In two parallel one-year studies, solution strategies for subtraction number facts and achievement patterns of matched groups of first graders in two different instructional programs were examined. Significant differences between groups were found favoring the strategy approach. (Author/CW)

Developed is a working definition of the concept of preformal proof through the analyses of an action proof, a geometric-intuitive proof, and a reality-oriented proof of a differential equation. Instructional problems for teachers and learners in connection with preformal proofs are pointed out. (MDH)

Reported is a naturalistic study of the role of mathematical paradoxes in the preservice education of high school mathematics teachers. Findings indicate that the model of resolving paradoxes as applied in this study has relevance to such aspects of mathematics education as cognitive conflicts, motivation, misconceptions, and constructive…

Probability theory can be developed from a theoretical or experimental probability approach. The problem, "The Gambler's Ruin," is used to study whether students are naturally sensitive to learning probability from an experimental probability approach through simulations. Results indicated that use of simulations can contribute to…

Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

Identified are three obstacles which students must overcome when examining and interpreting diagrams. The resources of the Geometric Supposer, a set of microcomputer tools designed to aid students, are outlined. The advantages of the use of this software are emphasized. (CW)

Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…

Proposes that although the past 30 years have seen increasing efforts to make mathematics more relevant and useful, schools continue to fail. Argues that forced rote learning is the direct cause of this failure and that improved teaching methods must be developed. Urges that shifts in methodology be phased in gradually. (TW)