Presents recommendations based on 13 years of work by the Study of Mathematically Precocious Youth. Holds that mathematically talented students are essential to our country's scientific and technological progress and that their abilities must be cultivated to a far greater extent than is permitted by current educational programs. (Author/GC)

Details of an 18-lesson unit of instruction that has been used successfully with eighth-, ninth-, and tenth-grade classes are presented. Each lesson centers around individual computer programs written in Applesoft BASIC. Copies of two programs are provided, and ways to acquire the other 16 are noted. (MP)

An examination of the way banks charge interest based on a 360-day year points out that excess interest may be charged if calculated rates are applied to a 365-day period. (MP)

An exploration of a problem called solving quadratic congruences modulo p is detailed and is built around an alternate method of deriving the quadratic formula. Three practical pedagogical values that have been experienced by students and instructor when the material was presented to classes are noted. (MP)

Continued fractions and associated sequences are viewed to constitute a rich area of study for mathematics students, by supporting instruction on algebraic and computational skills, mathematical induction, convergence of sequences, and interpretation of function graphs. An iterative method of approximating square roots opens suggestions for…

High school students are warned against service station fraud. A problem-solving section is designed to help students calculate consumer costs for various fraudulent transactions. Several ways of reducing fraud or of lessening the chances of problems are noted. (MP)

The use of mobiles to illustrate mathematical concepts, some areas for student investigation of the equation for the general form of a line that begins with switching the coefficients, and some examples of indeterminacy of the basic types of limits suitable for beginning students are presented and discussed. (MP)

The history of probability from ancient times is presented. The relationship between the mathematical and experimental definitions of probability are detailed. (MP)

Cardinal infinities, the superrational numbers, and intuitions of infinity in limiting processes are discussed. (MP)

Several sample problems from the "Ladies Diary," published in the early 1700s, are reviewed. They provide a fascinating glimpse of the mathematics considered useful in the eighteenth and early nineteenth centuries. (MP)

The process that Hippasus of Metapontum (ca. 470 B.C.) may have used to discover irrational numbers is reconstructed. (MP)

Magic squares are developed beginning with square arrays of playing cards. (SD)

The famous birthday problem is discussed and activities which can be used with it as an introduction to probability are examined. (SD)

Discusses a number series made from the multiplication of numbers to digits. Presents a number series for diverse multiplication numbers. (YP)

Develops a general computer algorithm to obtain a magic square having a number of rows that is a multiple of four. Presents a BASIC program and sample runs. (YP)