Mental computation helps children understand how numbers work, how to make decisions about procedures, and how to create different strategies to solve math problems. Although researchers agree on the importance of mental computation skills, they debate how to help students develop these skills. The present study explored the existing literature in…

This longitudinal study investigated the academic and cognitive characteristics of persistent mathematics difficulty (MD-p) from first to fourth grade. Ninety-nine children were retrospectively categorized into one of three groups: MD-p, transient mathematics difficulty (MD-t), or typically developing. MD-p was defined as persistently low…

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)

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)

In the first experiment, observations were made of children ages four-and-a-half to five-and-a-half years of age who were induced to use counting or matching in a Piagetian number conservation task. The spontaneous matching and counting behavior of a more mature but not yet conserving sample was investigated in the second experiment. (RH)

A biologically detailed computational model is described of how categorization judgments become automatic in tasks that depend on procedural learning. The model assumes 2 neural pathways from sensory association cortex to the premotor area that mediates response selection. A longer and slower path projects to the premotor area via the striatum,…

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)

An explicit model of the process of quantification which involves the operations of subitizing and counting is described. The general model states that quantification of n items takes place via subitizing when n is less than five and via subitizing and addition (that is, counting) when n is five or larger. The explicit model is stated in the form…

The cognitive and psychomotor processes involved in working with the modern Japanese version of the abacus were investigated by distracting expert abacus operators in various ways. (Author/MV)

Changes in children's cognitive strategies for solving simple subtractions were studied by analyzing verbal reports given immediately after each problem. The development of children's cognitive processes involved a gradual shift from more primitive and less demanding memory strategies to reconstructive memory processes to retrieval processes.…

This study examined the extent to which children's cognitive abilities in kindergarten and their mothers' education predict their single-digit and procedural calculation skills and the covariance of these with reading skill in Grade 4. In kindergarten, we assessed children's (N=178) basic number skills, linguistic skills, and visual attention. In…

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

An interpretation is provided of the philosopher L. Wittgenstein's analyses of mental states. The theoretical implications of these analyses for cognitive development and qualitatively oriented researchers are discussed. The mental states examined are: (1) pain; (2) remembering; (3) calculating/adding; (4) following a rule; and (5) reading.…

Students in grades 1, 4, 7, and 10 were tested in a two-part investigation of simple and complex mental addition (with college students as a reference point). One session involved a normal reaction time task in which children made true/false judgments about a series of addition examples. The other session involved a verbal protocol interview, the…