Nine verbal behaviors of teachers were identified. After twenty Algebra I teachers taught a lesson on direct variation, their students took a posttest. Findings showed that lesson objectives, relevant examples, and "OK" responses correlated positively (p less than .05) with student posttest achievement. (DT)

Basic algebraic formulas for calculating research program budgets are explained, using time-tested examples of cost-sharing, fringe benefit, and indirect cost calculation. The method is suggested as a tool for teaching both novice research administrators and researchers. (MSE)

Reports on an experiment in which Algebra I students (N=181) learned to translate word problems with two unknowns from the prose representation to symbolic representation using two variables when first solving word problems with two unknowns. Concludes that students who had learned to solve equations with the new method scored higher than those…

Illustrates how many key algebraic concepts can be informally developed within the number and operations strand taught in the primary grades. Discusses expressions and equations, properties and conventions, relationships between operations, and variables from this perspective. (ASK)

Presents two games that provide practice with equivalent fractions, that were produced at three levels of difficulty, Level 1 being the simplest. Also describes another game for practice in solving simple linear equations. Appendices contain examples of materials used in the games. (ASK)

Describes a technique that uses cellular telephones and their rates to enliven the topic of linear equations in a college algebra course. Uses mathematics to select a cellular telephone plan from a vendor. Enables students to use and connect the ideas of functions, equations, graphs, and applications. (DDR)

Presents the findings of a study on the learning experiences of undergraduates enrolled in a writing-intensive algebra course. The study revealed that writing activities are successful in terms of facilitating student comprehension of mathematical content. The use of words allows student writers to gain ownership of the algebraic content. (DDR)

Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)

Describes an activity in which students examine bicycle chain-rings, cogs, and gear ratios as a means of exploring algebraic relationships, data collection, scatter plots, and lines of best fit. (KHR)

Comments on Gregory Trandel's article that explores two teaching strategies using geometry and algebra to demonstrate the equivalence between two methods of measuring excess burden. States that for students with limited mathematics skills, measuring excess burden can be expressed algebraically using a simple formula (excess burden…

Compared tutoring episodes where tutoring did and did not cause learning in university physics students to inform design of intelligent tutoring systems. Found that when students were not at an impasse, learning was uncommon regardless of the tutorial explanations employed. When students were at an impasse, tutorial explanations were sometimes…

Examines 8th grade units from the Connected Mathematics Project (CMP). Identifies differences in older and newer conceptions, fundamental objects of study, typical problems, and typical solution methods in algebra. Also discusses where the issue of what is new in algebra is relevant to many other innovative middle school curricula. (KHR)

Discusses the advantages to using on-line assessment for both the instructor and the learner. Reports on the use of an online assessment tool that provides interactive feedback to students learning linear algebra. Measures success in terms of improved pass rate and students' satisfaction with the flexible learning opportunities that the tool…

Uses the notion of focusing phenomena to explain how a teacher's actions were connected to her students' interpretations of a linear equation. Conducts interviews and analyzes a high-school classroom that emphasized dependency relationships in real-world situations. Describes how the teacher directed attention away from functional relationships…

Discusses representations in the context of solving a system of linear equations. Views representations (concrete, tables, graphs, algebraic, matrices) from perspectives of understanding, technology, generalization, exact versus approximate solution, and learning style. (KHR)