Shows a way in which algebra and geometry can be used together to find the lengths and areas of spirals. This method develops better understanding of shapes, similarity, and mathematical connections in students. Discusses spirals embedded in triangles and squares, the Pythagorean theorem, and the area of regular polygons. (MKR)

Discussed are the rationale for, and the benefits accrued from, the use of graphing calculators within all aspects of the secondary mathematics curriculum. Examples are included that highlight specific features of graphing calculators. (JJK)

Part I describes the presentation of six different proofs of the Pythagorean Theorem by groups of three students in a party atmosphere. Part II delineates the analysis behind a student conjecture concerning the area of certain closed polar-coordinate figures. Part III proposes a categorical worksheet for determining when to apply the proper rule…

The recursive model presented here involves the study of drugs in the bloodstream and their subsequent elimination from the body. Both a basic and a more realistic model are presented and discussed in terms of an algebraic approach, a recursive approach, the graphical representation, and other extensions and connections particularly with models…

Describes the Geometer's Sketchpad, a geometric construction kit composed of three manipulatable, dynamic, linked, multiple representation environments: the coordinate system, formulas, and graphs. Examines the use of the environments for studying parameter effects of linear and quadratic functions and for solving linear equations. (MDH)

A way for students to refresh and use their knowledge in both mathematics and physics is presented. By the study of the properties of the "Runge-Lenz" vector the subjects of algebra, analytical geometry, calculus, classical mechanics, differential equations, matrices, quantum mechanics, trigonometry, and vector analysis can be reviewed. (KR)

Presented is the solution to a quadratic expression and a variety of comments regarding this situation and implications for problem-solving instruction. A strategy for approaching similar problem-solving situations is discussed. (CW)

Presented are example activities which are typical of the topic focus and methods of approach evident in the Algebraic Thinking in Children (ATIC) project. This project is aimed at assisting children to ultimately make sense of formal algebra when it is presented. (CW)

Presented is a comparison of two major surveys of the teaching and learning of mathematics conducted by the International Association for the Evaluation of Educational Achievement. Surveys indicate that performance levels have declined in computational skills and increased in algebra. (Author/CW)

Investigates the impact of faculty and student characteristics on the performance of students in their last developmental mathematics course and in college algebra. Reveals that faculty gender and employment status, and student age, ethnicity, and enrollment status were significantly related to student performance in both developmental mathematics…

Features activities for advanced second-year algebra students in grades 11 and 12. Introduces three random variables and considers an empirical and theoretical probability for each. Uses coins, regular dice, decahedral dice, and calculators. (ASK)

Describes the development of an interactive teaching and learning model involving Desktop Videoconferencing (DVC) and other audiographic facilities for undergraduate mathematics. The experiment demonstrated that it was possible to integrate DVC with computer applications/graphics software to represent algebraic, geometric, and numeric concepts.…

Examines the reliability and validity of using a survey to gauge the percentage of time that algebra teachers use practices that are consistent with professional standards for teaching mathematics. Survey results from 28 teachers suggest that a composite of practices is quite reliable and somewhat valid but that it does not capture instructional…

Introduces mathematical guessing games to teach algebra that motivate students in learning mathematics by stimulating their curiosity and problem-solving abilities. (ASK)

Suggests a few alternative approaches to teaching algebra that allow students to construct and reflect upon meanings for expressions and equations. The three lessons, which require extended discussion and reflection, are "Representing Algebraic Expressions,""Evaluating Algebraic Statements," and "Generating Equations." (WRM)