Science and Mathematics Education Commons^™

Color Models As Tools In Teaching Mathematics, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

In this paper we discuss various situations how color models and patterns can be used to simplify the study of abstract mathematics and serve as tools in understanding mathematical ideas. We illustrate the realization of such models through the development of advanced computer technology. In particular, we present how a computer algebra software such as Mathematica, or a dynamic geometry environment, can be utilized to facilitate the study of transformation geometry and group theory.

The Awards Project: Promoting Good Practices In Award Selection, Betty Mayfield, Francis Su

All HMC Faculty Publications and Research

Every year the MAA honors many members of our community with a wide variety of prizes, awards, and certificates for excellence in teaching, writing, scholarship, and service (see maa.org/awards). The winners exemplify our ideals as an association; consequently, they are often viewed as role models and leaders. So it is important to ask: Do these awards, as a whole, reflect the outstanding contributions of the breadth of association membership?

Collaborative Research: Linking Researchers And Graduate Students Through Cosee Tools & Services, Annette V. Decharon

University of Maine Office of Research Administration: Grant Reports

This proposal will be awarded using funds made available by the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).

This award provides funds to conduct workshops aimed at improving the broader impacts efforts of scientists. Through professional development workshops, scientist-graduate student teams will produce interactive materials based on the ?Ocean Literacy? and ?Climate Literacy? principles that can be specifically designed for a variety of audiences. The primary target audiences for this project are the research scientists and graduate students who participate in the project workshops. Through team-building and COSEE-facilitated long-term contact, the project will provide sustained professional development …

General Aviation Weather Encounter Case Studies, John M. Lanicci, Massoud Bazargan, Daniel Halperin, Scott Shappell, Jaclyn Baron, Rebecca Iden, Carla Hackworth, Kali Holcomb

School of Graduate Studies - Daytona Beach

This study presents a compilation of 24 cases involving general aviation (GA) pilots’ weather encounters over the continental U.S. The project team interviewed pilots who had experienced a weather encounter, and we examined their backgrounds, flight experience, and weather encounter details. Results from meteorological data analysis for each weather encounter were consistent with findings of larger GA weather accident studies in terms of the types of hazards encountered and flight phase during which the encounters occurred. Investigation of pilot weather products and the sources from which they were obtained revealed a lack of uniformity of pre-flight data sources and underutilization …

An Item Response Curves Analysis Of The Force Concept Inventory, Gary A. Morris, Nathan Harshman, Lee Branum-Martin, Eric Mazur, Taha Mzoughi, Stephen D. Baker

Faculty and Research Publications

Several years ago, we introduced the idea of item response curves (IRC), a simplistic form of item response theory (IRT), to the physics education research community as a way to examine item performance on diagnostic instruments such as the Force Concept Inventory (FCI). We noted that a full-blown analysis using IRT would be a next logical step, which several authors have since taken. In this paper, we show that our simple approach not only yields similar conclusions in the analysis of the performance of items on the FCI to the more sophisticated and complex IRT analyses but also permits additional …

The Abundance And Distribution Of Gelatinous Zooplankton In The San Francisco Estuary, Amalia Borson, Lindsay Sullivan, Wim Kimmerer

STAR Program Research Presentations

Until recently, gelatinous zooplankton were not considered important components of the San Francisco Estuary (SFE) foodweb. However, anecdotal evidence, ongoing research, and a few published reports and papers suggest an increase in their abundance over the last 10 to 20 years. Of particular interests are three species of introduced hydromedusae (Blackfordia virginica, Maeotias marginata, and Moerisia lyonsi). All three inhabit the fresh to brackish regions of the estuary, including Suisun Bay, the channels of Suisun Marsh, and the western Sacramento-San Joaquin Delta, and are seasonally abundant throughout late summer and fall. As a result, they overlap …

Prime Ideals In Two-Dimensional Noetherian Domains And Fiber Products And Connected Sums, Ela Celikbas

Department of Mathematics: Dissertations, Theses, and Student Research

This thesis concerns three topics in commutative algebra:

1) The projective line over the integers (Chapter 2),

2) Prime ideals in two-dimensional quotients of mixed power series-polynomial rings (Chapter 3),

3) Fiber products and connected sums of local rings (Chapter 4),

In the first chapter we introduce basic terminology used in this thesis for all three topics.

In the second chapter we consider the partially ordered set (poset) of prime ideals of the projective line Proj(Z[h,k]) over the integers Z, and we interpret this poset as Spec(Z[x]) U Spec(Z[1/x]) with an appropriate identification. …

An Analysis Of Nonlocal Boundary Value Problems Of Fractional And Integer Order, Christopher Steven Goodrich

Department of Mathematics: Dissertations, Theses, and Student Research

In this work we provide an analysis of both fractional- and integer-order boundary value problems, certain of which contain explicit nonlocal terms. In the discrete fractional case we consider several different types of boundary value problems including the well-known right-focal problem. Attendant to our analysis of discrete fractional boundary value problems, we also provide an analysis of the continuity properties of solutions to discrete fractional initial value problems. Finally, we conclude by providing new techniques for analyzing integer-order nonlocal boundary value problems.

Adviser: Lynn Erbe and Allan Peterson

Commutative Rings Graded By Abelian Groups, Brian P. Johnson

Department of Mathematics: Dissertations, Theses, and Student Research

Rings graded by Z and Z^d play a central role in algebraic geometry and commutative algebra, and the purpose of this thesis is to consider rings graded by any abelian group. A commutative ring is graded by an abelian group if the ring has a direct sum decomposition by additive subgroups of the ring indexed over the group, with the additional condition that multiplication in the ring is compatible with the group operation. In this thesis, we develop a theory of graded rings by defining analogues of familiar properties---such as chain conditions, dimension, and Cohen-Macaulayness. We then study the …

The Weak Discrepancy And Linear Extension Diameter Of Grids And Other Posets, Katherine Victoria Johnson

Department of Mathematics: Dissertations, Theses, and Student Research

A linear extension of a partially ordered set is simply a total ordering of the poset that is consistent with the original ordering. The linear extension diameter is a measure of how different two linear extensions could be, that is, the number of pairs of elements that are ordered differently by the two extensions. In this dissertation, we calculate the linear extension diameter of grids. This also gives us a nice characterization of the linear extensions that are the farthest from each other, and allows us to conclude that grids are diametrally reversing.

A linear extension of a poset might …

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Department of Mathematics: Dissertations, Theses, and Student Research

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to …

College Of Engineering Senior Design Competition Spring 2018, University Of Nevada, Las Vegas

Fred and Harriet Cox Senior Design Competition Projects

Part of every UNLV engineering student’s academic experience, the senior design project stimulates engineering innovation and entrepreneurship. Each student in their senior year chooses, plans, designs, and prototypes a product in this required element of the curriculum. A capstone to the student’s educational career, the senior design project encourages the student to use everything learned in the engineering program to create a practical, real world solution to an engineering challenge. The senior design competition helps focus the senior students in increasing the quality and potential for commercial application for their design projects. Judges from local industry evaluate the projects on …

Roger Williams Park Edible Forest Garden, Mark S. Scialla

Senior Honors Projects

An edible forest garden is a low-maintenance system that uses edible native and regionally-adapted plants arranged in beneficial relationships to meet human, wildlife and ecosystem needs. The forest garden in Roger Williams Park will transform underutilized urban land into a highly productive parcel producing market-viable fruits, nuts, vegetables, medicine and fiber. Forest gardens mimic natural forest systems in architecture and complexity. The design follows ecological principles to create a system that promotes biodiversity and enhances the surrounding ecosystem. This project also demonstrates the potential to grow food and create land-based livelihoods in the city.

Located on the edge of a …

K-8 Preservice Teachers’ Inductive Reasoning In The Problem-Solving Contexts, Marta Magiera

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper reports the results from an exploratory study of K-8 pre-service teachers’ inductive reasoning. The analysis of 130 written solutions to seven tasks and 77 reflective journals completed by 20 pre-service teachers lead to descriptions of inductive reasoning processes, i.e. specializing, conjecturing, generalizing, and justifying, in the problem-solving contexts. The uncovered characterizations of the four inductive reasoning processes were further used to describe pathways of successful generalizations. The results highlight the importance of specializing and justifying in constructing powerful generalizations. Implications for teacher education are discussed.

The Mathematics Portfolio: An Alternative Tool To Evaluate Students’ Progress, Marla A. Sole

Publications and Research

This article describes the need for more thorough and varied forms of assessment to evaluate students’ level of understanding in mathematics. Portfolios are one type of assessment tool that, when added to a teacher’s repertoire can improve students’ comprehension and retention and enable students to monitor their own progress and to take more responsibility for their own learning. Portfolio assignments can also help students and teachers to detect and remedy weaknesses and misunderstandings and can increase students’ self-confidence in mathematics. This article discusses what a portfolio is, gives an example of a unit portfolio used in an undergraduate Finite Mathematics …

Systems Of Nonlinear Wave Equations With Damping And Supercritical Sources, Yanqiu Guo

Department of Mathematics: Dissertations, Theses, and Student Research

We consider the local and global well-posedness of the coupled nonlinear wave equations

u_tt – Δu + g₁(u_t) = f₁(u, v)

v_tt – Δv + g₂(v_t) = f₂(u, v);

in a bounded domain Ω subset of the real numbers (Rⁿ) with a nonlinear Robin boundary condition on u and a zero boundary conditions on v. The nonlinearities f₁(u, v) and f₂(u, v) are with supercritical exponents …

Combinatorics Using Computational Methods, Derrick Stolee

Department of Mathematics: Dissertations, Theses, and Student Research

Computational combinatorics involves combining pure mathematics, algorithms, and computational resources to solve problems in pure combinatorics. This thesis provides a theoretical framework for combinatorial search, which is then applied to several problems in combinatorics. Some results in space-bounded computational complexity are also presented.

Undergraduate Students' Self-Reported Use Of Mathematics Textbooks, Aaron Weinberg, Emilie Wiesner, Bret Benesh, Timothy Boester

Mathematics Faculty Publications

Textbooks play an important role in undergraduate mathematics courses and have the potential to impact student learning. However, there have been few studies that describe students' textbook use in detail. In this study, 1156 undergraduate students in introductory mathematics classes were surveyed, and asked to describe how they used their textbook. The results indicate that students tend to use examples, instead of the expository text, to build their mathematical understanding, which instructors may view as problematic. This way of using the textbook may be the result of the textbook structure itself, as well as students' beliefs about reading and the …

What Mathematics Do Elementary Education Teachers Need To Know?, Bret Benesh

Forum Lectures

Almost no one is happy with the state of America's mathematics education. I examine the mathematics textbooks elementary education majors commonly use in college to determine what effect this might be having on their future elementary school students. In this Thursday Forum, I report on what I found in these textbooks---and why I do not like them. I then supply an alternative vision that would better serve our elementary school students.

Following Student Gaze Patterns In Physical Science Lectures, David Rosengrant, Doug Hearrington, Kerriann Alvarado, Danielle Keeble

Faculty and Research Publications

This study investigates the gaze patterns of undergraduate college students attending a lecture-based physical science class to better understand the relationships between gaze and focus patterns and student attention during class. The investigators used a new eye-tracking product; Tobii Glasses. The glasses eliminate the need for subjects to focus on a computer screen or carry around a backpack-sized recording device, thus giving an investigator the ability to study a broader range of research questions. This investigation includes what students focus on in the classroom (i.e. demonstrations, instructor, notes, board work, and presentations) during a normal lecture, what diverts attention away …

Tackling Teaching: Understanding Commonalities Among Chemistry, Mathematics, And Physics Classroom Practices., Samuel Pazicni, Karen A. Marrongelle, Warren Christensen

Chemistry

Abstract:

Education research in chemistry, mathematics, and physics tends to focus on issues inherent to the discipline, most notably content. At this time, little literature evidence exists that documents fruitful collaborations between education specialists across the STEM disciplines. This work seeks to unite the disciplines by investigating a common task: teaching. This study explores how discipline-specific practices influence the common act of reformed teaching pedagogy with a focus on the use of inquiry. We seek to identify commonalities among classroom teaching practices in these disciplines and contribute to the development of analytical tools to study STEM teaching.

A College-Level Foundational Mathematics Course: Evaluation, Challenges, And Future Directions, Wes Maciejewski

Faculty Research, Scholarly, and Creative Activity

Recently in Ontario, Canada, the College Math Project brought to light startling data on the achievement of students in Ontario's College of Applied Arts and Technology System related to their performance in first-year mathematics courses: one-third of the students had failed their first-year mathematics course or were at risk of not completing their program because of their performance in such a course. Here I present the results of an attempt to address the findings of the College Math Project. A foundational mathematics course, based on the JUMP Math program, was designed and implemented at a college in Toronto, Ontario. Although …

Wind Power, Susn Reyes

Science and Engineering Saturday Seminars

No abstract provided.

Mathematical Competitions In Hungary: Promoting A Tradition Of Excellence & Creativity, Julianna Connelly Stockton

Mathematics Faculty Publications

Hungary has long been known for its outstanding production of mathematical talent. Extracurricular programs such as camps and competitions form a strong foundation within the Hungarian tradition. New types of competitions in recent years include team competitions, multiple choice competitions, and some exclusively for students who are not in a special mathematics class. This study explores some of the recent developments in Hungarian mathematics competitions and the potential implications these changes have for the very competition-driven system that currently exists. The founding of so many new competitions reflects a possible shift in the focus and purpose of competitions away from …

Biochemical Research On Mongolian Lichens, Bryophytes And Vascular Plants – In Memoriam, Dr. Siegfried Huneck (1928–2011), Hans D. Knapp

Erforschung biologischer Ressourcen der Mongolei / Exploration into the Biological Resources of Mongolia, ISSN 0440-1298

Dr. Siegfried Huneck, biochemist and lichenologist from the Institute for Biochemistry of Plants in Halle/Saale, died on September 9, 2011. He was a world wide leading expert on lichen substances. An obituary with curriculum vitae and a complete list of publications was published by Stordeur et al. (2011)

Elements Of Proximal Formative Assessment In Learners’ Discourse About Energy, Benedikt W. Harrer, Rachel E. Scherr, Michael C. Wittmann, Hunter G. Close, Brian W. Frank

Faculty Publications

Proximal formative assessment, the just-in-time elicitation of students' ideas that informs ongoing instruction, is usually associated with the instructor in a formal classroom setting. However, the elicitation, assessment, and subsequent instruction that characterize proximal formative assessment are also seen in discourse among peers. We present a case in which secondary teachers in a professional development course at SPU are discussing energy flow in refrigerators. In this episode, a peer is invited to share her thinking (elicitation). Her idea that refrigerators move heat from a relatively cold compartment to a hotter environment is inappropriately judged as incorrect (assessment). The "instruction" (peer …

Math Department Newsletter, 2011-2012 (Year In Review), Mathematics Department

Mathematics Newsletter

No abstract provided.

Learning Interdisciplinary Pedagogies, Alison J. Friedow, Erin E. Blankenship, Jennifer L. Green, Walter Stroup

Department of Statistics: Faculty Publications

Advocates of interdisciplinary teaching and learning in higher education suggest that interdisciplinary courses “promise a wide range of desirable educational outcomes for students” (Newell 1994: 35). These outcomes include enhanced affective and cognitive abilities, increased understanding of multiple perspectives, greater appreciation for ambiguity, and superior capacities for creative thinking, among others (35). Despite claims about the possibilities interdisciplinary learning offers, we have few examples of how faculty from different disciplines work together to create interdisciplinary classroom environments where such outcomes can occur. In short, more examples of how faculty from different disciplines actually develop, engage, and revise interdisciplinary pedagogies with …

Which Accelerates Faster A Falling Ball Or A Porsche?, James D. Rall, Wathiq Abdul-Razzaq

Faculty & Staff Scholarship

An introductory physics experiment has been developed to address the issues seen in conventional physics lab classes including assumption verification, technological dependencies, and real world motivation for the experiment. The experiment has little technology dependence and compares the acceleration due to gravity by using position versus time graphs and the kinematic equation. The students are then asked to compare the acceleration they found to the one of a Porsche car which they seem surprised when they learn about it. This experiment may contribute significantly to the understanding of the concept of acceleration and the appreciation for the force of gravity.

What Does It Take To Teach Nonmajors Effectively?, Feryal Alayont, Gizem Karaali, Lerna Pehlivan

Pomona Faculty Publications and Research

Most MAA members teach mathematics at the college level, and many often teach courses intended for nonmajors. Indeed this is one of the main responsibilities of a mathematics department: offering service courses for client departments and general education courses for nonmajors. The three of us have been thinking about the question of how to teach nonmajors successfully for a while now. Finally we decided on a time-tested method of figuring things out: if you don't know what to do, ask the experts. We organized a panel titled "Effective Strategies for Teaching Classes for Nonmajors" for MAA MathFest 2012 and invited …