The purpose of this article is twofold. The first is to provide evaluative information on the recovery of model parameters and their standard errors for the two-parameter item response theory (IRT) model using different estimation methods by Mplus. The second is to provide easily accessible information for practitioners, instructors, and students…

This book provides prospective and practicing teachers with research insights into the mathematical difficulties of students with learning disabilities and classroom practices that address these difficulties. This linkage between research and practice celebrates teachers as learners of their own students' mathematical thinking, thus contributing…

Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression estimate as an orthogonal projection and the estimation error as the distance (which is minimized by the projection). Linear…

The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…

We study different ways of determining the mean distance (r[subscript n]) between a reference point and its nth neighbour among random points distributed with uniform density in a D-dimensional Euclidean space. First, we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating…

A concise roadmap for using computational chemistry programs (i.e., Gaussian 03W) to predict the color of a molecular species is presented. A color-predicting spreadsheet is available with the online material that uses transition wavelengths and peak-shape parameters to predict the visible absorbance spectrum, transmittance spectrum, chromaticity…

Describes a model for geometrical probability. Presents two examples of basic theories of probability using geometrical probability. Provides three problems using the described theorem. (YP)

Discusses a revised and extended version of the Mulliken electronegativities. Describes applications and limitations implied by this version. (CW)

Mastering the basic number combinations involves discovering, labeling, and internalizing relationships, not merely drill-based memorization. Counting procedures and thinking strategies are components, and it may be that using stored procedures, rules, or principles to quickly construct combinations is cognitively more economical than relying…

This essay clarifies what it means to know mathematics by examining ways of knowing multiplication and explores what those ways of knowing imply for the teaching and learning of mathematics in schools. It reviews the perennial argument about whether computational skill or conceptual understanding should guide the school curriculum. A mathematical…

Uses chaos theory to investigate the nonlinear phenomenon of population growth fluctuation. Illustrates the use of computers and computer programs to make calculations in a nonlinear difference equation system. (MDH)

Arithmetic programming for students with mild mental disabilities requires a comprehensive perspective that includes attention to curriculum, instruction, and appraisal. Arithmetic computation should not dominate educational programming, but should be included in ways that are functionally relevant and meaningfully presented within a framework of…

Describes a five-dice game, horse. Discusses the offensive player's strategy using the ideas of probability, such as counting outcomes, mutually exclusive events, conditional probabilities, zero sum games, and the use of computer. (YP)

Studies of word problem solving of story problems are reviewed and six immature strategies commonly used by elementary and junior high school students are highlighted. Suggested are some recommendations for mathematics instruction. (YP)

This document describes the contributions of African peoples to the science of mathematics. The development of a number system is seen as related to need. Names of numbers, time reckoning, gesture counting, and counting materials are examined. Mystical beliefs about numbers and special meanings in pattern are presented. Reproductions of patterns,…