting the "effect size" of research findings in addition to the outcome of any tests of significance. However, some confusion may result from the fact that there are three distinct uses of effect sizes in the psychological literature, namely, power analysis, research synthesis, and research…

In this paper we analyze class size effects in the case of primary schools in Poland. We use two empirical strategies to avoid endogeneity bias. First, we use average class size in a grade as an instrumental variable for actual class size. This allows us to control for within school selection of pupils with different abilities to classes of…

Purpose: We examine the methodological and economic policy implications of three operationalizations of retirement migration. Design and Methods: We compared the traditional age-based definition of retirement migration and two retirement-based definitions, based on degree of labor-force participation and retirement income, by using the 2000 U.S.…

This article challenges the traditional model for teaching computation in the primary grades. It describes a model in which students are encouraged to invent and use alternative computation procedures.

This mixed-methods study assessed the effects of Enhanced Anchored Instruction (EAI) on the math performance of adolescents with learning disabilities in math (MLD). A quasi-experimental pretest-posttest control group design with switching replications was used to measure students' computation and problem-solving skills on EAI compared to control…

Managing the pedagogical aspects of the "computational turn" that is occurring within the Humanities in general and the disciplines associated with cognitive science and neuroscience in particular, first implies facing the challenge of introducing students to computation. This paper presents what has proven to be an efficient approach to bringing…

Over the last three decades 45 states have been confronted with school finance lawsuits. This phenomenon has led to a proliferation of school funding equity studies. However, to date, most studies of the equity of state school finance systems have focused on differences in expenditures between school districts. More recent research has found…

Private tutoring is a widespread phenomenon in many developing countries, including Vietnam. Using the Vietnam Living Standards Surveys 1997-1998 and 1992-1993 for analysis, this paper finds evidence that private tutoring in Vietnam is a necessity in the household budget for both primary students and lower secondary students, and the trend to…

The purpose of this study was to document the instrument development of maze measures for grades 3-8. Each maze passage contained twelve omitted words that students filled in by choosing the best-fit word from among the provided options. In this technical report, we describe the process of creating, reviewing, and pilot testing the maze measures.…