Physical Sciences and Mathematics Commons^™

The International Crisis In Numeracy Education, Nathan D. Grawe

Numeracy

The OECD recently released results from the 2022 administration of the Programme for International Student Assessment test. As other studies suggest, pandemic mitigation policies resulted in deep learning loss including in basic mathematics which forms the foundation of numeracy. Perhaps of greater concern, however, in many countries pandemic effects amplify declining performance that dates back a decade or more. Losses of two or more years' worth of mathematics education are not uncommon among developed countries. The editorial makes an urgent call for research that identifies practical steps to reverse these trends.

An Introduction To The Algebra Revolution, Art Bardige

Numeracy

Bardige, Art. 2022. The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education; (Bookbaby) 135 pp. UNSPSC 55111505.

The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education argues that Algebra 1 can be eliminated by teaching mathematics through spreadsheets. Such a change would eliminate the greatest roadblock to student achievement.

“Math Talks Are Like An Alarm Clock Waking You Up”: Language’S Crucial Role In Mathematics, Gabriella M. Wasser

Journal of Practitioner Research

Whole group math talks, or number talks, are a common practice to get students talking about their own understanding of mathematical concepts. The purpose of this study was to implement math talks in small group settings to see what would happen, specifically to students’ conceptual understanding as well their general perceptions of math talks. This study took place in a fourth-grade math classroom, and math talks were implemented with the whole class for a week and then moved to small groups for the remaining three weeks of the study. During the study, a pre-and post-assessment was given, field notes were …

Educating Consumers And Producers Of Data: Review Of Making Sense Of Numbers By Jane E. Miller (2022), Andrew J. Miller

Numeracy

Author Jane E. Miller has brought her considerable experience writing and teaching about numerate communication to a new textbook, Making Sense of Numbers. Miller uses clear prose, timely and authentic examples, and thought-provoking exercises to educate the next generation of consumers and producers of data, students in introductory quantitative reasoning, research methods, or data analysis courses. While the textbook does not fit the mold of a "typical" quantitative literacy course, creative instructors may find ways to use it in innovative quantitative literacy, data literacy, or introductory data science courses.

The Use Of Calculus To Determine Efficient Fertilizer Levels For Crop Production, Cole Loadholtz

Undergraduate Journal of Mathematical Modeling: One + Two

For this project, I wanted to incorporate calculus into agriculture and environmental science methods. More in detail, the problem used asked for the maximum levels of nitrogen (N) and phosphorus (P) that would be best for a current crop yield. This allowed incorporating partial derivatives, and critical points to find the maximum values for the equation. The results show that in order to demonstrate maximum crop yield production, the levels of nitrogen (N) and phosphorus (P) were to be both at 2, with the correct corresponding units. The drawback from this problem is that although the problem showed effective nitrogen …

The Effects Of Effluent Discharge Into The Santa Fé River, João Vito Bezerra Dragone

Undergraduate Journal of Mathematical Modeling: One + Two

The discharge of effluents into rivers is something that has occurred a lot throughout our history, rivers like the Mississippi River and the Tiete River (São Paulo, Brazil) have been targets for many years. Therefore, in this paper I choose to show, through hard data and some assumptions, the impact of sewage dumping in water bodies, in this case the Santa Fé River, Florida and the reason why we should avoid dumping these effluents into the rivers.

Internal Combustion Engines: Modeling Internal Temperature As A Function Of Time, Garrett Fandrich

Undergraduate Journal of Mathematical Modeling: One + Two

Just like any thermodynamic system, combustion engines must be cooled to eliminate friction due to heat. Without proper cooling, internal components, such as connecting rods, rod bearings, and pistons can be severely damaged due to thermal expansion, leading to severe damage to the engine block or outright catastrophic failure. Modern engines are cooled using coolant, which flows through internal passageways within the engine block to pull heat away from the system. The use of coolant and external components, such as a water pump, radiator, and thermostat allow an engine to efficiently warm to standard operating temperature and remain at said …

The Distribution Of Energies, Dung Tien Do

Undergraduate Journal of Mathematical Modeling: One + Two

The application of calculus is of great importance in physics. It is used to calculate energy, acceleration, velocity, and much more. In this paper, to calculate the internal energy of an ideal gas (gas molecules) we will use Maxwell-Boltzmann statistical distribution based entirely on calculus. The technique represents the mathematical concept that depends on integration and substitution in calculus to solve a problem.

Application Of Calculus In The Elastic Curve (Deflection), Ryan Hillock

Undergraduate Journal of Mathematical Modeling: One + Two

Beams are extremely important structure members that are used in nearly every application where significant loads need to be supported. In mechanical and civil engineering being able to appropriately design beams to withstand the expected-to-be loads is a foundational skill. Proper beam design is what keeps large machines from failing and buildings from collapsing. One important aspect of beam design to consider is the deflection of the beam due to the applied loads. It is often useful to determine the deflection along any given point in the beam in order to make sure the loaded beam does not displace any …

Converting Velocity Pressure Into Cubic Feet Per Minute (Cfm), Darrian Robinette

Undergraduate Journal of Mathematical Modeling: One + Two

Almost every building in the United States has a HVAC (Heating, ventilation, and air conditioning) system that relies on balancing Velocity Pressure and calculated CFM to properly control the atmosphere in a building. This is ensured and tested by Field Engineers whose job it is to maintain the efficiency and proper output of these HVAC systems. These systems are used to improve indoor air quality, control moisture and condensation, and contaminants while satisfying comfort needs of occupants. Just with any mechanical system, HVAC systems function efficiently with multiple formulas derived from calculus and physics. Every building is equipped with a …

Volume And Cost Of Longboard Using Aircrete, Mira Stimac

Undergraduate Journal of Mathematical Modeling: One + Two

This project utilizes integral calculus to find the volume of a longboard-style surfboard. The cost for using AirCrete as the material for the longboard will then be calculated. Due to the longboard's shape, the longboard is divided into four sections, and the volume of each is found. The final volume for the longboard with the measurements provided is approximately 3821 cubic inches. The cost of making the longboard out of AirCrete was then calculated by using ratios. The final cost for the longboard is $4.70.

Monitoring Drug Concentration In Emergency Medicine, Andrew Woods

Undergraduate Journal of Mathematical Modeling: One + Two

The careful monitoring of a drug’s concentration in the body of a patient is of the utmost importance in modern medicine. Many of the lifesaving medications that are administered in an emergency medicine environment have a narrow window of efficacy. This effective concentration is in an ever-changing state, as the body processes and eliminates exogenous compounds that are introduced to maintain homeostasis. To ensure the proper treatment and/or management of ailments, special attention must be given to the concentration of a given drug in the body as time progresses. These changing concentrations can be evaluated and tracked using the mathematical …

An Introduction To Calling Bullshit: Learning To Think Outside The Black Box, Jevin D. West, Carl T. Bergstrom

Numeracy

Bergstrom, Carl T. and Jevin D. West. 2020. Calling Bullshit: The Art of Skepticism in a Data-Driven World. (New York: Random House) 336 pp. ISBN 978-0525509202.

While statistical methods receive greater attention, the art of critically evaluating information in everyday life more commonly depends on thinking outside the black box of the algorithm. In this piece we introduce readers to our book and associated online teaching materials—for readers who want to more capably call “bullshit” or to teach their students to do the same.

An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

Numeracy

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

Looking Back At Quantitative Reasoning, William Briggs

Numeracy

A teacher looks back on three decades of teaching, pondering, and writing about quantitative reasoning (QR) and shares a few lessons learned. The skills that we teach in QR courses are more important than ever in providing students with a sense of civic virtue: the ability to be engaged and informed citizens in an increasingly complex and quantitative world.

Review Of Social Workers Count: Numbers And Social Issues By Michael Anthony Lewis, Michael T. Catalano

Numeracy

Lewis, Michael Anthony. 2017. Social Workers Count: Numbers and Social Issues. 2019. New York: Oxford University Press. 223 pp. ISBN 978-019046713-5

The numeracy movement, although largely birthed within the mathematics community, is an outside-the-box endeavor which has always sought to break down or at least transgress traditional disciplinary boundaries. Michael Anthony Lewis’s book is a testament that this effort is succeeding. Lewis is a social worker and sociologist with an impressive resume, author of Economics for Social Workers, co-editor of The Ethics and Economics of the Basic Income Guarantee, and member of the faculty at the Silberman School …

Area Of Irregular Shaped Roof, Omar Alkhawaldeh

Undergraduate Journal of Mathematical Modeling: One + Two

This project makes use of calculus, specifically integration, to find the exact area of a roof garden to minimize the cost of material used in flooring it. Since the roof is of irregular shape, it is divided into four sections, the integral of each section is taken, and a relationship between the integrals is generated. Positive results are found, and the data reveal that the area of the grass floor is 175.3 m² while the area of the wooden floor is 23.4 m² with the total price being 2472 US dollars.

Using Calculus To Plan An Open-Air Concert, Timur Kalandarov

Undergraduate Journal of Mathematical Modeling: One + Two

A concert is a mass entertainment event held indoors, at concert halls, or outdoors (open-air festivals). These two formats differ greatly from each other. However, the goal of both events remains the same – to allow the audience to enjoy the musical performance. Indoor halls are designed for the best acoustics of sound. They are often circular and let sound waves travel around the inside of the building, like an echo bouncing back and forth. This makes the audience feel like they are surrounded by sound. Such places already have outlined spots for mounting music equipment with the highest efficiency. …

The Dangers Of Lift On Parked Planes: General Aviation Airport Safety, Robert Malloy

Undergraduate Journal of Mathematical Modeling: One + Two

The focus of this paper is to investigate proper aircraft management for safety on an airfield. This is accomplished by looking at lift caused by powerful winds to the aircrafts stored on an airfield, and the tension it places on the rope that secures them. This work could be used to determine when aircrafts are in high-risk and need to be stored either in hangars or moved to other airports prior to storms. The calculations used to determine these conclusions are also explored in the paper.

Mathematical Reconstruction Of A Traffic Crash, Benjamin Covert

Undergraduate Journal of Mathematical Modeling: One + Two

The objective is to find the impact speeds of two motor vehicles involved in a traffic crash. The calculations take into account the approach (pre-collision) and departure (post collision) angles, as well as weights and post collision speeds of both vehicles. The data is provided by Timothy Sleyzack who investigated this traffic collision. The conclusions confirm the validity of the use of Conservation of Linear Momentum in the field of traffic crash reconstruction.

Calculating Probable Theoretical Offspring Genotype In Fruit Flies, Megan Keller

Undergraduate Journal of Mathematical Modeling: One + Two

Being able to calculate an offspring's theoretical genotype is critical in genetic sciences. We calculate the theoretical genotype and phenotype of fruit fly offspring. Using the product rule, we determine the probability for each trait and then for each genotype. In conclusion, we calculate 64 different genotypes that are supposed to be possible, but only 8 phenotypes are possible.

Emergency Communications Deficiency Locator, Austin Collins

Undergraduate Journal of Mathematical Modeling: One + Two

The Bi-Directional Amplifier (BDA) is the newest edition to Life Safety in the state of Florida. The Florida Fire Prevention Code (NFPA 1) section 11.10.1 states that “In all new and existing buildings, minimum radio signal strength for fire department communications shall be maintained at a level determined by the authority having jurisdiction (Committee NFPA 1: Fire Code 2018). That authority having jurisdiction for our local Tampa Bay area is the Hillsborough County Fire Rescue department and they have posted their own requirements along with the Florida Senate for emergency communication standards. All existing “Hi-rise” buildings, 75 feet tall …

Analyzing Piney Point’S Wastewater Discharge Rate, Josephina Reyman

Undergraduate Journal of Mathematical Modeling: One + Two

Implicit differentiation is used in order to find the cubic feet of water dumped into Tampa Bay per hour from the Piney Point reservoir. To get to moles from cubic feet, a series of conversions is done while Le Chatelier’s principle explains how an increase in HPO₄ ^2- (hydrogen phosphate) in Tampa Bay is going to affect algae growth. The rate of moles of HPO₄ ^2- is analyzed as well as the consequences that come with dumping copious amounts of fertilizer water into an aquatic environment.

Evaluating The Improvement In Dna Fingerprinting, Dani Dray

Undergraduate Journal of Mathematical Modeling: One + Two

DNA fingerprinting is a forensic technique used to create patterns that are unique to a person’s DNA. Previously, these fingerprints were made from 13 different segments of DNA, but today they are made from the 20 ones. The fundamental principle of counting is used to determine how much of an improvement was made after adding the 7 additional DNA segments. It is found that this addition greatly reduces the likelihood of two people having the same exact fingerprint, therefore improving the accuracy and reliability of DNA fingerprinting.

Predicting The Cost Of Dental Care Using A Probability Model, Nadine Wehbe

Undergraduate Journal of Mathematical Modeling: One + Two

This paper uses survey data to present a probability model that allows dental offices to predict patient costs. The quantitative model is useful for developing and accepting capitation rates. It accounts for whether the care is initial care or maintenance care, the type of dental care (such as operative, prosthetics, or periodontics), and different age groups, all of which affect the cost of dental treatment.

Possible Contamination From Rainwater In Community Pool, David Mcgregor

Undergraduate Journal of Mathematical Modeling: One + Two

The project is meant to create an equation that can be used to estimate the amount of organic pollutant – bacteria - that is present in a swimming pool per day from rainwater. This equation is derived through a differential equation of the rate in minus the rate out. The created differential equation is an ordinary linear differential equation and is solved using an integration factor. The general solution is then converted into a specific equation using an initial condition. The resulting equation provides an approximate number of organic contaminants x(t) present in the pool after an …

Volume And Cost Of Cylindrical Shaped Silo With Conical Roof, Gabriel Mitzakoff Parola

Undergraduate Journal of Mathematical Modeling: One + Two

This project utilizes integral calculus to find the exact volume of a non-uniform cylindrical-shaped silo used to store wheat and calculate the cost of material utilized to build such silo. Due to its non-uniform shape, the silo is divided into two sections and the volume of each is calculated. The final volume for the silo with the measurements provided is approximately 2330.02 meters cubic and surface area of 1074.96 meters squared, which is considered to be a large capacity silo. With such a large capacity silo there are costs to be considered, such as the material cost which is calculated …

Calculating The Probability Of Constitutional Isomers Of Pentane, Mary-Margaret Dare

Undergraduate Journal of Mathematical Modeling: One + Two

Depending on the reagent, and orientation of collisions within a chemical reaction, organic molecules can be present as different constitutional isomers of the same molecule. We can analyze the likelihood of getting a mixture of pentane with certain conformers. Based on this, we find that there are 16 potential conformers, but 13 are identical structures, meaning only three are distinct from each other. Using the product rule, we then demonstrate how to go about calculating the probability of specific conformers, including specific identical structures, being present in a mixture, and then we demonstrate that process is strictly within the three …

Surge Functions And Drug Interactions, Olta Tarko

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project is to analyze how surge functions work to understand the way drug concentration levels in the bloodstream of a human body vary over time after an initial dose. A surge function increases rapidly at the beginning of the dosage and drops slowly after it reaches its peak. It is important to realize when a certain drug reaches its peak and how long the effects will last on a patient, so a second drug can be administered without risking negative interactions. We explain the calculations used in order to properly understand the curve of a drug’s …

Moment Of Inertia In Applied Calculus, Saad Habib

Undergraduate Journal of Mathematical Modeling: One + Two

This paper demonstrates the usefulness of calculus in structural/continuum mechanics. Calculus in structural/continuum mechanics is used to calculate mass, volume, centre of mass, moment of inertia and in solutions of differential equations. In this paper, we will use calculus to calculate moment of inertia. The area moment of inertia of a surface measures the resistance to deflection of the cross section to bending or buckling. Moment of inertia is used by engineers of inertia to determine the state of stress in a cross section and the amount of inertia. It represents a mathematical concept that depends on the size and …