If equivalent operations are performed on the left term and right term of an equation, a new equation results. This principle allows one to produce equations with a variable isolated on one side and its value(s) on the other. It also underlies problem-solving in situations where equations are not explicitly used, but the problem calls for…

The purpose of this study was to determine if the use of Learning Logic, an integrated-learning system, by high school students in Algebra I had a significant effect on the performance of these students when they subsequently enrolled in a traditionally taught Algebra II course. Four high schools were selected in which Learning Logic was used for…

Examines arithmetic and algebra knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Presents results of a longitudinal study designed to investigate students' readiness for algebra. Proposes a model for the transition from arithmetic to pre-algebra to algebra. Contains 29…

Mathematical meanings can be developed when individuals construct translations between algebra symbol systems and physical systems that represent one another. Previous research studies indicated (1) few high school students connect whole number manipulations to algebraic manipulations and (2) students who encounter algebraic ideas through…

A series of studies were conducted at Evergreen Valley College in San Jose, California, to evaluate the persistence of three groups of new mathematics students entering Arithmetic, Algebra, and Intermediate Algebra courses in the fall of 1988. In particular, the studies examined students' persistence from the initial mathematics course,…

A series of studies were conducted at San Jose City College (SJCC) in San Jose, California, to evaluate the persistence of three groups of new mathematics students entering Arithmetic, Algebra, and Intermediate Algebra courses in the fall of 1988. In particular, the studies examined students' persistence from the initial mathematics course,…

Examines the potential role for Computer Algebra Systems (CAS) when teaching courses as functions, calculus, and linear algebra to students with low prerequisite algebra skills. A study reports the rationale, planning, and implementation of a functions course integrating Maple CAS into instruction. (MDH)

Research indicates that students have great difficulty solving algebra word problems and that few high school seniors have mastered the fundamentals of algebra, let alone algebra problem-solving skills. Improving students' algebra problem solving skills is considered to be critically important by those who have worked on reforming mathematics…

The purpose of this study was to determine teachers' views of learning algebra and to investigate if any relationship exists between their views of learning algebra and the ways that they use graphing calculators in their algebra classes. The 48 algebra teachers who participated in the study were from Allen, Putnam, and Van Wert counties in…

Twelve adolescents with learning disabilities were trained to use a cognitive strategy in algebra problem solving. The two-phase strategy (problem representation and problem solution) was effective in improving algebra performance on algebra word problems, and maintenance and transfer of the strategy were evident. (JDD)

Students (n=61) in an experimental course stressing active student involvement and the use of a computer algebra system scored higher than students (n=76) in a traditional college algebra course on final measures of inductive reasoning, visualization, and problem solving while maintaining equivalent manipulation and computation skills. (Author/MLB)

Data from the High School and Beyond survey for 1,076 students who took algebra before high school and 5,818 who took algebra in high school demonstrated that early access to algebra had an effect beyond increased knowledge, and that it might socialize a student into taking more mathematics. (SLD)

Data from (n=470) students at Owens Technical College in Fall 1991 showed that high school GPA was the best predictor of grades in Basic Algebra, followed by high school rank, college GPA, ACT natural sciences, ASSET numerical skills, and ASSET elementary algebra scores. (11 references) (SW)

This study reports evaluation data from a statewide inservice project to retrain mathematics teachers to implement a new algebra curriculum required by all students for high school graduation. The new course places more emphasis on problem solving, use of graphing calculators, and real-life applications. Pretest and posttest data were collected…

Analyzes student construction of function-based problem solving methods in introductory algebra. Describes longitudinal observation of a pair of students that studied algebra for three years using the function approach including intensive use of graphing technology. Offers terms for describing and explaining what and how do learners appreciate and…