We present an experiment, well adapted for students of introductory optics courses, for the visualization of the impact of spherical aberration in the point spread function of imaging systems. The demonstrations are based on the analogy between the point-spread function of spherically aberrated systems, and the defocused patterns of 1D slit-like…

The synthesis of "N"-benzyl-2-azanorbornene via aqueous hetero Diels-Alder reaction of cyclopentadiene and benzyliminium chloride formed in situ from benzylamine hydrochloride and formaldehyde is described. Characterization of the product was achieved by IR and NMR spectroscopies. The spectral data acquired are thoroughly discussed. Numerous…

Using an easy-to-make cylindrical resonator, students can measure the speed of sound in a gas, u, with sufficiently high precision (by locating standing-wave Lissajous patterns on an oscilloscope) to observe real gas properties at one atmosphere and 300 K. For CO[subscript 2] and SF[subscript 6], u is found to be 268.83 and 135.25 m s[superscript…

As a result of conversations with students, previous teaching experiences, and through reading relevant literature, this author was aware that many students struggle with understanding fraction concepts. In particular, she knew that students had difficulty with reading, renaming, ordering, interpreting, and applying common fractions, fraction…

This article describes instructional activities designed to help students develop an understanding of the multiple relationships between fractions and percents and unit price as they develop their mental-math abilities. (Contains 4 figures.)

The cognitive underpinnings of arithmetic calculation in children are noted to involve working memory; however, cognitive processes related to arithmetic calculation and working memory suggest that this relationship is more complex than stated previously. The purpose of this investigation was to examine the relative contributions of processing…

Theoretical analyses of the development of numerical representations suggest that playing linear number board games should enhance young children's numerical knowledge. Consistent with this prediction, playing such a game for roughly 1 hr increased low-income preschoolers' (mean age = 5.4 years) proficiency on 4 diverse numerical tasks: numerical…

Benford's law of the "first digits" states that in spite of intuitively expected equal frequency of 1/9 of the decimal digits r = 1, ... , 9 appearance on the first place of any number, various empirical studies show another pattern of these frequencies distribution, which is log[subscript 10](1 + 1/r). The article considers this law and other…

This article considers two methods of estimating standard errors of equipercentile equating: the parametric bootstrap method and the nonparametric bootstrap method. Using a simulation study, these two methods are compared under three sample sizes (300, 1,000, and 3,000), for two test content areas (the Iowa Tests of Basic Skills Maps and Diagrams…

Approximately 93 percent of Americans indicate that they experience some level of math anxiety. Math anxiety is defined as negative emotions that interfere with the solving of mathematical problems. Studies have found that some students who perform poorly on math assessments actually have a full understanding of the concepts being tested; however,…

A grounded theory approach was employed to explore the variation in strategies used by students when solving mental multiplication problems. Metacognitive prompts, externally generated stimuli that activate thoughtful cognition, were automatically generated via computer during the solving of mental multiplication problems to elicit awareness,…

This study identified 10 savants with developmental disabilities and an exceptional ability to calculate calendar dates. These "calendar calculators" were asked to demonstrate their abilities, and their strategies were analyzed. The study found that the ability to calculate dates into the past or future varied widely among these…

Addition strategies used by 36 kindergarten children were examined. Children were given written stimuli (such as "2+5" and "3+7") during two sessions taking place a week apart. Results indicated that once children came to rely on mental addition strategies, they often quickly invented more economical procedures to compute sums. Also confirmed was…

D. von Winterfeldt, N.-K. Chung, R. D. Luce, and Y. Cho (see record 1997-03378-008) provided several tests for consequence monotonicity of choice or judgment, using certainty equivalents of gambles. The authors reaxiomatized consequence monotonicity in a probabilistic framework and reanalyzed von Winterfeldt et al.'s main experiment via a…

This article proposes an item response model that incorporates response time. A parameter estimation procedure using the EM algorithm is developed. The procedure is evaluated with both real and simulated test data. The results suggest that the estimation procedure works well in estimating model parameters. By using response time data, estimation…