Science and Mathematics Education Commons^™

The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown

Honors Theses

The Creation of a Video Review Guide for the Free-Response Section of the Advanced Placement Calculus Exam follows the creation of a resource to help students prepare for the College Board’s Advanced Placement Calculus Exam. This project originated out of the authors personal experiences in preparing for this exam. The goal of the project was to create an accessible resource that reviews content, provides insights into the Advanced Placement exam, and creates successful habits in student responses. This paper, chronologically, details the development of the resource and a reflection on the final product and future uses.

Pedagogical Moves As Characteristics Of One Instructor’S Instrumental Orchestrations With Tinkerplots And The Ti-73 Explorer: A Case Study, James L. Kratky

Dissertations

Those supporting contemporary reform efforts for mathematics education in the United States have called for increased use of technologies to support student-centered learning of mathematical concepts and skills. There is a need for more research and professional development to support teachers in transitioning their instruction to better meet the goals of such reform efforts.

Instrumental approaches to conceptualizing technology use in mathematics education, arising out of the theoretical and empirical work in France and other European nations, show promise for use to frame studies on school mathematics in the United States. Instrumental genesis is used to describe the bidirectional and …

Going For Gold In The International Math Olympiad, Queena N. Lee-Chua

Mathematics Faculty Publications

In July 2016, two high school students in the Philippine team garnered gold at the 57th International Mathematics Olympiad (IMO) in Hong Kong, capping a three-decade long quest for the top prize in the most prestigious high school math competition in the world. The four other team members also brought home honors, boosting our country to its highest rank ever, 17th out of 109 countries. This article discusses the history of the Philippine participation in the IMO, and examines the critical factors that have led to the victory. For Philippine team participants in general, these include: institutionalized and refined search …

Race, Space, And The Conflict Inside Us, Francis Su

All HMC Faculty Publications and Research

Talking about race is hard. Our nation is wrestling with some open wounds about race. These sores have been around a while, but they have been brought to light recently by technology, politics, and an increasingly diverse population. And regardless of the outcome of the U.S. presidential election, we will all need to work at healing these sores, not just in our personal lives, but in our classrooms and in our profession.

Exploring Connections Between Advanced And Secondary Mathematics, Erin E. Baldinger, Eileen Murray, Diana White, Shawn Broderick, Nicholas Wasserman

Department of Mathematics Facuty Scholarship and Creative Works

The second meeting of this Working Group continues to explore questions about the connections between abstract algebra and school mathematics. Our goal is to focus in on questions around the way in which teachers’ practice might be influenced based on their understanding of such connections. In particular, we will gather interested individuals in an effort to deepen our understanding of existing connections between abstract algebra and secondary mathematics and which of these connections are important for secondary teachers to know and understand. Moreover, we aim to further research in this area by first considering connections between abstract algebra and school …

Life After Calculus: 20 Years Later, Darren B. Glass

Math Faculty Publications

In 1996 Math Horizons interviewed a group of students at the Joint Mathematics Meetings; now, 20 years later, one of those students, Darren Glass, interviews another group of students.

Designing And Mentoring In A Research Experience For Undergraduates, Alex Capaldi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Freedom Through Inquiry, Francis Su

All HMC Faculty Publications and Research

I delivered this speech at the Inquiry‐Based Learning Forum & 19th Annual Legacy of R.L. Moore Conference on August 4, 2016. It is partly an homage to an influential teacher, partly an excuse to articulate what makes some styles of teaching so effective, and partly an excuse to talk about difficult issues facing our nation and our classrooms today.

Definition Of A Method For The Formulation Of Problems To Be Solved With High Performance Computing, Ramya Peruri

Master of Science in Computer Science Theses

Computational power made available by current technology has been continuously increasing, however today’s problems are larger and more complex and demand even more computational power. Interest in computational problems has also been increasing and is an important research area in computer science. These complex problems are solved with computational models that use an underlying mathematical model and are solved using computer resources, simulation, and are run with High Performance Computing. For such computations, parallel computing has been employed to achieve high performance. This thesis identifies families of problems that can best be solved using modelling and implementation techniques of parallel …

Stop Ruining Math! Reasons And Remedies For The Maladies Of Mathematics Education, Rachel M. Steinig

Journal of Humanistic Mathematics

Did you love math as a kid? Or was it ruined for you? Sadly, many people have had math ruined for them for various reasons. Some might say that it was because of not understanding what was going on, being bored in class, parental or societal pressure to achieve in math, not seeing a point in learning math, wrong amount of homework, grades, curriculum, physical concerns, mean teachers, or any number of things. This article delves into the many common reasons why math is ruined for so many kids, and offers solutions so that math can be enjoyable for everyone. …

On A Desert Island With Unit Sticks, Continued Fractions And Lagrange, Victor J. Ricchezza, H. L. Vacher

Numeracy

GLY 4866, Computational Geology, provides an opportunity, welcomed by our faculty, to teach quantitative literacy to geology majors at USF. The course continues to evolve although the second author has been teaching it for some 20 years. This paper describes our experiences with a new lab activity that we are developing on the core issue of measurement and units. The activity is inspired by a passage in the 2008 publication of lectures that Joseph Louis Lagrange delivered at the Ecole Normale in 1795. The activity envisions that young scientists are faced with the need to determine the dimensions of a …

Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis, Janet Heine Barnett

Analysis

No abstract provided.

Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett

Analysis

No abstract provided.

Richard Dedekind And The Creation Of An Ideal: Early Developments In Ring Theory, Janet Heine Barnett

Abstract Algebra

No abstract provided.

The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry, Jerry Lodder

Geometry

No abstract provided.

Pythagorean Combinations For Lego Robot Building., Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

This paper provides tips for LEGO robot construction involving bracing or gear meshing along a diagonal using standard Botball kits.

Critical Thinking Skills And Academic Maturity: Emerging Results From A Five-Year Quality Enhancement Plan (Qep) Study, Ian N. Toppin, Shadreck Chitsonga

Journal of Inquiry and Action in Education

The QEP that was implemented in this study focused on enhancing students’ critical thinking skills. A pretest/ posttest approach was used to assess students’ critical thinking progress in freshman level core English and Math courses. An intervention was performed involving intensive instruction and assignments relating to a set of reasoning strategies such as: analytical, analogical, inductive, deductive, and comparative reasoning, among others. When students performed well on assignments by applying the reasoning strategies, it was assumed that critical thinking occurred. However, pre/ posttest results in these classes were often disappointing, and seemed at times to suggest that freshmen are not …

Math Department Newsletter, 2015-2016, Mathematics Department

Mathematics Newsletter

No abstract provided.

Exploring Argumentation, Objectivity, And Bias: The Case Of Mathematical Infinity, Ami Mamolo

OSSA Conference Archive

This paper presents an overview of several years of my research into individuals’ reasoning, argumentation, and bias when addressing problems, scenarios, and symbols related to mathematical infinity. There is a long history of debate around what constitutes “objective truth” in the realm of mathematical infinity, dating back to ancient Greece (e.g., Dubinsky et al., 2005). Modes of argumentation, hindrances, and intuitions have been largely consistent over the years and across levels of expertise (e.g., Brown et al., 2010; Fischbein et al., 1979, Tsamir, 1999). This presentation examines the interrelated complexities of notions of objectivity, bias, and argumentation as manifested in …

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]

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.

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- …

Connecting Connectedness, Nicholas A. Scoville

Topology

No abstract provided.

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.

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

Geometry

No abstract provided.

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 …

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

All Student Theses

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. …

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.

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, …