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A Comparison Of Learning Subjective And Traditional Probability In Middle Grades, Jeanne D. Rast

Middle-Secondary Education and Instructional Technology Dissertations

The emphasis given to probability and statistics in the K-12 mathematics curriculum has brought attention to the various approaches to probability and statistics concepts, as well as how to teach these concepts. Teachers from fourth, fifth, and sixth grades from a small suburban Catholic school engaged their students (n=87) in a study to compare learning traditional probability concepts to learning traditional and subjective probability concepts. The control group (n=44) received instruction in traditional probability, while the experimental group (n=43) received instruction in traditional and subjective probability. A Multivariate Analysis of Variance and a Bayesian t-test were used to analyze pretest …

Maximum Size T-Cross-Intersecting And Intersecting Families With Degree Conditions, Yongbin Ou

Graduate Theses, Dissertations, and Problem Reports

We present four main results: (1) A solution to the problem of finding two set systems A and B such that A is r1-intersecting, B is r2-intersecting, A,B are t-cross-intersecting and A+ B is a maximum; (2) A solution to the problem of finding two set systems A and B such that A,B are Sperner, t-cross-intersecting and A+ B is a maximum; (3) A solution to the problem of finding the maximum size of an intersecting set system F such that the complementary degree c( F ) = s for a specified value s; (4) An asymptotic result on the …

Mathematical Functions: An Interactive Emodule, Sarah Jean Moody

Undergraduate Honors Capstone Projects

The National Library of Virtual Manipulatives (NLVM, http://nlvm.usu.edu/) is a widely used and highly praised teaching/learning resource for school mathematics. The NLVM is the result of a four-year USU project, funded primarily by the National Science Foundation, Award #9819107, to create a web-based, freely accessible, library of interactive virtual manipulatives to help students learn basic mathematics concepts. During a typical school day, the NLVM server receives more than 3 million hits.

All-Boy Mathematics Classes In Middle School., Amanda Neel Davis

Electronic Theses and Dissertations

A comparative case study focused on six mathematics teachers of all-boy classes in three middle schools. Each school chose to experiment with gendered classes to improve specific, yet somewhat different, outcomes. A purpose of this study was not to compare single-gender schooling with coeducation, but rather, to focus on each school's implementation process and to identify school and classroom factors that seemed to contribute to success of the single-gender program. Another purpose was to examine mathematics teaching. Observational analysis used as a framework the Five Strands of Mathematics Proficiency. Related areas of inquiry were classroom time allocation, textbook selection and …

The Importance Of Mental Calculation Skills: A Review Of The Literature, Robert Gusty

Theses

This paper reviewed research related to phonological awareness in deaf and hearing individuals. A number of studies showed that individuals skilled in memory tasks and reading achievement utilize a phonological voice. Often referred to as inner voice or the articulatory loop, phonology was used by both hearing and deaf individuals considered to be skilled readers. The evidence also shows that the use of phonology for coding information is related to the ability to use memory efficiently. As reading achievement is very important in a deaf child's education, so is mathematics. Compared to hearing students, deaf students do not perform at …

The Relationship Between Teaching Experience And Style And Primary Student Gains In Mathematics Using An Integrated Learning System, Marilyn N. Meub

USF Tampa Graduate Theses and Dissertations

The purpose of this mixed methods study was to ascertain using multiple tools and methods, the impact of teachers' interaction with primary students on mathematics performance using the Successmaker Integrated Learning System to determine effective teacher practices. The sample of nineteen primary teachers from an elementary school in southwest Florida included five first grade teachers, seven second grade teachers, and seven third grade teachers.

Data analysis included total years of teaching experience, years of experience in Florida schools, and years of experience at each grade. Both the total years of teaching and the years of teaching at the research site …

Nonlinear Multiregressions Based On Choquet Integral For Data With Both Numerical And Categorical Attributes., Jin Hui

Student Work

Based on generalized Choquet integrals with respect to signed fuzzy measures, a model of nonlinear multiregression that can catch the interaction among predictive attributes toward the objective attribute can be established. In this model, some predictive attributes are numerical while the others are categorical. A numericalization technique is adopted to project each state of a categorical attribute that has more than two states to a multi-dimensional space optimally through a genetic algorithm, in which some regression coefficients are determined from data. To reduce the complexity of the genetic algorithm, the other regression coefficients such as the values of the signed …

Elementary Cellular Automata, Fractal Dimensions And Mutual Information., Naomi Kochi

Student Work

We explore a quantitative description of Wolfram's classification of elementary cellular automata based on fractal dimensions. We find the· fractal dimension to be a global measure in classifying elementary cellular automata independent of initial conditions. On the other hand, the results of our analysis of rules in Class 3 numerically confirm the existence of a wide range of dynamics among rules in Class 3. The main reason for this is due to the fact that the rules with the Sierpinski structure in Class 3 have the capacity to behave like rules in Class 2 depending on their initial conditions. Furthermore, …

Claw -Free Graphs And Line Graphs, Yehong Shao

Graduate Theses, Dissertations, and Problem Reports

The research of my dissertation is motivated by the conjecture of Thomassen that every 4-connected line graph is hamiltonian and by the conjecture of Tutte that every 4-edge-connected graph has a no-where-zero 3-flow. Towards the hamiltonian line graph problem, we proved that every 3-connected N2-locally connected claw-free graph is hamiltonian, which was conjectured by Ryjacek in 1990; that every 4-connected line graph of an almost claw free graph is hamiltonian connected, and that every triangularly connected claw-free graph G with |E( G)| ≥ 3 is vertex pancyclic. Towards the second conjecture, we proved that every line graph of a 4-edge-connected …

The Hyperspace Graph Of Connected Subgraphs, Likin C. Simon Romero

Graduate Theses, Dissertations, and Problem Reports

Given a connected graph G, the hyperspace graph of connected subgraphs C (G) is defined. The graph C (G) is such that every vertex represents a connected subgraph of G. It is shown that every connected graph G has a unique graph C (G). A characterization of a path, a cycle and the 3-star by their corresponding hyperspace graphs of connected subgraphs is shown. A special geometric representation R (G) of C (G) in an euclidean space is presented. A set P (G) is constructed based on R (G). When G is a topological tree, P (G) and the hyperspace …

Applications Of The Covering Property Axiom, Andres Millan Millan

Graduate Theses, Dissertations, and Problem Reports

The purpose of this work is two-fold. First, we present some consequences of the Covering Property Axiom CPA of Ciesielski and Pawlikowski which captures the combinatorial core of the Sacks' model of the set theory. Second, we discuss the assumptions in the formulation of different versions of CPA.;As our first application of CPA we prove that under the version CPAgamecube of CPA there are uncountable strong gamma-sets on R . It is known that Martin's Axiom (MA) implies the existence of a strong gamma-set on R . Our result is interesting since that CPAgamecube implies the negation of MA.;Next, we …

Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff

Theses and Dissertations

The first part of our work is a statistical and geometric study of properties of Thompson's Group F. We enumerate the number of elements of F which are represented by a reduced pair of n-caret trees, and give asymptotic estimates. We also discuss the effects on word length and number of carets of right multiplication by a standard generator x0 or x1. We enumerate the average number of carets along the left edge of an n-caret tree, and use an Euler transformation to make some conjectures relating to right multiplication by a generator. We describe a computer algorithm which produces …

Solving Nonlinear Optimization Problems That Have A Nondifferentiable Objective Function By Using A Pseudo Gradient Search., Marie Louise Spilde

Student Work

The gradient search fails in an optimization problem where the objective function is not differentiable--such as nonlinear multiregressions based on generalized Choquet integrals. In cases such as this, we may replace the gradient search with a pseudo gradient search to determine the optimal search direction. The pseudo gradient can be obtained algorithmically from a data set containing the objective attribute and relevant arguments of the objective function. The algorithm for the pseudo gradient search is based on a neural network model which uses statistical techniques such as root mean square error to determine the optimal search direction and the optimal …

Hand-Held Calculators And Mathematics Achievement: What The 1996 National Assessment Of Educational Progress Eighth-Grade Mathematics Exam Scores Tell Us, Kenneth L. Wareham

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this study was to analyze the 1996 National Assessment of Educational Progress data to identify the relationship between calculator use and student performance on the National Assessment of Educational Progress Mathematics Assessment. This general purpose includes several sub issues. In addition to being interested in the overall relationship between use and National Assessment of Educational Progress achievement (including the effort to control for spurious factors), this study examined the contextual factors that moderate the impact of calculator use. Similarly, it analyzed the relationship between calculator use and student performance on calculator-allowed and calculator-restricted items, as well as …

Enumeration Of The Generalized Catalan Numbers, Steven L. Richardson Jr.

Graduate Theses, Dissertations, and Problem Reports

The sequence of numbers given by the equation Cn=1n +12nn are widely known as the Catalan numbers, because they were first studied by Catalan. The ways to enumerate these numbers are similarly widely known and studied, as can be seen in Gould's catalog of Catalan numbers. Our objective is to find ways to enumerate this larger and generalized set of sequences, using multiple methods that will build on known enumerations of the Catalan numbers.

Some Nonparametric And Semiparametric Methods For Discriminant Analysis., Anil Kumar Ghosh Dr.

Doctoral Theses

Discriminant analysis (see e.g., Devijver and Kittler, 1982; Duda, Hart and Stork, 2000; Hastle, Tibahirani and Friedman, 2001) deals with the separation of different groups of obaervationa and allocation of a new oboervation to one of the previously delined grouga. In a J-class discriminant analysis problem, we usually hae a training sample of the form {(xk, ck) : k = 1,2,...,N}, where xk = (Ik1,Ik2,...J) is a d-dimensional measarement vector, and ca € {1,2,...,J} is its class label. On the basis of thia training sample, one aims to form a decision rule d(x) : Rd + (1,2,...,J} for clasifying the …

Noise Reduction In Time Series Data From Dynamical Systems., Richard Lyman Warr

Student Work

Introduction: The objective of this thesis is to determine if the amount of noise in the observed time series data has affected the outcome of the chaotic descriptors. To thoroughly analyzed this problem I will first introduce how the data was obtained, next how to find the chaotic descriptors, and then discuss and apply noise reduction techniques.

Developing A B -Tagging Algorithm Using Soft Muons At Level-3 For The Dø Detector At Fermilab, Mayukh Das

Doctoral Dissertations

The current data-taking phase of the DØ detector at Fermilab, called Run II, is designed to aid the search for the Higgs Boson. The neutral Higgs is postulated to have a mass of 117 GeV. One of the channels promising the presence of this hypothetical particle is through the decay of b-quark into a muon. The process of identifying a b-quark in a jet using muon as a reference is b-tagging with a muon tag.

At the current data taking and analysis rate, it will take long to reach the process of identifying valid events. The triggering mechanism of the …

Differences In Teacher Qualifications And The Relationship To Middle School Student Achievement In Mathematics, Carrie R. Ferguson

Doctoral Dissertations

The purpose of the study was to compare mathematics teacher preparation and experience to the achievement of middle school students (grades 6–8) on the mathematics section of the Texas Assessment of Knowledge and Skills (TAKS). Using a theoretical framework, the research examined the extent to which the teacher qualification variables were related to the student achievement. Measures of teacher qualifications included four independent variables: (a) number of mathematics content hours, (b) level of teaching certification, (c) number of years teaching experience, and (d) number of years teaching middle school/junior high mathematics. Participants in this causal-comparative study included 97 teachers and …

Using Teacher Instructional Time More Efficiently Through The Use Of Madminute Software: A Tool For Teaching Elementary Children Basic Mathematics Facts, Jeremy Tinsley

Master of Education Program Theses

Time constraints often force elementary mathematics teachers to teach only from the textbook and sacrifice conceptual, hands-on approaches to mathematics instruction. This study explores the potential time-saving benefits of using MadMinute computer software to teach elementary students basic mathematics facts. Data was collected by administering pretests and posttests to participating students, and through time logs kept by participating teachers. Results showed that teachers who used MadMinute software saved a mean of 20.4 minutes of instructional time per day, compared to teachers who used traditional methods of mathematics facts instruction. Students receiving traditional methods of instruction had higher levels of growth, …

Cryptographic And Combinatorial Properties Of Boolean Functions And S-Boxes., Kishan Chand Gupta Dr.

Doctoral Theses

In this thesis we study combinatorial aspects of Boolean functions and S-boxes with impor- tant cryptographic properties and construct new functions possesing such properties. These have possible applications in the design of private key (symmetric key) cryptosystems.Symmetric key cryptosystems are broadly divided into two classes.1. Stream Ciphers,2. Block Ciphers.Some recent proposals of stream ciphers are SNOW [37], SCREAM [52], TURING (98], MUGI (117), HBB (102], RABBIT (9), HELIX (38] and some proposals of block ciphers are DES, AES, RC6 [97), MARS (12], SERPENT (6], TWOFISH (104].In stream cipher cryptography a pseudorandom sequence of bits of length cqual to the message …

On Some Generalized Transforms For Signal Decomposition And Reconstruction., Yumnam Singh Dr.

Doctoral Theses

In this thesis, we propose two new subband transforms entitled ISITRA and YKSK transforms and their possible applications in image compression and encryption. Both these transforms are developed based on a common model of multiplication known as Bino’s model of multiplication. ISITRA is a convolution based transforms i.e., that both forward and inverse transform of ISITRA is based on convolution as in DWT or 2-channel filter bank. However, it is much more general than the existing DWT or 2-channel filter bank scheme in the sense that it we can get different kinds of filters in addition to the filters specified …

Integrating Award Winning Literature Into A Constructivist Based Middle School Mathematics Curriculum, Michael Douglas Martone

All Graduate Projects

The purpose of this project was to design three independent units that integrate award winning literature and mathematics to be used in middle school mathematics classrooms. Numerous educators have been linking mathematics and literature in their classrooms. Children's literature gives students context in mathematics that can lead to an increase in students understanding of concepts. This project includes three independent units that are aligned with the national standards set forth by the National Council of Teachers of Mathematics. Suggestions for further study on the connection between literature and mathematics are discussed.

Collaborating With Colleagues To Improve Student Learning Using The Connected Mathematics Project, Margaret D. Seifer

Graduate Student Independent Studies

I am a teacher of mathematics at Millburn Middle School, Millburn, New Jersey. During my nine years at Millburn, I have taught using the Connected Mathematics Program (CMP) for seven years to eighth graders and before that, I taught CMP in it's pilot stage to sixth graders.

This guide is a result of my thinking and learning during my time at Bank Street College. The guide is based on a journey through my learning as a professional developer. It is a tool which, I hope, will be of some use to other CMP leaders. It is hoped that if such …

Cognitively Guided Instruction (Cgi) For Mathematics At The Elementary School Level, Henry, Cho

Capstone Projects and Master's Theses

This Senior Capstone project investigates the approach to teaching elementary school mathematics known as Cognitively Guided Instruction, or CGI. It addresses questions surrounding CGIś origin, development, effectiveness, and additional benefits stemming from its implementation. Furthermore, topics such as the differences between CGI and traditional math instruction and the multiple ways that CGI alters the way that teachers instruct their students in mathematics are explored.

Evaluating The Middle School Mathematics Teacher Preparation Program At Riyadh Teachers' College, Maher M. Alghanem

Doctoral Dissertations

Continuous evaluation and feedback are essential to improving the quality of teacher preparation programs. The purpose of this study was to evaluate the perceptions of various aspects of the preparation of preservice middle school mathematics teachers at Riyadh Teachers' College, Saudi Arabia, from the perspective of both preservice middle school mathematics teachers and mathematics department faculty members. The focus of this study was on the mathematics department's theoretical framework, its governance and resources, faculty qualifications and performance, courses and field experiences, approaches of teaching, and assessment forms. Two research questionnaires were developed for the purpose of collecting research data: one …

Burnside Factors, Amenability Defects And Transitive Families Of Projections In Factors Of Type Ii(1), Jon P. Bannon

Doctoral Dissertations

We introduce a notion of transitive family of projections in a type II1 factor and prove that there exists (i) a 5 element transitive family in the hyperfinite II1 and (ii) a 12 element free transitive family. We then prove that the group von Neumann algebras of the known infinite free Burnside groups are all type II1 factors. Our investigation of weak-amenability properties of Burnside groups leads us to consider the Connes theory of correspondences. From this investigation we are able to define a new Folner invariant for type II1 factors. We prove a monotonicity result and find a positive …

Stable Invariant Subspaces, Reflexivity, And Bmo, Hassan Yousefi

Doctoral Dissertations

In the first part of the thesis we obtain some new results in Hadwin's general version of reflexivity and apply them in the classical cases. We prove that the image of any C*-algebra under any bounded unital homomorphism into B(W) is approximately reflexive, where W is a Banach space. We also introduce two new versions of reflexivity, approximate algebraic reflexivity and asymptotic reflexivity, and study their properties.

In the second part of the thesis we construct a general setting in which functions of bounded mean oscillation (BMO) and vanishing mean oscillation (VMO) can be studied. In this setting we prove …

Nonunital Multiplier Pairs And Remarks On Generalized Group C*-Algebras, Sandra E. Zak

Doctoral Dissertations

In the first part of this paper we will consider a generalization of D. Hadwin and E. Nordgren's work on multiplier pairs. Here we will not assume the existence of an identity, but rather just ask for the existence of a bounded approximate identity. Without the assumption of the identity, we find a new result concerning the relationship between the norm closure of the left multiplication operators and the approximate double commutant of the left multiplication operators.

In the second part we will suppose f, g : T→T are continuous functions on the unit circle T and let B (f, …

The Process Of Integration And The Concept Of Integral: How Does Success With Applications And Comprehension Of Underlying Notions Such As Accumulation Relate To Students' Mathematical Fluency, Mariana Montiel

Doctoral Dissertations

At the end of the standard first calculus course, the student is expected to learn the Fundamental Theorem of Calculus, and to be able to use the integral to produce new functions, or numbers which, they are told, represent the "area under the curve". At the beginning of the standard second calculus course, students are expected to generalize their knowledge, and use the integration process to generate solids of revolution, surface areas, arc length and work, among other applications. Looking at students' success or failure in these endeavors, it was detected that there are marked differences in an aspect that, …