Digital Commons Network^™

Student Thinking Driving Collaboration And Teacher Knowledge, Rachel Cheney

Theses and Dissertations

The study in this paper examined how teachers engaged in their structured Professional Learning Community (PLC) time in a manner that focused their work on student mathematical thinking. The participants included two third-grade teachers and two fourth-grade teachers engaged in an alternative PLC process during their collaboration time. Interviews were conducted and focused on how the teachers thought about student thinking as the driving force of their collaboration. The teachers found their PLC time was more focused, student thinking led the discussions and lessons, they were more responsive to student needs, and their own mathematical understanding increased. The teachers also …

Parents' Perceptions Of The Importance Of Teaching Mathematics: A Q-Study, Ashlynn M. Holley

Theses and Dissertations

Mathematics education has gone through multiple reform efforts over the last century and continues to be the target of improvement efforts. Past changes in curriculum and goals have sometimes led to heated debates between various stakeholders. Knowing the views of different stakeholders can help determine what common ground there is between these different groups and where areas of disagreement might arise. Parents are especially important to understand because they have been influential in past reform efforts. Despite the importance of parents' opinions, little research has been conducted concerning their perspectives on the importance of mathematics teaching. Using Q-methodology, I was …

Reconstructing Historical Earthquake-Induced Tsunamis: Case Study Of 1820 Event Near South Sulawesi, Indonesia, Taylor Jole Paskett

Theses and Dissertations

We build on the method introduced by Ringer, et al., applying it to an 1820 event that happened near South Sulawesi, Indonesia. We utilize other statistical models to aid our Metropolis-Hastings sampler, including a Gaussian process which informs the prior. We apply the method to multiple possible fault zones to determine which fault is the most likely source of the earthquake and tsunami. After collecting nearly 80,000 samples, we find that between the two most likely fault zones, the Walanae fault zone matches the anecdotal accounts much better than Flores. However, to support the anecdotal data, both samplers tend toward …

Understanding College Students' Use Of Written Feedback In Mathematics, Erin Loraine Carroll

Theses and Dissertations

Many teachers want to help their students develop a growth mindset about their ability to do mathematics. Research has shown, however, that teachers simply do not know how to promote growth mindsets in their classrooms. Existing research suggests that one way teachers can support students' development of a growth mindset is through the written feedback they provide students. This study combines the research done on students' mindsets and written feedback to examine the interaction between student mindset and written feedback by analyzing written feedback provided to students in a College Algebra class and how students used that feedback based on …

The Relationship Between The Use Of Curriculum Materials And Inquiry-Based Pedagogy, Laura Jo Elzinga

Theses and Dissertations

Little change has resulted from decades of attempts at reforming the teaching of mathematics (Davis et al., 1990). This study involved approximately 43 teachers who had completed an inquiry-based professional development program prior to being provided with a new mathematics curriculum designed to support inquiry-based teaching. It analyzed the relationships between their implementation of the inquiry-based teaching and their use of the curriculum materials. A series of bivariate correlations were run to investigate the relationships between the professional development and aspects related to the implementation of the new curriculum. The factors being so inter-related, it was hypothesized that relationships would …

The Principal’S Impact On The Success Of Mathematics Professional Development, Michael Chad Staheli

Theses and Dissertations

Principal involvement is recognized as a key component to success in professional development implementation. Both the principal efforts undertaken, and the visions stated influence teacher development and student achievement. Using the instructional, transformational, and learning-centered models of leadership, as well as frameworks in vision, and organizational theory, this research sought to clarify the impact of principal involvement on student performance. Interview data was collected from 16 principals participating in a mathematics professional development program entitled the Comprehensive Mathematics Initiative. Of the participants, 9 of the principals were from schools that achieved high levels of student performance on standardized mathematics tests …

The Principles Of Effective Teaching Student Teachershave The Opportunity To Learn In An Alternativestudent Teaching Structure, Danielle Rose Divis

Theses and Dissertations

Research has shown that the focus of mathematics student teaching programs is typically classroom management and non-mathematics specific teaching strategies. However, the redesigned BYU student teaching structure has proven to help facilitate a greater focus on mathematics-specific pedagogy and student mathematics during post-lesson reflection meeting conversations. This study analyzed what specific principles of NCTM’s standards of effective teaching were discussed in the reflection meetings of this redesigned structure. This study found that the student teachers extensively discussed seven of the eight principles NCTM considers to be necessary for effective mathematics teaching. Other pedagogical principles pertaining to student mathematical learning not …

Examining The Effects Of College Algebra On Students' Mathematical Dispositions, Kevin Lee Watson

Theses and Dissertations

As Mathematics Educators, we want to help our students not only develop a deep, conceptual understanding of mathematical concepts and processes, but also a positive disposition towards mathematics. Despite the importance of helping students develop a positive mathematical disposition, little research has been conducted examining how students' dispositions develop as they progress through their mathematical studies. In particular, the effects of college algebra on students' mathematical dispositions is not well understood. To examine the influence of college algebra on students' dispositions, students using two different college algebra curriculums were studied at Brigham Young University. Using a mathematical disposition survey, student …

Comparing Two Different Student Teaching Structures By Analyzing Conversations Between Student Teachers And Their Cooperating Teachers, Niccole Suzette Franc

Theses and Dissertations

Research has shown that preservice teachers participating in traditional student teaching programs tend to focus on classroom management, with very little focus on student mathematical thinking. The student teaching program at BYU has been redesigned in the hopes of shifting the focus of student teachers away from classroom management toward student mathematical thinking. This study compared conversations between student teachers and cooperating teachers before and after the redesign of the program to work towards determining the effectiveness of the refocusing of the new student teaching program. The study found that STs and CTs in the different student teaching structures were …

The Effects Of Video Self-Modeling On The Math Performance Of Adolescents With Developmental Disabilities, Cami Elizabeth Burton

Theses and Dissertations

The current study examined the effects of video self-modeling (VSM) via an iPad on the mathematics performance of students with developmental disabilities. The learning task was presented from the consumers' point of view; students learned to estimate the amount of money they should use to pay for a given item and the amount they should receive back to help ensure that they are treated honestly by merchants. Through VSM, video clips showing the step-by-step problem solving process were synchronized onto an iPad. Students were shown how to use the iPad and access the video clips in order to watch themselves …

Investigating The Influence Of Computer Programs On Perception And Application Of Mathematical Skills, Neil M. Bly

Theses and Dissertations

Existing research suggests an intuitive relationship between mathematics and computer programming. These previous studies have focused primarily on the cognitive connection and have ignored the potential impact of programming on an individual's perception and application of mathematical skills. By surveying and interviewing a variety of participants, this study aims to provide a descriptive foundation for the experiential side of cognitive correlations and causalities. These phenomenological accounts, garnered from individual interviews of seven different programmers, indicate four specific areas of interest. First, learning to program provided context for many abstract concepts. Second, programming illustrated the important distinction between understanding the application …

Mathematics Vocabulary And English Learners: A Study Of Students' Mathematical Thinking, Hilary Hart

Theses and Dissertations

This study examined the mathematical thinking of English learners as they were taught mathematics vocabulary through research-based methods. Four English learners served as focus students. After administering a pre-performance assessment, I taught a 10-lesson unit on fractions. I taught mathematics vocabulary through the use of a mathematics word wall, think-pair-shares, graphic organizers, journal entries, and picture dictionaries. The four focus students were audio recorded to capture their spoken discourse. Student work was collected to capture written discourse. Over the course of the unit, the four focus students used the mathematics vocabulary words that were taught explicitly. The focus students gained …

Hokua – A Wavelet Method For Audio Fingerprinting, Steven S. Lutz

Theses and Dissertations

In recent years, multimedia identification has become important as the volume of digital media has dramatically increased. With music files, one method of identification is audio fingerprinting. The underlying method for most algorithms is the Fourier transform. However, due to a lack of temporal resolution, these algorithms rely on the short-time Fourier transform. We propose an audio fingerprinting algorithm that uses a wavelet transform, which has good temporal resolution. In this thesis, we examine the basics of certain topics that are needed in understanding audio fingerprinting techniques. We also look at a brief history of work done in this field. …

An Investigation Of The Support For Literacy Instruction In Elementary Mathematics Textbooks, Wendy Ann Williams

Theses and Dissertations

The purpose of this study was to investigate the kinds of support offered for integrating literacy strategies into mathematics instruction in elementary mathematics textbooks so that students are given opportunity to achieve the vision NCTM (2000) has for mathematical power for all. The research methodology for this was a qualitative content analysis using a priori codes. Two textbook series were chosen for this study. In each series examples of literacy integration ideas based on Trabasso's and Bouchard's (2002) effective comprehension strategies to teach comprehension were cited and analyzed. The results show that there is support for teachers to integrate literacy …

Effects Of After School Programs On Elementary School Students' Language Arts And Mathematics Achievement, Jennifer Lynn Presnell

Theses and Dissertations

This study evaluated after school program participation on student academic achievement as a way of helping schools meet Adequate Yearly Progress (AYP) standards set by the No Child Left Behind Act. After school programs were divided into academic after school programs and traditional after school programs. Student achievement was measured through Criterion Referenced Tests in Language Arts and Mathematics. This study took place in a small urban school district located in the Intermountain West. Students in after school programs were matched with students not participating in the programs on several background characteristics including socioeconomic status, English language proficiency status, school …

The Expectation Of Transition Events On Finite-State Markov Chains, Jeremy Michael West

Theses and Dissertations

Markov chains are a fundamental subject of study in mathematical probability and have found wide application in nearly every branch of science. Of particular interest are finite-state Markov chains; the representation of finite-state Markov chains by a transition matrix facilitates detailed analysis by linear algebraic methods. Previous methods of analyzing finite-state Markov chains have emphasized state events. In this thesis we develop the concept of a transition event and define two types of transition events: cumulative events and time-average events. Transition events generalize state events and provide a more flexible framework for analysis. We derive computable, closed-form expressions for the …

Numerical Solutions For Stochastic Differential Equations And Some Examples, Yi Luo

Theses and Dissertations

In this thesis, I will study the qualitative properties of solutions of stochastic differential equations arising in applications by using the numerical methods. It contains two parts. In the first part, I will first review some of the basic theory of the stochastic calculus and the Ito-Taylor expansion for stochastic differential equations (SDEs). Then I will discuss some numerical schemes that come from the Ito-Taylor expansion including their order of convergence. In the second part, I will use some schemes to solve the stochastic Duffing equation, the stochastic Lorenz equation, the stochastic pendulum equation, and the stochastic equations which model …

Uncovering Transformative Experiences: A Case Study Of The Transformations Made By One Teacher In A Mathematics Professional Development Program, Rachelle Myler Orsak

Theses and Dissertations

Effective professional development is vital for improving mathematics teaching (National Council of Teachers of Mathematics [NCTM], 2007), so studying effective professional development programs is important to the field of mathematics education. This case study presents findings on one teacher, Rebecca, and her experiences in a five-semester mathematics professional development for elementary teachers. The participants in this professional development engaged in collaborative problem solving of challenging mathematical tasks over extended periods of time. I used qualitative research methods based on grounded theory methodology (Charmaz, 2006) to analyze Rebecca's entrance and exit surveys, video data of Rebecca's individual interviews, and video data …

One Problem, Two Contexts, Danielle L. Gigger

Theses and Dissertations

In this study, a group of students were presented with two mathematically isomorphic problems but in radically different contexts. Analysis of their thinking and reasoning as they worked to solve and explain each problem demonstrates that the thinking and reasoning that emerged in each problem responded to clear purposes that the problems elicited in these students. The first problem was posed in a context that relied on experience and intuition rather than a formal mathematical description. The second problem was posed in a formal, set-theoretic context. While the analysis offered here reveals similarities in the students' final reasoning in the …

Second Graders' Solution Strategies And Understanding Of A Combination Problem, Tiffany Marie Hessing

Theses and Dissertations

I inquire about second graders' capabilities of developing solution strategies and the original variety of strategies they bring forth while solving a combination problem. Based on analysis of the data presented in this paper, students developed five different general strategies. After analyzing what the second grade students were capable of developing, we can conclude that young children are capable of developing powerful systematic strategies grounded in their personal experiences. This research shows that even when the teacher does not foster personal agency, children will still exercise agency. The social interactions in the classroom helped students learn to propose mathematical ideas, …

On The Combinatorics Of Certain Garside Semigroups, Christopher R. Cornwell

Theses and Dissertations

In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups.

What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses?, Matthew M. Webb

Theses and Dissertations

Lesson study is a form of professional development for teachers adopted in recent years from Japan. Introducing lesson study to U.S. teachers and researchers has been the focus of most of the literature on this subject. Much of the literature outlines how lesson study works and describes its essential features. One of the features of lesson study is anticipating student responses, also known as anticipating student thinking. Anticipating student responses is passingly described in lesson study literature. This research was conducted to understand what it means to anticipate student responses for preservice mathematics teachers in a lesson study group. Lesson …

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 …

Reasoning About Motion: A Case Study, Tiffini Lynn Glaze

Theses and Dissertations

Several dance and industrial design students were given the opportunity to attend a non-traditional mathematics course. The nature of this course prompted student interaction and expected collaboration. My research focuses on one dance student, Sara, who did not consider herself a strong mathematics student, but who understood physical motion very well. This paper explores the evolution of Sara's representations for physical motion in a given task, and discusses her reasoning for keeping or dismissing various parts of her representations during the course of this task. I examine first how Sara learns mathematics with understanding in this task, and second how …

Bounding The Number Of Graphs Containing Very Long Induced Paths, Steven Kay Butler

Theses and Dissertations

Induced graphs are used to describe the structure of a graph, one such type of induced graph that has been studied are long paths.

In this thesis we show a way to represent such graphs in terms of an array with two colors and a labeled graph. Using this representation and the techniques of Polya counting we will then be able to get upper and lower bounds for graphs containing a long path as an induced subgraph.

In particular, if we let P(n,k) be the number of graphs on n+k vertices which contains P_n, a path on n vertices, as …