The design and development of a program of computer-assisted instruction (CAI) which assists the student in learning elementary algorithms of an undergraduate numerical methods course is presented, along with special programing features such as partial precision arithmetic, computer-generated problems, and approximate matching of mathematical expressions. The program, designed to operate under the Purdue Instructional and Computational Learning System (PICLS) language, is described in detail: first, there is a tutorial presentation of the mathematical development surrounding an algorithm, the student then formulates the solutions to several problems to display a working knowledge of the algorithm, and, finally, the student progresses to an exploratory stage where he may formulate the solution to his own problems (all computation is assumed by the computer). An experiment to test this program is also described; results include analyses of student attitudes and performances, cost factors, and efficiency. (Author/SP)