Latent curve models have become a popular approach to the analysis of longitudinal data. At the individual level, the model expresses an individual's response as a linear combination of what are called "basis functions" that are common to all members of a population and weights that may vary among individuals. This article uses…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

Background: Government projections in the USA indicate that the country will need a million more science, technology, engineering, and mathematics (STEM) graduates above and beyond those already projected by the year 2022. Of crucial importance to the STEM pipeline is success in Calculus I, without which continuation in a STEM major is not…

The "gender gap" on various physics conceptual evaluations has been extensively studied. Men's average pretest scores on the Force Concept Inventory and Force and Motion Conceptual Evaluation are 13% higher than women's, and post-test scores are on average 12% higher than women's. This study analyzed the gender differences within the…

Multiple representations, multiple modalities, and technology can be helpful in the understanding of mathematical concepts when used in an appropriate manner (Shah & Freedman, 2003; Goldman, 2003), but this alone does not account for the student benefits of creating and using dynamic models over teacher generated graphs to construct…

Many business schools or colleges require calculus as a prerequisite for certain classes or for continuing to upper division courses. While there are many studies investigating the relationship between performance in calculus and performance in a single course, such as economics, statistics, and finance, there are very few studies investigating…

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for…

Value-added models have been widely used to assess the contributions of individual teachers and schools to students' academic growth based on longitudinal student achievement outcomes. There is concern, however, that ignoring the presence of missing values, which are common in longitudinal studies, can bias teachers' value-added scores.…

The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common…

Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying…

Social cognitive research has linked students' perceived academic capabilities, or self-efficacy, to academic choices, self-regulation, and performance in diverse contexts from reading comprehension to mathematical problem solving. This study addressed a need to investigate the interactions among prior achievement, self-efficacy, calibration (the…

Maintains that most economics textbooks continue to repeat past mistakes concerning returns to scale and economies of scale under assumptions of constant and nonconstant input prices. Provides an adaptation for a calculus-based intermediate microeconomics class that demonstrates the pointwise relationship between returns to scale and economies of…

In response to the increasing importance of student performance in required classes, research was conducted to compare two prediction procedures, linear modeling using multiple regression and nonlinear modeling using AID3. Performance in the first college math course (College Mathematics, Calculus, or Business Calculus Matrices) was the dependent…