Discusses the problem of finding the amount of fence it would require for the outfield fence of a baseball field of given dimensions. Presents different solution methods for each of the levels from grades 9-12. The different methods incorporate geometry, trigonometry, analytic geometry, and calculus. (MDH)

Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)

Described are student/consultant reports, turned in as homework, that reflected their abilities to distinguish useful from irrelevant information, solve the underlying calculus extremum problem, and reconcile the individual mathematical solutions with the ethical considerations surrounding the moral dilemma of the hypothetical consulting client.…

Identified are three obstacles which students must overcome when examining and interpreting diagrams. The resources of the Geometric Supposer, a set of microcomputer tools designed to aid students, are outlined. The advantages of the use of this software are emphasized. (CW)

Biomedical, logistic, economic, social, and psychosocial issues related to the successful distribution and use of a vaccine for human immunodeficiency virus (HIV) are reviewed. A mathematical model is introduced as an aid in conceptualizing these issues. The HIV vaccine should be seen as an adjunct to behavioral modification. (SLD)

The ability of 3-way INDSCAL and ALSCAL models to recover true structure in proximity data based on 2-dimensional configurations varying in number of subjects (15 and 20) and stimuli, amount of error, and monotonic transformation is examined. INDSCAL outperformed metric and nonmetric ALSCAL in all conditions. (SLD)

Three variations of a least squares regression model are presented that are suitable for determining and correcting for rating error in designs in which examinees are evaluated by a subset of possible raters. Models are applied to ratings from 4 administrations of a medical certification examination in which 40 raters and approximately 115…

Explains how students can perform a refutation of the ether theory using information from the Global Positioning System (GPS). Discusses the functioning of the GPS, qualitatively describes how position determination would be affected by an ether wind, and illustrates the pertinent ideas with a simple quantitative model. (WRM)

Statistical data can be represented in a number of qualitatively different ways, the choice depending on the following three conditions: the concepts to be investigated; the nature of the data; and the purpose for which they were collected. This paper begins by setting out frameworks that describe the nature of statistical thinking in schools, and…

Whenever teachers of young children get together there will be differences of opinion about how far children should be taught to count. Some will argue that the focus should be on small numbers to 9, building up the notion of what, say, the name 5 means, what it looks like, and how it can be represented. Others argue that with ice blocks retailing…

The purpose of this article is to identify the difficulty of learning materials in the network by using learner's portfolio in the asynchronous learning system. Asynchronous learning takes the advantage of information technology that records the learning portfolio of the learner. The data of the learning portfolio reflects the characteristics of…

Making connections becomes increasingly important as students proceed through middle school and high school. This book shows ways of embedding connective processes in instruction in grades 9-12. Problems invite mathematical modeling, unify diverse content, call for different representations, and encourage students to look back at their work to…

This study investigated the convergent validity of expert-system scores for four mathematical constructed-response item formats. A five-factor model was proposed comprised of four constructed-response format factors and a Graduate Record Examinations (GRE) General Test quantitative factor. Subjects were drawn from examinees taking a single form of…

This paper outlines the development of a quantitative instrument designed to measure students' multiple achievement goals and key aspects of their cognitive engagement in Australian educational settings. The paper demonstrates the use of congeneric measurement models in assessing and improving the validity of the scales comprising the Goal…

A multidimensional item response theory (IRT) model for polytomously scored items, based on the graded response model and using the normal ogive, is developed; and an EM algorithm that may be used to estimate the parameters of the model is also discussed. The model is illustrated through a simulation study in which the polytomous item responses of…