Young children increasingly interact with technological devices, either as a form of entertainment or for educational purposes. This research sought to investigate the early symbolic understanding of an interactive, three-dimensional digital image presented on a tablet. Two studies were designed in which the children had to use the image as a…

Symbolic objects are cognitive tools children must learn to master very early in life. A crucial factor in cognitive development is the instruction or informational support children receive in social contexts. While numerous studies have investigated the relation between instruction and development in various domains, like language or symbolic…

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)

After describing desirable characteristics of a student's first encounter with proof, and listing skills prerequisite for the proposed lesson (knowledge of some operational systems), the author describes in detail an introductory session in which students prove consequences of commutativity and associativity for a system supposedly encountered on…

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.

High school and undergraduate subjects were randomly assigned to either a semantic or symbolic learning program concerning the computation of the derivative of an algebraic expression and the multiplication of vectors in order to study aptitude-achievement interaction. Results of achievement and ability tests indicated that there does exist…

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…

Students were measured on eleven aptitudes from Guilford's structure-of-intellect cube, and randomly assigned to symbolic or figural instructional modes for a unit on functions. Achievement was measured and compared for students with different aptitudes. (SD)

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;…

The purpose of this project was to relate mathematics studies to the students' natural enthusiasm for popular music and favorite performers. Learning modules rather than lesson plans were used as the teaching approach in the experimental music-mathematics classes. Stated objectives of the project were (1) to motivate students to learn to code and…

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…