This response to Usiskin's editorial comment on calculator use in the May 1983 issue considers why arithmetic is taught. The belief that mathematics improves thinking and the humanist position that it is part of our cultural heritage are noted. The role of mathematics in the curriculum should be reconsidered. (MNS)

A general framework for conducting generalizability analyses is presented. Generalizability theory is extended to situations in which the objects of measurement are not persons but other factors, such as instructional objectives, stages of learning, and treatments. (Author/PN)

This paper describes an intelligent spelling error correction system for use in a word processing environment. The system employs a dictionary of 93,769 words and, provided the intended word is in the dictionary, it identifies 80 percent to 90 percent of spelling and typing errors. Nine references are cited. (Author/EJS)

The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)

The first section promotes use of student notebooks in mathematics instruction as incentives for pupils to do daily work. Part two looks at a geometric interpretation of the Euclidean algorithm. The final section examines an open box problem that is thought to appear in virtually every elementary calculus book. (MP)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

The hypothesis investigated is that understanding of the long division algorithm requires a higher cognitive level than understanding of fundamental division concepts. Sixth-grade children were tested on performance and understanding of a given algorithm and concepts of division. (MP)

Data indicated that high percentages of fifth- through eighth-grade low achievers had high algorithm confidence for the operations of addition, subtraction, and multiplication. A substantial proportion in each grade expressed a low degree of confidence in their computational method for division. (CM)

Some techniques for developing the ability to multiply and divide by powers of ten with ease and understanding are presented. (Author/MK)

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

Examines notion of algorithms and describes variety of roles they take in educational endeavors. Problems in their development and application are explored, and implications for future use and research are presented. References are included. (BK)

Computer science education for the liberal arts student has both a practical value (creating an intelligent consumer) and an appreciative value (teaching algorithmic thinking). A computer literacy course can be structured to harmonize with the aims of liberal education. (SK)

An unusual algorithm for approximating square roots is presented and investigated using techniques common in algebra. The material is presented as a tool to interest high school students in the logic behind mathematics. (MP)

Describes ways in which algorithms which refer to underlying procedures should be represented in order to improve communication in educational and/or training materials. Representations of linear procedures, decision rule procedures, and complex procedures are provided. (MER)

The time at which component skills are taught is studied to see whether it is a significant instructional variable. This research involved the instruction of a multiplication algorithm to 15 below-average first graders. (MP)