Physical Sciences and Mathematics Commons^™

An Analysis Of Preservice Elementary Teachers’ Professional Noticing Skills In A Mathematics Education Setting, Liza Bondurant, Lisa Poling, Diana Moss

Journal of Practitioner Research

Prospective elementary mathematics teachers (PTs) were asked to analyze 28 videos of cognitive interviews. The purpose of this study was to determine if experiences analyzing videos would lead to improvements in PTs’ professional noticing skills. Using a coding schema that reflected three levels of understanding (periphery, transitional, and accomplished), a frequency table was constructed that allowed PTs’ use and understanding of a noticing framework to be analyzed. Findings indicate that experiences analyzing videos leads to improvements in PTs’ professional noticing skills.

Development And Assessment Of A Continuing Education Unit In Quantitative Literacy For High School Stem Teachers, Craig P. Mcclure

Numeracy

Influencing the teaching of quantitative literacy at all levels of education can be difficult due to the many demands placed on educators. In a continuing education course, public high school science teachers participated in a pilot study of a program on quantitative literacy, involving defining quantitative literacy, how it is beneficial to students, examples of quantitative literacy education, and how it may be supported in the science classroom. Surveys administered before and after the unit indicate an improvement in the teachers’ understanding of quantitative literacy, and a follow-up survey indicates that the unit impacted classroom practice. Results support the conclusion …

Art, Artfulness, Or Artifice?: A Review Of The Art Of Statistics: How To Learn From Data, By David Spiegelhalter, Jason Makansi

Numeracy

David Spiegelhalter. 2019. The Art of Statistics: How to Learn From Data. (London: The Penguin Group). 444 pp. ISBN 978-1541618510

The author successfully eases the reader away from the rigor of statistical methods and calculations and into the realm of statistical thinking. Despite an engaging style and attention-grabbing examples, the reader of The Art of Statistics will need more than a casual grounding in statistics to get what Spiegelhalter, I believe, intends from his book. It should be viewed as a companion to a more rigorous textbook on statistical methods but not necessarily a book that makes statistics any …

Calculating The Area Within The Orbit Of Arrokoth, Aurielle Collins

Undergraduate Journal of Mathematical Modeling: One + Two

The area within the orbit of the Kuiper Belt object (KBO) Arrokoth (or 2014MU₆₉) is approximated using the corresponding ellipse. The fact that the Sun lies at a focus of the ellipse is of interest. Attention is made to the known deviations of orbits from their models. It is at least of interest that the ellipse model is still essentially valid. Theoretically, if there were only the Sun and Arrokoth in the Universe, the orbit would be precisely described by the ellipse model.

Probabilistic Machine Learning Using Bayesian Inference, Mayank Pandey

Undergraduate Journal of Mathematical Modeling: One + Two

Machine Learning is a branch of AI (Artificial Intelligence) which expands on the idea of a computational system extending its knowledge about set methodical behaviors from the data that is fed to it to essentially develop analytical skills that can help in identifying patterns and making decisions with little to no participation of a real human being. Computer algorithms help in gaining experience to improve the facility over time for use by both consumers and corporations. In today’s technologically advanced world, Machine Learning has given us self-driving cars, speech recognition software, and AI agents like Siri and Google assistant. This …

The Relationship Between Suicide Rates And Mental Health Provider Ratio, Christian Bates

Undergraduate Journal of Mathematical Modeling: One + Two

This project is an analysis of the relationship between suicide rates and mental health provider ratio within the United States. Data from 2018 are collected for each state regarding its suicide rate, mental health provider ratio, and percent of population unable to receive treatment for mental health problems. An initial analysis is made using suicide rates and mental health provider ratio, with no correlation being found. A second analysis is conducted, using multiple linear regression with the percent of individuals within each state who were unable to access treatment for their mental health problems being the confounding variable. Controlling for …

A Mathematical Modeling Of Infrared Neural Stimulation, Cesil S. Alex

Undergraduate Journal of Mathematical Modeling: One + Two

Electrical stimulation is the gold standard for artificial neural stimulation. The greatest disadvantage with electrical stimulation is that it scatters in space and it is difficult to achieve specific point stimulation. Recently, infrared stimulation attracted attention to address this issue. Infrared stimulation works on the principle of heating the tissue, exploiting the energy of infrared lasers to heat the cellular aqueous solution that helps transfer the energy to the cell membrane without direct contact, and provides a discrete localization of stimulation as it does not spread in space like electric fields. In the present study, a heat transfer model for …

Prosthetic Leg Model, Dang Nguyen

Undergraduate Journal of Mathematical Modeling: One + Two

The main goal of this paper is to introduce an imitated prosthetic leg model by analyzing the applied forces. Even though the model is based on the idea of a prosthetic leg, it is also applicable to people without disabilities. The same concept of the model can be seen in the circus, where a person maintains a balanced state while on an incredible height without falling. When all the applying forces in the system are calculated, the design achieves the ideal state which allows it to function most effectively. One of the essential factors applied to the imitated prosthetic leg …

An Exploration Of Wind Energy, Bianca De Haan

Undergraduate Journal of Mathematical Modeling: One + Two

Wind energy is renewable energy extrapolated from the wind that has the potential to revolutionize our power supply in the near future as fossil fuels become outdated. Wind turbines capture the energy as the wind spins the blades of the turbine, transforming wind energy into mechanical energy and then into electrical energy through a generator. One of the techniques utilized to understand wind energy is to manipulate various variables in the formula for wind power. These variables such as the power coefficient, wind velocity, number and length of blades are explored to find its optimal value. The variable of turbine …

Finding The Growth Rate Of A Tumor, Christine Staat

Undergraduate Journal of Mathematical Modeling: One + Two

The Gompertz method is used to analyze the growing glioblastoma data and estimate how accurate the results of growth over time are. The Gompertz curve is expressed as V(t) = αe^-βe-γt. The data from the tumor is graphed in Excel along with the values from the Gompertz equation. Excel solver is used to assist in determining the constant values of α, β, and γ. The data of the tumor is overall very close to the outcome of the Gompertz model following a sigmoidal “S” curve.

Optimization Of Handicap Ramp, Tyler Schilling

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project is to minimize the cost of building a handicap ramp. This is done by introducing an equation that represents the total cost of the construction, including labor and materials. Variables are then defined in terms of block length l, allowing for an equation with one variable to be graphed and derived. This equation then undergoes the first derivative test to find a value of l that would create a minimum output for cost. This value is then compared to the physical constraints of the project allowing for a realistic minimum cost to be found. …

Role Of Paleomagnetism In The Construction Of Earth’S Geographic Past, Stephanie Robinson

Undergraduate Journal of Mathematical Modeling: One + Two

Rocks have the ability to preserve magnetic information used in determining past geographic formations. The purpose of this report is to determine the past location of a site from a given data set’s magnetic information and the calculations found through their application to paleomagnetism. Magnetic information includes the rock sample’s location and concentration of trace magnetic particles which were used to find declination and inclination on site. The sample’s paleolatitude and paleolongitude are calculated using trigonometric equations that are derived using calculus. After a statistical analysis, these results are compared to the present day’s magnetic poles to determine the past …

Hyperelastic Bone Involving The Washer Method, Kristin Jones

Undergraduate Journal of Mathematical Modeling: One + Two

The research conducted focuses on 3D printing and its application in medical equipment. A recent breakthrough in modern material science was made with the creation of hyperelastic bone. This exploration looks at how hyperelastic bone is created, the cost comparison to older tools, and the possible design for hyperelastic bone. Detailed calculations and descriptions are also included to explain the reasoning behind the work conducted.

Calculating Ambu Bag Dimensions For Use In Portable Ventilators, Camden Smith

Undergraduate Journal of Mathematical Modeling: One + Two

Based on the design of non-portable ventilators, this project examines and analyzes the primary individual component used within a motorized AMBU bag ventilator - the AMBU bag. Calculations are conducted to assess the minimum volume for an AMBU bag to provide sufficient oxygen for average total lung capacity. It allows to determine the feasibility and effectiveness of an electrical, portable AMBU bag ventilator under the reduced size requirements. A calculus-based formula, known as the Disk Method, is utilized for these calculations. It is shown that the Disk method can be reversed to find a shape of an AMBU bag given …

The Famous Coin Change Problem And Its Possible New Applications, Quang Vu

Undergraduate Journal of Mathematical Modeling: One + Two

The classical problem “Coin change” in Computer Science has become a key problem to a number of subsequent problems in different areas: finance, algorithm study, sports, etc. Mathematicians have been paying attention to only two possible outcomes of the problem: the most time/resource efficient solution and the total number of solutions. However, solutions among the “normal solutions” can be beneficial in certain situations, if carefully considered with math and economic phenomena in the past. Our work describes some of such possible beneficial solutions that are worth paying attention to and its application in finance and fiscal policy. Now it is …

Locating The Center Of Mass Of Various Simplified Car Designs For The Problem Of Flipping Over An Incline, Sullivan Musgrove

Undergraduate Journal of Mathematical Modeling: One + Two

The center of mass of a given system is referred to as a position that is the average of all of its components. I am given two cases in which I need to find the center of mass for the problem of flipping over an incline. To solve the problem given, I utilize many equations that are derived to find the center of mass of both cases and then test each system when it is encountered with three different inclines increasing by fifteen degrees increments. The tests prove that the probability that a system will flip on an incline is …

Calculating Resonance Angle For Surface Plasmon Resonance Activation On Different Metals, Dang Nguyen

Undergraduate Journal of Mathematical Modeling: One + Two

Surface plasmon resonance (SPR) is the technique that has been used in many fields including biomedical science, optic, biosensing, photothermal plasmon and medicine. With the help of Kretschmann configuration, the setup allows to excite the electrons located around the metal which results in electron oscillation, also known as the plasmonic effect. However, SPR requires many factors in order to be activated. This paper approaches and analyzes two crucial features, the incident angle of incoming light and the effect of permittivity that different metals have in order to determine the sufficient value for the plasmon to exist. Different metals including gold, …

Measuring The Rate Of Heat Loss Across Selected Building Materials, Genesis Zambrano

Undergraduate Journal of Mathematical Modeling: One + Two

The rate of heat loss is analyzed for three materials: glass, brick and wood. To do this, the initial and final temperatures are set to 75℉ and 100℉, respectively, and the dimensions of each material are chosen to be 5ft by 5ft with a thickness of 2 inches. The objective of this paper is to see which material is best for insulating heat, thus enhancing the thermal performance of a building. Results from this study suggest that glass and brick have a higher rate of heat loss (high thermal conductance values and low thermal resistance values) compared to wood and …

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 …

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 …