Physical Sciences and Mathematics Commons^™

Parts Of The Whole: Learn More, Learn Better, Dorothy Wallace

Numeracy

Building on previous columns in Numeracy, this column analyzes various teaching techniques in terms of their ability to build cognitive schema, extend existing schema, reinforce learning, move mean understanding of a group of students, and reduce variance in understanding of a group. We offer a pedagogical cycle as an example of how to address multiple learning goals using common teaching methods.

Incorporating Quantitative Reasoning In Common Core Courses: Mathematics For The Ghost Map, John R. Jungck

Numeracy

How can mathematics be integrated into multi-section interdisciplinary courses to enhance thematic understandings and shared common readings? As an example, four forms of quantitative reasoning are used to understand and critique one such common reading: Steven Berlin Johnson’s "The Ghost Map: The Story of London's Most Terrifying Epidemic - and How it Changed Science, Cities and the Modern World" (Riverhead Books, 2006). Geometry, statistics, modeling, and networks are featured in this essay as the means of depicting, understanding, elaborating, and critiquing the public health issues raised in Johnson’s book. Specific pedagogical examples and resources are included to illustrate applications and …

If Only Math Majors Could Write..., Bernard L. Madison

Numeracy

This text of the opening plenary address to the 2011 Summit of the Appalachian College Association and the meeting of the National Numeracy Network makes an argument that quantitative reasoning and writing should be taught together. The argument is set up by noting that humanists have historically banished quantitative issues from their study of the liberal arts and that science, engineering, and mathematics education suffers from lack of approaches to learning that promote complex, deeper understanding, most notably integrative and reflective learning. Therefore, everyone would profit from combining writing and quantitative reasoning. Five more specific reasons are discussed, drawing evidence …

Period Life Tables: A Resource For Quantitative Literacy, Thomas J. Pfaff, Stanley Seltzer

Numeracy

A period life table provides an estimate of the probability that a person will die at a particular age. Using data available online, we examine tables of expected years to live for males and females against age for three populations: the United States in 2007, the U.S. at the turn of the twentieth century, and the Roman Empire. Scatter plots of males and females for each population show how life expectancy increases with age (e.g., U.S. 2007: 50 year-old female > 40 year-old female > 45 year-old male). The three data sets allow historical comparisons (e.g., of gender disparity, larger now; of …

Motivation For Achievement And Attitudes Toward Mathematics Instruction In A Required Calculus Course At The Norwegian University Of Science And Technology, Donna Sundre, Carol Barry, Vidar Gynnild, Erin Tangen Ostgard

Numeracy

This study from the Norwegian University of Science and Technology (NTNU) examines students’ learning goals and attitudes toward mathematics in a first-year calculus course in undergraduate engineering education. Achievement motivation research using the Achievement Goal Questionnaire (AGQ) is advanced from current literature with two additions: (1) a course specific context using introductory college calculus students, and (2) participation of Norwegian students.

Pre- and posttest measures of attitudes indicate that students do change learning goals over time, unfortunately opposite to the instructors’ aspirations. A significant increase in “Mastery Avoidance” and “Work Avoidance” was accompanied with a drop in “Mastery Approach” and …

Quantitative Literacy Interventions At University Of Cape Town: Effects Of Separation From Academic Disciplines, Vera Frith

Numeracy

The aim of the Numeracy Centre at the University of Cape Town is to develop students’ quantitative literacy (QL) in a manner consistent with their programmes of study and intended roles in the community. Our theoretical perspective on the nature of QL is in line with that of the New Literacies Studies and sees academic QL as practices in different academic disciplinary contexts. This means that for us the ideal curriculum structure for developing QL would fully integrate it into the teaching of the disciplines. This is in practice not achievable in most cases, especially since many students do not …

Numeracy, Financial Literacy, And Financial Decision-Making, Annamaria Lusardi

Numeracy

Financial decisions, be they related to asset building or debt management, require the capacity to do calculations, including some complex ones. But how numerate are individuals, in particular when it comes to calculations related to financial decisions? Studies and surveys implemented in both the United States and in other countries that are described in this paper show the level of numeracy among the population to be very low. Moreover, lack of numeracy is not only widespread but is particularly severe among some demographic groups, such as women, the elderly, and those with low educational attainment. This has potential consequences for …

The Joy Of Quantitative Reasoning, Caren Diefenderfer

Numeracy

One of the advantages of focusing on quantitative reasoning is that it spans a wide variety of topics. As incoming president of the National Numeracy Network, I would like to take the opportunity of this editorial to tell my story of intellectual reward from finding common purpose in quantitative reasoning with colleagues from disciplines outside of mathematics. The story starts with an NSF-funded faculty development project (DUE-9952807) to further a QR across-the-curriculum program and the finding from that program that merging authentic context with mathematics brings interaction and collaboration. That joy in learning from and working with colleagues in other …

Overfishing Of The Common Snook, Allison Ashcroft

Undergraduate Journal of Mathematical Modeling: One + Two

The chief aim of this project is to determine if the populations of the common snook, Centropomus Undecimalis, in the Atlantic and Gulf coast are being affected by overfishing. This is established by evaluating the intrinsic rate of change for these populations and their carrying capacities. It turns out that the carrying capacity for the population of the Atlantic coast is approximately one million snook and its intrinsic rate is 0.00621, while the carrying capacity of the Gulf coast's population is 2.9 million snook and its intrinsic rate is 0.00165. The decline of both populations is most likely due …

The Elevation To Area Relationship Of Lake Behnke, Kaitlin Deutsch

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project was to determine the area-to-depth relationship in Lake Behnke, which acts as the principal stormwater drainage basin for the University of South Florida campus in Tampa, Florida. Data previously collected in a stormwater management study by Jeffery Earhart illustrated a linear correlation between the lake's area and depth; however, that study was conducted in 1998, and this present work serves to double check that correlation. We analyzed a bathymetric map of Lake Behnke that displayed several contour lines indicating depth and approximated the area inside each closed curve with a contour integral. The resulting relationship …

U.S. Oil Reserves And Peak Oil, Trang Luong

Undergraduate Journal of Mathematical Modeling: One + Two

We use calculus methods to estimate the quantity of U.S. oil reserves. We consider a model that consists of an exponential function with four unknown constants. We fit real oil production data to determine the unknown constants. With the constants determined we use the function to find the year in which the U.S. oil production reached its peak. We also estimate the amount of petroleum produced until the end of 2006, and the undiscovered oil reserves to be produced in the future.

The Subset Sum Problem: Reducing Time Complexity Of Np-Completeness With Quantum Search, Bo Moon

Undergraduate Journal of Mathematical Modeling: One + Two

The Subset Sum Problem is a member of the NP-complete class, so no known polynomial time algorithm exists for it. Although there are polynomial time approximations and heuristics, these are not always acceptable, yet exact-solution algorithms are unfeasible for large input. Quantum computation offers new insights for not only the Subset Sum Problem but also the entire NP-complete class; most notably, Grover's quantum algorithm for an unstructured database search can be tailored to identify solutions to problems within mathematics and computer science. This paper discusses the physical and conceptual feasibility of quantum computation and demonstrates the utility of quantum search …

Complexity Of Mitochondrial Genome Sequences, Brandon Toun

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project is to compare the complexities of different species' mitochondrial genome sequences. Using an implementation of Deflate compression algorithm from Java standard library, we were able to compress mitochondrial genomes of nine different species. The complexity of each sequence is estimated as a ratio of the original sequence length to the length of the compressed sequence. In addition, we show how a notion of topological entropy from symbolic dynamics can be used as another complexity measure of nucleotide sequences.

Modeling Flow Rate To Estimate Hydraulic Conductivity In A Parabolic Ceramic Water Filter, Ileana Wald

Undergraduate Journal of Mathematical Modeling: One + Two

In this project we model volumetric flow rate through a parabolic ceramic water filter (CWF) to determine how quickly it can process water while still improving its quality. The volumetric flow rate is dependent upon the pore size of the filter, the surface area, and the height of water in the filter (hydraulic head). We derive differential equations governing this flow from the conservation of mass principle and Darcy's Law and find the flow rate with respect to time. We then use methods of calculus to find optimal specifications for the filter. This work is related to the research conducted …

Speleothem Laminae Counting And Growth Rate, Corey Wilson

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to determine if there is a correlation between annual laminae in speleothems and Uranium dating. To do this, we counted laminae using high-resolution images and calculated a line of the best fit for the resulting data. We found that our data could supplement Uranium dating, but unless more data is obtained, laminae counting gives relatively imprecise age and growth rate estimates.