A Toolkit For The Construction And Understanding Of 3-Manifolds,
2010
Brigham Young University - Provo
A Toolkit For The Construction And Understanding Of 3-Manifolds, Lee R. Lambert
Theses and Dissertations
Since our world is experienced locally in three-dimensional space, students of mathematics struggle to visualize and understand objects which do not fit into three-dimensional space. 3-manifolds are locally three-dimensional, but do not fit into 3-dimensional space and can be very complicated. Twist and bitwist are simple constructions that provide an easy path to both creating and understanding closed, orientable 3-manifolds. By starting with simple face pairings on a 3-ball, a myriad of 3-manifolds can be easily constructed. In fact, all closed, connected, orientable 3-manifolds can be developed in this manner. We call this work a tool kit to emphasize the …
Vanishing Of Ext And Tor Over Complete Intersections,
2010
University of Nebraska-Lincoln
Vanishing Of Ext And Tor Over Complete Intersections, Olgur Celikbas
Department of Mathematics: Dissertations, Theses, and Student Research
Let (R,m) be a local complete intersection, that is, a local ring whose m-adic completion is the quotient of a complete regular local ring by a regular sequence. Let M and N be finitely generated R-modules. This dissertation concerns the vanishing of Tor(M, N) and Ext(M, N). In this context, M satisfies Serre's condition (S_{n}) if and only if M is an nth syzygy. The complexity of M is the least nonnegative integer r such that the nth Betti number of M is bounded by a polynomial of degree r-1 for all sufficiently large n. We use this notion of …
A Hybrid Radial Basis Function-Pseudospectral Method For Thermal Convection In A 3-D Spherical Shell,
2010
Boise State University
A Hybrid Radial Basis Function-Pseudospectral Method For Thermal Convection In A 3-D Spherical Shell, Grady Wright, Natasha Flyer, David A. Yuen
Mathematics Faculty Publications and Presentations
A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral methods in a “2 + 1” approach is presented for numerically simulating thermal convection in a 3‐D spherical shell. This is the first study to apply RBFs to a full 3‐D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface‐based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be “scattered” over …
Comprehensive Peroxidase-Based Hematologic Profiling For The Prediction Of 1-Year Myocardial Infarction And Death,
2010
Cleveland Clinic
Comprehensive Peroxidase-Based Hematologic Profiling For The Prediction Of 1-Year Myocardial Infarction And Death, Marie Luise Brennan, Anupama Reddy, W.H. Wilson Tang, Yuping Wu, Danielle M. Brennan, Amy Hsu, Shirley A. Mann, Peter L. Hammer, Stanley L. Hazen
Mathematics and Statistics Faculty Publications
Background— Recognition of biological patterns holds promise for improved identification of patients at risk for myocardial infarction (MI) and death. We hypothesized that identifying high- and low-risk patterns from a broad spectrum of hematologic phenotypic data related to leukocyte peroxidase-, erythrocyte- and platelet-related parameters may better predict future cardiovascular risk in stable cardiac patients than traditional risk factors alone. Methods and Results— Stable patients (n=7369) undergoing elective cardiac evaluation at a tertiary care center were enrolled. A model (PEROX) that predicts incident 1-year death and MI was derived from standard clinical data combined with information captured by a high-throughput peroxidase-based …
Parts Of The Whole: Thinking About Variance: Standards, Targets, Tracking, And Other Thoughts,
2010
Dartmouth College
Parts Of The Whole: Thinking About Variance: Standards, Targets, Tracking, And Other Thoughts, Dorothy Wallace
Numeracy
Variation is a natural result of any process, including education. Understanding how variation propagates and increases is necessary for designing educational interventions that work for the intended population. We show how common strategies such as setting standards and tracking can accidentally produce unintended and undesirable results due to the way variation moves through a system.
Creating A Masters In Numeracy Program,
2010
Bowdoin College
Creating A Masters In Numeracy Program, Eric Gaze
Numeracy
The Master of Science in Numeracy program at Alfred University received full approval from the New York State Education Department (NYSED) in May of 2007. This first-of-its-kind program seeks to provide teachers at all levels, from across the curriculum, the skills, and more importantly the confidence, to introduce relevant quantitative concepts in their own disciplines. Created to be a complement of the MS Ed. in Literacy, the 30-hour MS in Numeracy program consists of four required core courses (Teaching Numeracy, Teaching with Data, Assessment and Learning Theories in Numeracy, and Doing Science and Numeracy), five electives from a list of …
Reorganizing School Mathematics For Quantitative Literacy,
2010
Valparaiso University
Reorganizing School Mathematics For Quantitative Literacy, Rick Gillman
Numeracy
This paper offers an alternative curriculum for high school mathematics. It proposes replacing the Algebra-Geometry-Algebra rush to calculus model with one which focuses on improving student problem-solving skills and general quantitative literacy skills while reinforcing basic manipulative skills. Most of these goals are gained by expanding the current single-year algebra-one course into two years. The model proposes moving “learning to write proofs” from the traditional geometry course into a separate discrete mathematics course. It requires statistics for every student, and requires a senior-level modeling course for every college-going student. In addition, the proposed model creates opportunities for students to move …
Spreadsheets Across The Curriculum, 1: The Idea And The Resource,
2010
Department of Geology, University of South Florida, Tampa
Spreadsheets Across The Curriculum, 1: The Idea And The Resource, H L Vacher, Emily Lardner
Numeracy
This paper introduces Spreadsheets Across the Curriculum, a workshop-based educational materials development project to build a resource to facilitate connecting mathematics and context in undergraduate college courses where mathematical problem solving is relevant. The central idea is “spreadsheet modules,” which, in essence, are elaborate word problems in the form of short PowerPoint presentations with embedded Excel spreadsheets. Students work through the presentations on their own, making and/or completing the spreadsheets displayed on the slides in order to perform calculations or draw graphs that address the issue (context) posed in the word problem. The end result of the project is the …
Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community,
2010
University of Arkansas
Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community, Bernard L. Madison, Shannon W. Dingman
Numeracy
Numerous questions about student learning of quantitative reasoning arose as we developed, taught and assessed the Quantitative Reasoning in the Contemporary World course described in the companion paper in this issue of Numeracy. In this paper, we present some of those questions and describe the context in which they arose. They fall into eight general problem areas: learning that is context-bound and does not easily transfer (i.e., situated learning); the need for a productive disposition regarding mathematics; the connection between QL and mathematical proficiency; the persistence of students, despite our efforts, for using the wrong base for percents; the inconsistent …
Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:,
2010
University of Arkansas - Main Campus
Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:, Shannon W. Dingman, Bernard L. Madison
Numeracy
The authors describe successes and challenges in developing a QL-friendly course at the University of Arkansas. This work is part of a three-year NSF project Quantitative Reasoning in the Contemporary World (QRCW) that supported the expansion of the course. The course, MATH 2183, began experimentally in Fall 2004 as a section of finite mathematics known informally as “News Math” for 26 students from arts and humanities disciplines. Over the past six years, the course has evolved and now MATH 2183 is approved to satisfy the College of Arts and Sciences mathematics requirement for the Bachelor of Arts degree. In 2009-2010, …
Quantitative Literacy: Does It Work? Evaluation Of Student Outcomes At Colby-Sawyer College,
2010
Colby-Sawyer College
Quantitative Literacy: Does It Work? Evaluation Of Student Outcomes At Colby-Sawyer College, Benjamin Steele, Semra Kilic-Bahi
Numeracy
Colby-Sawyer College has adopted a mission for quantitative literacy (QL) to give students the “necessary skills to understand and use quantitative information in their personal and professional lives.” We have implemented an across-the-curriculum approach to develop these skills. As part of this QL program, we administer two assessment tests, one in basic mathematical skills and one that applies those skills, plus an attitude survey to both freshmen and seniors. Three years of data show that seniors score about 10 percentage points higher than freshmen on these tests. However, seniors still scored below 55 percent on both tests, and many cannot …
Advancing Assessment Of Quantitative And Scientific Reasoning,
2010
James Madison University
Advancing Assessment Of Quantitative And Scientific Reasoning, Donna L. Sundre, Amy D. Thelk
Numeracy
Advancing Assessment of Quantitative and Scientific Reasoning is a four-year NSF Project (DUE-0618599) in part designed to evaluate the generalizability of quantitative (QR) and scientific reasoning (SR) assessment instruments created at James Madison University to four other four-year institutions with very distinct missions and student demographics. This article describes the methods, results, and findings we obtained in our studies. More specifically, we describe how to conduct content-alignment exercises in which faculty members map each item from a prospective test to the student learning objectives taught at the institution. Our results indicated that 92-100% of the QR and SR items were …
Science Literacy: Hand In Glove With Numeracy,
2010
University of South Florida, Tampa
Science Literacy: Hand In Glove With Numeracy, Gerry G. Meisels
Numeracy
Science Literacy requires numeracy as part of its foundation, and much of Numeracy draws on examples and applications from the sciences. They share the goal of creating a society that is mathematics numerate and science literate, and are interrelated. National priorities to strengthen both among all our students are driven by practical considerations of economic competitiveness that increasingly depend on technological innovation. It is also critical to each individual for long-term job opportunities and for informed citizenship. With up to 80% of 21st century jobs requiring mathematics and science skills, a large majority of the 2,900,000 students who graduate from …
Extension Of Plurisubharmonic Functions With Growth Control,
2010
Syracuse University
Extension Of Plurisubharmonic Functions With Growth Control, Dan Coman, Vincent Guedj, Ahmed Zeriahi
Mathematics - All Scholarship
Suppose that X is an analytic subvariety of a Stein manifold M and that varphi is a plurisubharmonic (psh) function on X which is dominated by a continuous psh exhaustion function u of M. Given any number c > 1, we show that varphi admits a psh extension to M which is dominated by cu on M. We use this result to prove that any omega-psh function on a subvariety of the complex projective space is the restriction of a global omega-psh function, where omega is the Fubini-Study Kahler form.
Rules Without Reason: Allowing Students To Rethink Previous Conceptions,
2010
University of Montana
Rules Without Reason: Allowing Students To Rethink Previous Conceptions, Mary Mueller, Dina Yankelewitz, Carolyn Maher
The Mathematics Enthusiast
This paper reports on the strategies chosen by a group of sixth-grade students in an urban informal learning program as they worked to solve an open-ended, nonroutine task. In particular, the paper focuses on the ability of these students to rise above their previous, procedure-based misconceptions and arrive at a mathematically reasonable solution. Aspects of the problem task, the problem-solving environment, and, importantly, of the nature of the teacher’s interventions are analyzed to determine the conditions that encouraged students to approach mathematics as a logical, meaningful, sense-making activity.
Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment,
2010
University of Montana
Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment, Anne Birgitte Fyhn
The Mathematics Enthusiast
In this innovative teaching experiment, the context of climbing is used to induce the teaching and learning of angle concepts. This article reports on the outcomes of a three day teaching and climbing experiment and the impact of this experience on the teacher’s understanding of meso and micro embodiments of mathematics, angle representations, as well as shifts in their attitudes about teaching/learning geometry.
Rehearsal Or Reorganization: Two Patterns Of Literacy Strategy Use In Secondary Mathematics Classes,
2010
University of Montana
Rehearsal Or Reorganization: Two Patterns Of Literacy Strategy Use In Secondary Mathematics Classes, Anne Adams
The Mathematics Enthusiast
This study presents two critical cases illustrating distinct patterns in teachers' use of literacy strategies in secondary mathematics classes. The cases are part of a professional development project designed to enhance teachers' pedagogical skills by developing content literacy strategies for use in secondary mathematics and science classrooms. Teachers' beliefs about teaching mathematics, their uses of writing and vocabulary development strategies, and goals for student learning were examined via interviews, classroom observations, reflections on teaching, and teacher posts to an online discussion forum. Results show patterns of literacy strategy use were related to teachers' views of pedagogy and of mathematics. Ned, …
Population Models With Allee Effect: A New Model,
2010
Trinity University
Population Models With Allee Effect: A New Model, Saber Elaydi, Robert J. Sacker
Mathematics Faculty Research
In this paper we develop several mathematical models of Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model that is our focus of study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.
Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers",
2010
University of Montana
Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers", Miriam Amit
The Mathematics Enthusiast
This paper describes a singular process that has been transforming mathematics education in Israel over the past 20 years, as a result of a massive influx of mathematics teachers from the former Soviet Union (FSU). It traces the key points of conflict that marked the initial contact between Israel's mathematical and educational culture and the codes and values brought with the immigrant teachers from the FSU. It then shows how this conflict is gradually becoming resolved, as the two disparate cultures merge into a single, new culture, based on 'the best of both worlds.' This case, we claim, can serve …
Some Reflections On Hernández And López’S Reflections On The Chain Rule,
2010
University of Montana
Some Reflections On Hernández And López’S Reflections On The Chain Rule, Michael N. Fried
The Mathematics Enthusiast
To shed light on how history of mathematics can play a role in mathematics education, Hernández and López chose well in focusing on the chain rule as a case study. Generally speaking, it is, as they point out, a topic students find difficult to grasp: it is a rule involving a different order of complexity than, say, the rule for differentiating functions of the form f(x)=xn, and, although it can eventually become intuitive, it is far from intuitive at the start. Harel et al. (2009) have pointed out that students’ difficulties with the chain rule involve: “...coordinating three or more …
