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A thorough understanding of the key concepts of logic is critical for student success. Logic is often not explicitly taught as its own subject in modern curriculums, which results in misconceptions among students as to what comprises logical reasoning. In addition, current standardized testing schemes often promote teaching styles which

A thorough understanding of the key concepts of logic is critical for student success. Logic is often not explicitly taught as its own subject in modern curriculums, which results in misconceptions among students as to what comprises logical reasoning. In addition, current standardized testing schemes often promote teaching styles which emphasize students' abilities to memorize set problem-solving methods over their capacities to reason abstractly and creatively. These phenomena, in tandem with halting progress in United States education compared to other developed nations, suggest that implementing logic courses into public schools and universities can better prepare students for professional careers and beyond. In particular, logic is essential for mathematics students as they transition from calculation-based courses to theoretical, proof-based classes. Many students find this adjustment difficult, and existing university-level courses which emphasize the technical aspects of symbolic logic do not fully bridge the gap between these two different approaches to mathematics. As a step towards resolving this problem, this project proposes a logic course which integrates historical, technical, and interdisciplinary investigations to present logic as a robust and meaningful subject warranting independent study. This course is designed with mathematics students in mind, with particular stresses on different formulations of deductively valid proof schemes. Additionally, this class can either be taught before existing logic classes in an effort to gradually expose students to logic over an extended period of time, or it can replace current logic courses as a more holistic introduction to the subject. The first section of the course investigates historical developments in studies of argumentation and logic throughout different civilizations; specifically, the works of ancient China, ancient India, ancient Greece, medieval Europe, and modernity are investigated. Along the way, several important themes are highlighted within appropriate historical contexts; these are often presented in an ad hoc way in courses emphasizing technical features of symbolic logic. After the motivations for modern symbolic logic are established, the key technical features of symbolic logic are presented, including: logical connectives, truth tables, logical equivalence, derivations, predicates, and quantifiers. Potential obstacles in students' understandings of these ideas are anticipated, and resolution methods are proposed. Finally, examples of how ideas of symbolic logic are manifested in many modern disciplines are presented. In particular, key concepts in game theory, computer science, biology, grammar, and mathematics are reformulated in the context of symbolic logic. By combining the three perspectives of historical context, technical aspects, and practical applications of symbolic logic, this course will ideally make logic a more meaningful and accessible subject for students.
ContributorsRyba, Austin (Author) / Vaz, Paul (Thesis director) / Jones, Donald (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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Previous research discusses students' difficulties in grasping an operational understanding of covariational reasoning. In this study, I interviewed four undergraduate students in calculus and pre-calculus classes to determine their ways of thinking when working on an animated covariation problem. With previous studies in mind and with the use of technology,

Previous research discusses students' difficulties in grasping an operational understanding of covariational reasoning. In this study, I interviewed four undergraduate students in calculus and pre-calculus classes to determine their ways of thinking when working on an animated covariation problem. With previous studies in mind and with the use of technology, I devised an interview method, which I structured using multiple phases of pre-planned support. With these interviews, I gathered information about two main aspects about students' thinking: how students think when attempting to reason covariationally and which of the identified ways of thinking are most propitious for the development of an understanding of covariational reasoning. I will discuss how, based on interview data, one of the five identified ways of thinking about covariational reasoning is highly propitious, while the other four are somewhat less propitious.
ContributorsWhitmire, Benjamin James (Author) / Thompson, Patrick (Thesis director) / Musgrave, Stacy (Committee member) / Moore, Kevin C. (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / T. Denny Sanford School of Social and Family Dynamics (Contributor)
Created2014-05
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Grade inflation in modern universities across the United States has been documented since the 1960's and shows no signs of disappearing soon. Responses to this trend have ranged from mild worry to excessive panic. However, is the concern justified? How significant are the effects, if any, of grade inflation on

Grade inflation in modern universities across the United States has been documented since the 1960's and shows no signs of disappearing soon. Responses to this trend have ranged from mild worry to excessive panic. However, is the concern justified? How significant are the effects, if any, of grade inflation on students? Specifically, does grade inflation on the aggregate level have any effect on how much an individual will learn from their courses? This is precisely the question my project hoped to address. Grade inflation in U.S. colleges has played a central role in student-teacher relationships and the way university classrooms run. Through teacher interviews, student surveys, and a literature review, this paper investigates the nuanced effects grade inflation is having on student motivation and learning. The hypothesis is that the easier it is for a student to obtain their desired grade, the less they will end up engaging in and learning from a given course. Major findings of the literature include: grade inflation has robbed grades of their signaling power, grade inflation has helped create students are too grade-oriented, student evaluations of teaching have prompted higher grades, higher expectations for high grades induce greater study times, and open dialogue can help reverse grade inflation trends. The student surveys and faculty interviews agreed with much of the literature and found that professors believe grade inflation is real but do not believe its effects are significant, students admit to being primarily motivated by grades, and students find grades critically important to their future. The paper concludes that grade inflation is not as detrimental to student outcomes as ardent critics argue and offers practical ways to address it.
ContributorsGregory, Austin Scott (Author) / Ruediger, Stefan (Thesis director) / Goegan, Brian (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Economics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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Description
A working knowledge of mathematics is a vital requirement for introductory university physics courses. However, there is mounting evidence which shows that many incoming introductory physics students do not have the necessary mathematical ability to succeed in physics. The investigation reported in this thesis used preinstruction diagnostics and interviews to

A working knowledge of mathematics is a vital requirement for introductory university physics courses. However, there is mounting evidence which shows that many incoming introductory physics students do not have the necessary mathematical ability to succeed in physics. The investigation reported in this thesis used preinstruction diagnostics and interviews to examine this problem in depth. It was found that in some cases, over 75% of students could not solve the most basic mathematics problems. We asked questions involving right triangles, vector addition, vector direction, systems of equations, and arithmetic, to give a few examples. The correct response rates were typically between 25% and 75%, which is worrying, because these problems are far simpler than the typical problem encountered in an introductory quantitative physics course. This thesis uncovered a few common problem solving strategies that were not particularly effective. When solving trigonometry problems, 13% of students wrote down the mnemonic "SOH CAH TOA," but a chi-squared test revealed that this was not a statistically significant factor in getting the correct answer, and was actually detrimental in certain situations. Also, about 50% of students used a tip-to-tail method to add vectors. But there is evidence to suggest that this method is not as effective as using components. There are also a number of problem solving strategies that successful students use to solve mathematics problems. Using the components of a vector increases student success when adding vectors and examining their direction. Preliminary evidence also suggests that repetitive trigonometry practice may be the best way to improve student performance on trigonometry problems. In addition, teaching students to use a wide variety of algebraic techniques like the distributive property may help them from getting stuck when working through problems. Finally, evidence suggests that checking work could eliminate up to a third of student errors.
ContributorsJones, Matthew Isaiah (Author) / Meltzer, David (Thesis director) / Peng, Xihong (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
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Description
Millennial involvement levels in the stock market are startlingly low. But what has caused this disconnect between America's younger generation and the financial sector? Stress from past financial crises, distrust of Wall Street, corporate greed, or a dislike of capitalism could surely all be viable culprits. Through our mutual experiences

Millennial involvement levels in the stock market are startlingly low. But what has caused this disconnect between America's younger generation and the financial sector? Stress from past financial crises, distrust of Wall Street, corporate greed, or a dislike of capitalism could surely all be viable culprits. Through our mutual experiences and research, however, we have found that most millennials aren't cynical anarchists avoiding the stock market in an attempt to fight against the system. Rather, they are individuals who have the desire to learn about investing but are clueless as to where/how to start. We both began investing in the stock market early in our college careers by opening online brokerage accounts and developing investment portfolios based on knowledge we learned within our Finance degrees and through independent research. Word of our involvement in the stock market began to spread in our social circles and people would consistently approach either of us and ask a variety of questions regarding investing. Questions such as: Can you sit down and help me open up an account and pick some stocks? What type of things do you invest in? How do I get started? How much money have you made? (always a favorite). Pre-med students, engineers, business, science, and technology majors alike all showed interest in the stock market. The more and more we talked to people, the more we realized that the problem was not a lack of desire or a lack of intellect. The problem was a lack of logically presented information, and barriers to entry that were far too high. We want to fix that. Investnet will be an online educational platform that will teach anyone the basics of investing, in plain, easy to understand terms. Whether the individual has absolutely zero knowledge of finances, or has some familiarity with investing, Investnet will provide them with the knowledge and confidence necessary to start investing in the stock market (or choose not to, but at least they'll know how).
ContributorsMcKenzie, Connor (Co-author) / Shatila, Jordan (Co-author) / Budolfson, Arthur (Thesis director) / Hoffman, David (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Finance (Contributor) / W. P. Carey School of Business (Contributor) / Economics Program in CLAS (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
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Description
Upon hiring a new college graduate, employers are left with limited information about the true productivity of the individual, mainly based on the information provided via resume and other related documents. Based on the information, which may include (and is not limited to) education years, grade point average(s), the institution

Upon hiring a new college graduate, employers are left with limited information about the true productivity of the individual, mainly based on the information provided via resume and other related documents. Based on the information, which may include (and is not limited to) education years, grade point average(s), the institution one attended, majors, etc., employers attempt to differentiate between the candidates. Existing employer learning literature, such as Altonji and Pierret (2001) and Peter Arcidiacono, Patrick Bayer, and Aurel Hizmo (2010), have found that employers statistically discriminate upon hiring and estimate wages based on expected productivity conditional to observable characteristics--specifically education. As one's work experience accumulates, the wages are adjusted to the newly learned characteristics correlated with productivity. Thus, college graduates are more appealing as job candidates than high school graduates, with little learning done with experience in the labor market as employers have a more accurate depiction on productivity with more education years. With rising demands for high-skilled labor, there is a growing interest on what employers learn about from the name of the college listed on one's resume, as varying ability students sort into varying quality colleges. I include a one-dimensional index of college quality, as similarly constructed by Eleanor Dillon and Jeffrey Smith (2015), to measure the effects of attending a highly-selective institution in predicting individual ability. This paper provides additional support for the employer learning model on college graduates, with an emphasis on the direct role that college quality has at the start of one's career. Although college quality appears to be influential in providing employers additional information on one's productivity, unlike education, the weight placed on it by employers does not change with experience in the labor market. I further investigate within the college market and provide possible explanations behind learning on the basis of college quality, including: the possibility of information explained by quality unrelated to one's ability and the effects of attending a highly selective college.
ContributorsNam, Jimin (Author) / Veramendi, Gregory (Thesis director) / Dillon, Eleanor (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Economics (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
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Description

This study estimates the effect of district wealth on Arizona Empowerment Scholarship Account program participation using data from the Arizona Department of Education. We find that students from poor districts are not more likely to participate as school performance decreases.Conversely, those from wealthy districts do increase participation as school

This study estimates the effect of district wealth on Arizona Empowerment Scholarship Account program participation using data from the Arizona Department of Education. We find that students from poor districts are not more likely to participate as school performance decreases.Conversely, those from wealthy districts do increase participation as school performance decreases. We briefly try to explain the observed heterogeneity through survey results and commenting on the program design.

ContributorsAngel, Joseph Michael (Author) / Kostol, Andreas (Thesis director) / Kuminoff, Nicolai (Committee member) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Description

As we count down the years remaining before a global climate catastrophe, ever increases the importance of teaching environmental history and fostering environmental stewardship from a young age. In the age of globalization, nothing exists in a vacuum, yet our traditional education system often fails to reflect the abundant connections

As we count down the years remaining before a global climate catastrophe, ever increases the importance of teaching environmental history and fostering environmental stewardship from a young age. In the age of globalization, nothing exists in a vacuum, yet our traditional education system often fails to reflect the abundant connections between content areas that are prevalent outside of schools. In fact, many of the flaws of the field of education have been exacerbated by the COVID-19 pandemic and a forced transition to online schooling, with many educators reverting to outdated practices in a desperate attempt to get students through the year. The aim of this project was to design a unit curriculum with these issues in mind. This month-long environmental history unit engages students through the use of hands-on activities and promotes interdisciplinary connections. The unit can be taught in a physical, online, or hybrid American history class, and will hopefully inspire and motivate students to become environmental stewards as they look toward their futures on this planet.

ContributorsColeman, Lauren Jean (Author) / Walters, Molina (Thesis director) / Anthony, Charles (Committee member) / School of International Letters and Cultures (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Division of Teacher Preparation (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description

The incidence of childhood obesity has become increasingly prevalent in the United States in recent years. The development of obesity at any age, but especially in adolescence, can have lasting negative effects in the form of cardiometabolic disease, increased incurred healthcare costs, and potential negative effects on quality of life.

The incidence of childhood obesity has become increasingly prevalent in the United States in recent years. The development of obesity at any age, but especially in adolescence, can have lasting negative effects in the form of cardiometabolic disease, increased incurred healthcare costs, and potential negative effects on quality of life. In recent years, a rising trend of obesity, in both adults and adolescents, has been observed in lower income and ethnic groups. Increased adiposity can be influenced by modifiable factors -(physical activity, caloric intake, or sleep) or by non-modifiable factors (ethnicity, genetic predispositions, and socioeconomic status). The influence of these factors can be observed in individuals of all ages, including infants. A common indicator of the development of childhood obesity is rapid weight gain (RWG) within an infant’s first year of life. The composition of the gut microbiome can act as a predictor for RWG and the development of childhood obesity. Infants are exposed to an immense microbial load when they are born and their gut microbiome is continually diversified through their method of feeding and the subsequent introduction to solid foods. While currently understudied, it is understood that cultural and socioeconomic factors influence the development of the gut microbiome, which is further explored in this analysis. The DNA from 51 fecal samples from infants ranging from 3 weeks to 12 months in age was extracted and sequenced using next-generation sequencing, and the resulting sequences were analyzed using QIIME 2. Results from alpha-diversity and beta-diversity metrics showed significant differences in the gut microbiome of infants when comparing groups based on baby race/ethnicity, household income, and mom’s education. These findings suggest the importance of sociodemographic characteristics in shaping the gut microbiome and suggest the importance of future studies including diverse populations in gut microbiome work.

ContributorsGallello, Chloe (Author) / Whisner, Corrie (Thesis director) / Petrov, Megan (Committee member) / Redding, Kevin (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Molecular Sciences (Contributor) / School of Life Sciences (Contributor)
Created2023-05
Description

This paper encompasses a reflection of my experience engaging Algebra 1 students in a math classroom. 5 main strategies were focused on: incorporating games in the classroom, asking students to create (projects, word problems, etc), using technology in the classroom, fostering student collaboration, and allowing student choice. Each strategy was

This paper encompasses a reflection of my experience engaging Algebra 1 students in a math classroom. 5 main strategies were focused on: incorporating games in the classroom, asking students to create (projects, word problems, etc), using technology in the classroom, fostering student collaboration, and allowing student choice. Each strategy was implemented three times in the classroom, student feedback collected, and the level of student engagement was assessed.

ContributorsGeorge, Ejlal (Author) / Trombley, Nicole (Thesis director) / Miiller, Samantha (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05