Presents a method for solving linear equations involving the use of inverses instead of memorizing rules. (MKR)

Circuits are described, with discussion on how to help students find the algorithms to solve a variety of problems involving circuits. (MNS)

Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)

A real world sample of actual data that students can use to see the application of the Hardy-Weinberg law to a real population is provided. The directions for using a six-step algorithmic procedure to determine Hardy-Weinberg percentages on the data given are described. (KR)

Described is a simple algorithm that can be used for the input, arithmetic manipulation, and output of large integers in their exact representations. Three BASIC programs are included that apply this method to the problem of multiplication of large integers, computation of factorials, and the generation of palindromic integers. (MNS)

Considered are what discrete mathematics includes, some parallels and differences between new math and discrete mathematics (listed in a table), and lessons to be learned. A list of references is included. (MNS)

Presents two methods for replacing a series by one converging more rapidly: regrouping the terms of a series and manipulations of power series. Describes a general algorithm for approximating the natural logarithm of any number. (YP)

Explains an algorithm which details procedures for solving a broad class of genetics problems common to pre-college biology. Several flow charts (developed from the algorithm) are given with sample questions and suggestions for student use. Conclusions are based on the authors' research (which includes student interviews and textbook analyses).…

Shows how to model Newton's method for approximating roots on a spreadsheet. (MKR)

Provides a short list of integral triples for the design of problems employing unit fractions (so solutions will be positive integers). Also presents an algorithm whereby both primary and imprimitive sets of triples can be easily obtained and shows how to extend the algorithm to solve three-variate unit fraction equations. (JN)

Described is a way to use knots to relate a three-dimensional object to a two-dimensional representation of the object. The results are used to produce an algorithm or rule to explain a general case. Included are examples, diagrams, procedures, and explanations. (KR)

The four-color theorem stating that any map in a plane can be colored using no more than four colors represents a problem suitable for the liberal arts student. Presented is an algorithm for coloring familiar maps through the temporary removal of states bordering three or fewer states. (MDH)

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

Presents the algorithm to approximate square roots as reproduced from the 1579 edition of an algebra book by Rafael Bombelli. The sequence of activities illustrates that the process of understanding an original source of mathematics, first at the algorithmic level and then with respect to its mathematical validity in modern terms, can be an…

Investigates high school students' understanding of the physical relationship of chromosomes and genes as expressed in their conceptual models and in their ability to manipulate the models to explain solutions to dihybrid cross problems. Describes three typical models and three students' reasoning processes. Discusses four implications. (YP)