This study investigated two methods used to teach multidigit multiplication to fourth-grade students: the lattice method and the distributive method. Classes from four schools were randomly assigned so that the two treatment groups contained two each or urban, rural and inner city classrooms. A series of 15 lessons was prepared for each treatment…

Computational algorithms appearing in early American arithmetic text are discussed. (SD)

Described is a case in which a young student stumbles upon the "integer" technique for subtraction which differs from the techniques of decomposition and equal addition. (MN)

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

Second-grade students were randomly assigned to either an instructional unit within which addition and subtraction of two digit numbers were treated as a single integrated process of regrouping or one which developed the addition and subtractive algorithms sequentially. Periodic assessments favored the sequential approach, but differences were not…

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

The following ideas are shared: (1) a low-stress subtraction algorithm that eliminates the traditional borrowing process, and (2) an approach to graphing circular functions that looks at the process of modifying simple functions as a series of shifting, sliding, and stretching adjustments, with its biggest advantage viewed as its generality. (MP)

Results of this study indicated calculator algorithms can serve as an effective alternative instructional strategy where computational skill is an instructional goal. (MP)

The author feels teaching division of fractions is worthwhile because it will help students understand other algorithms. (MK)

Three short essays provide teaching suggestions for lessons on base two, order of operations, and ratios used to motivate a number of mathematical ideas. (MK)

Encourages teachers to allow opportunities for students to present alternative algorithms, whether the students invent them or learn them, then lead a discussion about the meaning of the operations with the goal of students understanding why the algorithm works. Teachers with students of similar racial and ethnic backgrounds should encourage the…

Reviews research using diagrams, number sentences, and algorithms to help students learn to add and subtract; poses questions on the relationship of instruction to children's knowledge construction; and proposes a research agenda in this area. (86 references) (MKR)

Compares the approaches to teaching division in Britain and in Holland where different emphasis is placed on the development of mental and written methods. Describes how it is common for pupils in Britain to work from an early stage with pencil and paper rather than mentally whereas early emphasis is placed on mental strategies in Holland. (ASK)