An Experiment in Three Approaches to Teaching Average to Elementary School Children

The types of experiences children should encounter to best understand average were investigated in this study. Using a traditional approach with problem solving, a concrete approach with manipulatives, or a visual approach with computer spreadsheets, similar lessons on the arithmetic mean were taught to 22 children in grades 4–6, in three multiage groups. Differences among pretest, posttest, and interview performances suggest some advantage in the use of a visual instructional style. Continued gains in performance were found after 4 months without further instruction. An algorithmic-like definition of average corresponded to better long-term performance than less precise definitions. Collaborative deliberations resulted in positive implications for the researchers' teaching.     

An order-statistics-based method for constructing multivariate distributions with fixed marginals

A new system of multivariate distributions with fixed marginal distributions is introduced via the consideration of random variates that are randomly chosen pairs of order statistics of the marginal distributions. The distributions allow arbitrary positive or negative Pearson correlations between pairs of random variates and generalise the Farlie–Gumbel–Morgenstern distribution. It is shown that the copulas of these distributions are special cases of the Bernstein copula. Generation of random numbers from the distributions is described, and formulas for the Kendall and grade (Spearman) correlations are given. Procedures for data fitting are described and illustrated with examples.     

The occurrence of operational anomalies in spacecraft and theirrelationship to space weather

Modern spacecraft systems and subsystems appear to show an increasing susceptibility to effects of the space environment. This trend is probably due to “softer” designs of electronic components, reduction in subsystem sizes, and increases in performance demands and number of components within spacecraft. The major agents within the space environment that contribute to spacecraft anomalies can be reasonably well described. This paper reviews operational anomaly trends and assesses the identification and potential prediction of causative space weather agents     

Determination of cobalamins using capillary electrophoresis inductively coupled plasma mass spectrometry

The determination of cobalamins using capillary electrophoresis inductively coupled plasma mass spectrometry (CE-ICP-MS) was investigated. Both capillary zone electrophoresis (CZE) and micellar electrokinetic chromatography (MEKC) modes of operation were studied. The optimal separation of four cobalamin species (cyanocobalamin, hydroxocobalamin, methylcobalamin, and 5′-deoxyadenosylcobalamin) and a potentially harmful corrinoid analogue (cobinamide dicyanide) was obtained using CZE at a pH of 2.5. Both 20 mM phosphate and 20 mM formate buffers were used with success, although the formate buffer provided improved resolution. The CZE-ICP-MS method was used to quantify cyanocobalamin in a vitamin supplement and the analytical results were in good agreement (±5%) with values obtained by ICP-MS for total Co levels. The solution detection limits for cobalamins using CZE-ICP-MS were approximately 50 ng/ml. MEKC was found to be useful for the screening of vitamin preparations because it provided a rapid means of distinguishing cyanocobalamin (the form most commonly used in vitamin preparations) from free cobalt. The separation of free cobalt and cyanocobalamin using MEKC was achieved in less than 10 min.     

The millimeter-wave spectrum of acetaldehyde in its two lowest torsional states

A large number of new millimeter-wave spectral lines of gaseous acetaldehyde have been measured at frequencies up to 250 GHz. These lines arise from rotational transitions of acetaldehyde in its two lowest (v_t = 0,1) torsional states and involve angular momentum quantum numbers J ≤ 12 and K ≤ 10. A global data set consisting of 562 lines has been obtained by combining the millimeter-wave lines with previously measured lower frequency data involving the two lowest torsional states. This data set has been analyzed via an internal axis method previously used to study the spectra of CH₃OH and CH₃SH. The root-mean-square deviation of the fit is only 685 kHz. An analogous least-squares fit to 335v_t = 0 lines yields a root-mean-square deviation of 269 kHz.