Reported is a study which investigated four strategies of instruction for promoting higher levels of awareness of certain mathematical probability concepts. Strategies were identified on the basis of characterization moves and exemplification moves. College freshmen were presented the concepts via specific strategies by following programmed…

Four methods of teaching algebra to educationally disadvantaged students entering college were compared. (SD)

General verbal problem solving techniques and a modified wanted-given technique were compared. Fifth graders using either of these two techniques did not score higher than control groups. Those using the wanted-given technique used correct procedures significantly more often. (DT)

Reported is a study of the interaction between figural and semantic abilities (as defined in Guilford's Structure of the Intellect") and success in a programmed unit in modular arithmetic. The subjects were prospective elementary teachers. Significant interactions were found between both figural and semantic factors and methods of instruction.…

A test of the relative effects of verbal definitions and numerical examples as correctional feedback in a computer-assisted learning task. (MM)

The "Descriptor for Individualized Instruction" described here is a paradigm developed for use in describing individualized instruction and conceptualizing related research. The paradigm concerns itself with aspects of aims, instruction, and management. (SD)

Programed units of instruction designed with four different sequences of characterizations and exemplifications of disjunctive concepts were given to preservice elementary school teachers. Students were tested on three levels of concept attainment, with differences between strategies resulting, as one moves through the levels of cognitive…

A reply to questions raised by Leroy G. Callahan in the "Journal for Research in Mathematics Education," volume 5, 1974, pages 60-63. (JP)

The article critiqued is contained in the "Journal for Research in Mathematics Education," volume 4, 1973, pages 6-19. (JP)

This critique points out some possible limitations of a previously reported study on the relative efficacy of two feedback modes during CAI instruction. Researchers are cautioned about using results to suggest classroom instructional practices. See also SE 508 622. (LS)

The author answers the questions posed in a critique of his previously published study on the relative efficacy of two feedback modes during CAI instruction. Details which were originally omitted due to lack of space are provided for further clarification. See also SE 508 621. (LS)

This study examined the effects of using materials, modeled on programmed instruction, in which questions were posed after each paragraph. It was found that average and below average students studying matrix algebra benefited significantly from the experimental treatment. (SD)

Examined was the effect of teacher attitude on student achievement in arithmetic in grade four. The students were presented a lesson involving division via a modified programed learning sequence and teachers were given bias statements regarding the effectiveness of the programs. The results indicated no significant differences among students…

This critique discusses Gagne's position that students should understand how to mathematize a concrete situation and validate a solution but need not understand how a solution is derived. Reconciling his views with those of mathematics educators and raising questions are both included. (MNS)

Gagne's reply to critiques by Wachsmuth and by Steffe and Blake notes that their approaches are from different points of view. He urges that mathematics educators examine critically the view that understanding involves some aspects of the structure of mathematics. (MNS)