Physical Sciences and Mathematics Commons^™

The Power Of X, Darren B. Glass

Math Faculty Publications

In his recent book, The Math Myth: And Other STEM Delusions, political scientist Andrew Hacker argues, among other things, that we should not require high school students to take algebra.

Part of his argument, based on data some have questioned, is that algebra courses are a major contributor to students dropping out of high school. He also argues that algebra is nothing more than an "enigmatic orbit of abstractions" that most people will never use in their jobs. [excerpt]

Introducing Complex Systems Analysis In High School Mathematics Using System Dynamics Modeling: A Potential Game-Changer For Mathematics Instruction, Diana Marie Fisher

Dissertations and Theses

Complex systems abound on this planet, in the composition of the human body, in ecosystems, in social interaction, in political decision-making, and more. Analytical methods allowing us to better understand how these systems operate and, consequently, to have a chance to intervene and change the undesirable behavior of some of the more pernicious systems have developed and continue to be enhanced via quickly changing technology. Some of these analytical methods are accessible by pre-college students, but have not been widely used at that level of education. Jay Forrester, the founder of one of the methodologies, System Dynamics (SD), used to …

College Of Engineering Senior Design Competition Spring 2016, University Of Nevada, Las Vegas

Fred and Harriet Cox Senior Design Competition Projects

Part of every UNLV engineering student’s academic experience, the senior design project stimulates engineering innovation and entrepreneurship. Each student in their senior year chooses, plans, designs, and prototypes a product in this required element of the curriculum. A capstone to the student’s educational career, the senior design project encourages the student to use everything learned in the engineering program to create a practical, real world solution to an engineering challenge. The senior design competition helps focus the senior students in increasing the quality and potential for commercial application for their design projects. Judges from local industry evaluate the projects on …

Math Education: A Messy Problem, Gizem Karaali

Pomona Faculty Publications and Research

The current state of math education in America is certainly not ideal, writes Gizem Karaali, but mathematicians, researchers, policy makers and others are working on it -- and it is definitely a problem worth working on.

Exploring Elementary Students’ Agricultural And Scientific Knowledge Using Evidence Centered Design, Molly R. Brandt

School of Natural Resources: Dissertations, Theses, and Student Research

The public is more disconnected from agriculture than ever. Americans are two to four generations removed from the farm, and a majority of Americans, even in rural agricultural states have no direct link to agriculture. As a result, the public lacks the knowledge and appreciation of the food, fuel, and fiber it demands. The National Center for Agricultural Literacy (NCAL) uses National Agricultural Learning Objectives (NALOs) to measure student’s agricultural knowledge. The purpose of this project is to develop assessments aligned with the NALOs and to use results from the assessments to further understand students’ agricultural literacy. This study focuses …

Multivariate Thinking In An Intro Stats Course – Is It Possible?, Beverly Wood

Publications

Many of our students have an intuitive sense that there is more to the story than univariate or bivariate data can tell us. We can acknowledge and encourage that habit of digging deeper by demonstrating some ways to look at additional variables. Simpson’s paradox and side-by-side scatter plots are ways to provide a glimpse of more complex analysis that are accessible to students in an introductory course with or without strong quantitative skills.

Facilitating Conceptual Learning In Quantitative Chemistry, Sarah R. Johnson

Electronic Theses and Dissertations

Traditional chemistry laboratory courses have a manual consisting of “step-by-step” experiments; instructions are given to complete experiments, requiring minimal information/concepts processing to be successful. This experience leaves students unprepared for the real-world, where critical thinking skills are needed to conduct research. This study focused on building analytical techniques, conceptual knowledge, and critical thinking skills used to solve research problems. A new quantitative chemistry laboratory manual was developed to transition students from traditional to inquiry-based experiments, requiring analytical method development. Data showed students having less difficulty using the new manual (0.8281 average difficulty) on method development exam questions and experiments, compared …

Teaching Numerical Methods In The Context Of Galaxy Mergers, Maria Kourjanskaia

Physics

Methods of teaching numerical methods to solve ordinary differential equations in the context of galaxy mergers were explored. The research published in a paper by Toomre and Toomre in 1972 describing the formation of galactic tails and bridges from close tidal interactions was adapted into a project targeting undergraduate physics students. Typically undergraduate physics students only take one Computational Physics class in which various techniques and algorithms are taught. Although it is important to study computational physics techniques, it is just as important to apply this knowledge to a problem that is representative of what computational physics researchers are investigating …

A Modularized Tablet-Based Approach To Preparation For Remedial Mathematics, Kenneth A. Parker

Publications and Research

Basic arithmetic forms the foundation of the math courses that students will face in their undergraduate careers. It is therefore crucial that students have a solid understanding of these fundamental concepts. At an open- access university offering both two-year and four-year degrees, incoming freshmen who were identified as lacking in basic arithmetic skills were engaged in an experimental technology-enhanced workshop designed to provide them with a deeper understanding of arithmetic prior to their initial remedial coursework. Customized online content was created specifically for this experiment, and the first implementation (n=27) yielded statistically significant improvement, not only from pretest to post- …

Concepts About Sedimentology And Stratigraphy In Undergraduate Geoscience Courses, Bailey Z. Kreager

Department of Earth and Atmospheric Sciences: Dissertations, Theses, and Student Research

This two-part study examines sedimentologic and stratigraphic concepts in undergraduate geoscience courses. The first part seeks to identify the various types of interactive engagement strategies used in undergraduate science courses, how they are used and in what fields. It also looks at areas in which the geosciences have excelled in interactive engagement strategies. Published studies describing interactive engagement strategies in college-level courses were collected and coded, which identified six emergent types of interactive engagement strategies: (1) Polling, (2) Full-Class Discussion and Activities, (3) In-Class Group Work, (4) Out-Of-Class Group Work, (5) Online Work, and (6) Other types. Interactive engagement strategies …

The Cantor Set Before Cantor, Nicholas A. Scoville

Topology

A special construction used in both analysis and topology today is known as the Cantor set. Cantor used this set in a paper in the 1880s. Yet it appeared as early as 1875 in a paper by the Irish mathematician Henry John Stephen Smith (1826 - 1883). Smith, who is best known for the Smith normal form of a matrix, was a professor at Oxford who made great contributions in matrix theory and number theory. In this project, we will explore parts of a paper he wrote titled On the Integration of Discontinuous Functions.

Topology From Analysis, Nicholas A. Scoville

Topology

Topology is often described as having no notion of distance, but a notion of nearness. How can such a thing be possible? Isn't this just a distinction without a difference? In this project, we will discover the notion of nearness without distance by studying the work of Georg Cantor and a problem he was investigating involving Fourier series. We will see that it is the relationship of points to each other, and not their distances per se, that is a proper view. We will see the roots of topology organically springing from analysis.

Cuny Elementary Algebra Final Examination (Ceafe) Practice Tests, Olen Dias

Open Educational Resources

No abstract provided.

The Singing Cymbal: Is It Really Photon Momentum?, Thomas R. Moore, Samantha Collin, Nikki Etchenique

Student-Faculty Collaborative Research Publications

A simple demonstration that is occasionally used in the classroom to show that light carries momentum involves making an orchestral cymbal audibly ring using light from a common photoflash. A metal plate or a piece of foil can also be used, however, it appears that many people use a cymbal because the sound is easily heard at a reasonable distance. It is such an impressive example of the effects attributable to photon momentum that it is posted on the CERN website for educational under the name “singing cymbal.” Although it is an impressive demonstration, a series of simple classroom experiments …

Undergraduate Students' Goals For Chemistry Laboratory Coursework, Brittland K. Dekorver

Open Access Dissertations

Chemistry laboratory coursework has the potential to offer many benefits to students, yet few of these learning goals are realized in practice. Therefore, this study seeks to characterize undergraduate students’ learning goals for their chemistry laboratory coursework. Data were collected by recording video of students completing laboratory experiments and conducting interviews with the students about their experiences that were analyzed utilizing the frameworks of Human Constructivism and Self-Regulated Learning. A cross-sectional sampling of students allowed comparisons to be made among students with varying levels of chemistry experience and interest in chemistry. The student goals identified by this study were compared …

Trigonometry: An Overview Of Important Topics, Lauren Johnson

All Capstone Projects

The purpose of this project was to help students achieve a better understanding of Trigonometry, in order to better prepare them for future Calculus courses. The project is a tutorial that walks the student through important Trigonometry topics. The topics range from, but are not limited to, finding the measure of an angle to analyzing the graphs of Trigonometric Functions. Each topic allows an opportunity for the student to assess their understanding by working through practice problems and checking their solutions.

At any university, incoming students will have a wide variety of mathematical backgrounds. These students differ in age, in …

Analysis Of Scientific Argumentation In Two Physical Chemistry Classrooms Using The Pogil Approach, Alena C. Moon

Open Access Dissertations

The benefits of facilitating argumentation in science education have been well reported (Jimenez-Aleixandre & Erduran, 2007). Engaging in argumentation has shown to model authentic scientific inquiry as well as promote development of content knowledge. However, less emphasis has been placed on facilitating argumentation in upper level undergraduate courses, though it is important for evaluating undergraduate curricula to characterize upper level students’ scientific reasoning. This work considers two implementations of the POGIL physical chemistry curriculum and evaluates the classroom argumentation. The researchers aimed to consider the content of the arguments and dialectical features characteristic of socially constructed arguments (Nielson, 2013). To …

Connecting Connectedness, Nicholas A. Scoville

Topology

No abstract provided.

The Exigency Of The Euclidean Parallel Postulate And The Pythagorean Theorem, Jerry Lodder

Geometry

No abstract provided.

The Impact Of Students’ Attitudes After Implementing A Leadership Collaborative Grouping Method In A Collegiate Technical Mathematics Class, Robert J. Belin

All Student Theses and Dissertations

This research paper explored students’ attitudes towards mathematics before and after the implementation of an experimental instructional method. The measurement tool that was used is the Mathematics Attitude Inventory for Students (ATMI). The experimental methodology implemented in the collegiate class is a leadership based cooperative learning model. Students were surveyed twice. The first installment of the ATMI was conducted prior to a mathematics unit that spanned three classes. The second installment of the ATMI survey was conducted after the unit was completed. Student surveys were assessed and determined if the experimental model had any impact of students’ attitudes towards mathematics. …

The Promise Of An Energy Tracker Curriculum For Promoting Home-School Connections And Youth Agency In Climate Action, Elizabeth M. Walsh, Derek Jenkins, Eugene Cordero

Faculty Research, Scholarly, and Creative Activity

Formal classroom learning experiences that support sustainable behaviors outside the classroom necessarily must bridge students’ home and school lives, as knowledge and practice learned in the classroom is implemented outside of school. To this end, we study the impact of the Green Ninja Energy Tracker curriculum, which uses students’ home energy data in the classroom to promote engagement in climate change and conservation behaviors. Data is drawn from class observations, a focus group, and pre- and post- surveys of a pilot implementation of this curriculum in a diverse 12th-grade Earth Science classroom at an alternative school. We investigate what factors …

Using Ipads And Video-Based Instruction To Teach Algebra To High School Students With Disabilities, Elias Clinton, Tom J. Clees

National Youth Advocacy and Resilience Conference

This presentation targets a study in which four high school students with disabilities were taught to solve algebraic equations using iPads and video-based instruction. All students showed immediate increases in accurate responding following the introduction of the video-based intervention. This presentation provides practitioners with a flexible technology-based intervention for students with disabilities in need of grade-level academic instruction. The intervention could be used across a variety of subjects and academic tasks.

Guest Editors' Introduction: Research On Equity And Sustained Participation In Engineering, Computing, And Technology, Tiffany Barnes, Jamie Payton, George K. Thiruvathukal, Kristy Elizabeth Boyer, Jeff Forbes

Computer Science: Faculty Publications and Other Works

The guest editors introduce best papers on broadening participation in computing from the RESPECT'15 conference. The five articles presented here are part one of a two-part series representing research on broadening participation in computing at all levels of education: from K-12 schools through graduate school, with a focus on diversity with regard to gender, race, and ethnicity.

The Need For Research In Broadening Participation, Tiffany Barnes, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

Underrepresentation in computing is a global problem, marked by a disturbing lack of access to computing resources and education among people underrepresented by race, ethnicity, gender, income, disability, and sexual-orientation status. It is urgent that we address this divide between those with and without the knowledge to create computational artifacts or even basic functional literacy. Important alliances for broadening participation (BP) are catalyzing efforts to engage more people in computing, but they are not enough. We need solid research as well.

The Impact Of The Exploring Computer Science Instructional Model In Chicago Public Schools, Lucia Dettori, Ronald I. Greenberg, Steven Mcgee, Dale Reed

Computer Science: Faculty Publications and Other Works

As part of the Taste of Computing project, the Exploring Computer Science (ECS) instructional model has been expanded to many high schools in the Chicago Public Schools system. We report on initial outcomes showing that students value the ECS course experience, resulting in increased awareness of and interest in the field of computer science. We compare these results by race and gender. The data provide a good basis for exploring the impact of meaningful computer science instruction on students from groups underrepresented in computing; of several hundred students surveyed, nearly half were female, and over half were Hispanic or African-American.

Innumeracy: The Product Of Misrepresentation, Elizabeth Cundiff

Missouri S&T’s Peer to Peer

Innumeracy refers to one’s inability to understand mathematics. Or, more simply, innumeracy is mathematical illiteracy. The main problem with innumeracy is the fact that most of society does not see it as a problem. In fact, many people boast about their innumeracy. Consider a table of five people at a restaurant: they split the check and attempt to calculate the tip. More often than not, at least one individual at the table will joke about the fact that they don’t know how to do make that simple calculation. This flippancy toward the prevalence of mathematics has become an accepted norm, …

Knowledge And Tasks Connecting Elementary, Secondary, And Disciplinary Mathematics, Yvonne Lai

DBER Speaker Series

A well-prepared teacher should be able to help her students see mathematics as ideas that develop over time. Mathematics courses designed specifically for prospective secondary teachers aim for prospective teachers to see and find connections across elementary, secondary, and disciplinary mathematics, and beyond that to be able to use those connections in their future teaching. While there is broad agreement with these aims, there is also little consensus around how to carry them out. Two challenges in meeting these aims are identifying content that lends itself to such connections and designing tasks that can be used to engage with that …

Jay Leno And Abstract Algebra, Adam Glesser, Martin Bonsangue

Journal of Humanistic Mathematics

The Jay Leno skit Jaywalking, showing ordinary people struggling to answer basic questions, is both entertaining and applicable to teaching. This article describes how an instructor can strengthen students' conceptual understanding by creating an element of confusion, or "cognitive dissonance," in the students' minds using Jaywalking-style interactions in the classroom.

Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.

What If?: Mathematics, Creative Writing, And Play, Emily Clader

Journal of Humanistic Mathematics

Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.