Document retrieval tasks composed of human relevance judgments need test sets that allow comparison of human retrieval and automated retrieval and that place absolute limits on performance by any method. Results suggest that it should be possible to improve retrieval system performance within recommended limits by incorporating specific subject…

Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)

Based on Gestalt theory, the author assumes the existence of a field-force equilibrium to explain how, according to the conciseness principle, mathematically precise gestalts could exist in coauthorship networks. Develops a mathematical function to describe these gestalts in scientific literature and discusses structural characteristics of…

In response to Fischer (HE 527 626), the author considers his proposal to simplify need analysis in Pell grants and other federal need-based student aid as ignoring important considerations. It is suggested that a single formula will be difficult to derive until a coherent philosophy of needs analysis and specific current purpose for the grant…

Applies a probabilistic model to a contingency table with cross-citation frequency counts between scientific journals. The differences between model-based expected citation frequencies and observed frequencies (net citation balances) are used to derive an interjournal influence score. This measure of overall influence is compared with two other…

Developed are simple recursion formulas for generating the exact distribution of the longest run of heads, both for a fair coin and for a biased coin. Discusses the applications of runs-related phenomena such as molecular biology, Markov chains, geometric variables, and random variables. (YP)

Describes the development of the concept of function including changes of mental images, from the geometric conception versus the algebraic conception and the logical conception versus the algebraic conception. Lists 27 references. (YP)

Discusses the use of the recursive method to permutations of n objects and a problem making c cents in change using pennies and nickels when order is important. Presents a LOGO program for the examples. (YP)

A model for student retention and attrition is presented. Focus is on alternative models for the "dampening" in attrition rates as educational programs progress. Maximum likelihood estimates for the underlying parameters in each model and a Bayesian analysis are provided. (TJH)

Investigates the value of applying principles derived from simulated annealing to clustering tuples in database design, and compares this technique with a graph-collapsing clustering method. It is concluded that, while the new method does give superior results, the expense involved in algorithm run time is prohibitive. (24 references) (CLB)

Explores the basic physical laws of the juggling activity. Derives some equations involving height, angle, time, and distance for common juggling objects. Describes the relationships among height, length, mass, number of clubs, number of spins, angular velocity, time, and angle in club juggling. (YP)

Offers an approach to the understanding and to the teaching of the fundamental theorem of calculus. Stresses teaching the relation between a function and its derivative and the functions themselves. (YP)

Presents an example from the combinatorial theory of partially ordered sets. Discusses algorithms of on-line antichain partitioning problems, a topic in discrete optimization. (YP)

Presents an example of a mathematical question to illustrate an approach to simultaneous equations. Provides an example with diagrammatic and numerical representations. Suggests some possible developments. (YP)

Presents an approach to Vieta's formula involving pi and infinite product expansions of the sine and cosine functions. Indicates how the formula could be used in computing approximations of pi. (MVL)