Discusses the nature of tasks used to elicit the development of such systems by middle school students. Analyzes mathematical reasoning development of students across tasks and the diversity of thinking patterns identified on problem tasks. Discusses student reasoning about the relationships between and among quantities and their application in…

Develops covariational reasoning and proposes a framework for describing mental actions when interpreting and representing dynamic function events. Investigates calculus students' ability to reason about covarying quantities in dynamic situations. Suggests that curriculum and instruction should emphasize moving students to a coordinated image of…

Presents a case study in which two 8th grade students developed knowledge for modeling a physical device called a winch. Demonstrates that students have and can use criteria for evaluating algebraic representations. Explains how students can develop modeling knowledge by coordinating criteria with knowledge for generating and using algebraic…

Discusses how nature can illustrate mathematical structures and concepts in the classroom. For example, the upper surface of a typical leaf structure illustrates the notion of tessellating with polygons. Also lists classroom applications and hands-on activities such as growing crystals to investigate the natural forms of polyhedra and measuring…

Describes a classroom project involving the construction of a holiday mobile. Necessary supplies include a lightweight hanger, construction paper, string, scissors, protractors, compasses, and rulers. Concepts involved in the construction of the project include illustrating a chord, radius, diameter, shapes, metric measuring, circumference, area,…

Studied the teaching and learning of fractions in two matched groups of 10 9-10-year-olds in the Netherlands. In the experimental group, fractions were introduced using the bar and number line as mental models, while the control group used fair sharing and the circle model. The experimental group showed more proficiency in fractions after 1 year.…

Describes similarities and differences between modeling cycles and stages of development. Includes examples of relevant constructs underlying children's developing ways of thinking about fractions, ratios, rates, proportions, or other mathematical ideas. Concludes that modeling cycles appear to be local or situated versions of the general stages…

Refutes Peter Mueser's criticisms of the author's position on formalistic research approaches. Restates that statistical significance is virtually useless. Claims mathematical economists take their intellectual positions from mathematics departments bringing irrelevant intellectual values into economics. (NL)

Relationships among individual- and group-directed measures of leader behavior descriptions and five variables were examined using 54 law enforcement agency personnel associated with a large public university. Data on a questionnaire completed by participants during an interview were studied. Explicit consideration was given to multiple levels of…

A meta-analysis of studies conducted between 1974 and mid-1987 on sex differences in mathematical tasks is presented. Methods used include estimations of: (1) parameters for a random effects model, and (2) coefficients for a linear-regression equation, all based on effect sizes calculated from each study. Differences have been decreasing. (TJH)

Single construct validity is examined, and appropriate statistical tests are described when criterion information is available for: (1) examinees selected at random; (2) examinees selected on the basis of the current test; and (3) examinees selected using other measures of the latent construct. Discriminant validity is also discussed. (SLD)

Some extensions of the partial credit model are presented. A marginal maximum likelihood estimation procedure is developed to allow for incomplete data and linear restrictions on the item and population parameters. Two statistical tests for evaluating model fit are also presented. (SLD)

A computationally efficient three-stage estimator of thresholds and covariance structure parameters is prepared for analysis of structural equation models with polytomous variables. The method is based on partition maximum likelihood and generalized least squares estimation. An analysis of questionnaire responses of 739 young adults illustrates…

A method of estimating conditional standard error of measurement at specific score/ability levels is described that avoids theoretical problems identified for previous methods. The method focuses on variance of observed scores conditional on a fixed value of an observed parallel measurement, decomposing these variances into true and error parts.…

Mixed integer linear programing models for customizing two-stage tests are presented. Model constraints are imposed with respect to test composition, administration time, inter-item dependencies, and other practical considerations. The models can be modified for use in the construction of multistage tests. (Author/TJH)