A study of 29 students enrolled in Algebra II in an 8-week summer instructional program for minority students was conducted to reveal the skills that students have in translating among representational forms in mathematics problems where the representational form is varied in the given problem and in the required form of the answer. All students…

This study of 16 learning-disabled high school students in algebra classes found that their help-seeking behavior was similar to that of 16 normal-achieving peers, differing only in that subjects sought instrumental help from peers significantly more often than from the teacher. (Author/JDD)

As almost every state attempts to reform mathematics instruction by implementing new teaching standards, state testing practices remain largely unchanged. Is there a mismatch between these new standards and the old tests? This question is investigated by examining whether middle school and high school algebra students taught in a manner consistent…

Tests of (n=105) ninth-grade algebra students involving the addition and multiplication of monomials found that common, systematic errors made when multiplying monomials were related logically to the symbolism used and the algebraic convention of using an implicit 1 as an exponent. (16 references) (MKR)

In 2 experiments with 74 high school students, subjects studied worked examples while learning how to translate English expressions into algebraic equations. Those using worked examples outperformed the control group on posttests, made fewer errors, completed work more rapidly, and required less assistance from the teacher. (SLD)

A mathematical model is used to represent a physical problem. The resulting polynomial is graphed and analyzed. Students are asked to plot families of related polynomial functions and observe patterns. A partial list of possible observations is included. End behavior, complete graph, and classroom use of technology are discussed. (GW)

The cognitive structure of an algebra test was defined and validated using the linear logistic test model (LLTM) and quadratic assignment (QA). A 29-item test was administered to 235 ninth graders. Results suggest the benefits of applying both LLTM and QA to test construction and analysis. (SLD)

The use of restricted item response models to test hypotheses regarding item difficulty ordering and slope uniformity was demonstrated in a study in which 597 algebra students were asked to solve word problems reflecting various types of cognitive processing. Benefits and limitations of the procedures are discussed. (SLD)

Demonstrates examples, one of which is an extension of "guess and check," to include variables rather than numbers. The quadratic equation az2+bz+c=0, is solved by assuming a complex solution of the form z=x+iy. Explores the use of deMoivre's theorem in deriving trigonometric identities with other examples. (Author/ASK)

This report describes a program for improving homework on-time completion with high school Fundamental Algebra students in an urban gifted and arts magnet high school. The Grade Control Chart was selected as a strategy for presenting students with a visual reminder of the value of timely completion of homework. The skills needed to produce this…

Discussed are supercalculator capabilities and possible teaching implications. Included are six examples that use a supercalculator for topics that include volume, graphing, algebra, polynomials, matrices, and elementary calculus. A short review of the research on supercomputers in education and the impact they could have on the curriculum is…

Current educational reform movements focus on mathematics teaching for the empowerment of students and on the classroom as a mathematical community in which students themselves actively question, negotiate, and construct mathematical ideas through classroom discourse. This paper discusses a study that focused on students' use and perception of…

Examines research on the influence of classroom design on student learning attitudes and behavior and presents two case studies on the remodeling of five classrooms in two high schools to accommodate new instructional technology for teaching algebra. Highlights include lighting, color, surface materials, noise, climate control, and seating.…

Describes a project that features a video in the form of a documentary built around a series of six case studies in mathematical thinking: geometry, number, measurement, algebra, chance and data, functions, and calculus. Chooses an example from each area to illustrate inductive and deductive thinking-patterns and proof. (ASK)

Analyzes the construction of mathematical concepts and techniques developed by high school algebra students in computer-assisted instruction; examines learning styles of the most inventive students; and discusses the use of student-generated mathematical techniques in the development of new software intended to cultivate mathematical inventiveness…