This article discusses the rationale for the classroom use of manipulative materials. Selection criteria are presented for the guidance of teachers, together with advice on how and how not to use the materials. (MM)

A report of an experimental study regarding learning by sixth grade students. (MM)

Children were pretested and assigned to one of three treatments: training with three dimensional manipulanda; the same program except that the instructional materials were line drawings; and a control. On the posttest, both experimental groups were significantly superior to control group. (Author)

Several issues concerning mathematics curriculum for the primary grades are discussed. Five considerations necessary for building a balanced curriculum are defined and discussed: broadening content, providing variety in learning and thinking strategies, balancing emphasis on skills, concepts and applications, discretion in use of manipulative…

Three instructional settings were compared to determine which was most effective: no aids, two-dimensional aids, or three-dimensional aids. Results favored the three-dimensional aids. (MP)

A presentation of learning experiences involving materials is recommended which reflects the sequence of the developmental stages. This sequence is concrete, concrete-abstract, pictorial-abstract, and abstract. Instructional examples at each level are presented. (JP)

Activities, instructional methods, and some ideas from educational psychology used in tutoring a second grader in addition and subtraction are described. (DT)

This study focused on (1) the relation or transition between the measurement and partitive settings for division, and (2) the study of these two interpretations in general case where the remainder is not necessarily zero. Ninety-four second-grade pupils from four classrooms (two in each of two schools) were presented, through individual…

An exploratory investigation designed to gain insights into children's mathematical formulation of observed actions upon objects is presented. Eight episodes in which first and second graders were asked to interpret, in terms of number sentences, a sequence of actions with unifix cubes are also presented. Results of analysis of the videotaped…

This study examined the effects of a specified set of activities on the ability of educable mentally retarded (EMR) children to use the transitive property and conserve the three relations "same number as,""more than," and "fewer than." Thirteen EMR students, aged 12 to 15, were taught eleven lessons on establishing and conserving these relations,…

A concrete and a symbolic approach to learning multiplication in the second grade are studied. The results, indicating that children using the symbolic model performed at a higher level than those using a concrete model, are discussed. (DT)

In the experiment discussed, three modes of presenting materials to second grade students were compared. Data analysis showed that the abstract mode was less successful than the others, but there was no clear difference between the manipulative and pictorial modes. (SD)