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The Impact Of Secondary Mathematics Methods Courses On Preservice Secondary Teachers’ Beliefs About The Learning And Teaching Of Mathematics, Ronald Gene Smith Ii

Doctoral Dissertations

The Comprehensive Framework for Teacher Knowledge provides a model that describes an approach to the secondary mathematics methods course, as described by Robert Ronau and P. Mark Taylor. The model includes the orientation of preservice teachers toward mathematics and the teaching of mathematics, which includes the beliefs of the preservice teachers. The first questions deal with identifying the methods used in the methods course to address beliefs. The second set of questions deal with the effects of the methods course on the beliefs that preservice teachers hold on the learning and teaching of mathematics.

The study included 16 different universities …

Affective Socialization Processes In Mathematics Doctoral Study: Gaining Insight From Successful Students, Lauren L Wagener

Doctoral Dissertations

Mathematics has the highest attrition rate among all liberal arts disciplines (and among all disciplines, except for health professions) and the second highest attrition rate of all doctoral programs in the United State. In order to prevent the loss of so many students, mathematics departments must consider the root causes for attrition and determine what individual skills and knowledge and departmental systems and support will help more mathematics doctoral students to succeed. The purpose of this qualitative interview study was to explore the interactions mathematics doctoral candidates at one institution have had during graduate school and the value that the …

Creating And Validating An Instrument To Measure Middle School Mathematics Teachers’ Technological Pedagogical Content Knowledge (Tpack), Geri A. Landry

Doctoral Dissertations

Due to the pervasiveness of technology, the role and preparation of teachers as they strategically use technology for teaching mathematics needs to be examined. Technological pedagogical content knowledge (TPACK) is a framework for knowledge as teachers develop meaningful learning experiences for their students while integrating strategic use of technology (Mishra & Koehler, 2006). The purpose of this study was to develop a survey for measuring mathematics teachers’ Mathematical Technological Pedagogical Content Knowledge (M-TPACK). The survey measures the domains of mathematics content, pedagogy and technology. This mixed methods study first examined middle school mathematics teachers’ TPACK through the use of an …

Bimodule Categories And Monoidal 2-Structure, Justin Greenough

Doctoral Dissertations

We define a notion of tensor product of bimodule categories and prove that with this product the 2-category of C -bimodule categories for fixed tensor C is a monoidal 2-category in the sense of Kapranov and Voevodsky ([KV91]). We then provide a monoidal-structure preserving 2-equivalence between the 2-category of C -bimodule categories and Z( C )-module categories (module categories over the center of C ). The (braided) tensor structure of C1⊠D C2 for (braided) fusion categories over braided fusion D is introduced. For a finite group G we show that de-equivariantization is equivalent to the tensor product over Rep( G). …

Conjecturing In Dynamic Geometry: A Model For Conjecture-Generation Through Maintaining Dragging, Anna Baccaglini-Frank

Doctoral Dissertations

The purpose of this research is to study aspects of the impact of Dynamic Geometry Systems (DGS) in the process of producing conjectures in Euclidean geometry. Previous research has identified and classified a set of dragging schemes spontaneously used by students. Building on these findings, the study focuses on cognitive processes that arise in correspondence to particular dragging modalities in Cabri. Specifically, we have conceived a model describing what seems to occur during a process of conjecture-generation that involves the use of a particular dragging modality, described in the literature as dummy locus dragging. In order to accomplish this goal, …

The Impact Of A Mathematics Research Experience On Teachers' Conceptions Of Student Learning, Todd Abel

Doctoral Dissertations

Many mathematics teacher professional development programs have either incorporated or been organized around a goal of providing "research-like" (Cuoco, 2001) experiences. That is, teachers participate in a project that somehow simulates the mathematics research process. Though some research studies have shown positive outcomes from such programs, researchers have cautioned against assuming universally positive benefits without sufficient evidence (Proulx and Bednarz, 2001). Teacher conceptions of student learning play an important role in lesson development and preparation for classroom work (Penso & Shoham, 2003). Similarities between the processes of mathematics research and student learning (Dreyfus, 1991) beg the question of whether experience …

Admissible Orders On Quotients Of The Free Associative Algebra, Jeremiah William Johnson

Doctoral Dissertations

An admissible order on a multiplicative basis of a noncommutative algebra A is a term order satisfying additional conditions that allow for the construction of Grobner bases for A -modules. When A is commutative, a finite reduced Grobner basis for an A -module can always be obtained, but when A is not commutative this is not the case; in fact in many cases a Grobner basis theory for A may not even exist.

E. Hinson has used position-dependent weights, encoded in so-called admissible arrays, to partially order words in the free associative algebra in a way which produces a length-dominant …

Mf Algebras And A Bishop -Stone -Weierstrass Theorem Result, Qihui Li

Doctoral Dissertations

This dissertation consists of two parts. In the first part, we obtain many new results about MF algebras. First, we continue the work on D. Voiculescu's topological free entropy dimension deltatop (x1, ..., xn) for an n-tuple x&ar; = (x1, ..., xn) of elements in a unital C*-algebra. We also introduce a new invariant that is a C*-algebra analog of the invariant K3 introduced for von Neumann algebras. Second, we discuss a full amalgamated free product of unital MF (and residually finite-dimensional) algebras with amalgamation over a finite-dimensional C*-subalgebra. Necessary and sufficient conditions are given in this situation. In the …

Von Neumann Algebras, Affiliated Operators And Representations Of The Heisenberg Relation, Zhe Liu

Doctoral Dissertations

Von Neumann algebras are self-adjoint, strong-operator closed subalgebras (containing the identity operator) of the algebra of all bounded operators on a Hilbert space. Factors are von Neumann algebras whose centers consist of scalar multiples of the identity operator. In this thesis, we study unbounded operators affiliated with finite von Neumann algebras, in particular, factors of Type II1. Such unbounded operators permit all the formal algebraic manipulations used by the founders of quantum mechanics in their mathematical formulation, and surprisingly, they form an algebra. The operators affiliated with an infinite von Neumann algebra never form such an algebra. The Heisenberg commutation …