Digital Commons Network^™

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 …

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 …

Rebuilding Our Math Community, Jessica Feiwus

Graduate Student Independent Studies

This study investigates the attitudes of second grade students in mathematics. It looks into what research states about student attitudes and anxieties in school age children and different methods of keeping them positive. Over a two-month period, a teacher conducted a study in her classroom in New York City to assess change in student mathematical attitudes over time. A survey was given to her second grade students and changes were made in the classroom environment during math times, as well as within the TERC Investigations curriculum that the school follows. During and following the two-month study, two additional surveys were …

An Investigation Of Air Resistance On Projectile Motion From Aristotle To Euler, Michael Edward Clayton

Theses Digitization Project

From antiquity until today, mathematicians have tried to develop a theory of projectile motion. The development of a theory of projectile motion began with just a basic observation of motion by the great Greek mathematician Aristotle and has evolved to become more than conjecture or hypothesis, but a well developed science of prediciting the flight and accuracy of a projectile in motion. This thesis traces the development of the theory of projectile motion from Greek antiquity to about the mid 1700's.

Teaching Mathematics In The Classroom With Powerpoint Software, Robert Ward Kopp

Theses Digitization Project

This study will look at at how to better student achievement in an Algebra II course. Specifically this study examines two different modifications made during the second semester of an Algebra II course taught at a high school in Riverside County. The modifications that were made were based on a detailed literature review that suggested looking at how students learn while using PowerPoint software as an instructional tool and at the same time investigate the consequence of rearranging a fairly common and predetermined curriculum pattern.

Greenstem@Vcu: An Innovative Program For Integrating Service-Learning Into Middle School Science, Technology And Mathematics Instruction, Suzanne Kirk, Kelly Lockeman, Lynn Pelco

Division of Community Engagement Resources

GreenSTEM integrates science, technology, engineering and math (STEM) education with a focus on energy and the environment using service-learning techniques for middle school science, mathematics and technology teachers.

Cayley-Dickson Loops, Jenya Kirshtein

Electronic Theses and Dissertations

In this dissertation we study the Cayley-Dickson loops, multiplicative structures arising from the standard Cayley-Dickson doubling process. More precisely, the Cayley-Dickson loop Q_n is the multiplicative closure of basic elements of the algebra constructed by n applications of the doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, sedenions). Starting at the octonions, Cayley-Dickson algebras and loops become nonassociative, which presents a significant challenge in their study.

We begin by describing basic properties of the Cayley–Dickson loops Q_n. We establish or recall elementary facts about Q_n, e.g., inverses, …

Leonhard Euler's Contribution To Infinite Polynomials, Jack Dean Meekins

Theses Digitization Project

This thesis will focus on Euler's famous method for solving the infinite polynomial. It will show how he manipulated the sine function to find all possible points along the sine function such that the sine A would equal to y; these would be roots of the polynomial. It also shows how Euler set the infinite polynomial equal to the infinite product allowing him to determine which coefficients were equal to which reciprocals of the roots, roots squared, roots cubed, etc.

How Much Do Our Incoming First Year Students Know?:Diagnostic Testing In Mathematics At Third Level, Blathnaid Sheridan

Teaching Fellowships

A continuing cause for concern in higher education institutions is the poor core mathematical skills of incoming students. Many institutions now offer mathematics support services such as drop-in centres, online resources and short “refresher courses” in an attempt to alleviate the problem. The majority of third level institutions in Ireland and internationally now make use of diagnostic testing of incoming first year students that both predict subsequent success and select groups for remediation. This project was developed to explore the issues around diagnostic testing and follow up support for incoming students in the College of Sciences and Health. A large …

Humanistic Mathematics: An Oxymoron?, Gizem Karaali

Pomona Faculty Publications and Research

Mathematics faculty are trained as mathematicians, first and foremost. If we did not experience the soul-expanding possibilities of liberal education during our own undergraduate years, we may hesitate to bridge disciplinary divides when pursuing our core human need to inquire and understand. Although most mathematicians I know are amazing teachers, communicators, and mentors, many still teach the same material that their professors and their professors’ professors taught. This time-tested approach can be powerful, fascinating, and even quite entertaining. But it can also seem far removed from the world we inhabit. Yes, we teach “real world applications” of mathematical concepts. Yet …

Should Electrical Apprentices Study More Mathematics, David Lalor

Conference papers

The Department of Electrical Services Engineering, formerly known as the Installation Department, Kevin St., train Electrical Apprentices to become Qualified Electricians, has recently started to award Degrees in Electrical Services Engineering which includes the built environment. These students come from CAO applicants and from phase 6 students who have passed through the school. It is a popular and well subscribed course. I am involved in teach Phase 4 and 6. To progress to phase 6, phase 4 students must pass four examinations of which Electric Science is by all accounts the most difficult. To qualify as Electricians phase 6 also …

Adventures In Teaching: A Professor Goes To High School To Learn About Teaching Math, Darryl H. Yong

All HMC Faculty Publications and Research

During the 2009–2010 academic year I did something unusual for a university mathematician on sabbatical: I taught high school mathematics in a large urban school district. This might not be so strange except that my school does not have a teacher preparation program and only graduates a few students per year who intend to be teachers. Why did I do this? I, like many of you, am deeply concerned about mathematics education and I wanted to see what a typical high school in my city is like. Because I regularly work with high school mathematics teachers, I wanted to experience …

Delay-Periodic Solutions And Their Stability Using Averaging In Delay-Differential Equations, With Applications, Thomas W. Carr, Richard Haberman, Thomas Erneux

Mathematics Research

Using the method of averaging we analyze periodic solutions to delay-differential equations, where the period is near to the value of the delay time (or a fraction thereof). The difference between the period and the delay time defines the small parameter used in the perturbation method. This allows us to consider problems with arbitrarily size delay times or of the delay term itself. We present a general theory and then apply the method to a specific model that has application in disease dynamics and lasers.

Neuropsychological Predictors Of Math Calculation And Reasoning In School-Aged Children, Dana Schneider

Electronic Theses and Dissertations

After multiple reviews of the literature, which documented that multiple cognitive processes may be involved in mathematics ability and disability, Geary (1993) proposed a model that included three subtypes of math disability: Semantic, Procedural, and Visuospatial. A review of the extant literature produced three studies that examined Geary's three subtypes, which provided some support for Geary's model. Given the paucity of research examining Geary's subtypes of math disability, this study aimed to add to the literature by exploring the presence of these three subtypes in a sample of school-aged children. The sample consisted of 60 participants (30 males, 30 females) …

Boundary Values In Range Spaces Of Co-Analytic Truncated Toeplitz Operator, William T. Ross, Andreas Hartmann

Department of Math & Statistics Faculty Publications

Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some distribution condition on the zeros and the singular measure of the inner function, it is possible to obtain non-tangential boundary values of every function in the backward shift invariant subspace as well as for their derivatives up to a certain order. Here we will investigate, at least when the inner function is a Blaschke product, the non-tangential boundary values of the functions of the backward …

Mathematical Analysis Of The Problems Faced By The People With Disabilities (Pwds), Florentin Smarandache, W.B. Vasantha Kandasamy, A. Praveen Prakash

Branch Mathematics and Statistics Faculty and Staff Publications

The authors in this book have analyzed the socio-economic and psychological problems faced by People with Disabilities (PWDs) and their families. The study was made by collecting data using both fuzzy linguistic questionnaire / by interviews in case they are not literates from 2,15,811 lakhs people. This data was collected using the five Non Government Organizations (NGOs) from northern Tamil Nadu. Now any reader would be interested to know whether the Tamils (natives of Tamil Nadu) had ever spoken about people with disability. Even before 2000 years tamils had heroic poetry Purananuru (28th poem) about the war fare methods. In …

Mathematic Strategies For Teaching Problem Solving: The Influence Of Teaching Mathematical Problem Solving Strategies On Students' Attitudes In Middle School, Kelly Lynn Klingler

Electronic Theses and Dissertations

The purpose of this action research study was to observe the influence of teaching mathematical problem solving strategies on students’ attitudes in middle school. The goal was to teach five problem solving strategies: Drawing Pictures, Making a Chart or Table, Looking for a Pattern, Working Backwards, and Guess and Check, and have students reflect upon the process. I believed that my students would use these problem solving strategies as supportive tools for solving mathematical word problems. A relationship from the Mathematics Attitudes survey scores on students’ attitudes towards problem solving in mathematics was found. Students took the Mathematics Attitudes survey …

The Effects Of Journaling And Vocabulary Strategies On Elementary Students' Attitudes Towards Mathematical Performance, Renee Marie Janzen

Electronic Theses and Dissertations

In an attempt to examine the effects of journaling and vocabulary strategies on elementary students’ attitudes towards mathematical performance, I embedded reflective journaling and vocabulary strategies into my fourth grade mathematics curriculum. The mathematics content focused on whole number place value, multiplication, and division. My study revealed the positive effects these interventions can have on elementary students’ attitudes towards mathematics.

Numerical And Analytical Methods For Variational Inequalities And Related Problems With Applications, Zhenyu Huang, Ram N. Mohapatra, Muhammad Aslam Noor, Hong-Kun Xu, Qingzhi Yang

Faculty Bibliography 2010s

No abstract provided.

Improving Student Learning In Undergraduate Mathematics, Gabrielle Rejniak

Electronic Theses and Dissertations

The goal of this study was to investigate ways of improving student learning, par- ticularly conceptual understanding, in undergraduate mathematics courses. This study focused on two areas: course design and animation. The methods of study were the following: Assessing the improvement of student conceptual understanding as a result of team project-based learning, individual inquiry-based learning and the modi ed empo- rium model; and Assessing the impact of animated videos on student learning with the emphasis on concepts. For the first part of our study (impact of course design on student conceptual understanding) we began by comparing the following three groups …

Monitoring Australian Year 8 Student Achievement Internationally : Timss 2011, Sue Thomson, Kylie Hillman, Nicole Wernert

TIMSS 2011 and PIRLS 2011

The Trends in International Mathematics and Science Study (TIMSS 2011) is an international study directed by the International Association for the Evaluation of Educational Achievement (IEA). In Australia, TIMSS was managed by the Australian Council for Educational Research (ACER), and funded by the Australian and state and territory governments.

The goal of TIMSS is to provide comparative information about educational achievement across countries to improve teaching and learning in mathematics and science. It also provides comparative perspectives on trends in achievement in the context of different educational systems, school organisational approaches and instructional practices and to enable this, TIMSS collects …

Iteration Digraphs, Hannah Roberts

Senior Independent Study Theses

No abstract provided.

Determining Impact: Using Formative Evaluation In A Professional Development Program For Teachers Of Mathematics And Science, Tiah B. Alphonso

LSU Master's Theses

The purpose of this study was to evaluate a professional development (PD) program for middle and high school teachers of mathematics and science which is funded by a $5 million National Science Foundation grant. The evaluation was internal and formative in nature and took place in two separate phases. The focus of the evaluation was not only on program improvement but also to extend the body of existing knowledge in the area of teacher professional development. Both the needs of project stakeholders and the findings of previous research in the areas of professional development and program evaluation were drawn on …

Algebraic Pairs Of Isometries, Jim Agler, Greg Knese, John E. Mccarthy

Mathematics Faculty Research

We consider pairs of commuting isometries that are annihilated by a polynomial. We show that the polynomial must be inner toral, which is a geometric condition on its zero set. We show that cyclic pairs of commuting isometries are nearly unitarily equivalent if they are annihilated by the same minimal polynomial.

Examination Of An Online College Mathematics Course: Correlation Between Learning Styles And Student Achievement, Bridget Steele

Electronic Theses and Dissertations

The purpose of this study was to determine if there was a significant relationship between learning styles and student learning outcomes in an online college mathematics course. Specifically, the study was guided by two research questions focused on (a) the extent to which learning styles had a predictive relationship with student achievement in an online college mathematics course and (b) the extent to which various learning styles among mathematics students in online versus face-to-face courses predicted mathematics achievement. The population for this study consisted of the 779 college mathematics and algebra (CMA) students who were enrolled in a private multimedia …

Enriching Students With Developmental Delays In An Early Childhood Classroom Using Ipads With Mathematics Applications, Selma Powell

Electronic Theses and Dissertations

Laws and legislation related to early childhood and special education have shaped the field and impacted the need for early intervention services, but the outcomes of those services both academically and socially at the forefront. Children with developmental delays today are eligible for school services beginning at birth across the country, the new challenging is determining the impact of services on the social and academic outcomes. Many children with developmental delays are served in inclusive early intervention classrooms. A need for developmentally appropriate quality mathematics instruction exists to prepare students to meet the demands of a global economy; students must …

Processes And Pathways: How Do Mathematics And Science Partnerships Measure And Promote Growth In Teacher Content Knowledge?, Patricia S. Moyer-Packenham, A. Westenskow

Teacher Education and Leadership Faculty Publications

Intense focus on student achievement results in mathematics and science has brought about claims that K-12 teachers should be better prepared to teach basic concepts in these disciplines. The focus on teachers' mathematics and science content knowledge has been met by efforts to increase teacher knowledge through funded national initiatives focusing on mathematics and science. The purpose of the present study was to look across projects in the National Science Foundation's Math and Science Partnership Program to determine how partnerships developed processes for measuring growth in teacher content knowledge. Pre- and post-testing was the most common process for measuring growth …

Equal Or Not? An Exploration Of Eighth-Grade Students' Experience Of Algebra, Janice L. Reyes

College of Graduate Studies: Theses & Dissertations

Over the past two decades, a considerable amount of algebra instruction nationwide has shifted from high school to middle school. In Georgia, all eighth-grade students have been required to take a course that is equivalent to about 80 percent of a traditional Algebra 1 course. The purpose of this qualitative study was to explore how a selected group of eighth-grade students in a suburban Georgia middle school experience algebra within the eighth grade mathematics curriculum. A qualitative research design was used to investigate students’ perceptions of algebra, the strategies employed by teachers to teach algebra, students’ difficulties with algebra, and …

Daily Flash Card Drills And Systems Thinking To Master Math Addition Facts, Jerome Ravenna

Abraham S. Fischler College of Education ETD Archive

This applied dissertation was designed to provide better access to information for the students and staff in an elementary school regarding acquisition and retention of basic addition math facts. Teaching techniques and strategies were explored that would enable elementary students to master essential skills in mathematics.

By the end of the first semester in Grade 1, learners must demonstrate knowledge of basic mathematic facts, especially in addition. Learners are subjected to diversified instruction where schools strive to teach a wide variety of subject materials rather than focus on basic skills and mastery. The result is broader student awareness of many …

Cycles And Bases Of Graphs And Matroids, Ping Li

Graduate Theses, Dissertations, and Problem Reports (ETD)

The objective of this dissertation is to investigate the properties of cycles and bases in matroids and in graphs. In [62], Tutte defined the circuit graph of a matroid and proved that a matroid is connected if and only if its circuit graph is connected. Motivated by Tutte's result, we introduce the 2nd order circuit graph of a matroid, and prove that for any connected matroid M other than U1,1, the second order circuit graph of M has diameter at most 2 if and only if M does not have a restricted minor isomorphic to U2,6.;Another research conducted in this …