Describes a teaching experiment examining the possibility of the redefinition of a multiplication problem from a problem of remembering, to a problem of figuring out why arithmetic rules make sense. (YP)

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)

An approach to teaching factors and terms is offered that builds directly on students' knowledge of arithmetic. Errors arising from factor and term confusions are noted, followed by the pedagogical strategy of exploration, invention, and discovery. (MNS)

Call for reforming mathematics teaching has been sounded loudly and strongly. Change from teaching standard algorithms to having children invent their own methods requires major pedagogical shift. Teachers must trust students' inventiveness and ability to make sense of numerical situations, be committed to thinking and reasoning as cornerstone of…

This case study of a low-achieving first grader learning to subtract two-digit quantities with several different pedagogical objects demonstrates the complexities of the conceptual shift from the tens part of a number to the ones part. An appendix contains interview transcripts. Contains 52 references. (Author/MKR)

This article proposes use of a restructured hundreds chart that involves a right-to-left sequence of numbers (similar to the direction of computations) and inclusion of zero. Specific instructional activities using the restructured chart are suggested for teaching such skills as counting, number identification, numerical relationships, place…

The influence of reading comprehension level on solving verbally expressed arithmetic problems was studied with 12 students (ages 8 to 12) who were prelingually and profoundly deaf. Reading comprehension level was related to students' problem-solving level. Verbal arithmetic problems contained linguistic forms that were difficult for deaf…

Two experiments, one measuring eye fixations of 38 undergraduates and the other assessing memory of 37 undergraduates, provide evidence that unsuccessful problem solvers are more likely to comprehend by direct translation and that successful word problem solvers are more likely to build a problem model. (SLD)

Described is a strategy for teaching elementary or secondary level students to use a self-monitoring procedure and a mnemonic device to help students independently solve multidigit subtraction problems sometimes requiring regrouping. (DB)

Fourth grade students participated in mental arithmetic activities for eight weeks. Posttests revealed that the experimental group performed significantly higher than the control group on arithmetic problem solving and arithmetic computation. Females appeared to benefit more from the instructional program than males. (KS)

Fourth graders' (n=117) solutions to addition problems were analyzed in terms of standard or idiosyncratic written algorithms. Students had not previously been taught pencil-and-paper algorithms. Preference for horizontal layout, working from left to right, and a wide variety of written algorithms were found. (Contains 48 references.) (Author/MKR)

Explores the number problem of writing an expression for each of the unit fractions using any digit exactly four times. Includes tables of expressions for unit fractions. (MKR)

Assesses the competence of children (N=215) between the ages of 5 and 9 at addition by asking them to estimate the answers to addition sums. Reports that children at higher levels tend to produce more reasonable estimates than children at lower levels. Discusses the existence and nature of a zone of partial knowledge and understanding. Contains 31…

Examines adults from China and Canada solving single-digit multiplication problems. Reports that Chinese adults were faster and made fewer errors than Canadian adults, and Chinese adults made more errors that reflect verbal-production processes that may occur after retrieval whereas Canadian adults made more errors that reflect retrieval…

Presents a study to develop better understanding of the processes involved in the construction of oral and written symbolic systems and to grasp their role in the elaboration of the modeling function of numbers. Proposes ideas for teaching in light of this study and contributes better understanding of the relationship between numeration and…