Presents solutions for a problem concerning doubling a recipe from a previous article on number concepts in the October 1997 issue. (ASK)

Reacts to an article published in a previous issue of this journal on the effects of graphing calculators and computer algebra systems (CAS) on students' manual calculation and algebraic manipulation skills. Considers the contribution made by Jean-Baptiste Lagrange to thinking about the role of CAS in teaching algebra. (ASK)

Nigerian second graders (n=58) were given instruction on using counting and thinking strategies. Compared to 54 controls, they performed better on recall and retention of number facts. (SK)

Presents worksheets for students to practice substituting whole numbers into fairly simple symbolic expressions. (MKR)

Describes a strategy to make chi-square calculations and interpretations more understandable by presenting the theory behind the test to the students in a visual manner. Involves using dihybrid corn to generate a large sample of chi-squares followed by plotting a frequency distribution to get at the meaning behind the chi-square table. (JRH)

Debates the place of standard methods, the calculator, and mental mathematics in elementary education. Proposes a framework for computation that emphasizes a sequence for introducing computational procedures. (ASK)

Giving children time and encouragement to explain methods of calculation is a useful strategy. Uses this strategy with a group of children and discovers surprising thinking by one child on number facts. (ASK)

Discusses childrens books about money dealing with the recognition of coins, bills, and their value; counting and calculating; minting and printing; meaning of words, symbols, and pictures on money; history; and money from around the world. Describes activities and provides a bibliography. (PEN)

We consider power calculation in structural equation modeling with data missing completely at random (MCAR). Muth?n and Muth?n (2002) recently demonstrated how power calculations with data MCAR can be carried out by means of a Monte Carlo study. Here we show that the method of Satorra and Saris (1985), which is based on the nonnull distribution of…

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model,…

Interactions between (multiple indicator) latent variables are rarely used because of implementation complexity and competing strategies. Based on 4 simulation studies, the traditional constrained approach performed more poorly than did 3 new approaches-unconstrained, generalized appended product indicator, and quasi-maximum-likelihood (QML). The…

Confirmatory factor analysis (CFA) is widely used for examining hypothesized relations among ordinal variables (e.g., Likert-type items). A theoretically appropriate method fits the CFA model to polychoric correlations using either weighted least squares (WLS) or robust WLS. Importantly, this approach assumes that a continuous, normal latent…

The latent trait-state-error model (TSE) and the latent state-trait model with autoregression (LST-AR) represent creative structural equation methods for examining the longitudinal structure of psychological constructs. Application of these models has been somewhat limited by empirical or conceptual problems. In the present study, Monte Carlo…

In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the…

The Diels-Alder reaction is used as an example for showing the integration of computational and preparative techniques, which help in demonstrating the physical organic concepts in synthetic organic chemistry. These experiments show that the students should not accept the computational results without questioning them and in many Diels-Alder…