Reading mathematics differs from reading prose, and needs special treatment by the teacher. Thirteen necessary skills are described; these include knowing what to read next, using mathematical words, seeing and understanding symbols, reading charts, and searching for meaning. Techniques and activities to enhance these skills are discussed. (SD)

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.

Many of the difficulties that students have with mathematical symbolism seem to stem from the use of a horizontal form for an equation and a vertical form for computation. The differences between these two forms are discussed. (JT)

In the pair of experiments reported here the authors investigated the relationship between meaningfulness of problem statements and subjects' use of these statements in problem-solving tasks. Subjects (96 university students) were required to memorize meaningful formulae such as "volume = area x height" or corresponding symbolic formulae such as…

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)

This paper reports a study which attempted to generalize earlier results obtained by Eastman to another mathematical content area. Two hundred eight ninth-grade algebra students were randomly assigned to one of the two treatments. The figural-inductive treatment presented concepts of logic through the use of Euler diagrams in an inductive mode;…

This paper discusses six aspects of current practice in mathematics instruction of elementary school children: (1) use of symbolization, (2) use of models, (3) consideration of child development, (4) "logical" vs. "natural" approaches, (5) individualization, and (6) diagnosis and prescription. The author argues that symbols are frequently…

A review of several studies on the role of concrete and symbolic models in facilitating the learning of mathematical ideas, and a discussion of their implications for instruction are presented. (DT)