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

The necessity for developing computational estimation procedures has resulted from an increased availability of calculators and microcomputers in the classroom. This article reports on a study of middle school students who were given computational problems to estimate and explain how answers were obtained. Results are discussed. (Author/DF)

Investigates the calculation strategies used by female students in Grades Two and Three to solve word problems. Findings indicate that students used three main intuitive models: (1) direct counting; (2) repeated addition; and (3) multiplicative operation. Concludes that children acquire an expanding repertoire of intuitive models and the model…

Two experiments studied preschool children's ability to infer numerosity from correspondence between two sets. Found that children were able to make inferences as early as three years of age. However, differences between the two conditions suggest production deficiencies in young children's use of counting as a problem-solving strategy when they…

The strategies of four men with mild mental retardation when performing calendar calculations were investigated. Results suggested that subjects were aware of calendar rules and regularities, including knowledge of the 14 different calendar templates. Their strategies were rigidly applied and relied heavily on memory, with little manipulation of…

Examines the computational strategies of 10 young street vendors in Beirut by describing, comparing, and analyzing computational strategies used in solving three types of problems: (1) transactions in the workplace; (2) word problems; and (3) computation exercises in a school-like setting. Indicates that vendors' use of semantically-based mental…

Describes the success, the methods (mental, informal written, standard algorithm) and the strategies of informal written arithmetic to be observed when 300 elementary students worked on six addition and six subtraction problems with three-digit numbers. (Author/MM)

This study examined the hypothesis of superior quantification abilities of persons with high functioning autism (HFA). Fourteen HFA individuals (mean age: 15 years) individually matched with 14 typically developing (TD) participants (gender, chronological age, full-scale IQ) were asked to quantify as accurately and quickly as possible…

Meaningful visual experience requires computations that identify objects as the same persisting individuals over time, motion, occlusion, and featural change. This article explores these computations in the tunnel effect: When an object moves behind an occluder, and then an object later emerges following a consistent trajectory, observers…

Described in the context of a computer simulation are highlights of a program of research focusing on the storage of mathematics problem solving information in young children's memory and the development of such knowledge structures in older children. Specifically discussed are the problem size effect, the network nature of the memory…

Children use acquired knowledge as they learn basic multiplication facts. If informal thinking strategies are stressed, the border between "figuring out" and "knowing by heart" gradually disappears. Children will acquire a flexible mental structure of multiplication facts instead of a collection of rules. (MNS)

Indicates how thinking strategies help children learn the basic facts for whole numbers, listing several strategies involved in addition, subtraction, multiplication, and division. Also lists books and articles for illustrations of the strategies and how to teach them, and two sources for research findings on thinking strategies for basic facts.…

When the words "problem" and "answers" are used in connection with computational exercises, students think they are solving problems. Distinguishing between computational forms and problems is illustrated with a variety of topics. (MNS)

"Capture" is a game that requires players to perform several computations on each turn and to choose an optimal move, thus promoting higher-order thinking and probability notions. Rules are given, playing is described, and extension activities are noted. (MNS)

Presents a three-component model of arithmetical development in young children. Applies this model as a basis for analysis of developmental processes in early mathematics learning that may be universal. (RJC)