Illustrations are provided which show how some algebraic manipulations done prior to doing calculations can eliminate unnecessary storage of data, reduce the total number of needed steps, and avoid overflow. (MN)

Teacher planning procedures employing percentage-based measurement summaries and subsequent implementation of the results of planning with and without error analysis resulted in moderate increases in correct mathematics computation of learning disabled 10-13 year olds. No significant differences were found for presence or absence of error…

Assessment of effects of school principal involvement on acquisition of multiplication facts by 309 intermediate grade students found that taking the timed test three times per week resulted in consistent sustained gains and that a math game with the principal contingent on improved class performance was the most effective principal-initiated…

Discussed is the need to rethink computation in terms of what is critical, how computation is taught, and what constitutes computation. (MNS)

The mathematics associated with division is discussed, working from a theorem for the real division algorithm. Real-world, geometric, and algebraic approaches are discussed, as are related topics. (MNS)

A continuous and curriculum-based assessment method, Precision Learning Assessment (PLA), which integrates precision teaching and norm-referenced techniques, was applied to a math computation curriculum for 214 third graders. The resulting districtwide learning curves defining average annual progress through the computation curriculum provided…

Examines Kolers and Smythe's 1984 paper on the computational approach to cognition. Considers: (1) five specific criticisms of the computational approach, (2) their analysis of the conceptual basis of symbolization, and (3) their proposed alternative approach. Summarizes their position and discusses its shortcomings. (SED)

Discusses Kolers and Smythe's 1984 paper on the computational approach to cognition. Suggests some factors that support the continued emphasis on the analytic approach of the psychological representation of knowledge, but also acknowledges that they have provided a useful set of distinctions and at least one vocabulary for describing them. (SED)

Examines the implications of the following ways of computing forensic contest results: (1) sum-of-the ranks; (2) modified sum-of-the ranks; (3) majority rule; and (4) serial elimination. (PD)

This study of one part of the cognitive system of an illiterate Indian (his method of enumeration, computation, and evaluation) demonstrates the sophisticated conceptualization of which he is capable, independent of a writing system. (Author/CMG)

This paper describes a design research study with ten second-grade students who are part of the Measure Up (MU) research and development project underway at the University of Hawai'i. Students were asked how they counted in multiple bases, specifically how they knew when to go to a new place value and why it was necessary to do so. All ten…

Over the last 20 years, the use of calculators and digital measuring equipment has to some extent replaced mathematical mental/written activity and also the use of analogue measuring equipment. This paper explores some aspects of number concept, reading the number line, and estimation from scales. The students being considered are mainly part of a…

This textbook's goal is to train and develop the mind by means of the science of numbers. This work is designed both for primary and advanced classes. The first part is adapted to beginners, while the latter part is peculiarly fitted to give to the more advanced student that thorough mental drilling in the analysis of numbers, which furnishes the…