Gleason's Theorem Has a Constructive Proof

Gleason's theorem for R ³ says that if f is a nonnegative function on the unit sphere with the property that f(x) + f(y) + f(z) is a fixed constant for each triple x,y,z of mutually orthogonal unit vectors, then f is a quadratic form. We examine the issues raised by discussions in this journal regarding the possibility of a constructive proof of Gleason"s theorem in light of the recent publication of such a proof.     

Subjects' expectations,individual variability,and the scanning of mental images

The near-perfect correlation between mental imagery scanning times (averaged across subjects) and interobject distances on imaged maps has been cited as evidence for Kosslyn's (1981) analog theory of mental imagery. Present results (1) indicate that individual subjects' scanning-time/distance correlations vary as a function of instructional set (and, hence, a priori expectations), and (2) reveal a large degree of individual variability in scanning-time/distance correlations.     

Prerequisite vs. in vivo acquisition of self-feeding skill

Separating the acquisition of prerequisite skills from the learning of skills in vivo may be a more efficacious procedure for self-help training of low functioning developmentally delayed children. Two procedures for training independent use of a fork at meals were compared using two equivalent groups of three subjects each, in multiple baseline design. Using previously accepted procedures, one group was trained during meals while the experimental group received prerequisite training making use of simulated food (styrofoam pieces). Data during training, generalization-to-meal, and follow-up were collected. For 6 months following training, the efficacy of prerequisite training was upheld. The complexity of individual responses to the singular or conjunctive use of social and edible reinforcement for the purpose of self-feeding skill generalization and maintenance, is discussed.     

THE EFFECTS OF SELF-MONITORING AND SUPERVISOR FEEDBACK ON STAFF PERFORMANCE IN A RESIDENTIAL SETTING

We evaluated the effects of a self-monitoring procedure to increase staff on-task behavior and adherence to scheduled activities. Self-monitoring involved the use of activity cards that staff members completed and carried with them to assist in determining the activities for which they were responsible at any given time. Increases in both on-schedule and on-task behavior resulted. Supervisor feedback was subsequently added because some staff members did not maintain consistently high levels of performance. Generalization data indicated that staff members implemented the procedure during evening hours without specific programming. The advantages and limitations of using a self-monitoring procedure for improving performance of staff members in residential settings are discussed.