Explores the relationship between learners' actions, visualizations, and the means by which these are articulated. Describes a microworld called Mathsticks which is designed to help students construct mathematical meanings by forging links between the visual and symbolic representations they develop and their actions. Presents a case study of two…

Basic philosophical and statistical issues in structural equation modeling (SEM) are reviewed, including model conceptualization, identification, and parameter estimation and data-model-fit assessment and model modification. These issues should be addressed before the researcher uses any of the new generation of SEM software. (SLD)

A model projecting school enrollment by using births lagged an appropriate number of years and a model using lagged births and the previous year's enrollment were applied to two school grade levels and state and county levels in Kentucky. The model using lagged births and earlier figures provided better predictions. (SLD)

Studied modeling individual latent growth curves of older adults on measures of fluid intelligence by fitting second-order polynomial curves reflecting initial test performance improvement followed by relative stability/drop to the recorded scores of each of 248 subjects. Results suggest substantial plasticity in fluid intelligence of older…

Presents a typical cost-allocation problem with possible solutions, including geometric and combinatoric ones. Provides students with a real-life application of the mathematics that they know. (KHR)

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)