A principle of second-order isomorphism asserts that the functional similarities among internal representations parallel the functional similarities among the external objects to which those representations correspond. Research was conducted in accordance with this principle. (Author/BJG)

Three elementary-school students were exposed to Fractions 1, an instructional program for fraction problem-solving skills based on "direct instruction" principles. Fraction performance increases could reasonably be attributed to the instructional program. Improvements were durable across a short follow-up period and transfer occurred to similiar…

This textbook is a second reader for Catholic children. The contents include age-appropriate stories and passages on the importance of emphasis, consonant sounds, marked letters, and punctuation marks. A list of Roman and Arabic numbers is also included.

Three proofs for the problem show there exist irrational numbers a and b such that a to the b power is rational'' are presented and discussed. (DT)

This study was supported by a grant from the Carnegie Corporation to Educational Testing Service. (MH)