Computer-based adaptive instructional strategies for concept learning were investigated. Selection of the number of examples according to on-task information was more efficient than pretask or pretask plus on-task information. A response-sensitive strategy was preferable to a response-insensitive strategy to determine the presentation order of…

A three-way multidimensional scaling model is presented as a method for identifying classroom cliques, by simultaneous analysis of three variables (for example, chooser/choosen/criteria). Two scaling models--Carroll and Chang's INDSCAL and Lingoes' PINDIS--are presented and applied to two sets of empirical data. (CP)

Geometric axioms are discussed in terms of philosophy, history, refinements, and basic concepts. The triumphs and limitations of the formalism theory are included. Described is the status of high school geometry internationally. (KR)

A method is presented for using a restricted latent class model--a binary skills model--to determine skills required by a set of test items. Results from the method's application to reading achievement data for about 63,000 fourth graders indicate that the model offers useful information on test structure and examinee ability. (TJH)

Described is a game that is used to introduce the concept of multiplying integers. Serving as a physical model for the concept, "Froggie Frolic" races frogs along a number line by moves that indicate direction, magnitude, and number of jumps, thus modeling integer multiplication. A teacher's guide and worksheets are provided. (MDH)

Describes a project that uses a computer and a dot matrix printer to simulate the holographic recording process of simple object structures. The process' four steps are (1) superposition of waves; (2) representing the superposition of a plane reference wave on the monitor screen; (3) photographic reduction of the images; and (4) reconstruction of…

Describes an activity to construct polyhedra resembling molecular structures. Each face forms regular polygons made up of balls. Step-by-step directions are provided to perform the constructions. (MDH)

Discusses area models that can be used in grades three through nine, showing how the model generalizes from discrete situations involving the arithmetic of whole numbers to continuous situations involving decimals, fractions, percents, probability, algebra, and more advanced mathematics. (14 references) (MDH)

Describes how college students enrolled in a course in elementary algebra apply graphing and algebra to data collected from a seismic profile to uncover the structure of a subterranean rock formation. Includes steps guiding the activity. (MDH)

This study examined the hypothesis that prior experience with augmented-quotient problems would positively influence performance on remainder-only problems and quotient-only problems. Analysis of sixth through eighth grade students' (n=545) responses to test forms that systematically varied the order of appearance of these three division problems,…

A procedure for interpreting multiple-discrimination indices from a multidimensional item-response theory analysis is described and demonstrated with responses of 1,635 high school students to a multiple-choice test. The procedure consists of converting discrimination parameter estimates to direction cosines and analyzing the angular distances…

A mathematical model is used to represent a physical problem. The resulting polynomial is graphed and analyzed. Students are asked to plot families of related polynomial functions and observe patterns. A partial list of possible observations is included. End behavior, complete graph, and classroom use of technology are discussed. (GW)

Describes changes in scientific research methods that have been brought about by the use of computers. Presents an example of the falling of a body in a fluid to show students how computers can be used to experiment with mathematical models and to automate experiments. Contains 11 references. (Author/WRM)

This paper is about the structural equation modelling of quantitative measures that are obtained from a multiple facet design. A facet is simply a set consisting of a finite number of elements. It is assumed that measures are obtained by combining each element of each facet. Methods and traits are two such facets, and a multitrait-multimethod…

This study describes the learning of researchers who engage in mathematics teacher education as an integral part of their practice. As teacher educators working with teachers on the subject of proportional reasoning, the authors reflected on teachers solutions to a standard problem and analyzed answers that would conventionally be considered…