Mathematics Commons^™

If You Really Want To Get Ahead, Get A Bunch Of Theories… And Data To Test Them, Alan H. Schoenfeld

The Mathematics Enthusiast

This paper addresses questions of mathematics teachers’ professional development. My goal is not to provide “answers,” although I have worked for some years to enhance teachers’ capacity to create rich learning environments for their students. Rather, my goal is to problematize the issue, to ask: How do we frame questions of professional development in ways that are theoretically grounded? What theories do you need to know, in order do a good job of professional development? In the light of this kind of theoretical framing, I will discuss two related attempts at supporting teachers in their work.

The Teachers Institute Approach To Professional Development, Roger Howe

The Mathematics Enthusiast

The Yale New Haven Teachers Institute (YNHTI) provides a distinctive, perhaps nearly unique, approach to professional development. It originated in the 1978 as an outreach activity of Yale University to the New Haven Public Schools. For 20 years, it operated almost exclusively in New Haven. In 1998, under the leadership of its founder, James Vivian, YNHTI conducted a National Demonstration Project, and since 2004 has promoted a National Initiative, to spread the Teachers Institute model to other cities, with a focus on school districts with low income demographics. Currently there is a League of Teachers Institutes with Institutes operating in …

Teaching And Learning Mathematics With Math Fair, Lesson Study And Classroom Mentorship, Sharon Friesen, Krista Francis-Poscente

The Mathematics Enthusiast

For more than a decade, researchers, math educators and professional developers from the Galileo Educational Network (Galileo) in the Faculty of Education at the University of Calgary, to which the two of us are associated, have worked to improve the teaching of mathematics. Our focus has always been twofold: to improve teacher knowledge of mathematics and the pedagogy of teaching mathematics. We report on the extensive work we have conducted with teachers with lesson study, classroom mentorships and math fairs.

Teachers As Stakeholders In Mathematics Education Research, Michael Jarry-Shore, Sandra Mcneil

The Mathematics Enthusiast

In this paper, we report on our experiences with professional development at the Calgary Girls School in Alberta, Canada. In particular we reflect on factors such as mentoring and teacher coaching that contribute to higher student achievement as well as a culture of cooperation and collaboration in the context of the Alberta Initiative for School Improvement (AISI).

The Others’ Voice: Availing Other Disciplines’ Knowledge About Sustainable Impact Of Professional Development Programmes, Stefan Zehetmeier

The Mathematics Enthusiast

This paper deals with the sustainable impact of innovations and professional development programmes. While research on this issue is rather scarce in educational disciplines (and in particular in mathematics teacher education), some other domains like health care or development aid are well grounded in research results regarding this topic. This article gives an insight into the other disciplines’ knowledge concerning the impact of innovations and professional development programmes and the respective fostering and hindering factors. Moreover, possible implications for (mathematics) teacher education are discussed.

Tme Volume 11, Number 1

The Mathematics Enthusiast

No abstract provided.

The Impact And Effectiveness Of Student-Centered Classroom Structure, Amie P. Westberg

Mathematics Graduate Theses

The purpose of this paper is to explore the effectiveness of student-centered learning as an alternative classroom structure. It is important that we continually reflect on our teaching methods and explore alternatives that can help give our students the best chance to succeed. While the literature is mixed with regard to which classroom style is best, there are many sources showing the benefits of student-centered instruction over a strictly teacher- centered classroom. Sources also showed that teachers do not need to choose exclusively one style of teaching, and that a blended classroom using a variety of teaching styles can be …

When Semi-Monotone Implies Monotone, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The basic theme of this talk is the extrinsic description of objects by means of morphisms. One way to do this is to say that all monomorphisms from the object are “special” in some way; the dual of this is to single out epimorphisms to the object.

Professional Development: Possibilities And Restrictions For Mathematics Teachers In Lower Secondary School In Iceland, Guðný Helga Gunnarsdóttir

The Mathematics Enthusiast

Mathematics teachers in many parts of the world have been facing many challenges in recent years. In Iceland teachers in lower secondary school have been implementing a new reform oriented curriculum. Many researchers claim teachers need considerable support if they are to meet the demands of the current reforms in mathematics education. This paper explores whether mathematics teachers at lower secondary level in Iceland are given good opportunities to develop professionally during the last five years and if not what can possibly be done to improve the situation. My conclusion is that the opportunities given are limited and do not …

Lean, Green, And Lifetime Maximizing Sensor Deployment On A Barrier, Peter Michael Terlecky

Dissertations, Theses, and Capstone Projects

Mobile sensors are located on a barrier represented by a line segment, and each sensor has a single energy source that can be used for both moving and sensing. Sensors may move once to their desired destinations and then coverage/communication is commenced. The sensors are collectively required to cover the barrier or in the communication scenario set up a chain of communication from endpoint to endpoint. A sensor consumes energy in movement in proportion to distance traveled, and it expends energy per time unit for sensing in direct proportion to its radius raised to a constant exponent.

The first focus …

Quantifying The Statistical Impact Of Grappa In Fcmri Data With A Real-Valued Isomorphism, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

The interpolation of missing spatial frequencies through the generalized auto-calibrating partially parallel acquisitions (GRAPPA) parallel magnetic resonance imaging (MRI) model implies a correlation is induced between the acquired and reconstructed frequency measurements. As the parallel image reconstruction algorithms in many medical MRI scanners are based on the GRAPPA model, this study aims to quantify the statistical implications that the GRAPPA model has in functional connectivity studies. The linear mathematical framework derived in the work of Rowe , 2007, is adapted to represent the complex-valued GRAPPA image reconstruction operation in terms of a real-valued isomorphism, and a statistical analysis is performed …

An Abundant Dysfunctional Apolipoprotein A1 In Human Atheroma, Ying Huang, Joseph A. Didonato, Bruce S. Levison, Dave Schmitt, Lin Li, Yuping Wu, Jennifer Buffa, Timothy Kim, Gary S. Gerstenecker, Xiaodong Gu, Chandra S. Kadiyala, Zeneng Wang, Miranda K. Culley, Jennie E. Hazen, Anthony J. Didonato, Xiaoming Fu, Stela Z. Berisha, Daoquan Peng, Truc T. Nguyen, Shaohong Liang, Chia-Chi Chuang, Leslie Cho, Edward F. Plow, Paul L. Fox, Valentin Gogonea, W.H. Wilson Tang, John S. Parks, Edward A. Fisher, Jonathan D. Smith, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Recent studies have indicated that high-density lipoproteins (HDLs) and their major structural protein, apolipoprotein A1 (apoA1), recovered from human atheroma are dysfunctional and are extensively oxidized by myeloperoxidase (MPO). In vitro oxidation of either apoA1 or HDL particles by MPO impairs their cholesterol acceptor function. Here, using phage display affinity maturation, we developed a high-affinity monoclonal antibody that specifically recognizes both apoA1 and HDL that have been modified by the MPO-H2O2-Cl− system. An oxindolyl alanine (2-OH-Trp) moiety at Trp72 of apoA1 is the immunogenic epitope. Mutagenesis studies confirmed a critical role for apoA1 Trp72 in MPO-mediated inhibition of the ATP-binding …

The Mean Transform Of Bounded Linear Operators, Sang Hoon Lee, Woo Young Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we introduce the mean transform of bounded linear operators acting on a complex Hilbert space and then explore how the mean transform of weighted shifts behaves, in comparison with the Aluthge transform.

Optimal Control In The Treatment Of Retinitis Pigmentosa, Erika T. Camacho, Luis A. Melara, Cristina Villalobos, Stephen Wirkus

School of Mathematical & Statistical Sciences Faculty Publications

Numerous therapies have been implemented in an effort to minimize the debilitating effects of the degenerative eye disease Retinitis Pigmentosa (RP), yet none have provided satisfactory long-term solution. To date there is no treatment that can halt the degeneration of photoreceptors. The recent discovery of the RdCVF protein has provided researchers with a potential therapy that could slow the secondary wave of cone death. In this work, we build on an existing mathematical model of photoreceptor interactions in the presence of RP and incorporate various treatment regiments via RdCVF. Our results show that an optimal control exists for the administration …

Counting Conjugacy Classes Of Elements Of Finite Order In Lie Groups, Tamar Friedmann, Richard P. Stanley

Mathematics Sciences: Faculty Publications

Using combinatorial techniques, we answer two questions about simple classical Lie groups. Define N(G,m) to be the number of conjugacy classes of elements of finite order m in a Lie group G, and N(G,m,s) to be the number of such classes whose elements have s distinct eigenvalues or conjugate pairs of eigenvalues.What is N(G,m) for G a unitary, orthogonal, or symplectic group?What is N(G,m,s) for these groups? For some cases, the first question was answered a few decades ago via group-theoretic techniques.It appears that the second question has not been asked before; here it is inspired by questions related …

Teachers As Stakeholders In Mathematics Education Research, Konrad Krainer

The Mathematics Enthusiast

This paper states three claims dealing with the relationship between mathematics education researchers and mathematics teachers: (1) Mathematics education research is a highly diverse field; (2) Teachers have various roles as stakeholders in mathematics education research; (3) Regarding teachers as stakeholders in mathematics education research affords reflecting some (fruitful) „cultural differences”. The paper claims the necessity to regard researchers as key stakeholders in practice, and teachers as key stakeholders in research.

What Teachers’ Want: Identifying Mathematics Teachers’ Professional Learning Needs, Kim Beswick

The Mathematics Enthusiast

This paper reports on three differing approaches to ascertaining the professional learning (PL) needs of teachers of mathematics that were used in three PL projects. In each case the approach used was constrained to some extent by the project brief, practical considerations, and stakeholders’ preferences and abilities to contribute to determining the most useful focus of the PL. Nevertheless, there were consistent efforts to heed the advice in the literature about effective PL focusing on teachers’ needs in their particular contexts. The results of each approach are described and lessons about effective ways to identify mathematics teachers’ PL needs, and …

Approaching Professional Learning: What Teachers Want, Peter Liljedahl

The Mathematics Enthusiast

Teachers do not come to professional learning opportunities as blank slates. Instead, they come to these settings with a complex collection of wants and needs. The research presented here takes a closer look at these wants across five different professional learning settings distilling form the data a taxonomy of five categories of wants that teachers may approach professional learning with. The resultant taxonomy, as well as teachers behaviours vis-à-vis this taxonomy indicate that we need to rethink our role as facilitators within these settings as well as the role that single workshops can play in the professional learning of teachers.

Facilitating Stakeholders: Experiences From The Austrian Imst Project, Gertraud Benke, Angelika Kittner, Konrad Krainer

The Mathematics Enthusiast

In this paper, we will present an elaborate example of what can happen, if you give educational stakeholders a chance to participate and even more instigate change processes in a supportive environment. We report on experiences from the Austrian IMST (Innovations Make Schools Top) project.

Discovering Regularity In Point Clouds Of Urban Scenes, Sam Friedman

Dissertations, Theses, and Capstone Projects

Despite the apparent chaos of the urban environment, cities are actually replete with regularity. From the grid of streets laid out over the earth, to the lattice of windows thrown up into the sky, periodic regularity abounds in the urban scene. Just as salient, though less uniform, are the self-similar branching patterns of trees and vegetation that line streets and fill parks. We propose novel methods for discovering these regularities in 3D range scans acquired by a time-of-flight laser sensor. The applications of this regularity information are broad, and we present two original algorithms. The first exploits the efficiency of …

Odd Fibbinary Numbers And The Golden Ratio, Linus Lindroos, Andrew Sills, Hua Wang

Mathematical Sciences: Faculty Publications

The fibbinary numbers are positive integers whose binary representation contains no consecutive ones. We prove the following result: If the jth odd fibbinary is the nth odd fibbinary number, then j={nɸ²]-1.

Scheduling And Resource Allocation In Wireless Sensor Networks, Yosef Alayev

Dissertations, Theses, and Capstone Projects

In computer science and telecommunications, wireless sensor networks are an active research area. Each sensor in a wireless sensor network has some pre-defined or on demand tasks such as collecting or disseminating data. Network resources, such as broadcast channels, number of sensors, power, battery life, etc., are limited. Hence, a schedule is required to optimally allocate network resources so as to maximize some profit or minimize some cost. This thesis focuses on scheduling problems in the wireless sensor networks environment. In particular, we study three scheduling problems in the wireless sensor networks: broadcast scheduling, sensor scheduling for area monitoring, and …

Special Representations, Nathanson's Lambda Sequences And Explicit Bounds, Satyanand Singh

Dissertations, Theses, and Capstone Projects

{Let $X$ be a group with identity $e$, we define $A$ as an infinite set of generators for $X$, and let $(X,d)$ be the metric space with word length $d_{A}$ induced by $A$. Nathanson showed that if $P$ is a nonempty finite set of prime numbers and $A$ is the set of positive integers whose prime factors all belong to $P$, then the metric space $({\bf{Z}},d_{A})$ has infinite diameter. Nathanson also studied the $\lambda_{A}(h)$ sequences, where $\lambda_{A}(h)$ is defined as the smallest positive integer $y$ with $d_{A}(e,y)=h$, and he posed the problem to compute $\lambda_{A}(h)$ and estimate its growth rate. …

Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams, Karl-Dieter Crisman

Journal of Humanistic Mathematics

This review discusses Brams' wide-ranging book Game Theory and the Humanities and gives some basic examples of the methodology and style, including how the Theory of Moves contributes to understanding such games.

Promoting Active Studying: The Study Challenge, Christopher K. Storm, Salvatore Petrilli, Susan Petry

Journal of Humanistic Mathematics

We explore using a “Study Challenge” to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students’ to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom.

What Is So Negative About Negative Exponents?, Geoffrey D. Dietz

Journal of Humanistic Mathematics

While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …

Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta

Journal of Humanistic Mathematics

Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker’s naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers.

Improving Equity And Education: Why And How, Patricia Clark Kenschaft

Journal of Humanistic Mathematics

Progress is possible. When I graduated from college, only 5\% of the new U.S. doctorates in mathematics went to women; now it is about 30\%. There is of course room (and need) for more progress. This paper begins with an account of my research about women and black mathematicians. The latter group claimed that racial equality can be achieved only when better elementary school mathematics education is available to all children in this country. That motivated me to lead a seven-year, grant-supported program to work with elementary school teachers and children in nine New Jersey districts, including Newark, Paterson, and …

Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson

Journal of Humanistic Mathematics

This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the "is algebra necessary?'' discussion, teaching mathematics as a language, the transfer problem in learning, and the …

Galileo And Aristotle's Wheel, Olympia Nicodemi

Journal of Humanistic Mathematics

At the beginning of his last major work, Galileo tackles an old paradox, Aristotle's Wheel, in order to produce a model of the continuum that explains (at least to him) how line segments of different length could be put into a one-to-one correspondence. His argument seems like a playful digression. However, it is precisely this type of a one-to-one correspondence that he needs to support his work on free fall. In this article, we investigate how Galileo's model for the wheel paradox informs his work on free fall. We also examine some of the reasons his results on free fall---results …