Models for multidimensional scaling use metric spaces with additive difference metrics. Two important properties of additive difference metrics are decomposability and intradimensional subtractivity. A prediction was derived from these properties and tested experimentally. Eleven non-psychology students were used as subjects. Rectangles varying in…

An operations research method to optimize the teaching-learning process is introduced in this paper. In particular, a linear programing model is proposed which, unlike dynamic or control theory models, allows the computer to react to the responses of a learner in seconds or less. To satisfy the assumptions of linearity, the seemingly complicated…

This proceedings volume of a seminar on planning library services is the third in a series of papers, published at irregular intervals, to report on research work by members of the University of Lancaster library staff. From January 1967 until June 1969 the Office of Scientific and Technical Information (OSTI) organized regular meetings under the…

Consideration of computer-assisted instruction in the classroom has led to an analysis of the educational process including the need for developing more adequate models of the learning processes and increased attention to the function of the teacher (human or computer) as a decision maker. Given a descriptive model of the learning process, it is…

The augmented transition network described in this report was developed in the course of work in semantic interpretation in the context of a computer system which answers English questions. In order to provide mechanical input for the semantic interpreter, a parsing program based on the notion of a "recursive transition network grammar" was…

Ten highly motivated and above-average intermediate algebra students were selected to complete a ten-week schedule of activities involving the mathematizing of some physical representation of a phenomena and the studying of that model. Ten activity-based exercises, most adapted from LABORATORY MANUAL FOR ELEMENTARY MATHEMATICS by Fitzgerald, et…

Considerable thought, research, and concern has been expanded in an effort to determine whether the assumption of a quadratic relation between a single predictor and a criterion violated the assumptions which Johnson and Neyman (1936) state for calculating regions of significance about interacting regressions. In particular, there has been special…

When random assignment has been accomplished and an analysis of covariance (ANCOVA) is being used to correct for initial differences among treatment groups, use of unreliable covariables not only decreases the power of ANCOVA, but also causes ANCOVA to test biased treatment effects. Several correction procedures have been suggested for the single…

A theoretical basis was formulated for a model of individualized instruction. The theory is semi-axiomatic in nature so that the definitions and assumptions used are stated explicitly. Set theory and symbolic logic are the conceptual tools used. The model includes theories of subject-matter structure and student state description. These are…

Employing a computer-controlled experimental paradigm for studying coalition formation and bargaining, the present study tests three models for n-person games in characteristic function form, namely, the bargaining set and two of its subsets, the competitive bargaining set and the kernel. Twelve groups of subjects participated in several four…

This paper discusses Bayesian m-group regression where the groups are arranged in a two-way layout into m rows and n columns, there still being a regression of y on the x's within each group. The mathematical model is then provided as applied to the case where the rows correspond to high schools and the columns to colleges: the predictor variables…

This is the second unit in a series of 14 SMSG texts designed to cover mathematical concepts which the general population should know. One chapter of the unit discusses algorithms, flow charts, and computers; the second chapter tackles problem formulation procedures (not actual problem solving) and briefly covers mathematical models. For a special…

Three self-instructional episodes for use in physical science classes were written and tested with ninth grade students. The development was based on Piaget's learning theory leading students from actions with physical apparatus to the formulation of a mathematical equation. The episodes concerned: (1) equilibrium in a balance; (2) the oscillation…

This study is an analysis of the robustness of the Box-Tiao integrated moving averages model for analysis of time series quasi experiments. One of the assumptions underlying the Box-Tiao model is that all N values of alpha subscript t come from the same population which has a variance sigma squared. The robustness was studied only in terms of…

The Rasch model for the probability of a person's response to an item is extended to the case where this response depends on a set of scoring or category weights, in addition to person and item parameters. The maximum likelihood approach introduced by Wright for the dichotomous case is applicable here also, and it is shown to yield a unique…