Currently, dynamic structural equation modeling (DSEM) and residual DSEM (RDSEM) are commonly used in testing intensive longitudinal data (ILD). Researchers are interested in ILD mediation models, but their analyses are challenging. The present paper mathematically derived, empirically compared, and step-by-step demonstrated three types (i.e.,…

Through a series of explorations, this article will demonstrate how the Kentucky Derby winning times dataset provides various opportunities for introductory and advanced topics, from data processing to model building. Although the final goal may be a prediction interval, the dataset is rich enough for it to appear in several places in an…

Human beings are having a profound impact on the environment. The opportunity to investigate this timely issue during one or two class periods gives algebra and precalculus students insight into a sustainability topic of great international concern--carbon footprints. Students use mathematical thinking in matters that are pertinent to their…

This study examines whether the classification and regression tree (CART) model improves the early identification of students at risk for reading comprehension difficulties compared with the more difficult to interpret logistic regression model. CART is a type of predictive modeling that relies on nonparametric techniques. It presents results in…

Early in their study of one-dimensional kinematics, my students build an algebraic model that describes the effects of a rolling ball's (perpendicular) collision with a wall. The goal is for the model to predict the ball's velocity when it returns to a fixed point approximately 50-100 cm from the wall as a function of its velocity as it passes…

This article describes an empirical study concerning the mastering of the chemical equilibrium concept by prospective physical sciences teachers. The main objective was to check whether the concept of chemical equilibrium had become an integrating and unifying concept for them, that is to say an operational and functional knowledge to explain and…

In the early 1990s, the National Science Foundation funded many research projects for improving statistical education. Many of these stressed the need for classroom activities that illustrate important issues of designing experiments, generating quality data, fitting models, and performing statistical tests. Our paper describes such an activity on…

The paper reports some initiatives to freshen up the typical undergraduate business forecasting course. These include (1) students doing research and presentations on contemporary tools and industry practices such as neural networks and collaborative forecasting (2) insertion of Logistic Regression in the curriculum (3) productive use of applets…

A few kilometers from the shores of Palm Beach County, Florida, is the Gulf Stream current--a remarkable "river" within an ocean. The current's journey across the Atlantic Ocean connects southeast Florida and southwest Great Britain as it streams steadily north at speeds of 97 km a day; moving 100 times as much water as all the rivers on…

Describes features of a macroeconomics model that runs on a microcomputer and its solution, sometimes called a simulation. Specific uses of the model in the teaching of introductory and intermediate/advanced levels of macroeconomics are discussed, as well as use by economic planners in running alternative forecasts. (MBR)

This article details an exploration of exponential decay and growth relationships using M&M's and dice. Students collect data for mathematical models and use graphing calculators to make sense of the general form of the exponential functions. (Contains 10 figures and 2 tables.)

Describes activities in which students: (1) propose creative atomic models that account for observed properties and predict additional experimental data; (2) calculate empirical formulas for 27 binary compounds; (3) propose a model to explain why certain elements have certain valences; and (4) arrange hypothetical elements into a periodic chart.…

Describes a problem formulated by fourth-grade students about having more pizza for lunch, and the clarifying, predicting, modeling, simulating, comparing, and extending activities that occurred in addressing the problem from a probabilistic perspective. (MKR)

Describes a sustainable planet index (SPI) to gauge the survivability of the earth ecologically and economically. Compares the SPI to the consumer price index and general business cycle theory from which it draws constructs. Suggests that the SPI exhibits properties of a sine wave and is useable in mathematical formulations, explanation, and…

Uses the various strategies involved in baseball to illustrate basic concepts in game theory. Specifically discusses Willie Mays' base-stealing strategy and how it relates to probability and risk. Reminds students that expected results depend on adopted assumptions. (MJP)