Mastering the basic number combinations involves discovering, labeling, and internalizing relationships, not merely drill-based memorization. Counting procedures and thinking strategies are components, and it may be that using stored procedures, rules, or principles to quickly construct combinations is cognitively more economical than relying…

The author first corrects Baroody's description of the network retrieval model for basic number facts, in which facts are stored in memory and retrieved as needed. He then indicates weaknesses in Baroody's argument. (MNS)

The relationship between arithmetical concepts and solution methods is discussed. A case study illustrates the contention that some children with relatively sophisticated concepts express those concepts with primitive methods. (MNS)

A model of subtraction development and the computing difficulties and research issues suggested by the model are outlined. Demands of simultaneous processes, difficulties with informal subtraction, and the impact on the counting-up procedure are discussed. (MNS)

Discusses four ways in which subtraction is more difficult than addition: (1) verbal solutions do not always parallel object solutions; (2) methods may interfere with each other; (3) special problems exist with subtraction on the number line; and (4) subtraction has multiple situational interpretations. (MNS)

This critique focuses on Gagne's attempt to apply information-processing theory to mathematics education, noting that this distorts what it means to learn mathematics. This is discussed with specific illustrations. (MNS)

Mental arithmetic strategies were studied with 91 Dutch third graders who computed by splitting off 10s and units in both numbers or counting by 10s up or down from the first unsplit number. Results reveal flexibility in changing between and within strategy use. Implications for instruction are discussed. (SLD)

Fourth-grade students (n=45) either with or without learning disabilities and achieving or not achieving at grade level in math were asked to explain strategies used to solve computational problems. Strategies were classified as reproductive or reconstructive (which varied in applicability and efficiency). Significant group differences were found.…

Presents results from an Australian study examining whether children who use cognitive strategies in solving simple addition questions develop greater proficiency in addition than children who do not use such strategies. Describes the subjects, instruments, procedure, and instructional treatment. Concludes that the development of cognitive…

Speeded performance on simple mental addition problems of 6- and 7-year-olds with and without mild mental retardation was modeled from a person perspective and an item perspective, both inferred from Siegler's work. Models from item response theory were used to test hypotheses. Found that all children follow same developmental path in acquiring…

Magnitude is assumed to be represented along a holistic mental number line in adults. However, the authors recently observed a unit-decade compatibility effect for 2-digit numbers that is inconsistent with this "holisticness" assumption (H.-C. Nuerk, U. Weger, & K. Willmes, 2001). This study used the compatibility effect to examine whether the…

This research examined students' responses to mathematics problem-solving tasks and applied a general multidimensional IRT model at the response category level. In doing so, cognitive processes were identified and modelled through item response modelling to extract more information than would be provided using conventional practices in scoring…

In some settings, the validity of a battery composite or a test score is enhanced by weighting some parts or items more heavily than others in the total score. This article describes methods of estimating the total score reliability coefficient when differential weights are used with items or parts.

The purpose of this paper is to provide researchers with a shared framework, terminology and tool to improve the coherence of research into learning mathematics with CAS and to assist its findings to accumulate into a significant body of knowledge. Experience with calculators in arithmetic led to a framework for number sense. There is an obvious…

Three experiments investigated the route-angularity effect, which is demonstrated when a greater number of turns along a route increases the estimated length. So far, a route-angularity effect has not been demonstrated in school-age children. Because of the lack of a developmental theory, this finding could only be explained by a minor control of…