Results of two experiments support the view that logical development can occur when there is no direct internalization of a societal language and that deaf adolescents are capable of propositional thought despite their language deficiency. (Author/WY)

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…

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…

This study was designed to determine whether (1) rules are more easily memorized when stated in mathematical symbolism or when stated verbally, and whether (2) the ability to use constituent symbols correctly, assuming mastery of the underlying grammar, is a necessary and/or sufficient condition for applying a learned rule statement. Twenty-four…

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…

Aimed at advancement of the arts through improvement of education for both understanding and production, this long range basic research program dealt primarily with the study of the varieties and interaction of human abilities, the nature of the tasks involved in the several arts, and the available means for inculcating or fostering the abilities…

Two scales designed to measure cognitive preferences were constructed; this study was designed to validate these scales, and to investigate the relationship between instruction and cognitive preference. Items for both scales had elementary mathematics content. One scale was intended to measure deductive-inductive preference, the other…

Reviews approaches to machine learning (development of techniques to automate acquisition of new information, skills, and ways of organizing existing information) in symbolic domains. Four categorical tasks addressed in machine learning literature are examined: learning from examples, learning search heuristics, learning by observation, and…

Proposes that cognitive developmental stages can be accounted for in terms of information processing factors which limit the highest level of cognitive system which children can attain at any given age. Delineates four progressively more complex levels of cognitive mediation of the environment. Two experiments which support the developmental model…