Mathematics Commons^™

Promoting Reu Participation From Students In Underrepresented Groups, Heather M. Russell, Heather A. Dye

Department of Math & Statistics Faculty Publications

Research experiences for undergraduates (REUs) are an important component of undergraduate education. However, at the 2012 Trends in Undergraduate Research in the Mathematical Sciences conference, questions were raised about why many REU programs see few applications from students that are members of underrepresented groups. We examine the benefits of REUs and factors preventing or promoting participation in REUs.

Exploring The Effects Of Conversational Repair As A Scaffolding Strategy To Promote Mathematics Explanations Of Students With Learning Disabilities, Jia Liu

Open Access Dissertations

Conversational repair often occurs in conversations when people attempt to address communicative breakdowns or inaccuracy by way of repeating what have been said or putting them in another way. The review of literature on conversational repair revealed that as an important concept in pragmatic aspect of language, it is an effective strategy to improve communication of different populations with disabilities. However, it is rarely studied in the domain of mathematics and with the population with learning disabilities/difficulties (LD). In current reform-based, discourse-oriented mathematics classrooms, students with LD encounter difficulties articulating or explaining well their reasoning processes due to the mathematical …

Comparing The Impact Of Traditional And Modeling College Algebra Courses On Student Performance In Survey Of Calculus, Jerry West

Graduate Theses and Dissertations

Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to maximize students' potential in utilizing mathematics and gaining skills required in subsequent math-based courses when necessary. The Committee for Undergraduate Programs in Mathematics has gone through extensive work to help mathematics departments reform their college algebra courses in order to help students gain interest in the utilization of mathematics …

Some Results On Cryptanalysis Of Rsa And Factorization., Santanu Sarkar Dr.

Doctoral Theses

In this thesis, we propose some new results in Cryptanalysis of RSA and related Factorization problems. Till date, the best known algorithm to solve the Integer Factorization problem is the Number Field Sieve, which has a runtime greater than exp(log1/3 N) for factoring an integer N. However, if one obtains certain information about the RSA parameters, there are algorithms which can factor the RSA modulus N = pq quite efficiently. The intention of this thesis is to identify such weaknesses of the RSA cryptosystem and its variants. Further we study results related to factorization.In Africacrypt 2008, Nitaj presented a class …

What Does It Take To Teach Nonmajors Effectively?, Feryal Alayont, Gizem Karaali, Lerna Pehlivan

Pomona Faculty Publications and Research

Most MAA members teach mathematics at the college level, and many often teach courses intended for nonmajors. Indeed this is one of the main responsibilities of a mathematics department: offering service courses for client departments and general education courses for nonmajors. The three of us have been thinking about the question of how to teach nonmajors successfully for a while now. Finally we decided on a time-tested method of figuring things out: if you don't know what to do, ask the experts. We organized a panel titled "Effective Strategies for Teaching Classes for Nonmajors" for MAA MathFest 2012 and invited …

Medicine, Statistics, And Education: The Inextricable Link, Katharine K. Brieger '11, Johanna S. Hardin

Pomona Faculty Publications and Research

No abstract provided.

In Defense Of Frivolous Questions, Gizem Karaali

Pomona Faculty Publications and Research

Is there any reason for today's academic institutions to encourage the pursuit of answers to seemingly frivolous questions? The opinionated business leader who does not give a darn about your typical liberal arts classes "because they do not prepare today’s students for tomorrow's work force" might snicker knowingly here: Have you seen some of the ridiculous titles of the courses offered by the English / literature / history / (fill in the blank) studies department in the University of So-And-So? Why should any student take "Basketweaving in the Andes during the Peloponnesian Wars"? Just what would anyone gain from …

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 …

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 …

A Wealth Of Numbers: An Anthology Of 500 Years Of Popular Mathematics Writing, By Benjamin Wardhaugh. Princeton University Press: Princeton, 2012 (Book Review), John A. Adam

Mathematics & Statistics Faculty Publications

(First paragraph) To describe the landscape encompassed by this book I can do no better than to quote the dust jacket: "A Wealth of Numbers includes recreational, classroom, and work mathematics; mathematical histories and biographies; accounts of higher mathematics; explanations of mathematical instruments; discussions of how math should be taught and learned; reflections on the place of math in the world; and math in fiction and humor." More such details can be found on the Princeton University Press website. I shall use this as a point of departure to describe the highlights of my own trajectory through the book. Not …

Interactive Real-Time Embedded Systems Education Infused With Applied Internet Telephony, Kyle Persohn, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

The transition from traditional circuit-switched phone systems to modern packet-based Internet telephony networks demands tools to support Voice over Internet Protocol (VoIP) development. In this paper, we introduce the XinuPhone, an integrated hardware/software approach for educating users about VoIP technology on a real-time embedded platform. We propose modular course topics for design-oriented, hands-on laboratory exercises: filter design, timing, serial communications, interrupts and resource budgeting, network transmission, and system benchmarking. Our open-source software platform encourages development and testing of new CODECs alongside existing standards, unlike similar commercial solutions. Furthermore, the supporting hardware features inexpensive, readily available components designed specifically for educational …

Income Inequality And Spatial Distribution : Firm Location, Product Quality And Welfare Of Poor., Namrata Gulati Dr.

Doctoral Theses

The key idea explored in this thesis is the following: though being poor in itself is a huge disadvantage, the situation might be influenced considerably by the type of neighbourhood the poor lives in as private establishments like educational institutions, health care facilities or credit institutions take both the location and income mix of people into account while making strategic decisions like whether to enter into the neighbourhood at all, and, upon entry, what price and quality to choose for their products and services. Is staying with the rich a virtue for the poor or a source of resentment? Are …

Public Policy, Long Run Growth And Economic Transition From Agriculture To Industrial Mass Production., Rudrani Bhattacharya Dr.

Doctoral Theses

It has been recognized that the heart of the development process lies on the transformation of an economy from traditional activities in agriculture to industrial activities. As emphasized by Lewis (1954), the movement of labor from primary sector to industry is conducive to the rise of economy’s savings and investment rate and thus fostering economic growth. The core of this paradigm is the historically observed rapid growth in today’s developed countries associated with expansion of industrial activities.It is well-documented by now that at least over a few centuries leading up to 1800 AD there was little change in the world …

Wealth Inequality And Economic Performances., Sahana Roy Chowdhury Dr.

Doctoral Theses

Ever since the inception of Development Economics as a separate discipline inequality has been a major area of extensive study. Economists and researchers have deliberated both on the causes and the effects of inequality in a wide range of treatise, books and essays. So far, in this regard, two fundamental approaches came across viz., the Classical approach and the Credit Market Imperfection approach. The Classical approach was originated by Smith (1937) and was further interpreted and developed by Keynes (1920), Lewis (1954), Kaldor (1957), and Bourguignon (1981). According to this approach, savings rate is an increasing function of wealth and …

Gender Bias In Education In West Bengal., Chayanika Mitra Dr.

Doctoral Theses

There exists a vast literature with evidences of gender discrimination against females in allocation of goods and services at regional/national level in India. Evidence of gender bias on Indian data include, among many others, studies by Subramanian and Deaton (1991), Azam and Kingdon (2013), Kingdon (2005), Drèze and Kingdon (2001), Zimmerman (2012) and Lancaster, Maitra, and Ray (2008). India has a history of preference for sons over daughters for cultural and economic reasons. This is manifested through high birth sex ratios, which is possibly a result of female foeticide. The child sex ratio is within the normal natural range in …

The Influence Of Inclusion On Langauge Arts Literacy And Math Achievement On Non-Disabled Middle School Students, Faye Brady

Seton Hall University Dissertations and Theses (ETDs)

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Human Capital And Economic Growth: Theory And Policy., Bidisha Chakraborty Dr.

Doctoral Theses

Growth theory is one of the most important branches of macroeconomics. Growth theory helps us to understand the intertemporal behaviour of a dynamic economy and to understand the properties of the long-run rate of economic growth. It identifies the factors causing the deviation of the actual rate of growth from the socially efficient rate of growth and analyses the effectiveness of various policies in removing this gap. It analyses the condition of stability of the long-run equilibrium and also attempts to establish links between the long run equilibrium and the persistence of underdevelopment.With the emergence of the ‘new’ growth theory, …

Parts Of The Whole: Approaching Education As A System, Dorothy Wallace

Numeracy

An educational system is a highly coupled complex system of inputs, outputs, sensors and actuators. Using an engineering perspective, this column begins the process of naming and categorizing parts of the system. It then focuses on teachers as one part of a large system, and analyzes the forces that influence how teachers work, and that draw or repel individuals to a teaching career. The growing shortage of qualified teachers can be explained by properties of the system as a whole that determine the context in which teachers do their job.

Math Island At Brewer Elementary School: A Learner-Centered Model For Education, Vikki K. Collins, H. Marguerite Yates

Georgia Educational Researcher

This paper examines a learner-centered model for the teaching of elementary mathematics established at an urban Georgia school that serves a highly mobile, diverse population of approximately 475 students. The school was on its state’s list of schools needing improvement because students continued to perform poorly on standardized tests. Math Island, a support center for students designed to facilitate the conceptual understanding of mathematics, was created, and professional development programs were implemented to assist teachers in developing their pedagogical and content expertise in the teaching of mathematics. The school made substantial progress after these initiatives were employed and was removed …

All The More Reason For Qr Across The Curriculum, Bernard L. Madison

Numeracy

No abstract provided.

Empirical Development Of An Instructional Product And Its Impact On Mastery Of Geometry Concepts, Donaldson Williams

Dissertations

Problem

Relatively poor levels of mathematical thinking among American school children have been identified as a major issue over the past half century. Many efforts have been made to increase the mathematics performance of children in schools. Additionally, out-of-school-time programs have attempted to address this issue as well. Holistic development is one of the distinguishing features of Seventh-day Adventist instructional programs. Yet, as of 2007, the Pathfinder program, an informal educational program operated by the world-wide Seventh-day Adventist church, had no instructional product designed to foster participants’ cognitive development in mathematics. This study focused on the empirical development of an …

The Process Of Tracking In Mathematics In Box Elder School District, Megan Haramoto Bushnell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Educational policymakers have used tracking to instruct students in a variety of subjects, including mathematics. Tracking, which has also been called ability grouping, is a process by which students in the same grade are placed into different classes based on academic ability. Few educators and sociologists have looked at the process by which students are placed in different mathematics tracks. The research design of this study focused on accumulating, evaluating, and reporting the understanding and observations of 12 teachers and 4 counselors as they discussed their knowledge and involvement in the mathematics placement procedures from the intermediate and middle school …

Mathematicians Playing A Role In Math Education: What We Learned At The Ime/Mime Workshop, Anna Bargagliotti, Rama Chidambaram, Gizem Karaali

Pomona Faculty Publications and Research

In Hollywood, some actors are regularly cast as mean, others as sweet and endearing, and some typically play innocent big-eyed youths who inevitably succeed after awakening to the particular facts of life that their producer wants them to awaken to. It is unusual and difficult for actors to cross the bridge between different types on a regular basis. However, there are always exceptions to the rule.

In the seemingly unrelated world of academics, mathematics faculty may find themselves playing different roles. People with different skills and interests strive to balance their careers in ways that will be uniquely fulfilling to …

The Art Of Teaching Mathematics, Garikai Campbell, Jon T. Jacobsen, Aimee S A Johnson, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

On June 10–12, 2007, Harvey Mudd College hosted A Conference on the Art of Teaching Mathematics. The conference brought together approximately thirty mathematicians from the Claremont Colleges, Denison, DePauw, Furman, Middlebury, Penn State, Swarthmore, and Vassar to explore the topic of teaching as an art. Assuming there is an element of artistic creativity in teaching mathematics, in what ways does it surface and what should we be doing to develop this creativity?

Teaching Time Savers: The Exam Practically Wrote Itself!, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I first started teaching, creating an exam for my upper division courses was a genuinely exciting process. The material felt fresh and relatively unexplored (at least by me), and I remember often feeling pleasantly overwhelmed with what seemed like a vast supply of intriguing and engrossing exam-ready problems. Crafting the perfect exam, one that was noticeably inviting, exceedingly fair, and unavoidably illuminating, was a real joy.

Teaching Time Savers: Is Homework Grading On Your Nerves?, Lisette G. De Pillis, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

You have probably heard it said that we learn mathematics best when we do mathematics, or that mathematics is not a spectator sport. For most of our students, this means that their mathematics courses will involve a fair amount of homework. This homework is often used to evaluate individual student progress, but it can also be used, for example, as a catalyst for discussion, to emphasize a point made in class, and to identify common misunderstandings throughout the class as a whole. There is, however, the matter of grading homework.

Collected Papers Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Teaching Time Savers: Some Advice On Giving Advice, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

There are always a lot of questions that need to be answered at the beginning of a course. When are office hours? What are the grading policies? How many exams will there be? Will late homework be accepted? We have all seen the answers to these sorts of questions form the bulk of a standard course syllabus, and most of us feel an obligation (and rightly so) to provide such information.

Teaching Time Savers: Style Points, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I began as an assistant professor, I had a pretty good sense of how much time it would take for me to prepare for each class. After a few conversations with my new colleagues, I even had a good sense of how much time I should devote to tasks like office hours and committee work. Somewhere in the middle of grading my first exam, though, it became painfully clear that I had underestimated the amount of time I would need to grade exams!

How Have Teachers Affected The Disinterest Towards Mathematics?, Amy Brown

Senior Honors Projects

In our school system today there is a collective disinterest and lack of enthusiasm towards mathematics as a whole. This apathy is prevalent as early as elementary school and continues through higher education. It is disheartening that so many students avoid mathematics because of their misconception that it is too difficult and has little value in their future. How well prepared are our teachers to deal with this? I began my research by looking at the past perceptions of mathematics and how the reform movement has changed this perspective. I also looked at the changing standards and how the Principles …