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…

Cabri3D is a potentially very useful software for learning and teaching 3D geometry. The dynamic nature of the digital diagrams produced with it provides a useful aid for helping students to better develop concept images of geometric concepts. However, since any Cabri3D diagram represents three-dimensional objects on the two dimensional screen of…

This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, 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…

This paper examines 6th grade children's local conceptual development and mathematization processes as they worked a comprehensive mathematical modeling problem (creating a consumer guide for deciding the best snack chip) over several class periods. The children and their teachers were participating in a 3-year longitudinal teaching experiment in…

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…

Procedures used to map the achievement levels, expressed as total expected scores on the full set of items presented to a grade, onto the Mathematics Composite of the 1990 National Assessment of Educational Progress (NAEP) are described. The Composite, defined as a weighted average of subdomain scores, provides a global measure of mathematics…