Evaluates an instructional method in general chemistry that attempts to bridge the gap between algorithmic problem-solving abilities and conceptual understanding of chemistry students and emphasizes conceptual problem solving in the initial phase of a concept. Concludes that using a conceptual focus for the chemistry courses had many positive…

Adapts Stanic and McKillip's ideas for the use of developmental algorithms to propose that the present emphasis on symbolic manipulation should be tempered with an emphasis on the conceptual understanding of the mathematics underlying the algorithm. Uses examples from the areas of numeric computation, algebraic manipulation, and equation solving…

An approach to solving equations is presented. (SD)

CYBERNETICS IN EDUCATION IMPLIES COMPLETE CONTROL OF THE INSTRUCTIONAL PROCESS, WHOSE GOALS ARE SPECIFIED BY COMMUNIST POLICY. MODELS FOR INSTRUCTIONAL PROCESSES, INCLUDING BOTH LOGICAL ALGORITHMS, AND NON-ALGORITHMIC OR PROBABILITY PROBLEMS, MUST BE TESTED EXPERIMENTALLY SO SPECIFIC OBJECTIVES CAN BE STATED. THE INSTRUCTIONAL PROCESS ITSELF MUST…

The early use of the distributive law can aid students in learning addition of fractions and provide rapid approaches to computation involving other operations. (SD)

Two methods of adding columns of single digits were compared in terms of the speed and accuracy with which sums are produced. The direct method (successive addition) was found to be better than the method of looking for combinations which sum to ten. (SD)

Significant differences were found favoring skill-deficient second-graders (N=10) provided with repeated preteaching trials on a selected component skill of a subtraction algorithm before they worked the entire algorithm over students (N=10) who, from the beginning of training, received systematic instruction on working the entire algorithm.…

The role of division of whole numbers in problem solving and the implications for teaching division computation are examined. Deleting the teaching of division facts, and obtaining solutions by using multiplication facts, is advocated. (DT)

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)

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)

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)

A study to determine if "random" or "careless" errors in multiplication made by individual students take on discernible patterns is described. Implications for teaching are discussed. (MK)