The concepts of number sense and numeration, operations, and whole-number computations and their importance are discussed. Activities cover developing concepts of operations, exploring patterns and relationships, and building an understanding of mathematical structure. (KR)

A 2-year project helped Supai Middle Schools (grades 7-8; enrollment 600) in Scottsdale, Arizona, explore ways to use calculators as tools for learning and teaching mathematics. This project and other research indicate that students at every grade level can use calculators in classes to understand mathematical concepts. (MLF)

In 1992, the National Assessment of Educational Progress will assess math skills at fourth- and eighth-grade levels and reading skills among fourth graders. For the first time, the process will be designed to compare states. The historical background, rationale, and expected benefits of this new approach are summarized. Includes six references.…

Explored is young children's ability to estimate set sizes and use reference points such as 10. Results indicated that many children could accurately place sets somewhat smaller than a reference point but had difficulty placing sets somewhat larger than a reference point. (CW)

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)

Discussed are some applications of mathematics involved in actuarial science which may be taught in high school mathematics classes. Described are the importance of approximate solutions, multiple answers, and selling the solution to a problem. (CW)

This article presents 12 examples of the use of a calculator in the algebra class. The calculator codes and the mathematical formulas of the examples are presented in the appendix. (Author/YP)

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 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)

Investigated whether children who reflected the structure of word problems with their concrete models were successful in learning to symbolically represent problems with structure-based open number sentences. Forty-five first graders were taught to write canonical and noncanonical open number sentences. (Author/YP)