Investigated qualitative features of proportional reasoning on dimensional intensive variables by sixth- (N=116) and eighth- (N=137) grade students. These features included types of comparison and types of strategies employed. Results based on the administration of four proportional problems, varying in numerical and referential content, are…

Math teaching involves more development of computational skills than problem solving and concept analysis. Presented are four areas to consider in attacking the problem. (MD)

Presented is a mean-value theorem that generalizes the Taylor-Lagrange formula. Discussed is the asymptotic behavior of the remainder term of the formula. Several numerical schemes are derived to approximate the solution to initial-valued first order differential equations. (KR)

Presents an approach to the concept of absolute value that alleviates students' problems with the traditional definition and the use of logical connectives in solving related problems. Uses a model that maps numbers from a horizontal number line to a vertical ray originating from the origin. Provides examples solving absolute value equations and…

Explores alternative strategies to solve algebraic equations that do not lend themselves to traditional methods. Examines one nontraditional equation by a graphical approach using a graphing utility and by a numerical approach using spreadsheets. Discusses new basic skills for algebra utilizing technology. Provides a computer program to solve…

Since 1990, the January issue of "Teaching Pre K-8" has highlighted a school visit by the president of the National Council of Teachers of Mathematics. This article discusses Cathy Seeley's visit to a 6th grade classroom at the J. E. Pearce Middle School in Austin, Texas, where she participated in a math activity from the Connected…

Problems involving the generation and counting of isosceles triangles interior to a given isosceles triangle are described. (SD)

A series of interesting mathematical applications for the greatest integer function are presented. (JT)

A discussion of the classic probability hat check problem. The paper shows how the hat check problem can be viewed as a problem about enumerating certain members of the symmetric group of permutations on n symbols, with an ensuing generalization. (PK)

Two topics are discussed that can be presented in a discussion of the annual percentage rate (APR): difference equations and fixed-point iteration. A program in BASIC using the iteration procedure is included. (MNS)

Suggests that problems designed for classroom use should include such factors as ways to introduce the problem, the skills to be developed, the mathematical prerequisites for the problem, key questions, extensions, and solutions. An example is provided which illustrates these and other points. (JN)

This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…

Details of an instructor's attempt to solve a problem in combinatorics taken from a textbook used by some of his students are presented. It is felt the material raises a number of significant points about problem solving and mathematics. Teachers are encouraged to put themselves in such situations. (MP)

Incorporating problem solving as an integral part of mathematics programs in the classroom is discussed. The teacher's focus is seen as stretching pupil thinking. (MP)