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.

The use, learning and transfer of workplace numeracy skills, as well as current understandings of the term numeracy, are examined in this study. It also highlights the importance of numeracy as an essential workplace skill. The report challenges the training system and training organisations to provide numeracy training which makes links directly…

Using data from the Panel Study of Income Dynamics PSID, across the life course Socio Economic Status (SES) impacts future health outcomes, although the primary influence is education and not an individual's financial resources in whatever form they are received. That conclusion appears to be robust whether the financial resources are income or…

This article describes a model for response times that is proposed as a supplement to the usual factor-analytic model for responses to graded or more continuous typical-response items. The use of the proposed model together with the factor model provides additional information about the respondent and can potentially increase the accuracy of the…

"How much popcorn will our classroom hold?" This intriguing question sparked a terrific integrated science and math exploration that the author conducted with fifth-and sixth-grade students. In the process of finding the classroom's volume, students developed science-process skills (e.g., developing a plan, measurement, collecting and interpreting…

The issue of the disproportionate identification and placement of racial/ethnic minorities in special education has been investigated extensively. One of the most useful tools in this research is the risk ratio, which compares one racial/ethnic group's risk of receiving special education and related services to that of all other students. The risk…