Presents a model of the relation between the circulation at a large library, the collection at that library, and the size of the user population. Analysis of data at United States academic research libraries reveals a square-root law describing this relation. Explores theoretical foundations and speculates on bibliometric implications. (Author/AEF)

Models the motion of a gymnast around the high bar first as swinging around a rigid rod, then more accurately when the rod is considered to be elastic. Also considers how the gymnast should best move his hips. (Author/ASK)

Investigates determinants behind the spectacular higher education enrollment growth in Belgium since 1953, using a demand model that integrates consumption and investment aspects and empirically tests time-series data specifications between 1953 and 1992. Income and foregone earnings are driving enrollments. Income, opportunity costs, and the wage…

Uses a flexible modeling strategy to examine the roles of measured ability, family characteristics, and proxies for secondary schooling quality as determinants of the decision to enter college. Finds that the link functions and estimated impacts of ability and family characteristics on the probabilities of enrolling in college are not constant…

Promotes the use of logistic modeling in high school and early college mathematics, to compare this model to commonly used models, and to give an alternative to the TI-83 built-in logistic-regression key method when that method fails to converge or gives an inappropriate model. (ASK)

Compares sixth-grade American students to three samples of (Chinese, Japanese, and Taiwanese) sixth-grade Asian students to determine if the well-documented mathematical achievement of students from these Asian nations might be due in part to a greater understanding of mathematical representations. Indicates that all Asian samples scored…

Describes a study of the effectiveness of computer-simulation programs in enhancing biology students' familiarity with ecological modeling and concepts. Finds that computer simulations improved student comprehension of ecological processes expressed in mathematical form, but did not allow a full understanding of ecological concepts. Contains 28…

According to historical stories, the Saxons placed a bowl with a hole in its bottom in water and used the time it took the bowl to submerge to limit orations. Describes a science activity in which students find a relationship between the diameter of the hole and the time to submergence. (WRM)

Examines the definition, construction, and interpretation of social indicators. Shows how standard classes of formalisms used to construct models in contemporary sociology are derived from the general theory of models. Reviews recent model building and evaluation related to active life expectancy among the elderly, fertility rates, and indicators…

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…

The purpose of this article is to describe a middle school mathematics teacher's model of his students' responses to algebraic tasks involving equivalent expressions and the distributive property. The teacher engaged in two model-eliciting activities designed for teachers by creating a library of his students' work and an accompanying "Ways…

Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

This article proposes an item response theory (IRT) approach to constructing and scoring multidimensional pairwise preference items. Individual statements are administered and calibrated using a unidimensional single-stimulus model. Tests are created by combining multidimensional items with a small number of unidimensional pairings needed to…

Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem…

Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…