A subtraction algorithm for numbers having several digits is described. The algorithm requires that, for digits in the same place, the smaller is always subtracted from the larger. (SD)

A multiplication algorithm based on a perfect square is described. (SD)

Upper elementary school students created their own algorithms for finding products of whole numbers. The algorithms were similar to familiar ones for finding products involving 9 and 11. (SD)

A model of the division algorithm is described which relates step-by-step to the standard algorithm. Use of the model in instruction requires the distribution of a special worksheet. The focus of the instruction is on students sharing some amount of money equally among several friends. (MP)

Typical instruction of the division algorithm fails to justify why one brings down a number during the process. The construction and use of an aid is described which can be used to help explain the process of division to students. The aid emphasizes place-value aspects. (MP)

How teachers can diagnose difficulties with computation is discussed, with emphasis on how to develop diagnostic tests. How to use such tests to plan remediation is considered in terms of several types of errors. (MN)

Algorithms for the four basic operations on whole numbers are described; these algorithms provide for sequential recording of all steps in the operations. (SD)

The changing role of computational skills is discussed. A level of computational skill desirable in light of predictable future needs is proposed, and four reasons for advocating that level are discussed. (MN)

In a two-year study, frequencies and descriptions of systematic errors in four algorithms in arithmetic were studied in regular and special education classrooms. (Author/SD)

Two questions were investigated in this study: (1) How did the computational proficiency of sixth graders who had one year's experience with Developing Mathematical Processes (DMP) materials compare with an equivalent group of students who used the usual textbook program; and (2) What occurs when sixth graders study algorithms as sequences of rule…

The observations of a fifth-grade student concerning number patterns are recorded and discussed. (SD)

Alternative algorithms, "tricks," and shortcuts are viewed as ideally suited for inclusion in a systematic program of practice because of their motivational effect and the mental stimulation involved in discovering why they work. (MP)

The author suggests that, through using the outlined question model and suggested classroom activities, elementary students will improve their abilities to analyze routine, one-step word problems and make a plan for the solution. It is further argued that the same algorithm can be applied to multistep problems by using specified questions. (PK)

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…

The use of counting for subtraction was investigated. Counting for subtraction is related to counting-on for addition and to four skills: the ability to use the subtrahend cardinality to gain entry into the count sequence, the ability to use the minuend cardinality to gain entry into the count sequence, the ability to use the count sequence to…