Mathematics Commons^™

The Aerodynamics Of Frisbee Flight, Kathleen Baumback

Undergraduate Journal of Mathematical Modeling: One + Two

This project will describe the physics of a common Frisbee in flight. The aerodynamic forces acting on the Frisbee are lift and drag, with lift being explained by Bernoulli‘s equation and drag by the Prandtl relationship. Using V. R. Morrison‘s model for the 2-dimensional trajectory of a Frisbee, equations for the x- and y- components of the Frisbee‘s motion were written in Microsoft Excel and the path of the Frisbee was illustrated. Variables such as angle of attack, area, and attack velocity were altered to see their effect on the Frisbee‘s path and to speculate on ways to achieve maximum …

Embedded Systems - Missile Detection/Interception, Luis Cintron

Undergraduate Journal of Mathematical Modeling: One + Two

Missile defense systems are often related to major military resources aimed at shielding a specific region from incoming attacks. They are intended to detect, track, intercept, and destruct incoming enemy missiles. These systems vary in cost, efficiency, dependability, and technology. In present times, the possession of these types of systems is associated with large capacity military countries. Demonstrated here are the mathematical techniques behind missile systems which calculate trajectories of incoming missiles and potential intercept positions after initial missile detection. This procedure involved the use of vector-valued functions, systems of equations, and knowledge of projectile motion concepts.

The Sir Epidemiology Model In Predicting Herd Immunity, Joanna Nicho

Undergraduate Journal of Mathematical Modeling: One + Two

The Simple Epidemic Model uses three states to describe the spread of an infection: the susceptible (S), the infected (I), and the recovered (R). This model follows the trend of an infection over time and can predict whether an infection will spread. Using this model, epidemiologists may calculate the percentage of the population that needs to be vaccinated in order to provide a population immunity from a disease. This study will compare the vaccination percentage required for herd immunity to measles, mumps, and rubella against the current percentage of vaccinated individuals.

Locomotion Of A Running Quadruped Robotic System, Bradley Savon

Undergraduate Journal of Mathematical Modeling: One + Two

Very little is known about the locomotion of quadruped robotic systems. In Latin, the term quadruped means 'having four feet'. The robotic system analyzed in this project was a software simulation program modeled after a horse. Simulation data was recorded to resolve the relationship between foot position and impulses required to accelerate or to decelerate the system while trotting. These sets of data were then analyzed in MATLAB to produce graphical representations which allowed for a better understanding of the robot's motion in the simulation environment. A function was fit to the graph of discrete data values measured in the …

Pollination Of A Canary Tree Flower, Abbie O'Hern Weeks

Undergraduate Journal of Mathematical Modeling: One + Two

Pollination is an essential part of the life cycle of flowering plants. We perform an experiment to determine how long a canary tree flower is accessible to pollinating insects so that fertilization can take place. We conducted an observational study where we measured the size of the same flower and charted its growth each day. With the observational data we constructed a scatter plot and from the graph we fit a cubic function to the data. We conclude that in the lifespan of a canary tree flower, pollination begins at 5 1/2 days and ends approximately 9 days later.

Dosimetry Calculations Of Radiopharmaceuticals, Kelbe Jahnke

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to determine the absorbed dose of radiation to a patient using ^99mTc-MAA as a tracer for a lung scan using the MIRD formula accounting only for the radiation dose contributed by the target organ. The radiation dose for other organs to the target organ is considered negligible as the uptake of ^99mTc-MAA from other organs is less than 1%. In addition to calculating the absorbed dose of radiation, the initial dose rate was also calculated by back solving to determine the total mass of the lungs. The radiation dose to the patient …

Maximum Power From A Solar Panel, Michael Miller

Undergraduate Journal of Mathematical Modeling: One + Two

Solar energy has become a promising alternative to conventional fossil fuel sources. Solar panels are used to collect solar radiation and convert it into electricity. One of the techniques used to maximize the effectiveness of this energy alternative is to maximize the power output of the solar collector. In this project the maximum power is calculated by determining the voltage and the current of maximum power. These quantities are determined by finding the maximum value for the equation for power using differentiation. After the maximum values are found for each time of day, each individual quantity, voltage of maximum power, …

Escape Velocity, Nikola Vlacic

Undergraduate Journal of Mathematical Modeling: One + Two

In this project, we investigated if it is feasible for a single staged rocket with constant thrust to attain escape velocity. We derived an equation for the velocity and position of a single staged rocket that launches vertically. From this equation, we determined if an ideal model of a rocket is able to reach escape velocity.

Parts Of The Whole: Observing The State Of The System, Dorothy Wallace

Numeracy

This column draws on the approach of statistician J. Edwards Deming to analyze sources and consequences of variation in an education system. Educational systems are not immune from the effects of poor statistical control, which makes it difficult for teachers to teach effectively and for managers such as principals to improve on school performance. It is also argued that the need for statistical control in these areas is in tension, if not outright conflict, with our goals for educating students.

Two Popular Books For Quantitative Literacy: What The Numbers Say, And The Numbers Game, Robert G. Root

Numeracy

Niederman, Derrick, and Boyum, David. What the Numbers Say: A Field Guide to Mastering Our Numerical World. (New York: Broadway Books/Random House, 2003). 288 pp. Hardcover, ISBN 978-0-7679-0998-3. Paperback, 978-0-7679-0999-0. Available as an eBook.

Blastland, Michael, and Dilnot, Andrew. The Numbers Game: The Commonsense Guide to Understanding Numbers in the News, in Politics and in Life. (New York: Gotham Books/Penguin, 2009). 192 pp. Hardcover, ISBN 978-1-5924-0423-0. Paperback, ISBN 978-1-5924-0485-8. Available as an eBook.

Popular books on quantitative literacy need to be easy to read, reasonably comprehensive in scope, and include examples that are thought-provoking and memorable. In contrast …

Numeracy: Open-Access Publishing To Reduce The Cost Of Scholarly Journals, Todd A. Chavez

Numeracy

Each fiscal year, as academic librarians throughout the United States prepare materials budgets, a national “groan” ensues. Regardless of their format (i.e. print or digital), serial subscription costs are escalating, in the process impacting the role of the library in advancing scholarly communication . This paper examines some of the economic issues concerning open-access (OA) journal publishing. The importance of quantitative literacy is suggested for librarians and academics seeking a better understanding of alternatives to traditional journal subscription models and to anyone considering ventures into OA publishing. Quantitative literacy is essential for managing alternatives to the rising cost of scholarly …

College Algebra In Context: A Project Incorporating Social Issues, Michael T. Catalano

Numeracy

This paper discusses the development of an innovative college algebra text designed for use in a data-driven, activity-oriented college algebra course, incorporating realistic problem situations emphasizing social and economic issues, including hunger and poverty, energy, and the environment. The course incorporates quantitative literacy themes, is informed by existing college algebra texts within the college algebra reform movement, and implements a collaborative pedagogical approach intended to provide future K-12 teachers an alternative model for the teaching of mathematics. The paper contains a short history of the project development phase, supported by an NSF grant (DUE #0442979), as well as the perceived …

An Activity Promoting The Practice Of Quantitative Literacy For Pre– And In–Service Teachers Of Mathematics And Science, Timothy L. Sorey, Teri Willard, Duane Sholz

Numeracy

The purpose of this article is to describe a hands-on, laboratory activity that provided pre-service teachers in mathematics and science methods courses, and also some in-service mathematics teachers, with the opportunity to exercise quantitative literacy (QL) skills. The focus of the activity is electrical resistance, more particularly the resistance (in ohms) that is painted on small resistors by the use of color-coded bands, one of which is a band for % error. The activity consists of four parts. In the first, student teams familiarize themselves with the code, measure the ohmage of resistors for which the codes are visible, and …

Are Statistics Labs Worth The Effort?--Comparison Of Introductory Statistics Courses Using Different Teaching Methods, Jose H. Guardiola, Nadina Duran-Hutchings, Hassan Elsalloukh

Numeracy

This paper compares the academic performance of students in three similar elementary statistics courses taught by the same instructor, but with the lab component differing among the three. One course is traditionally taught without a lab component; the second with a lab component using scenarios and an extensive use of technology, but without explicit coordination between lab and lecture; and the third using a lab component with an extensive use of technology that carefully coordinates the lab with the lecture. Extensive use of technology means, in this context, using Minitab software in the lab section, doing homework and quizzes using …

Envisioning A Quantitative Studies Center: A Liberal Arts Perspective, Gizem Karaali, Philip I. Choi, Sara Owsley Sood, Eric B. Grosfils

Numeracy

Several academic institutions are searching for ways to help students develop their quantitative reasoning abilities and become more adept at higher-level tasks that involve quantitative skills. In this note we study the particular way Pomona College has framed this issue within its own context and what it plans to do about it. To this end we describe our efforts as members of a campus-wide committee that was assigned the duty of investigating the feasibility of founding a quantitative studies center on our campus. These efforts involved analysis of data collected through a faculty questionnaire, discipline-specific input obtained from each departmental …

A Rubric For Assessing Quantitative Reasoning In Written Arguments, Nathan D. Grawe, Neil S. Lutsky, Christopher J. Tassava

Numeracy

This paper introduces a rubric for assessing QR in student papers and analyzes the inter-rater reliability of the instrument based on a reading session involving 11 participants. Despite the disciplinary diversity of the group (which included a faculty member from the arts and literature, two staff members, and representatives from five natural and social science departments), the rubric produced reliable measures of QR use and proficiency in a sample of student papers. Readers agreed on the relevance and extent of QR in 75.0 and 81.9 percent of cases respectively (corresponding to Cohen’s κ= 0.611 and 0.693). A four-category measure of …

Confessions Of A Weak Tie, Joel Best

Numeracy

No abstract provided.

Five Thousand Downloads, H L Vacher

Numeracy

No abstract provided.

Parts Of The Whole: Approaching Education As A System, Dorothy Wallace

Numeracy

An educational system is a highly coupled complex system of inputs, outputs, sensors and actuators. Using an engineering perspective, this column begins the process of naming and categorizing parts of the system. It then focuses on teachers as one part of a large system, and analyzes the forces that influence how teachers work, and that draw or repel individuals to a teaching career. The growing shortage of qualified teachers can be explained by properties of the system as a whole that determine the context in which teachers do their job.

Review Of Super Crunchers By Ian Ayers, Eric Gaze

Numeracy

Ayers, I. Super Crunchers: Why Thinking-by-Numbers Is the New Way to be Smart. (Bantam Dell Publishing Group, 2007). 272 pp. Hard cover $25 ISBN 978-0-553-80540-6.

Super Crunchers tells the story of how analyzing data is changing the ways in which decisions are made. We in the National Numeracy Network make a case for the importance of quantitative literacy by referring to how much quantitative information is now available to each of us: “a world awash in numbers.” Ian Ayres zeroes in on the people who are making a living crunching all of these data. From the seemingly innocuous (how …

Review Of Stat-Spotting: A Field Guide To Identifying Dubious Data By Joel Best, Joe Swingle

Numeracy

Best, Joel. Stat-Spotting: A Field Guide to Identifying Dubious Data. (Berkeley: University of California Press, 2008) 144 pp. $19.95. ISBN 1-978-0-520-25746-7.

Stat-Spotting is a practical, do-it-yourself manual for detecting questionable claims reported in the media. Using examples drawn mostly from mass media sources, Stat-Spotting provides readers with a number of useful tips for identifying potentially problematic statistics. The author’s skillful analyses and explanations presented in clear and concise prose make Stat-Spotting an ideal guide for anyone who reads a newspaper, watches television, or surfs the Web. In short, everyone.

Review Of Calculation Vs. Context: Quantitative Literacy And Its Implications For Teacher Education By Bernard L. Madison And Lynn Arthur Steen (Editors), Maura B. Mast

Numeracy

Madison, Bernard L. and Steen, Lynn Arthur (Eds.). Calculation vs. Context: Quantitative Literacy and Its Implications for Teacher Education. (Washington, DC: Mathematical Association of America, 2009). 197 pp. Softcover. ISBN 978-0-88385-908-7. Available free on the MAA website at http://www.maa.org/ql/calcvscontext.html

The papers in Calculation vs. Context discuss the role of quantitative literacy in the K-12 curriculum and in teacher education. The papers present a varied set of perspectives and address three themes: the changing environment of education in American society; the challenges, and the necessity, of preparing teachers to teach quantitative literacy and of including quantitative literacy in the K-12 education; …

Engaging Math-Avoidant College Students, M. Paul Latiolais, Wendi Laurence

Numeracy

This paper is an informal, personal account of how we, as two college teachers, became interested in math anxiety, decided to explore it amongst students at our institution in order to inform our teaching, and became convinced that the massive problem is math avoidance. We tried discussion groups, but few students attended, although those that did made useful suggestions. Thus informed, we designed an innovative course, Confronting College Mathematics as a Humanities course with the possibility of credit toward the math requirement, but it was undersubscribed in its first offering and had to be canceled. How can we get college …

Measuring Resource Inequality: The Gini Coefficient, Michael T. Catalano, Tanya L. Leise, Thomas J. Pfaff

Numeracy

This paper stems from work done by the authors at the Mathematics for Social Justice Workshop held in June of 2007 at Middlebury College. We provide a description of the Gini coefficient and some discussion of how it can be used to promote quantitative literacy skills in mathematics courses. The Gini Coefficient was introduced in 1921 by Italian statistician Corrado Gini as a measure of inequality. It is defined as twice the area between two curves. One, the Lorenz curve for a given population with respect to a given resource, represents the cumulative percentage of the resource as a function …

Quantitative Literacy Assessments: An Introduction To Testing Tests, Dorothy Wallace, Kim Rheinlander, Steven Woloshin, Lisa Schwartz

Numeracy

This paper describes how professional evaluators construct assessment instruments that work properly to measure the right thing. Constructing an assessment tool begins with getting feedback from relevant experts on the content of questions. The tool is developed and refined through comparison with existing instruments, focus groups and cognitive interviews. The final instrument is formally tested for content validity, usability, reliability and construct validity through a variety of statistical measures. This process of construction is illustrated by two examples relevant to quantitative literacy: the Medical Data Interpretation Test and the Math Attitudes Survey.

Integration With Writing Programs: A Strategy For Quantitative Reasoning Program Development, Nathan D. Grawe, Carol A. Rutz

Numeracy

As an inherently interdisciplinary endeavor, quantitative reasoning (QR) risks falling through the cracks between the traditional “silos” of higher education. This article describes one strategy for developing a truly cross-campus QR initiative: leverage the existing structures of campus writing programs by placing QR in the context of argument. We first describe the integration of Carleton College’s Quantitative Inquiry, Reasoning, and Knowledge initiative with the Writing Program. Based on our experience, we argue that such an approach leads to four benefits: it reflects important aspects of QR often overlooked by other approaches; it defuses the commonly raised objection that QR is …

Assessing Quantitative Reasoning, Corrine H. Taylor

Numeracy

No abstract provided.

Parts Of The Whole: Is Everything Equally Important?, Dorothy Wallace

Numeracy

Two strategies are proposed for sorting out priorities and goals in education. At the college level the column argues that goals, and therefore requirements, should be set based on the desired knowledge base of the entire population rather than the individual. At the scale of a single K-12 classroom the column argues that priority be given to content requiring most instructor intervention, describing how the structure of class time and school activities would change as a result. Implementation of these strategies would lead to more efficient use of teacher’s time and effort, better allocation of systemic resources, and clarity of …

Review Of The Chicago Guide To Writing About Numbers By Jane E. Miller, Neil Lutsky

Numeracy

Miller, J. E. 2004. The Chicago Guide to Writing about Numbers. Chicago, IL: University of Chicago Press. 304 pp. Cloth $45 ISBN: 9780226526300, Softcover $17. ISBN: 9780226526317.

The Chicago Guide to Writing about Numbers is a reference work suitable for anyone interested in understanding, using, or promoting quantitative thinking. Its primary aim is to identify and illustrate ways in which information associated with numbers can be conveyed most effectively given a particular communication purpose and context. The book is directed at writers who incorporate numbers in verbal or visual displays in documents, in oral presentations, or on the Web. The …

Quantitative Literacy On The Web Of Science, 2 – Mining The Health Numeracy Literature For Assessment Items, H L. Vacher, Todd Chavez

Numeracy

A topic search of the Web of Science (WoS) database using the term “numeracy” produced a bibliography of 293 articles, reviews and editorial commentaries (Oct 2008). The citation graph of the bibliography clearly identifies five benchmark papers (1995-2001), four of which developed numeracy assessment instruments. Starting with the 80 papers that cite these benchmarks, we identified a set of 25 papers (1995-2008) in which the medical research community reports the development and/or application of health-numeracy assessments. In all we found 10 assessment instruments from which we have compiled a total of 48 assessment items. There are both general and context-specific …