Digital Commons Network^™

Student Interactions And Mathematics Discourse: A Study Of The Development Of Discussions In A Fifth-Grade Classroom, Sharon Marie Soucy Mccrone

Doctoral Dissertations

Mathematics reform efforts are gaining attention and support in the years since the dissemination of the National Council of Teachers of Mathematics (NCTM) Standards documents. Encouraging student interactions in small and large group settings, and promoting discussion and argumentation of mathematical ideas among students are two possible implications of the vision presented in the Standards. The goal of having mathematics discussions, however, can present a variety of classroom challenges. Many factors influence classroom discourse and need to be addressed in ways that inform teachers as they work toward creating a more interactive, discussion-based mathematics classroom.

The study examines the development …

On Some Range Inclusions, Mihaela Anca Poplicher

Doctoral Dissertations

The de Branges-Rovnyak spaces have been introduced by Louis de Branges and James Rovnyak, and have been studied by several authors, in particular by Donald Sarason. The object of this thesis is to study more extensively some properties of this class of spaces. In particular, which of these spaces are invariant under the action of which composition operators, or adjoints of composition operators.

Some known facts and a couple of new properties are included in Chapter 1. There it is shown that the norm of the kernel function for evaluation at a point in the unit disc (in the de …

A Vector-Valued Operational Calculus And Abstract Cauchy Problems., Boris Baeumer

LSU Historical Dissertations and Theses

Initial and boundary value problems for linear differential and integro-differential equations are at the heart of mathematical analysis. About 100 years ago, Oliver Heaviside promoted a set of formal, algebraic rules which allow a complete analysis of a large class of such problems. Although Heaviside's operational calculus was entirely heuristic in nature, it almost always led to correct results. This encouraged many mathematicians to search for a solid mathematical foundation for Heaviside's method, resulting in two competing mathematical theories: (a) Laplace transform theory for functions, distributions and other generalized functions, (b) J. Mikusinski's field of convolution quotients of continuous functions. …

Unavoidable Minors Of Graphs Of Large Type., John Joseph Dittmann Jr

LSU Historical Dissertations and Theses

In this paper, we study one measure of complexity of a graph, namely its type. The type of a graph G is defined to be the minimum number n such that there is a sequence of graphs $G = G\sb0, G\sb1,\... , G\sb{n},$ where $G\sb{i}$ is obtained by contracting or deleting one edge from each block of $G\sb{i-1}$, and where $G\sb{n}$ is edgeless. We show that a 3-connected graph has large type if and only if it has a minor isomorphic to a large fan. Furthermore, we show that if a graph has large type, then it has a minor …

Graphs And Number Theory., Brian Heck

LSU Historical Dissertations and Theses

In the 1930's, L. Redei and H. Reichardt used certain matrices to aid in the determination of the structure of ideal class groups of quadratic number fields. This is a classical number theoretic problem which in general presents diffculties. Ideal class groups are finite abelian groups, and it is a result of Gauss that allows us to determine their 2-rank, in other words the number of cyclic factors of even order. Redei and Reichardt worked on determining the 4-rank, the number of factors of order divisible by 4. Later, the classical study of circulant graphs was utilized to further help …

Designing And Developing A Model Applied Mathematics Curriculum For Taiwanese-Canadian Extension School Students, In Grades Ten Through Twelve In Vancouver, British Columbia, Canada, Timothy Kuo-Tung Liu

All Graduate Projects

The purpose of the project was to design and develop a model applied mathematics curriculum for Taiwanese-Canadian extension school students, in grades ten through twelve in Vancouver, British Columbia, Canada. To accomplish this purpose, a review of current research and literature regarding curriculum and instruction related to applied mathematics was conducted. Additionally, related information from selected schools with applied mathematics programs in Taiwan, Canada, and the United States of America, was obtained and analyzed. A handsearch of various other sources was also conducted.

Literature-Based Supplimental Activities In A Second Grade Classroom, Heidi Stevens

All Graduate Projects

The National Council of Teachers of Mathematics recommendations and the Washington State Commission on Student Learning Essential Academic Learning Requirements are addressed. The benefits of integrating mathematics and literature are studied. Integrated activities, materials, and a bibliography of children's literature that supplement a traditional mathematics CUITiculum for primary students are developed. Recommendations for implementing the project are given.

Lie Theory Of Differentiable Transformations On Banach-Type Manifolds., Amadou Belly Guisse

LSU Historical Dissertations and Theses

Let M be a manifold modeled on a Banach space B, and let U be an open subset of M containing the domain of some chart $\varphi$. The aim of this work is to set mathematical foundations (topological, algebraic geometrical) for the theory of pseudosemigroups of local transformations S on M and their infinitesimal generators $L\sp{r}(S,\ U).$ In the first part of this dissertation we define the topology of local uniform convergence, the most suitable in this case, similar to the compact open topology in the finite dimensional case, and show what relationship it has with different topologies. In the …

Pure Framed Braids And 3-Manifolds., Jonathan Natov

LSU Historical Dissertations and Theses

This dissertation looks at representations of framed pure braids and compact orientable three manifolds. A representation, $\Phi:Z\sp{n}\oplus P\sb{n}\to \Gamma\sb{n},$ is constructed from the framed pure braid group on n strands to the mapping class group on a surface of genus n. The representation is used to obtain a presentation of the fundamental group. The representation, like that of (M-P), is compatible with Heegaard and Surgery descriptions. An algorithm is presented for transforming mapping class group elements to a stably equivalent pure framed braid, under the correspondence given by the representation. A geometric description, using the representation, is given for multiplication …

Weak Convergence Of Interacting Stochastic Systems., George William Paslaski

LSU Historical Dissertations and Theses

The aim of the dissertation is to establish the weak convergence of mean-field interacting particle systems driven by Poisson random measures and semimartingales. The limit of the stochastic systems is identified by the use of martingale problems and Picard iteration schemes. The interacting systems driven by Poisson random measures are shown to be stable with respect to the coefficients of the system as well as the driving terms. The same results can be achieved when a random interaction term independent of the driving terms is introduced into the coefficients of the system. Equations driven by semimartingales do not neccesarily possess …

Collected Papers, Vol. 2, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Investigating Assessment Strategies In Mathematics Classrooms : A Cd-Rom Resource Enabling Teachers To Explore Assessment Strategies In Mathematics Education, Tony Herrington, Len Sparrow, Jan Herrington, Ron Oliver

Research outputs pre 2011

No abstract provided.

Number Sense In School Mathematics: Student Performance In Four Countries, Alistair Mcintosh, Barbara Reys, Robert Reys, Jack Bana, Brian Farrell

Research outputs pre 2011

Since 1988 teams of researchers in the United States, Japan and Australia have been involved in a collaborative research project to assess the mental computation ability of their students. The results of this research have been reported elsewhere (Mcintosh, Bana & Farrell 1995; Mcintosh, Nohda, Reys & Reys 1995). The researchers involved were Professors Robert and Barbara Reys of the University of Missouri - Columbia, Professor Nobuhiko Nohda of the University of Tsukuba and Alistair Mcintosh, Jack Bana and Brian Farrell of Edith Cowan University, Perth, Western Australia.

The United States and Australian researchers went on to assess the number …

Investigating Teaching Strategies In Mathematics Classrooms : A Cd-Rom Resource Enabling Teachers To Explore Teaching Strategies In Mathematics Education, Tony John Herrington, Len Sparrow, Jan Herrington, Ron Oliver

Research outputs pre 2011

Teaching mathematics has traditionally followed a standard pattern across the world. Students are placed in classrooms where they are seated individually, are required to listen passively and observe the teacher demonstrating mathematical procedure and then s1 end extensive time practicing the newly acquired ski ll s. Generally the content being taught comprises mathematical facts and skills taught sequentially in the order presented by a textbook. Students are then assessed by unseen pencil and paper tests for the purpose of grading and ranking. This cycle is then repeated with another mathematical topic which is viewed by students as discrete from the …

On Lucasian Numbers, Peter Hilton, Jean Pedersen, Lawrence Somer

Faculty Bibliography 1990s

No abstract provided.

Nsu Programs In Education And Technology Ed.D. Programs In Child And Youth Studies 1997–1998, Nova Southeastern University

Abraham S. Fischler College of Education and School of Criminal Justice College Archive

No abstract provided.

The Duals Of Warfield Groups, Peter Loth

Mathematics Faculty Publications

A Warfield group is a direct summand of a simply presented abelian group. In this paper, we describe the Pontrjagin dual groups of Warfield groups, both for the p-local and the general case. A variety of characterizations of these dual groups is obtained. In addition, numerical invariants are given that distinguish between two such groups which are not topologically isomorphic.

Vertical Equating Of Curriculum-Based Tests In Reading, Mathematics, And Language Arts, Judith Susan Gage Costa

UNLV Retrospective Theses & Dissertations

Vertical equating of a large urban school district's curriculum-based achievement tests for students in grades one through five was performed by using the BILOG-MG software package produced by Zimowski, Muraki, Mislevy, and Bock. This software extends the application of the item response theory (IRT) approach to test analysis to testing situations involving multiple groups BILOG-MG, item parameter estimates were derived using a marginal maximum a posteriori approach in combination with an expectation-maximization algorithm (EM). Estimates of examinee ability were produced using the Bayesian, or expected a posteriori, estimate with a normal prior distribution; Linkage of successive test forms was accomplished …

The Laws Of Complexity & The Complexity Of Laws: The Implications Of Computational Complexity Theory For The Law, Eric Kades

Faculty Publications

No abstract provided.

Calculator Use In Western Australian Primary Schools, Len Sparrow, Paul Swan

Research outputs pre 2011

There are very few issues in mathematics teaching over the past twenty five years which have caused so much debate among teachers, parents and the community than the use of calculators in primary schools. Letters to newspapers, magazine articles and public comment often express the opinion that the apparent decline in the ability of young people to calculate, even simple computations, is a direct result of the use of calculators in schools. Anecdotal evidence in the form of reports from teaching practice students, personal observation in schools and comments from teachers suggests there is, in fact, very little calculator use …

Extending And Exploring Students' Problem Solving Via Problem Posing, Elena N. Stoyanova

Theses: Doctorates and Masters

Despite the fact that problem posing has been recommended as a useful mathematical activity in the curriculum documents of several countries, research about the types of problem-posing situations in which students could be involved, and about the effects of these problem-posing activities on students' mathematical performance is limited. The application of problem posing in school mathematics has been hindered by the absence of a framework which links problem posing, problem solving and mathematics curricula

Teachers Of Mathematics Teach Mathematics Differently : A Case Study Of Two Teachers, Jennie Bickmore-Brand

Theses: Doctorates and Masters

This thesis investigates the different approaches adopted by two teachers for teaching mathematical content at the upper primary level of education. Questions have been raised by researchers about the impact teachers' philosophical background may have on their perception of how mathematics should be taught. Similarly questions have been asked about the role of content in mathematics education in relation to the process of education. The two teachers held different beliefs about what they were doing when they were teaching mathematics and why they were teaching that way. Their methodological emphases were different; one could be described as being more learner-centred …

Some Problems Of Continuum Percolation., Anish Sarkar Dr.

Doctoral Theses

The model of continuum percolation can be described as follows. We start with a homogeneous Poisson point process X. At each point of X we centre a ball with a random radius such that the radii corresponding to different points are independent of each other and also independent of the Poisson process X. In this way, the space is divided into two regiorns, the covered region or the occupied region consisting of the region which is covered by at least one ball, and the uncovered region or the vacant region which is complement of the covered region. In this dissertation …

Rethink The Aptitude Excuse, David E. Drew

CGU Faculty Publications and Research

The achievement problems in U.S. schools can be seen clearly at our border. Juarez, Mexico and El Paso, Texas, are about a mile apart, separated by the Rio Grande. For years, one of my former doctoral students was on the faculty of the University of Texas at El Paso and directed the remedial center. Students who were having trouble in a variety of subjects, including mathematics, came to the center for tutoring by undergraduates and graduate students. In reviewing who was hired by the center over a number of years, she observed that Americans were rarely hired to tutor in …

Chaotic Behaviour In Three Dimensional Quadratic Systems., Fu Zhang

Student Work

This thesis presents a part of the proof of that there is no chaos in three dimensional autonomous quadratic systems of four terms with one nonlinear term and without constant terms. The first step of the proof is identifying equivalent systems from all possible systems by the 3rd order permutation group and as a result 138 inequivalent patterns are found(refer to appendix A). And then for the solvable systems we show how to solve them. Some of the nonsolvable systems turn out to be 2nd order autonomous systems and they are resolved by analyzing the monotonicity of the solutions and/or …

Design,Analysis And Routing In Static Interconnection Networks., Rajib Kumar Das Dr.

Doctoral Theses

Many real-life applications such as image processing, weather forecasting, digital signal processing, etc., require large amount of computations. By distributing the task among several processors, one can appreciably reduce the computation time. To solve complex problems, several computer architectures using multiple processors have been introduced. Recent developments in IC technology have made it economically feasible to construct multiple processor systems consisting of hundreds or thousands of processors.There are two types of multiprocessor systems (PS87). One is tightly coupled, where the processors share a common clock and/or memory. The other is loosely coupled, where each processor runs independently with a local …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

All The Company Of Heaven, Milner S. Ball

Michigan Law Review

A Review of Joseph Vining, From Newton's Sleep

The Algebra Of Green And Mackey Functors, Florian Luca

Theses (Unassigned)

We investigate various Green and Mackey functor analogs of concepts from the theory of rings and modules. In particular, we consider ideals, chain conditions, Krull dimension, decomposition theorems and completion for these functors. We characterize the Jacobson radical and the prime and maximal ideals of an arbitrary Green functor A. We prove various properties of these ideals. We also investigate the Krull dimension of a commutative Green functor. We analyze the Green and Mackey functors satisfying various chain conditions. For left-modules over Green functors A satisfying a certain noetherian-like condition we study the analog of the tertiary decomposition theorem. For …

Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.

Doctoral Theses

No abstract provided.