This monograph focuses on the influence of meaning theory on elementary school mathematics programs and on mathematics instruction. Theories of arithmetic instruction up through 1935 are described, and the philosophy of meaning theory, contributions and discussions by mathematics educators, and applications to actual instruction are delineated for…

This volume contains a series of papers on algorithmic learning. Included are six reviews of research pertaining to various aspects of algorithmic learning, six reports of pilot experiments in this area, a theoretical discussion of "The Conditions for Algorithmic Imagination," and an annotated bibliography. All the papers assume a common…

The author develops a four-stage model for concept-internalization. The stages are: (1) concrete structure; (2) linguistic structure; (3) algorithm; and (4) mastery. The model is related to teaching methods and the teaching of long division is examined in detail. (SD)

Three perspectives of instruction that reflect applications of cognitive theory are transportation of knowledge, application of algorithms, and transfer of responsibility. To determine what kind of instructional theory is appropriate for vocational education in a rapidly changing, technological, and increasingly complex society and what…