## ASU Electronic Theses and Dissertations

This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.

In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.

Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.

- 40 Arizona State University
- 11 Middleton, James
- 10 Thompson, Patrick W
- 9 Sloane, Finbarr
- 6 Carlson, Marilyn
- 6 Milner, Fabio
- 6 Roh, Kyeong Hah
- more
- 5 Carlson, Marilyn P
- 5 Middleton, James A
- 4 Saldanha, Luis
- 4 Thompson, Patrick
- 4 Zandieh, Michelle
- 3 Buss, Ray
- 2 Atkinson, Robert K
- 2 Bitter, Gary G
- 2 Fishel, Susanna
- 2 Heck, Thomas
- 2 Van De Sande, Carla
- 2 Zambo, Ronald
- 2 Zazkis, Dov
- 1 Ann, Keith
- 1 Atkinson, Robert
- 1 Atkinson, Robert K.
- 1 Barber, Rebecca
- 1 Barnett, Joshua
- 1 Battey, Dan
- 1 Battey, Daniel
- 1 Battey, Daniel S
- 1 Berliner, David
- 1 Bicer, Alpay
- 1 Bitter, Gary
- 1 Bolley, Staci Ann
- 1 Bowling, Stacey Andrew
- 1 Burke, Margaret
- 1 Buss, Ray R
- 1 Byerley, Cameron O'Neill
- 1 Carlson, Marilyn P.
- 1 Castillo-Chavez, Carlos
- 1 Cavanagh, Mary C.
- 1 Colbourn, Charles
- 1 Cruz, Heather
- 1 Culbertson, Robert
- 1 Cunningham, James Allan
- 1 Currin van de Sande, Carla
- 1 Czocher, Jennifer
- 1 Czygrinow, Andrzej
- 1 David, Carlson L
- 1 David, Erika Johara
- 1 Dawkins, Paul C
- 1 Denham, Andre R.
- 1 Douglas, Ian
- 1 Elliott, Sherman
- 1 Elliott, Stephen N
- 1 Evangelista, Arlene Morales
- 1 Fischman, Gustavo
- 1 Flores, Alfinio
- 1 Foshee, Cecile Mary
- 1 Frank, Kristin Marianna
- 1 Ganesh, Tirupalavanam
- 1 Greenes, Carole
- 1 Greenes, Carole E
- 1 Halani, Aviva
- 1 Harel, Guershon
- 1 Hatfield, Neil
- 1 Herriman, Patricia Valles
- 1 Holmes, Raquell M
- 1 Hong, Yi-Chun
- 1 Horan, John
- 1 Jimenez, Rosa
- 1 Johnson, Jeffrey Ivan
- 1 Joshua, Surani Ashanthi
- 1 Judson, Eugene
- 1 Kang, Hyun Jung
- 1 Kierstead, H.A.
- 1 Kim, Seong Hee
- 1 Kulinna, Pamela
- 1 Kuper, Emily Ginamarie
- 1 Lee, Mi Yeon
- 1 Legacy, Jane
- 1 Legacy, Jane M
- 1 Lehrer, Richard
- 1 Llamas-Flores, Silvia
- 1 Macswan, Jeffrey
- 1 Marble, Cindy
- 1 Marfai, Frank Stephen
- 1 Marsh, Josephine
- 1 Marsh, Josephine P
- 1 McNamara, Allen
- 1 Medrano, Juan Candelario
- 1 Meylani, Rusen
- 1 Middleton, James A.
- 1 Moore, Kevin C
- 1 Mostofo, Jameel (Jim) Richard
- 1 Mubayi, Anuj
- 1 Nelson, Brian C.
- 1 Nicoloff, Stephen J.
- 1 O'Bryan, Alan Eugene
- 1 Orletsky, Darryl William
- 1 Pampel, Krysten Ashley
- 1 Reiser, Mark

- 40 English

- 40 Public

- Mathematics education
- 7 Educational technology
- 6 Mathematics
- 5 Teacher education
- 3 Education
- 3 Elementary education
- 3 Instructional design
- more
- 3 Mathematics Education
- 3 mathematics
- 2 Adult education
- 2 Calculus
- 2 Cognitively Guided Instruction
- 2 Collaboration
- 2 Cooperative learning
- 2 Curriculum development
- 2 English Language Learners
- 2 Function
- 2 Functions
- 2 Graphing
- 2 Higher education
- 2 Mathematical Knowledge for Teaching
- 2 Secondary education
- 2 Self-efficacy
- 2 mathematical knowledge for teaching
- 2 mathematics education
- 2 professional development
- 1 2
- 1 4-hour block
- 1 AP Calculus
- 1 Adaptive Learning
- 1 Adaptive learning
- 1 Adult Mathematics
- 1 Algebra
- 1 Algebraic reasoning
- 1 Applied mathematics
- 1 Blended Learning
- 1 CGI
- 1 Case Study
- 1 Community college
- 1 Community development
- 1 Composition
- 1 Computer Aided Instruction
- 1 Conceptual curriculum
- 1 Content
- 1 Conveyance of meaning
- 1 Covariational Reasoning
- 1 Covariational reasoning
- 1 Creativity
- 1 Derivative
- 1 Developmental education
- 1 Didactic Object
- 1 Distance Education
- 1 ELL
- 1 Early childhood education
- 1 Educational Data Mining
- 1 Educational leadership
- 1 Educational psychology
- 1 Embedded Assessments
- 1 Engineering Design Process
- 1 Error Analysis
- 1 Exponent
- 1 Exponential
- 1 Exponential functions
- 1 Expressions
- 1 Foundations of Algebra Class
- 1 Fraction
- 1 Frame of Reference
- 1 Functional Reasoning
- 1 Grades 1
- 1 Graduate Teaching Assistant
- 1 Hierarchical Linear Model
- 1 High School Freshmen
- 1 Higher education in STEM
- 1 Holzman's metaphor of becoming
- 1 Individualized learning
- 1 Instructional Constraints
- 1 Instructional Strategy
- 1 Interactive Multimedia
- 1 Key Pedagogical Understanding
- 1 Knowledge
- 1 Language Policy
- 1 Learning Analytics
- 1 Lesson Study
- 1 Lesson planning
- 1 Logarithm
- 1 Logarithmic
- 1 MKT
- 1 MOOCs
- 1 Mastery learning
- 1 Mathematical Meanings
- 1 Mathematical knowledge for teaching
- 1 Mathematics Teaching Cycle
- 1 Middle school education
- 1 Motivation
- 1 Online Education
- 1 Online Learning Environment
- 1 Partitive Division
- 1 Pedagogical
- 1 Pedagogical goals
- 1 Pedagogy

- Dwarf Galaxies as Laboratories of Protogalaxy Physics: Canonical Star Formation Laws at Low Metallicity
- Evolutionary Genetics of CORL Proteins
- Social Skills and Executive Functioning in Children with PCDH-19
- Deep Domain Fusion for Adaptive Image Classification
- Software Defined Pulse-Doppler Radar for Over-The-Air Applications: The Joint Radar-Communications Experiment

The mathematics test is the most difficult test in the GED (General Education Development) Test battery, largely due to the presence of story problems. Raising performance levels of story problem-solving would have a significant effect on GED Test passage rates. The subject of this formative research study is Ms. Stephens’ Categorization Practice Utility (MS-CPU), an example-tracing intelligent tutoring system that serves as practice for the first step (problem categorization) in a larger comprehensive story problem-solving pedagogy that purports to raise the level of story problem-solving performance. During the analysis phase of this project, knowledge components and particular competencies that enable …

- Contributors
- Ritchey, ChristiAnne Stephens, VanLehn, Kurt, Savenye, Wilhelmina, et al.
- Created Date
- 2018

Teachers must recognize the knowledge they possess as appropriate to employ in the process of achieving their goals and objectives in the context of practice. Such recognition is subject to a host of cognitive and affective processes that have thus far not been a central focus of research on teacher knowledge in mathematics education. To address this need, this dissertation study examined the role of a secondary mathematics teacher’s image of instructional constraints on his enacted subject matter knowledge. I collected data in three phases. First, I conducted a series of task-based clinical interviews that allowed me to construct a …

- Contributors
- Tallman, Michael Anthony, Carlson, Marilyn P, Thompson, Patrick W, et al.
- Created Date
- 2015

The principle purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK) and examine the development of that knowledge among pre-service and current math teachers. Seventy-eight current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT) - Mathematics assessment and nine of them took the Cognitively Activating Instruction in Mathematics (COACTIV) assessment. Participants answered questions that demonstrated their understanding of students' challenges and misconceptions, ability to recognize and utilize multiple representations and methods of presenting content, and understanding of tasks and materials that they may be using …

- Contributors
- Johnson, Jeffrey Ivan, Middleton, James A, Marsh, Josephine P, et al.
- Created Date
- 2016

The Mathematical and Theoretical Biology Institute (MTBI) is a summer research program for undergraduate students, largely from underrepresented minority groups. Founded in 1996, it serves as a 'life-long' mentorship program, providing continuous support for its students and alumni. This study investigates how MTBI supports student development in applied mathematical research. This includes identifying of motivational factors to pursue and develop capacity to complete higher education. The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to …

- Contributors
- Evangelista, Arlene Morales, Castillo-Chavez, Carlos, Holmes, Raquell M, et al.
- Created Date
- 2015

A teacher’s mathematical knowledge for teaching impacts the teacher’s pedagogical actions and goals (Marfai & Carlson, 2012; Moore, Teuscher, & Carlson, 2011), and a teacher’s instructional goals (Webb, 2011) influences the development of the teacher’s content knowledge for teaching. This study aimed to characterize the reciprocal relationship between a teacher’s mathematical knowledge for teaching and pedagogical goals. Two exploratory studies produced a framework to characterize a teacher’s mathematical goals for student learning. A case study was then conducted to investigate the effect of a professional developmental intervention designed to impact a teacher’s mathematical goals. The guiding research questions for this …

- Contributors
- Marfai, Frank Stephen, Carlson, Marilyn P., Ström, April D., et al.
- Created Date
- 2016

Past research has shown that students have difficulty developing a robust conception of function. However, little prior research has been performed dealing with student knowledge of function composition, a potentially powerful mathematical concept. This dissertation reports the results of an investigation into student understanding and use of function composition, set against the backdrop of a precalculus class that emphasized quantification and covariational reasoning. The data were collected using task-based, semi-structured clinical interviews with individual students outside the classroom. Findings from this study revealed that factors such as the student's quantitative reasoning, covariational reasoning, problem solving behaviors, and view of function …

- Contributors
- Bowling, Stacey Andrew, Carlson, Marilyn P, Thompson, Patrick W, et al.
- Created Date
- 2014

This study purposed to determine the effect of an endogenously designed instructional game on conceptual understanding of the associative and distributive properties of multiplication. Additional this study sought to investigate if performance on measures of conceptual understanding taken prior to and after game play could serve as predictors of game performance. Three versions of an instructional game, Shipping Express, were designed for the purposes of this study. The endogenous version of Shipping Express integrated the associative and distributive properties of multiplication within the mechanics, while the exogenous version had the instructional content separate from game play. A total of 111 …

- Contributors
- Denham, Andre R., Nelson, Brian C., Atkinson, Robert K., et al.
- Created Date
- 2012

This dissertation reports three studies about what it means for teachers and students to reason with frames of reference: to conceptualize a reference frame, to coordinate multiple frames of reference, and to combine multiple frames of reference. Each paper expands on the previous one to illustrate and utilize the construct of frame of reference. The first paper is a theory paper that introduces the mental actions involved in reasoning with frames of reference. The concept of frames of reference, though commonly used in mathematics and physics, is not described cognitively in any literature. The paper offers a theoretical model of …

- Contributors
- Joshua, Surani Ashanthi, Thompson, Patrick W, Carlson, Marilyn, et al.
- Created Date
- 2019

Researchers have postulated that math academic achievement increases student success in college (Lee, 2012; Silverman & Seidman, 2011; Vigdor, 2013), yet 80% of universities and 98% of community colleges require many of their first-year students to be placed in remedial courses (Bettinger & Long, 2009). Many high school graduates are entering college ill prepared for the rigors of higher education, lacking understanding of basic and important principles (ACT, 2012). The desire to increase academic achievement is a wide held aspiration in education and the idea of adapting instruction to individuals is one approach to accomplish this goal (Lalley & Gentile, …

- Contributors
- Foshee, Cecile Mary, Atkinson, Robert K, Elliott, Stephen N, et al.
- Created Date
- 2013

This action research study, set in a community college in the southwestern United States, was designed to investigate the effects of implementing cooperative learning strategies in a developmental mathematics course. Introductory algebra was formerly taught in a lecture based format, and as such regularly had a low course completion rate. To create a more engaging learning environment, formal and informal cooperative learning activities were integrated into the curriculum. Bandura's self-efficacy theory, Vygotsky's constructivist theory, and Deutsch's social interdependence theory guided this study. Qualitative and quantitative data were collected through pre and post self-efficacy surveys, semi-structured student interviews, student journal entries, …

- Contributors
- Rivera, Natalie, Zambo, Ron, Jimenez, Rosa, et al.
- Created Date
- 2013

This study was conducted to assess the performance of 176 students who received algebra instruction through an online platform presented in one of two experimental conditions to explore the effect of personalized learning paths by comparing it with linearly flowing instruction. The study was designed around eight research questions investigating the effect of personalized learning paths on students’ learning, intrinsic motivation and satisfaction with their experience. Quantitative results were analyzed using Analysis of Variance (ANOVA), Analysis of Covariance (ANCOVA) and split-plot ANOVA methods. Additionally, qualitative feedback data were gathered from students and teachers on their experience to better explain the …

- Contributors
- Bicer, Alpay, Bitter, Gary G, Buss, Ray R, et al.
- Created Date
- 2015

A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance with AP style Related Rate questions and changes in conceptions, beliefs, and influences. The research design followed a treatment-control multiple post-assessment model with three periods of data collection. Four high school calculus classes were selected for the study, with one class designated as the treatment and three as the controls. Measures for this study include a skills assessment, Related Rate word problem assessments, and a motivation problem solving survey. Data …

- Contributors
- Thieken, Johnny, Ganesh, Tirupalavanam, Sloane, Finbarr, et al.
- Created Date
- 2012

The research indicated effective mathematics teaching to be more complex than assuming the best predictor of student achievement in mathematics is the mathematical content knowledge of a teacher. This dissertation took a novel approach to addressing the idea of what it means to examine how a teacher's knowledge of mathematics impacts student achievement in elementary schools. Using a multiple case study design, the researcher investigated teacher knowledge as a function of the Mathematics Teaching Cycle (NCTM, 2007). Three cases (of two teachers each) were selected using a compilation of Learning Mathematics for Teaching (LMT) measures (LMT, 2006) and Developing Mathematical …

- Contributors
- Burke, Margaret, Middleton, James A, Sloane, Finbarr, et al.
- Created Date
- 2013

Researchers have documented the importance of seeing a graph as an emergent trace of how two quantities’ values vary simultaneously in order to reason about the graph in terms of quantitative relationships. If a student does not see a graph as a representation of how quantities change together then the student is limited to reasoning about perceptual features of the shape of the graph. This dissertation reports results of an investigation into the ways of thinking that support and inhibit students from constructing and reasoning about graphs in terms of covarying quantities. I collected data by engaging three university precalculus …

- Contributors
- Frank, Kristin Marianna, Thompson, Patrick W, Carlson, Marilyn P, et al.
- Created Date
- 2017

Many students in the United States are graduating from high school without the math skills they need to be considered college ready. For many of these graduates, who find themselves starting their higher education at a community college, remedial math can become an insurmountable barrier that ends their aspirations for a degree or certificate. Some students must take as many as four remedial courses before they are considered college ready. Studies report that between 60% and 70% of students placed into remedial math classes either do not successfully complete the sequence of required courses or avoid taking math altogether and …

- Contributors
- Bolley, Staci Ann, Schugurensky, Daniel, Cruz, Heather, et al.
- Created Date
- 2013

This dissertation report follows a three-paper format, with each paper having a different but related focus. In Paper 1 I discuss conceptual analysis of mathematical ideas relative to its place within cognitive learning theories and research studies. In particular, I highlight specific ways mathematics education research uses conceptual analysis and discuss the implications of these uses for interpreting and leveraging results to produce empirically tested learning trajectories. From my summary and analysis I develop two recommendations for the cognitive researchers developing empirically supported learning trajectories. (1) A researcher should frame his/her work, and analyze others’ work, within the researcher’s image …

- Contributors
- O'Bryan, Alan Eugene, Carlson, Marilyn P, Thompson, Patrick W, et al.
- Created Date
- 2018

In this mixed-methods study, I examined the relationship between professional development based on the Common Core State Standards for Mathematics and teacher knowledge, classroom practice, and student learning. Participants were randomly assigned to experimental and control groups. The 50-hour professional development treatment was administered to the treatment group during one semester, and then a follow-up replication treatment was administered to the control group during the subsequent semester. Results revealed significant differences in teacher knowledge as a result of the treatment using two instruments. The Learning Mathematics for Teaching scales were used to detect changes in mathematical knowledge for teaching, and …

- Contributors
- Rimbey, Kimberly Ann, Middleton, James A, Sloane, Finbarr, et al.
- Created Date
- 2013

Drawing on Lave and Wenger (1991) this study explores how preservice elementary teachers develop themselves as teachers of mathematics, in particular, from the time of their teacher education courses to their field experiences. This study also researches the critical experiences that contributed to the construction of their identities and their roles as student teachers in their identity development. The stories of Jackie, Meg, and Kerry show that they brought different incoming identities to the teacher education program based on their K-12 school experiences. The stories provide the evidence that student teachers' prior experience as learners of mathematics influenced their identities …

- Contributors
- Kang, Hyun Jung, Middleton, James A, Battey, Dan, et al.
- Created Date
- 2012

Researchers have described two fundamental conceptualizations for division, known as partitive and quotitive division. Partitive division is the conceptualization of a÷b as the amount of something per copy such that b copies of this amount yield the amount a. Quotitive division is the conceptualization of a÷b as the number of copies of the amount b that yield the amount a. Researchers have identified many cognitive obstacles that have inhibited the development of robust meanings for division involving non-whole values, while other researchers have commented on the challenges related to such development. Regarding division with fractions, much research has been devoted …

- Contributors
- Weber, Matthew Barrett, Strom, April D, Thompson, Patrick W, et al.
- Created Date
- 2019

In 2007, Arizona voters passed House Bill (HB) 2064, a law that fundamentally restructured the Structured English Immersion (SEI) program, putting into place a 4-hour English language development (ELD) block for educating English language learners (ELLs). Under this new language policy, ELL students are segregated from their English-speaking peers to receive a minimum of four hours of instruction in discrete language skills with no contextual or native language support. Furthermore, ELD is separate from content-area instruction, meaning that language and mathematics are taught as two separate entities. While educators and researchers have begun to examine the organizational structure of the …

- Contributors
- Llamas-Flores, Silvia, Middleton, James, Battey, Daniel, et al.
- Created Date
- 2013

The need for improved mathematics education in many of America's schools that serve students from low income households has been extensively documented. This practical action research study, set in a suburban Title I school with a primarily Hispanic, non-native English speaking population, is designed to explore the effects of the progression through a set of problem solving solution strategies on the mathematics problem solving abilities of 2nd grade students. Students worked in class with partners to complete a Cognitively Guided Instruction-style (CGI) mathematics word problem using a dictated solution strategy five days a week for twelve weeks, three or four …

- Contributors
- Spilde, Amy, Zambo, Ronald, Heck, Thomas, et al.
- Created Date
- 2013

More Math Minutes is an action research study, set in a high school in the southwestern United States, designed to examine the effects of collaborative peer-group learning for low-performing Algebra I and low-performing Algebra II students. This study is grounded in Social Cognitive Theory and Constructivist Theory including Bandura’s self-efficacy theory and Vygotsky’s theory of proximal development. Participants are comprised of 20 low-performing Algebra I students as the peer-learners and 20 low-performing Algebra II students as the peer-teachers participating in a peer tutoring intervention. Quantitative and qualitative data was collected through pre- and post-self-efficacy questionnaires, pre- and post-mathematics knowledge assessments, …

- Contributors
- Herriman, Patricia Valles, Kulinna, Pamela, Marsh, Josephine, et al.
- Created Date
- 2018

Let $G=(V,E)$ be a graph. A \emph{list assignment} $L$ for $G$ is a function from $V$ to subsets of the natural numbers. An $L$-\emph{coloring} is a function $f$ with domain $V$ such that $f(v)\in L(v)$ for all vertices $v\in V$ and $f(x)\ne f(y)$ whenever $xy\in E$. If $|L(v)|=t$ for all $v\in V$ then $L$ is a $t$-\emph{list assignment}. The graph $G$ is $t$-choosable if for every $t$-list assignment $L$ there is an $L$-coloring. The least $t$ such that $G$ is $t$-choosable is called the list chromatic number of $G$, and is denoted by $\ch(G)$. The complete multipartite graph with $k$ …

- Contributors
- Wang, Ran, Kierstead, H.A., Colbourn, Charles, et al.
- Created Date
- 2015

The advancement of technology has substantively changed the practices of numerous professions, including teaching. When an instructor first adopts a new technology, established classroom practices are perturbed. These perturbations can have positive and negative, large or small, and long- or short-term effects on instructors’ abilities to teach mathematical concepts with the new technology. Therefore, in order to better understand teaching with technology, we need to take a closer look at the adoption of new technology in a mathematics classroom. Using interviews and classroom observations, I explored perturbations in mathematical classroom practices as an instructor implemented virtual manipulatives as novel didactic …

- Contributors
- Pampel, Krysten Ashley, Currin van de Sande, Carla, Thompson, Patrick W, et al.
- Created Date
- 2017

While predicting completion in Massive Open Online Courses (MOOCs) has been an active area of research in recent years, predicting completion in self-paced MOOCS, the fastest growing segment of open online courses, has largely been ignored. Using learning analytics and educational data mining techniques, this study examined data generated by over 4,600 individuals working in a self-paced, open enrollment college algebra MOOC over a period of eight months. Although just 4% of these students completed the course, models were developed that could predict correctly nearly 80% of the time which students would complete the course and which would not, based …

- Contributors
- Cunningham, James Allan, Bitter, Gary, Barber, Rebecca, et al.
- Created Date
- 2017

This dissertation reports three studies of students’ and teachers’ meanings for quotient, fraction, measure, rate, and rate of change functions. Each study investigated individual’s schemes (or meanings) for foundational mathematical ideas. Conceptual analysis of what constitutes strong meanings for fraction, measure, and rate of change is critical for each study. In particular, each study distinguishes additive and multiplicative meanings for fraction and rate of change. The first paper reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on …

- Contributors
- Byerley, Cameron O'Neill, Thompson, Patrick W, Carlson, Marilyn P, et al.
- Created Date
- 2016

Public Mathematics Education is not at its best in the United States and technology is often seen as part of the solution to address this issue. With the existence of high-speed Internet, mobile technologies, ever-improving computer programming and graphing, the concepts of learning management systems (LMS’s) and online learning environments (OLE’s), technology-based learning has elevated to a whole new level. The new generation of online learning enables multi-modal utilization, and, interactivity with instant feedback, among the other precious characteristics identified in this study. The studies that evaluated the effects of online learning often measured the immediate impacts on student achievement; …

- Contributors
- Meylani, Rusen, Bitter, Gary G, Legacy, Jane, et al.
- Created Date
- 2016

There have been a number of studies that have examined students’ difficulties in understanding the idea of logarithm and the effectiveness of non-traditional interventions. However, there have been few studies that have examined the understandings students develop and need to develop when completing conceptually oriented logarithmic lessons. In this document, I present the three papers of my dissertation study. The first paper examines two students’ development of concepts foundational to the idea of logarithm. This paper discusses two essential understandings that were revealed to be problematic and essential for students’ development of productive meanings for exponents, logarithms and logarithmic properties. …

- Contributors
- Kuper, Emily Ginamarie, Carlson, Marilyn, Thompson, Patrick, et al.
- Created Date
- 2018

The primary purpose of this study is to examine the effect of knowledge for teaching mathematics and teaching practice on student mathematics achievement growth. Thirty two teachers and 299 fourth grade students in three elementary schools from one school district in urban area participated in the study. Most of them are Hispanic in origin and about forty percent is English Language Learners (ELLs). The two level Hierarchical Linear Model (HLM) was used to investigate repeated measures of teaching practice measured by Classroom Assessment Scoring System (CLASS) instrument. Also, linear regression and a multiple regression to examine the relationship between teacher …

- Contributors
- Kim, Seong Hee, Sloane, Finbarr, Middleton, James, et al.
- Created Date
- 2012

Functions represented in the graphical register, as graphs in the Cartesian plane, are found throughout secondary and undergraduate mathematics courses. In the study of Calculus, specifically, graphs of functions are particularly prominent as a means of illustrating key concepts. Researchers have identified that some of the ways that students may interpret graphs are unconventional, which may impact their understanding of related mathematical content. While research has primarily focused on how students interpret points on graphs and students’ images related to graphs as a whole, details of how students interpret and reason with variables and expressions on graphs of functions have …

- Contributors
- David, Erika Johara, Roh, Kyeong Hah, Thompson, Patrick W, et al.
- Created Date
- 2019

The concept of distribution is one of the core ideas of probability theory and inferential statistics, if not the core idea. Many introductory statistics textbooks pay lip service to stochastic/random processes but how do students think about these processes? This study sought to explore what understandings of stochastic process students develop as they work through materials intended to support them in constructing the long-run behavior meaning for distribution. I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I …

- Contributors
- Hatfield, Neil, Thompson, Patrick, Carlson, Marilyn, et al.
- Created Date
- 2019

Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative combinatorics problems and how students conceptualize the set of elements being counted in such problems, called the solution set. In particular, the focus was on the stable patterns of reasoning, known as ways of thinking, which students applied in a variety of combinatorial situations and tasks. This study catalogued students' ways of thinking about solution sets as they progressed through an instructional sequence. In addition, the relationships between the catalogued …

- Contributors
- Halani, Aviva, Roh, Kyeong Hah, Fishel, Susanna, et al.
- Created Date
- 2013

This dissertation describes an investigation of four students' ways of thinking about functions of two variables and rate of change of those two-variable functions. Most secondary, introductory algebra, pre-calculus, and first and second semester calculus courses do not require students to think about functions of more than one variable. Yet vector calculus, calculus on manifolds, linear algebra, and differential equations all rest upon the idea of functions of two (or more) variables. This dissertation contributes to understanding productive ways of thinking that can support students in thinking about functions of two or more variables as they describe complex systems with …

- Contributors
- Weber, Eric David, Thompson, Patrick, Middleton, James, et al.
- Created Date
- 2012

This study explores teacher educators' personal theories about the instructional practices central to preparing future teachers, how they enact those personal theories in the classroom, how they represent the relationship between content, pedagogy, and technology, and the function of technology in teacher educators' personal theories about the teaching of mathematics and their practices as enacted in the classroom. The conceptual frameworks of knowledge as situated and technology as situated provide a theoretical and analytical lens for examining individual instructor's conceptions and classroom activity as situated in the context of experiences and relationships in the social world. The research design employs …

- Contributors
- Toth, Meredith Jean, Middleton, James, Sloane, Finbarr, et al.
- Created Date
- 2014

The purpose of this study is to impact the teaching and learning of math of 2nd through 4th grade math students at Porfirio H. Gonzales Elementary School. The Cognitively Guided Instruction (CGI) model serves as the independent variable for this study. Its intent is to promote math instruction that emphasizes problem-solving to a greater degree and facilitates higher level questioning of teachers during their instructional dialogue with students. A mixed methods approach is being employed to see how the use of the CGI model of instruction impacts the math achievement of 2nd through 4th grade students on quarterly benchmark assessments …

- Contributors
- Medrano, Juan Candelario, Ann, Keith, David, Carlson L, et al.
- Created Date
- 2012

This dissertation reports three studies of the relationships between meanings teachers hold and meanings their students construct. The first paper reports meanings held by U.S. and Korean secondary mathematics teachers for teaching function notation. This study focuses on what teachers in U.S. and Korean are revealing their thinking from their written responses to the MMTsm (Mathematical Meanings for Teaching secondary mathematics) items, with particular attention to how productive those meanings would be if conveyed to students in a classroom setting. This paper then discusses how the MMTsm serves as a diagnostic instrument by sharing a teacher’s story. The data indicates …

- Contributors
- Yoon, Hyunkyoung, Thompson, Patrick W, Roh, Kyeong Hah, et al.
- Created Date
- 2019

Industry, academia, and government have spent tremendous amounts of money over several decades trying to improve the mathematical abilities of students. They have hoped that improvements in students' abilities will have an impact on adults' mathematical abilities in an increasingly technology-based workplace. This study was conducted to begin checking for these impacts. It examined how nine adults in their workplace solved problems that purportedly entailed proportional reasoning and supporting rational number concepts (cognates). The research focused on four questions: a) in what ways do workers encounter and utilize the cognates while on the job; b) do workers engage cognate problems …

- Contributors
- Orletsky, Darryl William, Middleton, James, Greenes, Carole, et al.
- Created Date
- 2015

This study investigated the current state of the U.S. and Chinese urban middle school math teachers' pedagogical content knowledge (PCK) for the topic of functions. A comparative, descriptive case study was employed to capture the PCK of 23 teachers in Arizona and of 28 teachers in Beijing, regarding their instructional knowledge, understanding of student thinking and curricular knowledge--three key components based on Shulman's conceptualization of PCK--related to functions. Cross-case comparisons were used to analyze the PCK of teacher groups across countries and socio-economic statuses (SES), based on the questionnaire, lesson plan, and interview data. This study finds that despite cultural …

- Contributors
- Zou, Hui, Fischman, Gustavo, Berliner, David, et al.
- Created Date
- 2014

ABSTRACT There is a continuing emphasis in the United States to improve student's mathematical abilities and one approach is to better prepare teachers. This study investigated the effects of using lesson study with preservice secondary mathematics teachers to improve their proficiency at planning and implementing instruction. The participants were students (preservice teachers) in an undergraduate teacher preparation program at a private university who were enrolled in a mathematics methods course for secondary math teachers. This project used lesson study to engage preservice teachers in collaboratively creating lessons, field testing them, using feedback to revise the lessons, and re-teaching the revised …

- Contributors
- Mostofo, Jameel (Jim) Richard, Zambo, Ronald, Elliott, Sherman, et al.
- Created Date
- 2013

The purpose of this study was to identify the algebraic reasoning abilities of young students prior to instruction. The goals of the study were to determine the influence of problem, problem type, question, grade level, and gender on: (a) young children’s abilities to predict the number of shapes in near and far positions in a “growing” pattern without assistance; (b) the nature and amount of assistance needed to solve the problems; and (c) reasoning methods employed by children. The 8-problem Growing Patterns and Functions Assessment (GPFA), with an accompanying interview protocol, were developed to respond to these goals. Each problem …

- Contributors
- Cavanagh, Mary C., Greenes, Carole E, Buss, Ray, et al.
- Created Date
- 2016