Mathematical computation consists of both written computation and mental computation. The strategies for mental computation can be used to check the reasonableness of written computations. Mental computation has two distinguishing characteristics: "it produces an exact answer, and the procedure is performed mentally, without using external…

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

With both energy usage and energy costs rising rapidly, people can benefit from paying closer attention to their consumption of energy. Students can gain greater awareness of their personal use of electricity and get some excellent experience with the practical application of mathematics by studying their families' consumption of electricity. A…

When there exist omitted effects, measurement error, and/or simultaneity in multilevel models, explanatory variables may be correlated with random components, and standard estimation methods do not provide consistent estimates of model parameters. This paper introduces estimators that are consistent under such conditions. By employing generalized…

In many practical situations scaling the data is necessary to solve linear programs. This note explores the relationships in translating the sensitivity analysis between the original and the scaled problems.

Under predetermined conditions on the roots and coefficients, necessary and sufficient conditions relating the coefficients of a given cubic equation x[cubed] + ax[squared] + bx + c = 0 can be established so that the roots possess desired properties. In this note, the condition for one root of a cubic equation to be "the negative reciprocal of…

The widely used PASCO laboratory equipment is an excellent way to introduce students to many topics in physics. In one case, PASCO's equipment may be too good! Various experiments exist for calculating the kinetic coefficient of friction by measuring the acceleration of a sliding object under some constant force. With ever more accurate equipment,…

Meta-analyses are presented of sex differences in (1) the (mental) arithmetic subtest of the Wechsler intelligence tests for children and adolescents (the WISC and WPPSI tests), showing that boys obtained a mean advantage of 0.11d; (2) the (mental) arithmetic subtest of the Wechsler intelligence tests for adults (the WAIS tests) showing a mean…

This study examined the efficacy of 4 different parceling methods for modeling categorical data with 2, 3, and 4 categories and with normal, moderately nonnormal, and severely nonnormal distributions. The parceling methods investigated were isolated parceling in which items were parceled with other items sharing the same source of variance, and…

A structural equation modeling method for examining time-invariance of variable specificity in longitudinal studies with multiple measures is outlined, which is developed within a confirmatory factor-analytic framework. The approach represents a likelihood ratio test for the hypothesis of stability in the specificity part of the residual term…

The increasing use of diary methods calls for the development of appropriate statistical methods. For the resulting panel data, latent Markov models can be used to model both individual differences and temporal dynamics. The computational burden associated with these models can be overcome by exploiting the conditional independence relations…

An experimental work on controller tuning for chemical engineering undergraduate students is proposed using a small heat exchange unit. Based upon process reaction curves in open-loop configuration, system gain and time constant are determined for first order model with time delay with excellent accuracy. Afterwards students calculate PID…

Within the framework of a laboratory-focused, guided-inquiry pedagogy, students discover the Nernst equation, the spontaneity of galvanic cells, concentration cells, and the use of electrochemical data to calculate equilibrium constants. The laboratory experiment we describe here is a continuation of curriculum reform and pedagogical innovation at…

Three widely used sixth-grade textbooks were studied to see how fraction concepts were represented. The textbooks selected were "Connected Mathematics," "Middle Grades MathThematics," and Glencoe's "Mathematics: Applications and Concepts Course 1." Three specific areas were examined: representation mode, model, and problem context. Results of…

We present a case study of the physical principles necessary to model the high altitude parachute jump made by Colonel Joseph Kittinger, USAF, in 1960, in order to determine the maximum speed attained and to calculate whether this speed was sufficient to exceed the speed of sound at that altitude. There is considerable discrepancy in the value of…