Presents Latin square mathematical techniques for assigning laboratory partners so that each pair of individuals work together only once. (MLH)

A game based on the group of permutations on four symbols is described. The game can be used in the study of many algebraic concepts. (SD)

Rewriting the usual relativistic equations in equivalent forms can help students recognize the relation between classical and relativistic mechanics. The derivation of relativistic equations is facilitated by means of simple algebraic generalizations of proofs often used in teaching their classical analogs to students who have not studied…

Work performed persuant to grant number 1-06, 1819-2240 from the U.S. Office of Education.

This paper reviews issues and analyses in bilingual switching, or intercalation, and offers a topological model to represent the activity of code switching, sometimes under the same environmental conditions and with the same interlocutors. The topological notion of catastrophe is proposed as a means to model the various factors that influence code…

In the past, several latent structure models have been proposed for handling problems associated with measuring the achievement of examinees. Typically, however, these models describe a specific examinee in terms of an item domain or they describe a few items in terms of a population of examinees. In this paper, a model is proposed which allows a…

An upper-asymptote parameter was added to the three-parameter logistic item response model. This four-parameter model was compared to the three-parameter model on four data sets. The fourth parameter increased the likelihood in only two of the four sets. Ability estimates for the students were generally unchanged by the introduction of the fourth…

Wilcox (1977) examines two methods of estimating the probability of a false-positive on false-negative decision with a mastery test. Both procedures make assumptions about the form of the true score distribution which might not give good results in all situations. In this paper, upper and lower bounds on the two possible error types are described…

Increasing the level of educational attainment of the population may not always increase the social benefits for those who receive the education. In fact, when a high percentage of the population attains a certain level of education, that attainment ceases to provide socioeconomic benefits; instead, those few who have not reached that educational…

The applicability of catastrophe theory to research in higher education is considered, with several problems that typically appear in the literature presented in a theoretical framework. A catastrophe model is attempted for each. The nature of mathematical modeling and the relationship between modeling continuous systems and discontinuous systems…

The relatively hard problem of transforming a given set of curves to curves with the same shape can sometimes be reduced to the easier problem of rendering curves parallel. In this paper a group is associated with the given curves, and it is shown that the reduction from the hard problem to the easy problem is valid whenever the group is…

The average cost pupil transportation reimbursement formula developed on the basis of 1976-1977 Illinois pupil transportation data and presented in this paper has several advantages over the current law. This formula would consider the factors that cause variations in the cost of providing the services to Illinois school districts: number and…