Mathematics Commons^™

Path Partitions Of Almost Regular Graphs, Colton Magnant, Hua Wang, Shuai Yuan

Mathematical Sciences: Faculty Publications

The path partition number of a graph is the minimum number of paths required to partition the vertices. We consider upper bounds on the path partition number under minimum and maximum degree assumptions.

A Transformation Class For Spatio-Temporal Survival Data With A Cure Fraction, Sandra M. Hurtado Rua, Dipak K. Dey

Mathematics and Statistics Faculty Publications

We propose a hierarchical Bayesian methodology to model spatially or spatio-temporal clustered survival data with possibility of cure. A flexible continuous transformation class of survival curves indexed by a single parameter is used. This transformation model is a larger class of models containing two special cases of the well-known existing models: the proportional hazard and the proportional odds models. The survival curve is modeled as a function of a baseline cumulative distribution function, cure rates, and spatio-temporal frailties. The cure rates are modeled through a covariate link specification and the spatial frailties are specified using a conditionally autoregressive model with …

Minimizing Differences Of Convex Functions With Applications To Facility Location And Clustering, Mau Nam Nguyen, R. Blake Rector, Daniel J. Giles

Mathematics and Statistics Faculty Publications and Presentations

In this paper we develop algorithms to solve generalized Fermat-Torricelli problems with both positive and negative weights and multifacility location problems involving distances generated by Minkowski gauges. We also introduce a new model of clustering based on squared distances to convex sets. Using the Nesterov smoothing technique and an algorithm for minimizing differences of convex functions called the DCA introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.

Tme Volume 13, Numbers 1 And 2

The Mathematics Enthusiast

No abstract provided.

Knowledge For Equitable Mathematics Teaching: The Case Of Latino Ells In U.S. Schools, Aaron T. Wilson

The Mathematics Enthusiast

This paper reports the exploration of an aspect of knowledge needed for equitable mathematics teaching. Pedagogical Content Knowledge for Teaching Mathematics to English Language Learners (PCK-MELL) was proposed as a theoretical knowledge construct, a subdomain of MKT, and the construct was investigated through a process of survey instrument development and administration. The survey contained items intended to measure teachers’ knowledge of the obstacles encountered by ELLs in math classes, of the resources that ELLs draw upon, and of instructional strategies for teaching ELLs. Analysis of middle school mathematics teachers’ responses (N = 42) offered insights into how to improve the …

Making Progress On Mathematical Knowledge For Teaching, Mark Hoover, Reidar Mosvold, Deborah L. Ball, Yvonne Lai

The Mathematics Enthusiast

Although the field lacks a theoretically grounded, well-defined, and shared conception of mathematical knowledge required for teaching, there appears to be broad agreement that a specialized body of knowledge is vital to improvement. Further, such a construct serves as the foundation for different kinds of studies with different agendas. This article reviews what is known and needs to be known to advance research on mathematical knowledge for teaching. It argues for three priorities: (i) finding common ground for engaging in complementary studies that together advance the field; (ii) innovating and reflecting on method; and (iii) addressing the relationship of such …

Use Of Mathematical Tasks Of Teaching And The Corresponding Lmt Meaures In The Malawi Context, Mercy Kazima, Arne Jakobsen, Dun N. Kasoka

The Mathematics Enthusiast

We discuss the adaptation and piloting of the previously developed U.S.-specific measures of mathematical knowledge for teaching to the Malawi context. The purpose is to produce measures that can be used to evaluate changes in mathematical knowledge for teaching gained through primary teacher education, thus informing teacher educators on the most effective evidence-based practices. By interviewing 14 teachers, we first examine whether the 16 recurrent mathematical tasks of teaching tasks identified in the U.S. are applicable to the Malawi context. This is followed by the discussion of the adaptability of the U.S. developed number concept and operations LMT measures. Next, …

In-Service Teachers' Reasoning About Scenarios Of Teaching Mathematics To English Language Learners, Sultan Turkan

The Mathematics Enthusiast

The student population in the U.S. and worldwide is becoming increasingly diverse, creating a need to support all learners, especially linguistically and culturally diverse subpopulations such as English language learners (ELLs). From a social equity standpoint, the need to support these learners is critical especially in mathematics classrooms. In the U.S, the demand for mathematics teachers who are adequately prepared to teach ELLs has in fact risen. Yet, little is known about what knowledge base is essential to teach mathematics to ELLs. Driven by the need to explore this knowledge base, in this paper I explore what is involved in …

What Does It Take To Develop Assessments Of Mathematical Knowledge For Teaching?: Unpacking The Mathematical Work Of Teaching, Sarah Kate Selling, Nicole Garcia, Deborah L. Ball

The Mathematics Enthusiast

In the context of the increased mathematical demands of the Common Core State Standards and data showing that many elementary school teachers lack strong mathematical knowledge for teaching, there is an urgent need to grow teachers’ MKT. With this goal in mind, it is crucial to have research and assessment tools that are able to measure and track aspects of teachers’ MKT at scale. Building on the concept of “mathematical tasks of teaching” (Ball et al., 2008), we report on a new framework that unpacks the mathematical work of teaching that could serve as a scaffold for item writers who …

Teachers And Their Educators - Views On Contents And Their Development Needs In Mathematics Teacher Education, Mika Koponen, Mervi A. Asikainen, Antti Viholainen, Pekka E. Hirvonen

The Mathematics Enthusiast

Finland has scored well in international assessments (e.g. PISA, TIMSS), and the pressure to attain excellent scores has activated a drive toward even more effective mathematics teacher education. This article presents the results of a qualitative assessment of the mathematics teacher education provided by the University of Eastern Finland. In this study, the views held by practicing teachers (N=101) and teacher educators (N=19) are compared so that the outstanding development needs of mathematics teacher education in terms of their contents can be revealed. The data was gathered via an electronic survey and was mainly analyzed using data-driven methods. In addition, …

Mindset Training For Undergraduates In Developmental Mathematics, Valorie L. Zonnefeld, Kate Van Weelden

Faculty Work Comprehensive List

This poster highlights the work of an individual study that student Kate Van Weelden did in Dr. Zonnefeld's Math 100 class. Kate was a teacher assistant who led a lab session for 6 of the students in the Math 100 course. Throughout the semester Kate implemented incremental mindset training for her 6 students. The results showed a promising avenue for improved achievement, especially among males.

Depression In Mexican Americans With Diagnosed And Undiagnosed Diabetes, Rene L. Olvera, Susan P. Fisher-Hoch, Douglas E. Williamson, Kristina Vatcheva, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Background: Depression and diabetes commonly co-occur; however, the strength of the physiological effects of diabetes as mediating factors towards depression is uncertain.

Method: We analyzed extensive clinical, epidemiological and laboratory data from n = 2081 Mexican Americans aged 35-64 years, recruited from the community as part of the Cameron County Hispanic Cohort (CCHC) divided into three groups: Diagnosed (self-reported) diabetes (DD, n = 335), Undiagnosed diabetes (UD, n = 227) and No diabetes (ND, n = 1519). UD participants denied being diagnosed with diabetes, but on testing met the 2010 American Diabetes Association and World Health Organization definitions of diabetes. …

Epistemic Considerations On Extensive-Form Games, Cagil Tasdemir

Dissertations, Theses, and Capstone Projects

In this thesis, we study several topics in extensive-form games. First, we consider perfect information games with belief revision with players who are tolerant of each other’s hypothetical errors. We bound the number of hypothetical non-rational moves of a player that will be tolerated by other players without revising the belief on that player’s rationality on future moves, and investigate which games yield the backward induction solution.

Second, we consider players who have no way of assigning probabilities to various possible outcomes, and define players as conservative, moderate and aggressive depending on the way they choose, and show that all …

Supplemental Instruction For Developmental Mathematics: Two-Year Summary, Olen Dias, Alice W. Cunningham, Loreto Porte

Publications and Research

Supplemental instruction—using trained peer tutors to conduct additional class sessions in a group-work format—has been in use for over forty years. However, its success in developmental mathematics has been inconclusive. In the two years since institution of the strategy for developmental mathematics students at Hostos Community College, overall results (n = 5403 students) show significantly improved course pass rates to at least a 99% confidence level. Although no significant course retention differences have yet appeared, academic success itself promotes future retention. The program has proved beneficial for the College’s developmental mathematics students and is being expanded. Future research including …

Approximating Optimal Release In A Deterministic Model For The Sterile Insect Technique, Sergio Ramirez, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Cost/benefit analyses are essential to support management planning and decisions before launching any pest control program. In particular, applications of the sterile insect technique (SIT) are often prevented by the projected economic burden associated with rearing processes. This has had a deep impact on the technique development and its use on insects with long larval periods, as often seen in beetles. Under the assumptions of long adult timespan and multiple mating, we show how to find approximate optimal sterile release policies that minimize costs. The theoretical framework proposed considers the release of insects by pulses and finds approximate optimal release …

The Log-Exponential Smoothing Technique And Nesterov’S Accelerated Gradient Method For Generalized Sylvester Problems, N. T. An, Daniel J. Giles, Nguyen Mau Nam, R. Blake Rector

Mathematics and Statistics Faculty Publications and Presentations

The Sylvester or smallest enclosing circle problem involves finding the smallest circle enclosing a finite number of points in the plane. We consider generalized versions of the Sylvester problem in which the points are replaced by sets. Based on the log-exponential smoothing technique and Nesterov’s accelerated gradient method, we present an effective numerical algorithm for solving these problems.

Unions Of Lebesgue Spaces And A1 Majorants, Greg Knese, John E. Mccarthy, Kabe Moen

Mathematics Faculty Research

We study two questions. When does a function belong to the union of Lebesgue spaces, and when does a function have an A1 majorant? We provide a systematic study of these questions and show that they are fundamentally related. We show that the union ofLwp(ℝn)spaces withw∈Apis equal to the union of all Banach function spaces for which the Hardy–Littlewood maximal function is bounded on the space itself and its associate space.

Knowledge For Equitable Mathematics Teaching: The Case Of Latino Ells In U.S. Schools, Aaron T. Wilson

School of Mathematical & Statistical Sciences Faculty Publications

This paper reports the exploration of an aspect of knowledge needed for equitable mathematics teaching. Pedagogical Content Knowledge for Teaching Mathematics to English Language Learners (PCK-MELL) was proposed as a theoretical knowledge construct, a subdomain of MKT, and the construct was investigated through a process of survey instrument development and administration. The survey contained items intended to measure teachers’ knowledge of the obstacles encountered by ELLs in math classes, of the resources that ELLs draw upon, and of instructional strategies for teaching ELLs. Analysis of middle school mathematics teachers’ responses (N = 42) offered insights into how to improve the …

Pythagoras Plays His Lyre, Sarah Glaz

Journal of Humanistic Mathematics

A poem about the Pythagoreans' beliefs and way of life.

Pension Building, Washington Dc, E Laura Golberg

Journal of Humanistic Mathematics

No abstract provided.