“Race” In Mathematics Education: Are We A Community Of Cowards?, 2011 Georgia State University

#### “Race” In Mathematics Education: Are We A Community Of Cowards?, David W. Stinson

*Middle-Secondary Education and Instructional Technology Faculty Publications*

In this editorial, the author revisits Attorney General Eric Holder's well-known 2009 statement that, "in things racial we have always been and continue to be, in too many ways, essentially a nation of cowards," examining the ways in which racial "cowardice" continues to impact urban mathematical education.

Tme Volume 8, Number 3, 2011 University of Montana

Can Dual Processing Theories Of Thinking Inform Conceptual Learning In Mathematics?, 2011 University of Montana

#### Can Dual Processing Theories Of Thinking Inform Conceptual Learning In Mathematics?, Ron Tzur

*The Mathematics Enthusiast*

Concurring with Uri Leron’s (2010) cross-disciplinary approach to two distinct modes of mathematical thinking, intuitive and analytic, I discuss his elaboration and adaptation to mathematics education of the cognitive psychology dual-processing theory (DPT) in terms of (a) the problem significance and (b) features of the theory he adapts. Then, I discuss DPT in light of a constructivist stance on the inseparability between thinking and learning. In particular, I propose a brain-based account of conceptual learning—the Reflection on Activity-Effect Relationship (Ref*AER) framework—as a plausible alternative to DPT. I discuss advantages of the Ref*AER framework over DPT ...

Editorial: “Glocal”, “Glocavores”: Good Gadgetry?, 2011 University of Montana

#### Editorial: “Glocal”, “Glocavores”: Good Gadgetry?, Bharath Sriraman

*The Mathematics Enthusiast*

No abstract provided.

Research On Practical Rationality: Studying The Justification Of Actions In Mathematics Teaching, 2011 University of Montana

#### Research On Practical Rationality: Studying The Justification Of Actions In Mathematics Teaching, Patricio Herbst, Daniel Chazan

*The Mathematics Enthusiast*

Building on our earlier work conceptualizing teaching as the management of instructional exchanges, we lay out a theory of the practical rationality of mathematics teaching—that is, a theory of the grounds upon which instructional actions specific to mathematics can be justified or rebuffed. We do that from a perspective informed by what experienced practitioners consider viable but also in ways that suggest operational avenues for the study of instructional improvement, in particular for improvements that enable students to do more authentic mathematical work. We show how different kinds of experiments can be used to engage in theory building and ...

2011 (Summer), 2011 University of Dayton

#### 2011 (Summer), University Of Dayton. Department Of Mathematics

*Colloquia*

Abstracts of the talks given at the 2011 Summer Colloquium.

Using Performance Assessments To Connect Fractions And Rational Expressions: Noyce Scholars As Mentors To Pre-Service Elementary Teachers, 2011 Georgia Southern University

#### Using Performance Assessments To Connect Fractions And Rational Expressions: Noyce Scholars As Mentors To Pre-Service Elementary Teachers, Joy W. Darley, Michelle Cawthorn, Marlynn Griffin, Brian P. Koehler, James Lobue

*Mathematical Sciences Faculty Presentations*

At Georgia Southern University, Noyce scholars are not only being mentored, but they are also serving as mentors to preservice elementary teachers. One topic that proves to be problematic for many students is the conceptual understanding of fractions and rational expressions. Since our Noyce scholars with mathematics degrees will be teaching algebra, it is important that they are fluent with the arithmetic to algebra connection. In addition, it is crucial that these mathematics majors become stakeholders in mathematics education at the elementary school level.

Performance assessments can provide the structure necessary for assisting pre-service elementary teachers in firmly establishing the ...

Careers In Mathematics, 2011 Cedarville University

#### Careers In Mathematics, Adam J. Hammett

*Science and Mathematics Faculty Presentations*

No abstract provided.

Mathematical Modeling And Dynamical Analysis Of The Operation Of The Hypothalamus - Pituitary - Thyroid (Hpt) Axis In Autoimmune (Hashimoto's) Thyroiditis, 2011 Marquette University

#### Mathematical Modeling And Dynamical Analysis Of The Operation Of The Hypothalamus - Pituitary - Thyroid (Hpt) Axis In Autoimmune (Hashimoto's) Thyroiditis, Balamurugan Pandiyan

*Dissertations (2009 -)*

This thesis is a mathematical modeling study of the operation of the negative feedback control through the hypothalamus-pituitary- thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis. Negative feedback control through the HPT axis is a mechanism in which the high levels of thyroid hormone; free thyroxine (FT4) in the blood inhibits the secretion of the pituitary hormone, thyroid stimulating hormone (TSH) into the blood. Similarly, the low levels of free thyroxine (FT4) sensed by the pituitary gland and then it secretes thyroid stimulating hormone (TSH) into the blood. Autoimmune (Hashimoto's) thyroiditis is a disease in which the immune system ...

A Characterization Of Ramsey Graphs For R(3,4), 2011 Louisiana Tech University

#### A Characterization Of Ramsey Graphs For R(3,4), Nicholas M. Richardson

*Doctoral Dissertations*

The Ramsey number *R*(ω, α) is the minimum number *n* such that every graph *G* with |*V*(*G*)| ≥ *n* has an induced subgraph that is isomorphic to a complete graph on ω vertices, *K*ω, or has an independent set of size α, *N*α. Graphs having fewer than *n* vertices that have no induced subgraph isomorphic to *K* ω or *N*α form a class of Ramsey graphs, denoted ℜ(ω, α). This dissertation establishes common structure among several classes of Ramsey graphs and establishes the complete list of ℜ(3, 4).

The process used to find the ...

Modeling And Control For Heave Dynamics Of A Flexible Wing Micro Aerial Vehicle Distributed Parameter System, 2011 Louisiana Tech University

#### Modeling And Control For Heave Dynamics Of A Flexible Wing Micro Aerial Vehicle Distributed Parameter System, Lisa M. Kuhn

*Doctoral Dissertations*

In recent years, much research has been motivated by the idea of biologically-inspired flight. It is a conjecture of the United States Air Force that incorporating characteristics of biological flight into air vehicles will significantly improve the maneuverability and performance of modern aircraft. Although there are studies which involve the aerodynamics, structural dynamics, modeling, and control of flexible wing micro aerial vehicles (MAVs), issues of control and vehicular modeling as a whole are largely unexplored. Modeling with such dynamics lends itself to systems of partial differential equations (PDEs) with nonlinearities, and limited control theory is available for such systems.

In ...

A Numerical Method For Studying Thermal Deformation In 3d Double-Layered Thin Films With Imperfect Interfacial Thermal Contact Exposed To Ultrashort-Pulsed Lasers, 2011 Louisiana Tech University

#### A Numerical Method For Studying Thermal Deformation In 3d Double-Layered Thin Films With Imperfect Interfacial Thermal Contact Exposed To Ultrashort-Pulsed Lasers, Runzhou Liu

*Doctoral Dissertations*

Micro heat transfer induced by Ultrashort-pulsed lasers is an important research topic in mechanical engineering and material science. In order to apply ultrashort-pulsed lasers successfully, studying the thermal deformation in double-layered thin films with imperfect thermal interfacial contact induced by ultrashort-pulsed lasers is important for preventing thermal damage. For the ultrashort-pulsed laser, the thermal damage is different from that caused by the long-pulsed lasers, and ultrafast cracks occur after heating.

This dissertation presents a new finite difference method for investigating the thermal deformation in a 3D gold-chromium thin film with imperfect interfacial thermal contact exposed to ultrashort-pulsed lasers. The method ...

A Characterization Of Ramsey Graphs For R(3,4), 2011 Louisiana Tech University

#### A Characterization Of Ramsey Graphs For R(3,4), Nicholas M. Richardson

*Doctoral Dissertations*

The Ramsey number *R*(ω, α) is the minimum number *n* such that every graph *G* with |*V*(*G*)| ≥ *n* has an induced subgraph that is isomorphic to a complete graph on ω vertices, *K*ω, or has an independent set of size α, *N*α. Graphs having fewer than *n* vertices that have no induced subgraph isomorphic to *K* ω or *N*α form a class of Ramsey graphs, denoted ℜ(ω, α). This dissertation establishes common structure among several classes of Ramsey graphs and establishes the complete list of ℜ(3, 4).

The process used to find the ...

On The Idea Of Learning Trajectories: Promises And Pitfalls, 2011 University of Montana

#### On The Idea Of Learning Trajectories: Promises And Pitfalls, Susan B. Empson

*The Mathematics Enthusiast*

Learning mathematics is a complex and multidimensional if not an inherently indeterminate process. A necessary goal of research on learning is to simplify this complexity without sacrificing the ability of research to inform teaching. This goal has been addressed in part by researchers focusing on how to represent research on learning for teachers and on how to support teachers to use and generate models of students’ learning (e.g., Franke, Carpenter, Levi, & Fennema, et al., 2001; Hammer & Schifter, 2001; Simon & Tzur, 2004; Steffe, 2004). Recently, the idea of learning trajectories has gained attention as a way to focus research on learning in service of instruction and assessment. It ...

Practical Rationality, The Disciplinary Obligation, And Authentic Mathematical Work: A Look At Geometry, 2011 University of Montana

#### Practical Rationality, The Disciplinary Obligation, And Authentic Mathematical Work: A Look At Geometry, Deborah Moore-Russo, Michael Weiss

*The Mathematics Enthusiast*

Grossman and McDonald (2008) recently argued that the research community needs to move its “attention beyond the cognitive demands of teaching … to an expanded view of teaching that focuses on teaching as a practice (p. 185).” Building on the work of Bourdieu (Bourdieu and Wacquent, 1992; Bourdieu, 1985, 1998), Herbst and Chazan (2003, 2006) have written about mathematics teaching as a practice, just as law and medicine are considered practices, in an attempt to better understand the rationality that produces, regulates, and sustains mathematics instruction. This practical rationality is the commonly held system of dispositions or the “feel for the ...

Complex Learning Through Cognitively Demanding Tasks, 2011 University of Montana

#### Complex Learning Through Cognitively Demanding Tasks, Lyn D. English

*The Mathematics Enthusiast*

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by “continuing education as usual” (The National Academies, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualization. These technologies have led to significant changes in the forms of mathematical thinking that are required beyond the classroom. This paper argues for the need to incorporate future-oriented understandings and competencies within the mathematics curriculum, through intellectually stimulating activities that draw upon multidisciplinary content and contexts. The paper also argues for greater recognition of ...

Conceptualizations And Issues Related To Learning Progressions, Learning Trajectories, And Levels Of Sophistication, 2011 University of Montana

#### Conceptualizations And Issues Related To Learning Progressions, Learning Trajectories, And Levels Of Sophistication, Michael T. Battista

*The Mathematics Enthusiast*

In this paper the nature of learning progressions and related concepts are discussed. The notions of learning progressions and learning trajectories are conceptualized and their usage is illustrated with the help of examples. In particular the nuances of instructional interventions utilizing these concepts are also discussed with implications for the teaching and learning of mathematics.

The Milnor Fiber Associated To An Arrangement Of Hyperplanes, 2011 University of Iowa

#### The Milnor Fiber Associated To An Arrangement Of Hyperplanes, Kristopher John Williams

*Theses and Dissertations*

Let *f* be a non-constant, homogeneous, complex polynomial in *n* variables. We may associate to *f* a fibration with typical fiber *F* known as the Milnor fiber. For regular and isolated singular points of *f* at the origin, the topology of the Milnor fiber is well-understood. However, much less is known about the topology in the case of non-isolated singular points. In this thesis we analyze the Milnor fiber associated to a hyperplane arrangement, ie, *f* is a reduced, homogeneous polynomial with degree one irreducible components in *n* variables. If *n* > 2then the origin will be a non-isolated singular point ...

N-Parameter Fibonacci Af C*-Algebras, 2011 University of Iowa

#### N-Parameter Fibonacci Af C*-Algebras, Cecil Buford Flournoy Jr.

*Theses and Dissertations*

An n-parameter Fibonacci AF-algebra is determined by a constant incidence matrix K of a special form. The form of the matrix K is defined by a given n-parameter Fibonacci sequence. We compute the K-theory of certain Fibonacci AF-algebra, and relate their K-theory to the K-theory of an AF-algebra defined by incidence matrices that are the transpose of K.

Superposition Of Zeros Of Automorphic L-Functions And Functoriality, 2011 University of Iowa

#### Superposition Of Zeros Of Automorphic L-Functions And Functoriality, Timothy Lee Gillespie

*Theses and Dissertations*

In this paper we deduce a prime number theorem for the L-function L(s; AIE=Q() AIF=Q(0)) where and 0 are automorphic cuspidal representations of GLn=E and GLm=F, respectively, with E and F solvable algebraic number elds with a Galois invariance assumption on the representations. Here AIF=Q denotes the automorphic induction functor. We then use the proof of the prime number theorem to compute the n-level correlation function of a product of L-functions dened over cyclic algebraic number elds of prime degree.