This module was initially developed for a course in applications of mathematics in biology. The objective of this lesson is to investigate how the allele and genotypic frequencies associated with a particular gene might evolve over successive generations. The lesson will discuss how the Hardy-Weinberg model provides a basis for comparison when…

The 3 most often-used performance measures in the cognitive and decision sciences are choice, response or decision time, and confidence. We develop a random walk/diffusion theory--2-stage dynamic signal detection (2DSD) theory--that accounts for all 3 measures using a common underlying process. The model uses a drift diffusion process to account…

Problems on the dynamics of changing mass systems often call for the more general form of Newton's second law Fnet = dp/dt. These problems usually involve situations where the mass of the system decreases, such as in rocket propulsion. In contrast, this experiment examines a system where the mass "increases" at a constant rate and the net force…

We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z greater than 0 and V(z) = [infinity] for z less than 0) and the symmetric linear potential…

Students who are deaf or hard of hearing are increasingly being educated in regular education classrooms along with their typical hearing peers. Establishing educational environments that address their unique needs is essential for their success. Response to intervention (RtI), as it is being implemented in the United States, provides a framework…

Recently, there has been growing emphasis on supporting robust learning within intelligent tutoring systems, assessed by measures such as transfer to related skills, preparation for future learning, and longer term retention. It has been shown that different pedagogical strategies promote robust learning to different degrees. However, the student…

A multilevel latent transition analysis (LTA) with a mixture IRT measurement model (MixIRTM) is described for investigating the effectiveness of an intervention. The addition of a MixIRTM to the multilevel LTA permits consideration of both potential heterogeneity in students' response to instructional intervention as well as a methodology for…

Students with autism spectrum disorders (ASD) present unique programming challenges to school personnel because of the wide variability of clinical symptoms and the high rates of emotional and/or behavior disorders (EBD) that can affect learning outcomes. Currently, there is little empirically based guidance to assist in determining the support…

Introduction: Response to intervention (RTI) has become widely recognized and used in education. Propelling its significance is its systematic and schoolwide approach and emphasis on using a problem-solving approach to providing appropriate instruction for each child. Children with visual impairments (that is, blindness and low vision) are…

Bandit problems provide an interesting and widely-used setting for the study of sequential decision-making. In their most basic form, bandit problems require people to choose repeatedly between a small number of alternatives, each of which has an unknown rate of providing reward. We investigate restless bandit problems, where the distributions of…

This dissertation is a qualitative study of the benefits of a student-initiated apartment theme-housing program at a small private university in the southern United States. This study used in-depth interviews to determine what benefits existed from participation in the theme-housing program, and to determine if the program was beneficial to…

In Thailand, the Center for Research in Mathematics Education (CRME) has been implementing Japanese Lesson Study (LS) since 2002. An adaptive feature of this implementation was the incorporation of four phases of the Open Approach as a teaching approach within the three steps of the LS process. Four phases of this open approach are: 1) Posing…

The purpose of this study was to analyze how school psychologists engaged in problem analysis during problem-solving consultation. Five aspects of the problem analysis process were examined: 1) the types of questions participants asked during problem identification, 2) the types of data participants requested, 3) the frequency of requests for each…

This article explores theoretical and methodological issues associated with task-based interviews conducted with pairs of children. We explore different approaches to interviews from sociological, psychological and subject-based perspectives. Our interviews, concerning mathematical questions and carried out with pairs of 10 and 11-year-olds, are…

What we're thinking about behaviorally challenging students and what we're doing to them requires a fresh look. When schools believe that parental discipline explains a child's misbehavior, educators are less likely to consider different explanations for the misbehavior and the full range of interventions that could be implemented at school. And…