Presented is a example that shows why a certain technical lemma is necessary for a valid proof of Galois Theory. The usual proof of Galois' Theory is included as well as one using the lemma. (KR)

Presented is an alternate way to derive R from Taylor's Theorem without involving the (n + 1)st derivative of f. Included is the procedure for estimating the bounds of R. (KR)

Developed is a condition, expressed in terms of an index, that ensures that a quasinormal subgroup is normal. The arguments suggest a variety of exercises for a course in group theory or Galois theory. Included are the definitions, lemmas, and proofs. (KR)

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

Presented are several applications of geometric concepts and measurement skills that are used daily by surveyors, real estate attorneys, and paralegal assistants. Described are the objectives and directions for this lesson. Activity sheets for students are included. (CW)

Described is an investigation into how the use of LOGO programing language affects children's basic knowledge of an angle. Findings indicate that children make erroneous adjustments to their conceptual knowledge of angle to accommodate the results of acquired procedural interaction with the computer. (Author/CW)

Describes four laboratory activities in algebra and precalculus classes that provide hands-on experiences related to functions: slowing down the acceleration of gravity; calculating the acceleration of gravity; generating a parabola using a steel ball and a tilted board; and photographing projectile motion. (YP)

Describes a way for students to learn to solve linear equations using physical objects (pan balances), diagrams, and symbols. Provides diagrams illustrating the method and five problems. Nine references are listed. (YP)

Elaborates the importance of transition to high school emphasized in the "Curriculum and Evaluation Standards for School Mathematics." Describes teaching examples related to each of three dimensions for change: from number to variable; from specifics to generalization; and from description to proof. (YP)

Discusses the use of flexible straws for teaching properties of figures and families of shapes. Describes a way to make various two- or three-dimensional geometric shapes. Lists eight advantages of the method. (YP)

Describes how Suzuki's methods of teaching young pupils to play the violin can be combined with Polya's ideas on problem solving to teach mathematics to elementary school pupils. Six references are listed. (YP)

The focus of this article is on the verification processes children use when assessing the equality of parts produced by them when partitioning geometric shapes. Different processes and children's verbal proofs of equality are presented. Activities for mathematics instruction are suggested. (YP)

Discusses the use of computer graphics in the teaching of geometry. Describes five types of geometry: Euclidean geometry, transformation geometry, coordinate geometry, three-dimensional geometry, and geometry of convex sets. (YP)

Investigates the ways children used their schemes of fractions to interpret fraction situations. Records clinical interviews with nine children (grades three through five). Reports that children do not establish relationships among different schemes when giving meaning to a given situation. (Author/YP)

Describes a graphical method of approximating roots of complex functions that uses the multicolor display capabilities of microcomputers. Theorems and proofs are presented that illustrate the method, and uses in undergraduate mathematics courses are suggested, including numerical analysis and complex variables. (six references) (LRW)