Mathematics Commons^™

High School Mathematics Teachers' Evolving Understanding Of Comparing Distributions, Sandra R. Madden

Dissertations

Statistics has achieved a position of status in the secondary curriculum (College Board, 2006b; Franklin et al., 2007; NCTM, 2000) and understanding of statistics is essential for high school mathematics teachers if they are to engage students in thoughtful pursuit of statistical ideas. High school teachers typically are ill-prepared in the area of statistics (Ben-Zvi & Garfield, 2004a; CBMS, 2001; Shaughnessy, 1992, 2007). Using methods of design research, this study investigated 56 high school mathematics teachers' understanding of the statistical concept ofcomparing distributions and demonstrated that a modest four-day, statistics-oriented, technology-rich, professional development program may significantly improve teachers' understanding. …

On The Rolling Motion Of Viscous Fluid On A Rigid Surface, Xinli Wang

Dissertations

This thesis considers two closely related problems. First, the influence of insoluble surfactant at a moving contact line is considered. This work is mostly motivated by the air entrainment during the coating process where there is a three-phase contact point (e.g., air, liquid and solid). For moving contact line problems, when the fluid is assumed to be an incompressible Newtonian fluid and a no-slip boundary condition is enforced at the solid boundary, the non-integrable stress singularity arises at the contact line, which is physically unrealistic. The contact angle of 180° is considered as a special case in which the singularity …

A Mathematical And Computational Exploration Of The Effect Of The A-Current In Determining The Activity Phase Of Follower Neurons, Yu Zhang

Dissertations

Bursting oscillations are prevalent in neurons of central pattern generators (CPGs) that produce rhythmic motor activity, and the activity phase plays an important role in determining the normal or dysfunctional network output. The activity phase is the delay time-with respect to some reference time in each cycle and normalized by the oscillation cycle period-of the onset of action potentials by a neuron. This dissertation investigates how the A-current, in conjunction with other intrinsic properties, sets the activity phase of a neuron driven by inhibition.

This dissertation is divided into two major components. In the first component, methods of dynamical systems …

Understanding Similarity: Bridging Geometric And Numeric Contexts For Proportional Reasoning, Dana Christine Cox

Dissertations

The concept of similarity is uniquely situated at the crossroads of geometric and numerical proportional reasoning. Although studies have documented the existence and nature of student difficulties with this topic, there exists a gap between documented visual insights of younger children and the quantitative inadequacies of older ones. Using a revised version of the Similarity Perception Test followed by 21 clinical interviews, this study investigated the visual and analytical strategies that are used by middle-school students to differentiate and construct similar figures.

New strategies for construction and differentiation were identified, and three overarching conclusions were drawn from the work. First, …

The Role Of Short Term Synamptic Plasticity In Temporal Coding Of Neuronal Networks, Lakshmi Chandrasekaran

Dissertations

Short term synaptic plasticity is a phenomenon which is commonly found in the central nervous system. It could contribute to functions of signal processing namely, temporal integration and coincidence detection by modulating the input synaptic strength. This dissertation has two parts. First we study the effects of short term synaptic plasticity in enhancing coincidence detecting ability of neurons in the avian auditory brainstem. Coincidence detection means a target neuron has a higher firing rate when it receives simultaneous inputs from different neurons as opposed to inputs with large phase delays. This property is used by birds in sound localization. When …

Roles Of Gap Junctions In Neuronal Networks, Joon Ha

Dissertations

This dissertation studies the roles of gap junctions in the dynamics of neuronal networks in three distinct problems. First, we study the circumstances under which a network of excitable cells coupled by gap junctions exhibits sustained activity. We investigate how network connectivity and refractory length affect the sustainment of activity in an abstract network. Second, we build a mathematical model for gap junctionally coupled cables to understand the voltage response along the cables as a function of cable diameter. For the coupled cables, as cable diameter increases, the electrotonic distance decreases, which cause the voltage to attenuate less, but the …

Instabilities Of Volatile Films And Drops, Nebojsa Murisic

Dissertations

We report on instabilities during spreading of volatile liquids, with emphasis on the novel instability observed when isopropyl alcohol (IPA) is deposited on a monocrystalline silicon (Si) wafer. This instability is characterized by emission of drops ahead of the expanding front, with each drop followed by smaller, satellite droplets, forming the structures which we nickname “octopi” due to their appearance. A less volatile liquid, or a substrate of larger heat conductivity, suppress this instability. In addition, we examine the spreading of drops of water (DJW)-JPA mixtures on both Si wafers and plain glass slides, and describe the variety of contact …

Signal Transmission In Epithelial Layers, Filippo Posta

Dissertations

Cell signaling is at the basis of many biological processes such as development, tissue repair, and homeostasis. It can be carried out by different mechanisms. Here we are focusing on ligand mediated cell-to-cell signaling in which a molecule (ligand) is free to move into the extra-cellular medium. On the cell layer surface, it can bind to its molecule-specific receptors located on the cell plasma membrane. This mechanism is the subject of many experimental and theoretical studies on many model biological systems, such as the follicular epithelium of the Drosophila egg, which motivates this work.

Here, we present a general mathematical …

The Role Of Prediction In The Teaching And Learning Of Algebra, Lisa Kasmer

Dissertations

Research has shown that including prediction questions within reading and science instruction has been advantageous for students, yet minimal research existed regarding the use of such questions within mathematics instruction. In order to extend and build on our knowledge about the effects of prediction in mathematics instruction, this study explored the impact of this paradigm in the teaching and learning of algebra. Specifically, this study probed whether utilizing prediction questions provided students opportunities for engaging in mathematical thinking, retrieving prior knowledge, and discussing related mathematical ideas, could increase such students' conceptual understanding and mathematical reasoning in the content area of …