Mathematics Commons^™

Undergraduate Research Fellowships: A Strategic Investment To Reduce Women Underrepresentation In The Mathematical Sciences, Janie L. Knell, Wilson Gonzalez-Espada

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

How Do Manipulatives Help Students Communicate Their Understanding Of Double-Digit Subtraction?, Rabab Abi-Hanna

Theses, Dissertations and Culminating Projects

Multi-digit subtraction is difficult for students to learn. The purpose of this study is to explore how second-grade students communicate their understanding of double-digit subtraction through the use of manipulatives/tools. This qualitative study reports on six case studies of second-grade students where clinical interviews were the main source of data. Findings suggest that manipulatives/tools helped reveal cognitive constructs and difficulties that the handwritten algorithms were not conveying. For example, students who exhibited an understanding of the subtraction process had not yet developed an understanding of ten and 10 ones interchangeability. These results highlight the potential role of manipulatives/tools as communication …

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- …

Dagum-Poisson Distribution: Model, Properties And Application, Broderick O. Oluyede, Galelhakanelwe Motsewabagale, Shujiao Huang, Gayan Warahena-Liyanage, Marvis Pararai

Mathematical Sciences: Faculty Publications

A new four parameter distribution called the Dagum-Poisson (DP) distribution is introduced and studied. This distribution is obtained by compounding Dagum and Poisson distributions. The structural properties of the new distribution are discussed, including explicit algebraic formulas for its survival and hazard functions, quantile function, moments, moment generating function, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics and R\'enyi entropy. Method of maximum likelihood is used for estimating the model parameters. A Monte Carlo simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the …

Bivariate Barycentric-Coordinate Berstein-Bezier Polynomial & C1 Quadratic Vertex Spline, Rui Jiang, Tian-Xiao He, Faculty Advisor

John Wesley Powell Student Research Conference

Poster presentation abstract.

Integer Antimagic Labeling For Cycle With One Chord, Jinze Zheng, Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

Poster presentation abstract.

Multidecomposition Of Complete Directed Graphs Into Directed Graph Pairs Of Order 3 And 4, Jacob Henry, Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

Oral presentation abstract.

Multidesigns For A Graph Pair Of Order 6, Yizhe Gao, Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

Oral presentation abstract.

Duals Of Bernoulli Numbers And Polynomials And Euler Numbers And Polynomials, Jinze Zheng, Tian-Xiao He, Faculty Advisor

John Wesley Powell Student Research Conference

Oral presentation abstract.

C7 And C7 Complement Multidecomposition Of Kn, Hang Phung, Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

Poster presentation abstract.

Generalized Catalan Numbers And Their Properties, Yuanziyi Zhang, Tian-Xiao He, Faculty Advisor

John Wesley Powell Student Research Conference

Poster presentation abstract.

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.

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.

Collaboration And Creativity In Southern Califonia: An Offering, Gizem Karaali, Ami Radunskaya

Pomona Faculty Publications and Research

WiMSoCal (Women in Math in Southern California) is a regional conference in its ninth incarnation. The conference is the result of the efforts of Professor Cymra Haskell (USC) to create a supportive local community for women mathematicians. At our first meeting in 2007, a confluence of Ami’s EDGE regional cluster and Cymra’s WISE group at USC, we socialized, got to know each other and brainstormed about what we, as a group, would like to see happen. It was clear that our younger colleagues wanted to meet as mathematicians, sharing intellectual ideas as well as anecdotes from the trenches.

Does Academic Performance Predict Workplace Productivity?, Jodie-Gaye Hunter

Honors Projects in Economics

This research examines if college GPA affects productivity and compensation in the workplace. It uses data collected from a survey of approximately 23,000 Bryant University graduates in different stages of their career. About 10 percent of the alumni surveyed completed the survey. The econometric model used in this study allows estimating the effect of GPA on income after controlling for various demographic and socioeconomic variables, including education, major, occupation, gender, among others. The empirical work provides evidence that GPA has a positive and statistically significant impact on workplace productivity for females, but GPA seems to be a weaker predictor of …

Exploring The Relationship Between High School Diploma Requirements In Mathematics And College Remediation Rates, Derek J. Brown

Doctor of Education (EdD)

This study examined the relationship between the essential skill of math and college remediation rates using a dataset of 1,858 recent high school graduates attending public, 4-year Oregon universities. Using a logistic regression methodology, this study explored (a) the extent to which the essential skill of math improved college remediation rates, (b) the association between allowable essential skill of math sources of evidence and college remediation rates, and (c) the impact of the essential skill of math on students from various demographic backgrounds. Results from this study suggest the essential skill of math graduation requirement significantly predicts the likelihood of …

Choosing The Right Tool, Stacy K. Boote

UNF Faculty Research and Scholarship

No abstract provided.

The Gold Standard And Education Intervention Research: A Consideration Of Middle School Mathematics Interventions As A Particular Case, Sarah Nielsen , '16

Senior Theses, Projects, and Awards

This thesis explores the benefits and drawbacks of various experimental designs, outcome measures, and specific methodological techniques in education intervention research. Through an analysis of nine top-tier journals in education, I describe which experimental designs and outcome measures are most commonly used in current middle school mathematics intervention research. Then, four case intervention studies with different experimental designs are closely examined. This discussion is juxtaposed with consideration of evaluation standards published by government agencies. Each study represents different discourses about the effectiveness of the intervention reported. Although the standards for intervention research no longer only promote randomized quantitative research, I …

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. …

Beta Linear Failure Rate Geometric Distribution With Applications, Broderick O. Oluyede, Ibrahim Elbatal, Shujiao Huang

Mathematical Sciences: Faculty Publications

This paper introduces the beta linear failure rate geometric (BLFRG) distribution, which contains a number of distributions including the exponentiated linear failure rate geometric, linear failure rate geometric, linear failure rate, exponential geometric, Rayleigh geometric, Rayleigh and exponential distributions as special cases. The model further generalizes the linear failure rate distribution. A comprehensive investigation of the model properties including moments, conditional moments, deviations, Lorenz and Bonferroni curves and entropy are presented. Estimates of model parameters are given. Real data examples are presented to illustrate the usefulness and applicability of the distribution.

Improved Full-Newton-Step Infeasible Interior-Point Method For Linear Complementarity Problems, Goran Lesaja, Mustafa Ozen

Mathematical Sciences: Faculty Publications

We present an Infeasible Interior-Point Method for monotone Linear Complementarity Problem (LCP) which is an improved version of the algorithm given in [13]. In the earlier version, each iteration consisted of one feasibility step and few centering steps. The improved version guarantees that after one feasibility step, the new iterate is feasible and close enough to the central path thanks to the much tighter proximity estimate which is based on the new lemma introduced in [18]. Thus, the centering steps are eliminated. Another advantage of this method is the use of full-Newton-steps, that is, no calculation of the step size …

Research And Evaluation Of The Effectiveness Of E-Learning In The Case Of Linear Programming, Ljiljana Miletić, Goran Lesaja

Mathematical Sciences: Faculty Publications

The paper evaluates the effectiveness of the e-learning approach to linearprogramming. The goal was to investigate how proper use of information andcommunication technologies (ICT) and interactive learning helps to improve high schoolstudents’ understanding, learning and retention of advanced non-curriculum material.The hypothesis was that ICT and e-learning is helpful in teaching linear programmingmethods. In the first phase of the research, a module of lessons for linear programming(LP) was created using the software package Loomen Moodle and other interactivesoftware packages such as Geogebra. In the second phase, the LP module was taught asa short course to two groups of high school students. …

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 Power Of Two: Two Tips For Mathematicians, Gizem Karaali

Pomona Faculty Publications and Research

This post is about two great tips involving the number 2 that I learned along the way. They will perhaps not double your happiness or fortune, but I promise you that you will not regret it if you do decide to take them along for the ride.

Applying Linear Controls To Chaotic Continuous Dynamical Systems, James P. Braselton, Yan Wu

Mathematical Sciences: Faculty Publications

In this case-study, we examine the effects of linear control on continuous dynamical systems that exhibit chaotic behavior using the symbolic computer algebra system Mathematica. Stabilizing (or controlling) higher-dimensional chaotic dynamical systems is generally a difficult problem, Musielak and Musielak, [1]. We numerically illustrate that sometimes elementary approaches can yield the desired numerical results with two different continuous higher order dynamical systems that exhibit chaotic behavior, the Lorenz equations and the Rössler attractor.

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

National Youth Advocacy & 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.

Session E-2: Function Fundamentals, More Than X And Y, Carlo Ordonez, Steven M. Condie

Professional Learning Day

How many of your students say that √9 = ±3? This may have to do with a lack of understanding of functions. This session will highlight some of the nuances of functions with less formal, non-formula driven examples with which students can expand their understanding.

Session D-3: The Mathematical Wonders Of Pascal's Triangle, Donald Porzio

Professional Learning Day

Most mathematics teachers are aware of the some of the more straightforward connections Pascal's Triangle has to mathematics. Come explore some of the lesser known connections that can be used to peak your students' interest and entice them into exploring the mathematics behind these connections.