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…

Upper primary school children often routinely apply proportional methods to missing-value problems, even when it is inappropriate. We tested whether this tendency could be weakened if children were not required to produce computational answers to such problems. A total of 75 sixth graders were asked to classify 9 word problems of three types (3…

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…

Problem-based learning (PBL) is an instructional approach that is organized around the investigation and resolution of problems. Problems are neither uniform nor similar. Jonassen (1997, 2000) in his design theory of problem solving has categorized problems into two broad types--well-structured and ill-structured. He has also described a host of…

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…

To explore student mathematical self-efficacy and understanding of graphical data, this dissertation examines students solving real-world problems in their neighborhood, mediated by professional urban planning technologies. As states and schools are working on the alignment of the Common Core State Standards for Mathematics (CCSSM), traditional…

Previous research shows that speed is one of the most difficult in the upper grades of primary school. It is because students must take into consideration two variables; distance and time. Nevertheless, Indonesian students usually learn this concept as a transmission subject and teacher more emphasizes on formal mathematics in which the concept of…

Investigating students' perceptions of their classroom environment is one of the ways researchers and educators can effectively determine what factors may benefit students' learning. Student Perceptions of Classroom Quality (SPOCQ; Gentry & Owen, 2004) was used with a group of Chinese gifted and general secondary students in the study. SPOCQ…

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…