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Are We At A Watershed Moment For The Quantitative Literacy Movement?: Review Of Shifting Context, Stable Core: Advancing Quantitative Literacy In Higher Education, By Luke Tunstall, Gizem Karaali, And Victor Piercey, Eds., Maura Mast

Numeracy

Luke Tunstall, Gizem Karaali, and Victor Piercey, eds. 2019. Shifting Concepts, Stable Core: Advancing Quantitative Literacy in Higher Education. Math Notes 88. (Mathematics Association of America, MAA Press). Print ISBN 978-0-88385-198-2. Electronic ISBN 978-1-61444-324-7.

The thematic approach of the edited MAA Notes volume Shifting Contexts, Stable Core: Advancing Quantitative Literacy in Higher Education is that the “construct” of quantitative literacy is now fairly stable, but the contexts in which quantitative literacy is taught (and practiced) continue to change. Several chapters give the reader much to consider regarding what constitutes the foundation of this stable core and, relatedly, how quantitative …

Taking Multiple Regression Analysis To Task: A Review Of Mindware: Tools For Smart Thinking, By Richard Nisbett (2015), Jason Makansi

Numeracy

Richard Nisbett. 2015. Mindware: Tools for Smart Thinking.(New York, NY: Farrar, Strauss, and Giroux). 336 pp. ISBN: 9780374536244

Nisbett, a psychologist, may not achieve his stated goal of teaching readers to “effortlessly” extend their common sense when it comes to quantitative analysis applied to everyday issues, but his critique of multiple regression analysis (MRA) in the middle chapters of Mindware is worth attention from, and contemplation by, the QL/QR and Numeracy community. While in at least one other source, Nisbett’s critique has been called a “crusade” against MRA, what he really advocates is that it not be used as …

Quantitative Literacy And The Mathematical Association Of America In The 2000’S: Ql Subcommittee Of Cupm , Sigmaa Ql, And Maa Notes #70, Rick Gillman

Numeracy

This Roots and Seeds article is a partial history of the quantitative literacy movement in the Mathematical Association of America in the first decade of the 21st century. It focuses on the inclusion of QL in the MAA Committee on the Undergraduate Program in Mathematics’ CUPM Curriculum Guidelines (2004), the creation of the special interest group for MAA members (SIGMAA QL, 2004), and the work of that body in subsequent years, in particular, the MAA Notes #70, Current Practices in Quantitative Literacy (2006). I discuss some issues that were problematic in the QL movement in the MAA in those years …

The Ultimatum Game: An Introduction To Quantitative Literacy In A Social Justice Context, Robert G. Root

Numeracy

The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social sciences to demonstrate the human propensity for costly punishment in response to inequitable treatment. The game serves to provide quantitative evidence for a diversity of fairness norms across cultures. The play of the game and its interpretation offer nuanced views of the nature and importance of quantitative literacy. Its use in a writing seminar connecting quantitative literacy and social justice is described.

Roots And Seeds: Finding Our Place In The Social Practice Nexus That Is Quantitative Literacy, H. L. Vacher, Nathan D. Grawe

Numeracy

The purpose of our new Roots and Seeds feature is to provide an open-access space to archive first-hand accounts of QL activities that have preceded our journal (2008). The first two contributions in the collection appeared last issue: Linda Sons on the making of what has come to be known as the 1994 Sons Report (Mathematics Association of America), and Dorothy Wallace on her path to the Quantitative Literacy Design Team for Mathematics and Democracy (2001), and the questions that bedeviled them then – and us now. In this issue, we get Rick Gillman’s account of how the committee that …

Hierarchical Self-Assembly And Substitution Rules, Daniel Alejandro Cruz

USF Tampa Graduate Theses and Dissertations

A set of elementary building blocks undergoes self-assembly if local interactions govern how this set forms intricate structures. Self-assembly has been widely observed in nature, ranging from the field of crystallography to the study of viruses and multicellular organisms. A natural question is whether a model of self-assembly can capture the hierarchical growth seen in nature or in other fields of mathematics. In this work, we consider hierarchical growth in substitution rules; informally, a substitution rule describes the iterated process by which the polygons of a given set are individually enlarged and dissected. We develop the Polygonal Two-Handed Assembly Model …

Reconstruction Of Radar Images By Using Spherical Mean And Regular Radon Transforms, Ozan Pirbudak

USF Tampa Graduate Theses and Dissertations

The goal of this study is the recovery of functions and finite parametric distributions from their spherical means over spheres and designing a general formula or algorithm for the reconstruction of a function f via its spherical mean transform. The theoretical study is and supported with a numerical implementation based on radar data. In this study, we approach the reconstruction problem in two different way. The first one is to show how the reconstruction problem could be converted to a Prony-type system of equations. After solving this Prony-type system of equations, one can extract the parameters that describe the corresponding …

Power Graphs Of Quasigroups, Dayvon L. Walker

USF Tampa Graduate Theses and Dissertations

We investigate power graphs of quasigroups. The power graph of a quasigroup takes the elements of the quasigroup as its vertices, and there is an edge from one element to a second distinct element when the second is a left power of the first. We first compute the power graphs of small quasigroups (up to four elements). Next we describe quasigroups whose power graphs are directed paths, directed cycles, in-stars, out-stars, and empty. We do so by specifying partial Cayley tables, which cannot always be completed in small examples. We then consider sinks in the power graph of a quasigroup, …

An Optimal Medium-Strength Regularity Algorithm For 3-Uniform Hypergraphs, John Theado

USF Tampa Graduate Theses and Dissertations

Szemere´di’s Regularity Lemma [32, 33] is an important tool in combinatorics, with numerous appli- cations in combinatorial number theory, discrete geometry, extremal graph theory, and theoretical computer science.

The Regularity Lemma hinges on the following concepts. Let G = (V, E) be a graph and let ∅ /= X, Y ⊂ V be a pair of disjoint vertex subsets. We define the density of the pair (X, Y ) by d_G(X, Y ) = |E[X, Y ]|/(|X||Y |) where E[X, Y ] denotes the …

Illuminating Changes In Preservice Teachers’ Perceptions About Teaching Elementary Mathematicsin An Introductory Methods Course, Elaine Cerrato

USF Tampa Graduate Theses and Dissertations

Producing highly skilled elementary mathematics teachers capable of facilitating mathematics learning in ways aligned with The Principles and Standards for School Mathematics (NCTM, 2000) and the Common Core State Standards for Mathematics (CCSSM), is a common objective of teacher preparation programs (National Governors Association & Chief Council of State School Officers, 2010). After decades of effort, Brown (2003) argues, teachers continue to teach in the way they were taught; thus, they disregard mathematics standards. As Abell, Appleton, and Hanuscin (2010) note, students’ preexisting ideas relevant to the nature of learning and teaching stem from experiences in their schooling, life, and …

The Systems Of Post And Post Algebras: A Demonstration Of An Obvious Fact, Daviel Leyva

USF Tampa Graduate Theses and Dissertations

In 1942, Paul C. Rosenbloom put out a definition of a Post algebra after Emil L. Post published a collection of systems of many–valued logic. Post algebras became easier to handle following George Epstein’s alternative definition. As conceived by Rosenbloom, Post algebras were meant to capture the algebraic properties of Post’s systems; this fact was not verified by Rosenbloom nor Epstein and has been assumed by others in the field. In this thesis, the long–awaited demonstration of this oft–asserted assertion is given.

After an elemental history of many–valued logic and a review of basic Classical Propositional Logic, the systems given …

Analyses Of Unorthodox Overlapping Gene Segments In Oxytricha Trifallax, Shannon Stich

USF Tampa Graduate Theses and Dissertations

A ciliate is a phylum of protozoa that has two types of nuclei, macronuclei and micronuclei. There may be more than one of each type of nucleus in the organism [1]. The macronucleus is the structure where protein synthesis and cell metabolism occur [1]. The micronucleus stores genetic information and is mobilized during a sexual reproduction process called conjugation [1]. The somatic macronucleus (MAC) is developed from the germ-line micronucleus (MIC) through genome rearrangement during a sexual reproduction process called conjugation [6, 8]. Segments of the MIC that form the MAC during conjugation are called macronuclear destined sequences (MDSs) [8]. …

Calculus Application To Topographic Mapping, Veronica Zapata

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of the paper is to find the volume of water in a ditch. An example image of ditch is given in Appendix C. The first act that before any calculation can be performed is to record the field work. Once at the property the ditch must be identified. Three points of elevations per section should be measured by the surveyor; one point is at the center of the ditch (the lowest point) and the two ones are at the ends (the highest points). The sections are detailed in Appendix A. Using the elevation points from the property, we …

Using The Sir Epidemiology Model With Vector Transmission To Predict The Effectiveness Of A Viral Marketing Campaign And The Spread Of Product Adoption, Michael Freed

Undergraduate Journal of Mathematical Modeling: One + Two

Stevelab, LLC is working on an app that will be released within the year. For planning purposes, the company needs to be able to predict how well the app will spread in its initial phase. Because the pilot launch will be limited to Hillsborough County, FL, there is a limited population. The marketing strategy is to sell the application to places where people gather to mingle and socialize, with a particular focus to the bar scene. Customers of the bar can use the app for free. In addition to our direct sales efforts, we can expect the bar owners to …

Equilibrium Ratio Of Polymers To Monomers In Cooperative Polymerization Of Amyloid-Β Protein, Tina Gagliardo

Undergraduate Journal of Mathematical Modeling: One + Two

Amyloid-β42 is a protein polymer that catalyzes the formation of pathogenic amyloid plaques that are a prominent feature in the brain tissue of patients who suffer from Alzheimer’s disease. Aβ42 polymerizes via a nucleation-elongation mechanism; several monomers must first congregate into a nucleus before it can elongate into a polymer. The nucleation step is energetically unfavorable since a nucleus smaller than 7 to 8 monomeric units is unstable, therefore the pieces tend to dissociate faster than they can bond together. A solution of Aβ42 will consist of 100% monomers and oligomers smaller than the nucleus when the total concentration is …

Calculating Water Wavelength Using Dispersion Relation And Approximation, Chantelle Lee

Undergraduate Journal of Mathematical Modeling: One + Two

The dispersion relation equation is used to directly compute wave number and wave length to compliment water wave pressure sensor readings. Waves are measured to help coastal engineering to better mitigate coastal infrastructures. Various given wave periods and water depths are used to show how the dispersion relation equation could compute wave length. Also, shallow and deep-water approximations are formulated from the dispersion relation equation and the results are compared.

Effects Of Change In Tire Pressure Upon Efficiency Of A Vehicle, Haider Ali Khan

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this paper is to compare the difference in the efficiency of acceleration, of a 2018 Audi A8, in two distinct scenarios where the tire pressure is kept at a maximum and partial level. The approach towards solving the issue is multi-faceted, the efficiency is dependent on the difference in the time it takes for the car to accelerate, thus to obtain the elapsed time, the foundational basis is set by the relations between Torque/Force, and RPM/Speed of the vehicle. All the calculations are completed by using the data extracted from the car’s specifications set (Automobile Catalog). Newton’s …

Population And Mortality Predictions Of The Florida Manatee – Ten Year Watercraft Mortality, Dylan Lehigh

Undergraduate Journal of Mathematical Modeling: One + Two

The West Indian Manatee is currently listed as a threatened species by the U.S Fish and Wildlife service. A threatened designation means population levels still are at risk of becoming endangered again in the foreseeable future. This project seeks to forecast how many manatees would perish from watercraft strikes (the greatest threat to their survival) based upon the most current method utilized for projecting manatee population growth.

The latest version, known as the Core Biological Model (version 6) or CBMv6, was employed along with the most current manatee population data, which was provided by Dr. Jeffrey A. Hostetler. Dr. Hostetler …

A Mathematical Model For The Upper Limits Of Thyroid Volume In Adolescents, Jacob Treanor

Undergraduate Journal of Mathematical Modeling: One + Two

This paper describes a mathematical model that relates age to the volume of the thyroid gland, given in milliliters, of adolescents based on data from a 1997 study by the World Health Organization (W.H.O.) (World Health Organization, 1997). Using the upper limit per age group provided by the data, a model was constructed through integration of the second derivative of the data for males and females, ages 6-15. It was concluded that the upper limit for the thyroid volume could be expressed by one of two second order polynomial equations, depending on gender, with any values significantly larger than those …

Locating Centers Of Mass With Image Processing, Amina Gahramanova

Undergraduate Journal of Mathematical Modeling: One + Two

The center of mass of a rigid body is a unique point that represents the mean position of all matter that composes it. Allowing representing complex bodies as a single point, this concept is underlying the basis of all essential mechanical calculations, and is therefore a crucial consideration in engineering. The paper shows how to devise a fast and convenient way of locating the centroid of planar objects of different shapes. For several shapes that can be represented as regions bounded by graphs of functions, this point can be found by using integral calculus. However, solving for the center of …

Using Moment Of Inertia And Observable Planetary Features To Approximate The Two-Layer Structure Of Earth, Jupiter, And Neptune, Selena Kimball

Undergraduate Journal of Mathematical Modeling: One + Two

This paper examines the interior structure and composition of Earth, Jupiter, and Neptune by using moment of inertia (MoI) and observable planetary features to create approximate two-layer interior structure models. The moment inertia of a uniform sphere, hollow sphere, and a sphere with a shell are derived to calculate the radius and density variables that identify the relationship between the different radii and densities of the two layers. A two-layer model of the planet’s interior can then be formulated based on the radius, density, known MoI factor and the surface density or the assumed composition density of the planet. The …

Using Matrices To Balance Chemical Reactions And Modeling The Implications Of A Balanced Reaction, Emilee Barrett

Undergraduate Journal of Mathematical Modeling: One + Two

This paper explores an alternative way to balancing equations of chemical reactions and understanding why it is necessary to use balanced equations in science. To balance a chemical equation chemists often guess the coefficients that would balance the equation and check if it works. An alternative method is to use matrices to determine the coefficients of a balanced chemical reaction through solving a system of linear Diophantine equations. After determining the coefficients, a balanced chemical reaction can be formed and used to model how the different coefficients impact the overall reaction. Then it can lead to larger applications within the …

Bicycle Speed Through Different Gears With Drag, Ian Larson

Undergraduate Journal of Mathematical Modeling: One + Two

When riding a bicycle, the rider experiences two forces: the force of the road that acts upon the rear wheel while pedaling, and an opposing force that exerts on the bicycle/cyclist, called aerodynamic drag force (drag). When adjusting Newton’s equation in the second law of motion, the instantaneous change in velocity is equal to the object’s net force divided by its mass. The corresponding differential equation has not been solved analytically. With the bicycle starting at rest at t=0, we solved the equation numerically for any time t by using what is known as Euler’s Method to plot the …

Integrating The Equation Of Hydrostatics For Groundwater Under Non-Isothermal Conditions, Megan A. Levine

Undergraduate Journal of Mathematical Modeling: One + Two

Groundwater is an important area of study for several scientific fields and is relevant to many problems in our everyday life. One way the study of groundwater has become different in this age of technology is through modeling. Modeling is used in numerous fields to visualize complex problems and view inaccessible areas, such as under the Earth. An essential part of groundwater modeling is to know water pressure at any depth underground. The difficulty in calculating this is that there are several variables that affect water pressure, all of which are affected by one another and all are calculated by …

Calculating The Electromotive Force Through A Loop, Esteban Leal

Undergraduate Journal of Mathematical Modeling: One + Two

This is a short article which utilizes the equations of Faraday’s law, Ampere’s law, and Ohm’s law. We manipulate the formulas to solve a practical application in which the electromotive force must be calculated. With the successful calculation of the electromotive force, we can use this technique in larger applications.

Acid-Base Titration, David Pierre

Undergraduate Journal of Mathematical Modeling: One + Two

Titration is an analytical method used in biomedical sciences and analytical chemistry laboratories to determine the quantity or the concentration of a known or unknown substance. There are many kinds of titrations, but this investigation is fundamentally based on acid-base titration, in which the development of a mathematical titration model is explained and determined. In a titration experiment, the concentration and volume of the base added is proportionally equal to those of the acid. The concentration of the substance is determined by following this principle. Moreover, these calculations are usually approximate. Thus, the construction of a titration model is done …

The Sons Report (1989-1994, Mathematical Association Of America): The Way It Was, Linda R. Sons

Numeracy

Recollections and commentary by Linda R. Sons on a 1994 national report entitled Quantitative Reasoning for College Graduates: A Complement to the Standards. Professor Sons chaired the committee which wrote the report and championed its use.

This paper traces the development of the 1994 MAA report Quantitative Reasoning for College Graduates: A Complement to the Standards--a report which is still surprisingly relevant. The paper highlights some major parts of the report, describing the context in which its conclusions were made. Additionally, it challenges and encourages those continuing the quest for QL in the nation by noting progress made …

Three Formative Questions In The Quantitative Literacy Movement, Dorothy Wallace

Numeracy

In this essay we remember early discussions attempting to answer three questions that played a formative role in our understanding of and approach to numeracy, quantitative literacy, and quantitative reasoning: (1) What is numeracy? (2) Should the QL movement promote any specific kind of pedagogy? (3) What organizational structure will best support QL?

As the QL movement has progressed, these three questions continue to be difficult to answer. As a result, they have been useful formative guides for institutions and organizations seeking to improve the quantitative reasoning of students. Now that the quantitative literacy movement has a firmer standing in …

The Second Decade Of Numeracy: Entering The Seas Of Literacy, H. L. Vacher

Numeracy

This multipurpose editorial explores and tries to count the many types of literacy that are referred to by name in Wikipedia and Numeracy. Wikipedia’s Category:Literacy page identifies 44 kinds of literacy that are the subject of articles, ranging from numeracy and graphicacy to braille literacy and diaspora literacy. In addition, searching Google finds more than 30 adjective-literacy or noun-literacy collocations, including quantitative literacy, adult literacy, and document literacy, that do not have Wikipedia pages of their own but are mentioned on other Wikipedia pages. The sum puts this modest literacy count in line with the more than 70 bodies …

Developing Mathematics Teachers’ Attention To Quantitative Reasoning In Task Design: A Modeling Approach, David Glassmeyer

Numeracy

This study examines how a models-and-modeling perspective affected teachers' attention to quantitative reasoning in task design. A Model-Eliciting Activity (MEA) was implemented with 21 teachers over four weeks, challenging teachers to design a quantitative reasoning task for their students. Teachers’ initial quantitative reasoning tasks did not incorporate quantities or quantitative relationships, two essential components of quantitative reasoning. As teachers revised their tasks through the MEA, most teachers began attending to these components. This article details how a modeling approach to teacher education provided a method to describe and support teachers to incorporate quantitative reasoning in their classroom tasks, though attending …