Percentages of mathematics content for 7 text series, grades 1-8, were compared with percentages on the Ohio Ninth Grade Proficiency Test. Ratios of text:test percentages were arithmetic (63:30), measurement (10:25), geometry (12:15), data analysis (11:15), and algebra (4:15). Implications are discussed. (MSD)

Investigates the construction of understanding of the motion of an object down an inclined plane which takes place through the process of model building in an integrated algebra, trigonometry, and physics class. Discusses four major themes related to student learning through modeling that emerged from the results. Discusses implications for…

Uses qualitative analysis to understand how middle school students thought about and approached problems while they wrote descriptions of why and how they solve problems. Indicates that rich learning experiences are possible when writing is used as a way to prepare for small group discussion in mathematics. (Contains 13 references.) (Author/ASK)

Presents alternative equation-solving procedures that emphasize an examination of the steps or operations necessary to perform a calculation, followed by the inversion of those steps. The approach is especially attractive to students with limited mathematical skills. (Author/MKR)

Shows how five points determine the formula of a conic section and uses the determinant as a computational device to find the coefficients in the formula. Uses symbolic, numerical, and graphical techniques. (Author/MKR)

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 the Treisman model which involves supplemental workshops in which college students solve problems in collaborative learning groups. Reports on the effectiveness of Math Excel, an implementation of the Treisman model for introductory mathematics courses at Oregon State University over five academic terms. Reveals a significant effect on…

Traces three major stages in the development of algebraic notation: (1) rhetorical or prose; (2) syncopated; and (3) symbolic. Illustrates the development of a standardized, efficient symbol system by tracing the evolution of some common symbols, including the symbols for equals, addition, subtraction, multiplication, and division. (Author/WRM)

Explores abundant numbers and presents a proof that abundant numbers of every order exist. Readers are encouraged to use the included computer program to explore abundant numbers for themselves, look for patterns in the output, and consider further questions. (Author/MKR)

Described is a strategy that allows students to experiment with probability without applying formulas to solve problems. Students are able to intuitively develop concepts of probability before formal definitions and properties. Sample problems are included along with BASIC programs for some of the problems. (KR)

Describes an activity in which students, grades 7-12, explore patterns and properties of repunits, an integer written as a string of ones. Includes extensions for exploring algebraic justifications. (MKR)

Investigated the effect of the choice of a model's medium (algebraic expression or computer program) on the performance of students. Student programers did not transfer the qualities of a computer program approach to their algebraic models. Provides items for five tests. (YP)

The ability of students to sort cards based on surface features and deep patterns is investigated. The effect of the presence of variables and what makes a pattern difficult or easy for students to recognize are discussed. Study revealed that students are unsuccessful at making connections between expressions, sentences, and sequences which share…

Describes the Secant Method, a numerical method to approximate solutions to equations for which symbolic solution methods do not apply. Illustrates the method using the EXCEL spreadsheet program. Discusses instructional implications of utilizing this method. (MDH)

P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)