To help the reader understand the scope and diversity of the Wisconsin R & D Center's research effort in mathematics, four perspectives are presented: (1) the Center's approach to research, development, and practice; (2) the origins of the current research effort; (3) a description of current research; and (4) a projection for future research. (JP)

Evidence is presented for the theory that the two brain hemispheres process stimuli differently: the left hemisphere is specialized for logico-analytic tasks and the right hemisphere for visuo-spatial tasks. They contend that cognitive ability is related to the development of hemispheric asymmetry and present implications for mathematics education…

Kindergartners appeared to differ in their readiness to use a concrete counting strategy for addition. Many persisted in counting with objects. Mental counting strategies were sequenced. (MNS)

Achievement of 20 Trainable Mentally Retarded and 67 Educable Mentally Retarded Students under manipulative and non-manipulative modes of mathematics instruction are compared. (MM)

The Piagetian area scores of 168 students in first, second, and third grades were used to predict mathematics achievement for each of four succeeding years. Conservation and measurement scores were highly predictive. (MP)

The ability of students in grades 1-12 to generate proofs of theorems in an unfamiliar, one axiom, abstract system was investigated. There were no significant differences in performance of two levels of secondary students; fourth- through sixth-grade students were also able to develop proofs, but needed more time. (SD)

A review of 25 years of Piagetian research in intellectual growth as it pertains to the learning and understanding of mathematics and implications for teaching. (MM)

An outline of a model that provides a new perspective on the conceptual foundations of mathematics and a new approach for the study of children's acquisition of numerical operations is proposed. Attention is viewed as a pulse-like succession of moments and is supported by recent data from neurophysiology. (MP)

Problem-solving processes used by concrete- and formal-operational eighth-grade pupils were investigated through interviews. Formal-operational pupils used a larger variety of processes. Also, a larger variety of processes were used on more complex problems. (MP)

The effects of numerical and visual cues, equality or inequality of initial volumes, size of measurement unit, and order of cue presentation on conservation of liquid volumes by first- and second-graders were investigated. Some findings extend, and others contradict, those of Piaget. (SD)

Nine children were tested to determine the appropriateness of Piaget's part-whole fraction concept interpretation for both the discrete case and the continuous cases of length and area. (MP)

First and second graders (n=81) were randomly partitioned into experimental and control groups. The experimentals were given experiences in sorting and seriating objects. Significant treatment and grade effects (p.01) were found on a seriation test, but no significant relationships between classification and transitivity nor seriation and…

Children were grouped according to ability to conserve number and then randomly assigned to training on arithmetic concepts or playing a game. The research hypothesis that there would be an interaction effect between conservation and effect of treatment was not confirmed. (SD)

Students were pretested, then 27 first graders were trained using a highly verbal procedure emphasizing class addition activities. On posttests, trained subjects significantly improved their class inclusion and number conservation scores, but no effects were found for substance conservation or transitivity. (DT)