A review of research involving the utilization of manipulative materials in improving mathematics learning is presented. Subsequent assessment and discussion is included. (JG)

The author cites studies concerning the effectiveness of manipulative and non-manipulative approaches to teaching mathematics in elementary schools. He concludes that, after the first grade, an instructional strategy that gives preeminence to the rise of manipulative materials is unwarrented. (MN)

Twelve fourth-grade classes in two schools were taught division using either the subtractive approach to the Greenwood algorithm or a partitioning approach to the standard algorithm. Analysis of class means on immediate, retention, and delayed retention tests indicated that use of the standard algorithm was more effective. (JP)

Seventy-one college students were taught probability and statistics for one month by one of three methods: MP, manipulative-pictorial; P, pictorial; and S, symbolic. Analysis of variance yielded significant differences (p.05) between treatment groups for selected subtests of an achievement test and generally favored MP and P over S.

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)

The enactive and iconic modes of instruction were compared in teaching preservice elementary teachers the mathematical concepts and skills necessary to teach mathematics via manipulative aids. No significant differences were found. (MP)

Students in second and third grades were given instruction on sentential logic. Different approaches were used in 3 classrooms at each grade level and a classroom at each level served as a control group. Posttests included tests of classification, sentential logic, and perceptual reasoning; experimental students outperformed controls. (SD)

Reports on a study to determine the development of children's understanding of seven properties of the arithmetic mean and to assess the effects of material used in the testing and the medium of presentation. Some differences were found in children's reasoning. No significant differences were found for materials or medium of presentation. (PK)

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)

Focuses on the strategies young children (N=115) use to solve rectangular covering tasks before they have been taught area measurement. Children's solution strategies were classified into five developmental levels. Emphasizes the importance of understanding the relationship between the size of a unit and the dimensions of the rectangle in learning…

The author criticizes an experiment of Moody, Abell and Bausell (EJ 038 323) on the grounds of inappropriate instruction and invalid tests. (MM)

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

Children attempted a division problem in one of four distraction settings: minimal, situational, color-attribute, or spatial-numerical. The effects of both grade level and distraction setting in problem-solving performance were highly significant, with children who used a manipulative approach being more prone to distraction than those using a…

Analysis of the role that (n=4) second graders' use of the hundred board played in supporting their conceptual development found that the board did not support the construction of increasingly sophisticated concepts of 10, but did support their ability to reflect on their mathematical activity. (54 references) (Author/MKR)