For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…

Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based…

Results of operations on the Pythagorean formula are interpreted pictorially to yield interesting art forms. (MP)

A coordinate system is imposed on a geoboard to form a table that leads to the discovery of the formula n[(n+1)(n+1)] (n+2)/12. Proof is by induction. (MP)

Describes an intuitive and discovery-oriented approach that can be used to develop formulas for rectangles, triangles, parallelograms, and trapezoids. The approach emphasizes the interrelationships between the formulas. (JN)

Examines the writing of two groups of students in a college-level calculus class to identify criteria that discriminate successful versus unsuccessful writers in mathematics. Discusses results from the mathematics writers' checklist and methods for its use as an instructional and assessment tool in the classroom. (Author/KHR)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

Describes three studies in which students (N=515; N=60; N=135) were asked to indicate appropriate operations and numbers used in solving open mathematical sentences. Analysis of data and interviews suggest two error patterns: "finding a solution" and "inverse operation." Indicates that "finding a solution" strategy…

The derivation of a method to drive the general term of a sequence is presented. The difference sequences and binomial coefficents are used in the derivation. An application of this method is made to solve Polya's problems concerned with dividing space in regions by a given number of planes. (JP)

Examines how selected U.S. and Asian mathematics curricula are designed to facilitate students' understanding of the arithmetic average. Discusses similarities and differences of learning goals, focuses, and concepts among U.S. commercial, Asian, and U.S. reform curriculum series. (Author/KHR)

Presents a short study of proper values of two-by-two matrices with real entries. Gives examples of symmetric matrices and applications to systems of linear equations of perpendicular lines intersecting at the origin and central conics rotated about the origin to eliminate the xy term from its equation. (MDH)

The authors derive distance formulas in two-and-three-dimensional coordinate geometry utilizing the concept of similar triangles and the Pythagorean theorem. (MN)