Discusses Newton's method for approximating the roots of functions, indicating that students who program in BASIC can learn and appreciate the method by writing their own programs. Includes a hypothetical dialogue between teacher and student about the topic; sample program listings; and problems assigned to students who have written programs. (JN)

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…

Discusses the use of Logo tools, spinners, dice, and coins for creating and understanding probability. Gives procedures for devising a spinner board and other necessary functions for performing the activity. Presents ideas for extending the experiment. (RT)

Describes three games that one can play with or without a computer involving arithmetic, strategy, and problem solving techniques. Lists an abbreviated program for BASIC. Provides information on availability of the variable number game and the ARITHMETICULATOR which does calculations of large numbers and runs on IBM PCs. (RT)

Discusses the process of mathematical iteration, its benefits as a problem-solving technique, and how to teach it. Presents a selection of mathematical ideas and problems that can be solved and explored using iteration, along with related BASIC computer programs. (MDH)

A computer program is given which will generate a list of descriptions of the items to which a student has responded incorrectly on the Keymath Diagnostic Arithmetic Test. It is designed for the TRS-80, Model III, with two disk drives. The documentation lists all required materials, describes the six options and how to use them, indicates the…

Graphs equations in two variables using a BASIC screen-sweep program that generates solutions to equations by applying the intermediate value theorem. Provides suggestions for investigations that result in graphs of a butterfly, the Cheshire cat, the Trisectrix of Catalna, E. T. waving goodbye, a praying mantis, and others. (MDH)

Examines the use of the computer to approximate the value of the definite integral normally calculated by mathematical means. Presents four examples using BASIC programs to approximate single and double integrals by numerical integration and the Monte Carlo method. Programs are provided. (MDH)

Presents a method for using matrix algebra and computers to encode and decode secret messages. Provides examples of coding procedures, a short review of matrix multiplication, and a BASIC program for use with secret messages containing up to 1000 numbers. (RT)

States the objectives and implementation procedures for this teacher-directed or individualized learning discovery unit. Describes the value of the program and additional activities that can be included. Shows a copy of the program. (RT)

Describes several phenomena in which interesting properties of numbers are demonstrated. Includes discussions of amicable, perfect, and sociable numbers. Presents computer programs for conducting a number chain search. (RT)

Describes the use of simulation to introduce the bootstrapping technique of creating confidence intervals for the mean, median, and variance. These bootstrap confidence intervals are compared to the traditional confidence intervals for the purpose of analyzing accuracy of the technique. A Minitab program to produce confidence intervals is…

Presents an algorithm to estimate pi by approximating a unit circle with a sequence of inscribed regular polygons. Demonstrates the application of the algorithm with a hand-held calculator and an Apple computer. Provides a program to calculate pi in Pascal programing language. (12 references) (MDH)

Offers examples of loss of accuracy when using digital computing devices. Discusses causes for loss of accuracy and methods of preventing loss. Presents implications that loss of accuracy has for mathematics instruction. (MDH)

Describes examples of student-centered activities for exploring mathematical induction using BASIC programs or spreadsheets. Discusses the advantages of using this medium to teach the concept and provides computer programs for the activities. (MDH)