Mathematics Commons^™

Prospective Elementary Mathematics Teacher Content Knowledge: What Do We Know, What Do We Not Know, And Where Do We Go?, Eva Thanheiser, Christine Browning, Alden J. Edson, Jane-Jane Lo, Ian Whitacre, Dana Olanoff, Crystal Morton

The Mathematics Enthusiast

In this Special Issue, the authors reviewed 112 research studies from 1978 to 2012 on prospective elementary teachers’ content knowledge in five content areas: whole numbers and operations, fractions, decimals, geometry and measurement, and algebra. Looking across these studies, this final paper identifies the trends and common themes in terms of the counts and types of studies and commonalities among findings. Analyses of the counts show that the number of articles published each year focusing on prospective teacher (PT) content knowledge is increasing. Most articles across the content areas show that PTs tend to rely on procedures rather than concepts. …

Appendix: References By Content Area

The Mathematics Enthusiast

No abstract provided.

Living At The Friendship House: Findings From Thetransition Planning Inventory, Jane E. Finn, Vicky-Lynn Holmes, Rebecca Johnson

Faculty Publications

A residential initiative, named the Friendship House, was created through advocates focused on helping people with intellectual disabilities live independently in affordable and safe housing on a university campus. The Friendship House is a small residence hall where individuals with intellectual disabilities live side-by-side with similarly aged and same gendered university students. Qualitative finding as in resident reports and observational data provides support that the Friendship House experience has been successful. However, to better equip these residents with intellectual disabilities, it is important to assess the program in terms of post school transition acquisition skills. This study focuses on whether …

Foreword, Lynn Hart

The Mathematics Enthusiast

The authors in this Special Issue of The Mathematics Enthusiast make an important contribution to the knowledge base in mathematics education. They examine a body of research on a significant issue. They review what we know and make suggestions about what we need to know. They move the field forward by taking the time to look back and learn.

Mathematical Content Knowledge For Teaching Elementary Mathematics: A Focus On Fractions, Dana Olanoff, Jane-Jane Lo, Jennifer Tobias

The Mathematics Enthusiast

This article presents a research summary of prospective elementary teachers’ (PTs’) mathematical content knowledge in the area of fractions. The authors conducted an extensive review of the research literature and present the findings across three time frames: a historical look (pre-­‐1998), a current perspective (1998–2011), and a look at the horizon (2011–2013). We discuss 43 articles written across these time frames that focus on PTs’ fraction knowledge. Consistent across these papers is that PTs’ fraction knowledge is relatively strong when it comes to performing procedures, but that they generally lack flexibility in moving away from procedures and using “fraction number …

Tme Volume 11, Number 2

The Mathematics Enthusiast

No abstract provided.

Boundary Value Problems Of Nabla Fractional Difference Equations, Abigail M. Brackins

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation we develop the theory of the nabla fractional self-adjoint difference equation,

∇_a^ν(p∇y)(t)+q(t)y(ρ(t)) = f(t),

where 0 < ν < 1.We begin with an introduction to the nabla fractional calculus. In the second chapter, we show existence and uniqueness of the solution to a fractional self-adjoint initial value problem. We find a variation of constants formula for this fractional initial value problem, and use the variation of constants formula to derive the Green's function for a related boundary value problem. We study the Green's function and its properties in several settings. For a simplified boundary value problem, we show that the Green's function is nonnegative and we find its maximum and the maximum of its integral. For a boundary value problem with generalized boundary conditions, we find the Green's function and show that it is a generalization of the first Green's function. In the third chapter, we use the Contraction Mapping Theorem to prove existence and uniqueness of a positive solution to a forced self-adjoint fractional difference equation with a finite limit. We explore modifications to the forcing term and modifications to the space of functions in which the solution exists, and we provide examples to demonstrate the use of these theorems.

Advisers: Lynn Erbe and Allan Peterson

The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs

Department of Mathematics: Dissertations, Theses, and Student Research

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects …

Algebraic Properties Of Ext-Modules Over Complete Intersections, Jason Hardin

Department of Mathematics: Dissertations, Theses, and Student Research

We investigate two algebraic properties of Ext-modules over a complete intersection R of codimension c. Given an R-module M, Ext(M,k) can be viewed as a graded module over a polynomial ring in c variables with an action given by the Eisenbud operators. We provide an upper bound on the degrees of the generators of this graded module in terms of the regularities of two associated coherent sheaves. In the codimension two case, our bound recovers a bound of Avramov and Buchweitz in terms of the Betti numbers of M. We also provide a description of the differential graded (DG) R-module …

Fejér And Suffridge Polynomials In The Delayed Feedback Control Theory, Dmitriy Dmitrishin, Anna Khamitova, Anatolii Korenovskyi, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

A remarkable connection between optimal delayed feedback control (DFC) and complex polynomial mappings of the unit disc is established. The explicit form of extremal polynomials turns out to be related with the Fejer polynomials. The constructed DFC can be used to stabilize cycles of one-dimensional non-linear discrete systems.

Bipartitions Based On Degree Constraints, Pamela I. Delgado

Electronic Theses and Dissertations

For a graph G = (V,E), we consider a bipartition {V₁,V₂} of the vertex set V by placing constraints on the vertices as follows. For every vertex v in V_i, we place a constraint on the number of neighbors v has in V_i and a constraint on the number of neighbors it has in V_3-i. Using three values, namely 0 (no neighbors are allowed), 1 (at least one neighbor is required), and X (any number of neighbors are allowed) for each of the four constraints, results in 27 distinct types of …

Acyclic And Indifference-Transitive Collective Choice Functions., Katey Bjurstrom

Electronic Theses and Dissertations

Arrow's classic theorem shows that any collective choice function satisfying independence of irrelevant alternatives (IIA) and Pareto (P), where the range is a subset of weak orders, is based on a dictator. This thesis focuses on Arrovian collective choice functions in which the range is generalized to include acyclic, indifference-transitive (ACIT) relations on the set of alternatives. We show that Arrovian ACIT collective choice functions with domains satisfying the free-quadruple property are based on a unique weakly decisive voter; however, this is not necessarily true for ACIT collective choice functions where Arrow's independence condition is weakened. For ACIT collective choice …

Functional Equations With Involution Related To Sine And Cosine Functions., Allison Perkins

Electronic Theses and Dissertations

Let G be an abelian group, C be the _eld of complex numbers, _ 2 G be any _xed, nonzero element and _ : G ! G be an involution. In Chapter 2, we determine the general solution f; g : G ! C of the functional equation f(x + _y + _) + g(x + y + _) = 2f(x)f(y) for all x; y 2 G. Let G be an arbitrary group, z0 be any _xed, nonzero element in the center Z(G) of the group G, and _ : G ! G be an involution. The main goals of …

Anxiety, Depression And Smoking Status Among Adults Of Mexican Heritage On The Texas-Mexico Border, Anna V. Wilkinson, Kristina Vatcheva, Adriana Pérez, Belinda M. Reininger, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical & Statistical Sciences Faculty Publications

The goal of the current analysis is to examine relationships between smoking status and anxiety and depression among adults of Mexican heritage to inform the development of culturally relevant smoking cessations efforts. Mexican heritage residents (N=1,791) of the city of Brownsville, TX, aged 18 years or older, enrolled in the Cameron County Hispanic Cohort, were selected through two stage cluster sampling of randomly selected census tracts from the first and third quartile of SES using Census 2000. Among current smokers, anxiety and depression scores were highest among women who had not completed high school (p<0.05). Former smoking women, but not men, with at least a high school education and former smoking women born in the United States reported higher levels of anxiety and depression than never smoking women. Negative affective states may represent a greater barrier to smoking cessation among women than men.

Balanced Modular Parameterizations, Esteban J. Melendez

Theses and Dissertations - UTB/UTPA

In this thesis, we show that Classical representations for certain modular forms have symmetric form. These symmetric formulations are interpreted in terms of more general balanced homogeneous polynomial representations resulting from a permutative action of Hecke congruence subgroups on quotients of theta functions. For prime levels between 5 and 19, sets of permuted theta quotients are constructed that generate the corresponding vector spaces of modular forms of weight one.

Dynamics For The Compound Burgers-Kdv Equation, Xiangqian Zheng

Theses and Dissertations - UTB/UTPA

In this thesis, we study the Two-Dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation and Two-Dimensional Compound Burgers-Korteweg-de Vries (2D-Compound BKdV) by analyzing the first integral equation, which indicates that under some particular conditions, the 2D-BKdV equation and 2D-Compound BKdV have exact traveling wave solutions. By using the elliptic integral and some transformations, traveling wave solution to the 2D-BKdV equation and 2DCompound BKdV are expressed explicitly.

An Empirical Study Of Some Branching Processes With Upper Barrier, Alejandro Aguilar

Theses and Dissertations - UTB/UTPA

We consider discrete time branching processes with a reflecting upper barrier. The processes differ in their offspring distributions being either binary splitting or binomial one. Two important factors for the behavior of the processes characteristics are studied as follows: time to extinction and total progeny up to the n th generation. More specifically, we investigate the distribution and expected value of the time to extinction as well as the probability mass functions of the total progeny. The tools used are basic results for a finite state Markov chain.

Properties Of Small Ordered Graphs Whose Vertices Are Weighted By Their Degree, Constance M. Blalock

Electronic Theses and Dissertations

Graphs can effectively model biomolecules, computer systems, and other applications. A weighted graph is a graph in which values or labels are assigned to the edges of the graph. However, in this thesis, we assign values to the vertices of the graph rather than the edges and we modify several standard graphical measures to incorporate these vertex weights. In particular, we designate the degree of each vertex as its weight. Previous research has not investigated weighting vertices by degree. We find the vertex weighted domination number in connected graphs, beginning with trees, and we define how weighted vertices can affect …

Problems In The Theory Of Convergence Spaces, Daniel R. Patten

Dissertations - ALL

We investigate several problems in the theory of convergence spaces: generalization of Kolmogorov separation from topological spaces to convergence spaces, representation of reflexive digraphs as convergence spaces, construction of differential calculi on convergence spaces, mereology on convergence spaces, and construction of a universal homogeneous pretopological space. First, we generalize Kolmogorov separation from topological spaces to convergence spaces; we then study properties of Kolmogorov spaces. Second, we develop a theory of reflexive digraphs as convergence spaces, which we then specialize to Cayley graphs. Third, we conservatively extend the concept of differential from the spaces of classical analysis to arbitrary convergence spaces; …

Prospective Elementary Teacher Mathematics Content Knowledge: An Introduction, Christine Browning, Eva Thanheiser, Alden J. Edson, Patrick Kimani, Dana Olanoff, Jennifer Tobias, Ian Whitacre

The Mathematics Enthusiast

This Special Issue on the mathematical content knowledge of prospective elementary teachers (PTs) provides summaries of the extant peer-­‐reviewed research literature from 1978 to 2012 on PTs’ content knowledge across several mathematical topics, specifically whole number and operations, fractions, decimals, geometry and measurement, and algebra. Each topic-­‐specific summary of the literature is presented in a self-­‐contained paper, written by a subgroup of a larger Working Group that has collaborated across several years, resulting in this Special Issue sharing the final work. The authors hope this summative look at prospective teacher content knowledge will be of interest to the mathematics education …