Examines several uses of the word cancel and suggests alternative terminology. In particular, arithmetic and algebraic examples are used to illustrate problems associated with the term cancel. (PK)

Defines and supports investigative mathematics for schools. Presents several results of an investigation of Fermat's Last Theorem. (PK)

Presented are two examples including data sets for which calculating various elementary statistics will reveal something new about the data. The objective of these examples is to show the student what various statistics may reveal, or not reveal, about a given data set. (PK)

The general combinatorial problem of counting the number of regions into which the interior of a circle is divided by a family of lines is considered. A general formula is developed and its use is illustrated in two situations. (PK)

Classroom ideas for teaching area and perimeter concepts are presented. Squares, circles and other shapes are examined. Further explorations are suggested. (PK)

Annual mathematics talent searches for 12-year-old students were conducted in Hamburg, West Germany. One-hundred-fifty students took part in a long-term Saturday enrichment program to train them in problem finding and problem solving. The philosophy of this program is explained and illustrated with preliminary data. (MNS)

The use of a synthetic division microcomputer program in searching for the zeros in polynomial functions is described. A program listing and outputs are included. (MNS)

Use of general mathematical strategies by Australian students in grades 8-10 was studied, with students required to describe their reasoning and articulate reasons for the choice of particular strategies. Main effects were found for cognitive level, year level, and sex. A taxonomy is also presented. (MNS)

Brief articles on producing videotapes of the execution of a program on a microcomputer, an illustration of the sums of numbers and squares, and the distance from a point to a line are included. (MNS)

Provides examples of if-then and combinatorial reasoning situations that have proved successful with college students and can be used with secondary school students. Proposes that practice with these problem solving processes can eliminate the need to memorize formulas that students may not understand. (ML)

Four methods of solutions and 12 calculative strategies were found from introspective reports of 15 skilled and 15 unskilled students in grades 11 and 12 doing mental multiplication. Unskilled students used strategies more suited to written than mental computation, while skilled students used strategies based on number properties. (MNS)

Programs are listed for integer powers and fractional powers, with discussion of how to use them in instruction. (MNS)

Some concrete examples of the use of historical materials in developing certain topics from precalculus and calculus are presented. Ideas which can be introduced with a reformulated curriculum are discussed in five areas: algorithms, combinatorics, logarithms, trigonometry, and mathematical models. (MNS)

Brief articles concern solving a polynomial equation of degree greater than two, an approach for teaching an ambiguous case in trigonometry, and built-in functions on calculators and computers. Two computer programs are listed. (MNS)

Provides results from a 1983 survey of secondary mathematics education in Wisconsin. Questions refer to graduation requirements, curriculum topics, nature of geometry classes, metric system, computers, and calculators. Items also collected data on district mathematics committees, policies, competency exams, computer access, and the nature of…