Discusses the loss of precision that normally results in solving equilibrium problems, particularly as presented through the use of quadratic formulas in most introductory college chemistry textbooks. Provides examples of demonstrations. (TW)

College students were asked to write equations using one of two sets of notational systems. Results indicate that the use of more explicit notation did not help problem-solving performance. (Author/PK)

This study investigated the performance of 14 Hispanic and Anglo ninth graders on several problem-solving tasks, with the focus on the interplay of language-related factors in translating several mathematical statements expressing relationships among variables into mathematical equations. (MNS)

Using data from High School and Beyond, this study empirically investigated the extent of within-variable, between-occasion error covariances among variables included in educational achievement models. Little evidence was found to support the statement that reliability estimates for social background variables are inflated because of correlated…

The various difficulties and cognitive obstacles that students face when they are introduced to algebra are well documented and described in the relevant bibliography. If it is possible, in order to avoid these difficulties, we have adopted the functional approach widening the meaning of algebraic thinking. In this paper, which is part of wider…

We are studying two groups of preservice teachers' conceptions, progression and especially the concept of function in connection to y=x+5 when they are taking a course in algebra or one in calculus in their third and sixth term, respectively, in a teacher preparation program. There is a similar development in that they use to a higher degree a…

Presented is a mean-value theorem that generalizes the Taylor-Lagrange formula. Discussed is the asymptotic behavior of the remainder term of the formula. Several numerical schemes are derived to approximate the solution to initial-valued first order differential equations. (KR)

Proposed is a flow-chart and related formulas to obtain expressions for the derivatives of the old thermodynamic function in terms of new variables, the new function and its derivatives, and derivatives of the old function, involving only measurable quantities. (CW)

Described are the use of spreadsheet programs in chemical engineering calculations using Lotus 1-2-3 macros. Discusses the macro commands, subroutine operations, and solution of partial differential equation. Provides examples of the subroutine programs and spreadsheet solution. (YP)

A generalized Rasch model is presented for measuring attitudes; it is based on the concepts of Thurstone's method of successive intervals. Benefits of the model are illustrated with a study of students' (N=4,035 fifth through ninth graders) interest in physics. (SLD)

Demonstrates how graphing calculators can be used by students to solve equations involving absolute value. Allows students to make connections between the algebraic and graphical representations of the problem. (MDH)

Presents an approach to the concept of absolute value that alleviates students' problems with the traditional definition and the use of logical connectives in solving related problems. Uses a model that maps numbers from a horizontal number line to a vertical ray originating from the origin. Provides examples solving absolute value equations and…

Discusses the equation and proportion methods for teaching how to solve percent problems. Supplements the teaching of each method by introducing a representational model that enhances understanding when solving percent problems. (MDH)

Explores alternative strategies to solve algebraic equations that do not lend themselves to traditional methods. Examines one nontraditional equation by a graphical approach using a graphing utility and by a numerical approach using spreadsheets. Discusses new basic skills for algebra utilizing technology. Provides a computer program to solve…

A method is proposed for constructing a population covariance matrix as the sum of a particular model plus a nonstochastic residual matrix, with the stipulation that the model holds with a prespecified lack of fit. The procedure is considered promising for Monte Carlo studies. (SLD)