In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

In this action research, first-graders were challenged to cope with a sequence of modelling tasks involving an analysis of given situations and choices of mathematical tools. In the course of the sequence, they underwent a change in the nature of their problem-solving processes and developed modelling competencies. Moreover, during the task…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

As Duncomb and Yinger (2001) have stated, "School consolidation represents the most dramatic change in education governance and management in the United States in the twentieth century. Over 100,000 school districts have been eliminated through consolidation since 1938, a drop of almost 90 percent (NCES 1999, Table 90). This longstanding…

The interest in developmental sequences and learning hierarchies is growing. One approach to the study of such sequences is to gather data on several variables, each of which corresponds to a stage, step, or phase in the sequence and to examine the associations between the variables as displayed in a contingency table. If the variables are…

It is shown that Trueswell's empirical 80/20 rule arises from type of stochastic model for library loans presented by Burrell and Cane. Particular attention is paid to previously suggested uses of rule in identifying "core collection" for library noting that length of time period is of crucial importance. (20 references) (EJS)

Discusses bibliometric studies of research collaboration and describes the development of a theoretical model for the distribution of authorship. The shifted Waring distribution model and 15 other probability models are tested for goodness-of-fit, and results are reported that indicate the shifted inverse Gaussian-Poisson model provides the best…

Presents Price's law, which states that half of the literature on a subject will be contributed by the square root of total number of authors publishing in that area, and assesses it against empirical evidence and simulated productivity distributions. The discussion covers this law's relation to Lotka's law and its empirical validity. (Author/CLB)

Empirical estimates of production frontiers and average production functions performed for selected public elementary school districts in California support the hypothesis of an optimal school size model. Some policy implications of the results are briefly analyzed. Appended are 16 references. (MLF)

The average citation per article in chemistry by age of citation is related to the Poisson frequency distribution. This provides a formula for calculation of a half-life for chemistry which depends on the structure of the research front exhibited in the literature. (Author/FM)

Examines the main mathematical approaches to information retrieval, including both algebraic and probabilistic models, and describes difficulties which impede formalization of information retrieval processes. A number of developments are covered where new theoretical understandings have directly led to improved retrieval techniques and operations.…

This study demonstrates that the number of references at the end of scientific research papers forms a strongly unimodal frequency distribution and that the generalized Gaussian-Poisson distribution fits such unimodal data extremely well. (three references) (Author/MES)

Argues that the gamma mixture of Poisson processes, for all its perceived defects, can be used to make predictions regarding future library book circulations of a quality adequate for general management requirements. The use of the model is extensively illustrated with data from two academic libraries. (Nine references) (CLB)

Examines relationships among the parameters of the Zipf size-frequency distribution as well as its sampling properties. Highlights include its importance in bibliometrics, tables for the sampling distribution of the maximal value of a finite Zipf distribution, and an approximation formula for confidence intervals. (Author/LRW)

Reviews the literature on Bradford's law (i.e., an empirical relationship describing the distribution of scholarly articles in relevant journals). A model for the distribution of articles, based on random partitioning, is presented; and a mathematical formulation for a law of scattering is derived. The relationship of the model to Bradford's law…