Doctor of Philosophy (PhD), Ohio University, 2024, Curriculum and Instruction Mathematics Education (Education)

Mathematics is central to human activity and hence to education. Although the usefulness and importance of mathematics are unquestioned, many students find mathematics difficult, uninteresting, and dry. Based on my personal experience as a mathematics teacher, teacher educator, and researcher, I have witnessed numerous students expressing their dislike for school mathematics. There is a lack of research specifically exploring the perspectives of students who dislike mathematics. In this research, I explore the factors contributing to the dislike of mathematics and identify ways to mitigate these factors. The study comprises of two phases: the first phase explores students' perspectives on their dislike of school mathematics and the contributing factors. The second phase explores aspects of the undergraduate Quantitative Reasoning (QR) course that help mitigate this dislike. I chose the undergraduate Quantitative Reasoning course for its emphasis on innovative educational approaches such as real-world connection, project-based learning, and formative assessment. In this study, I selected a purposive sample of undergraduates who self-reported their dislike of school mathematics in the Spring of 2023 at a university in Midwestern part of the United States. Fifteen (15) participants took part in the Phase 1 of the study, and 14 continued and completed Phase 2. For each phase, I conducted a semistructured interview of each participant, one at the beginning of the semester and another near the end, except for one participant there were two interviews for Phase 2. Each interview lasted for about one hour. The interviews were audio or audio-video recorded and transcribed and coded using NVivo, a qualitative transcription and coding software. In Phase 1, most students first developed a dislike of mathematics in experienced elementary school, struggling particularly with multiplication and division. This dislike deepened in the middle and high school with subjects like (open full item for complete abstract)

Doctor of Education (EdD), Wright State University, 2020, Leadership Studies

In this study, the investigator sought to determine the extent to which mathematics self-efficacy affects mathematics growth among students in grades four and five. Included in this investigation is a hypothesized structural model that reflects Bandura's (1977a, 1986, 1989) theory of self-efficacy. In part one of the investigation, each variable in the model (mathematics self-efficacy, self-regulation in mathematics, mathematics avoidance, mathematics anxiety, attitude toward mathematics, and mathematics growth) was analyzed to determine whether there were significant differences between genders in those specified variables. Findings revealed gender differences in two of the six variables, self-regulation in mathematics and mathematics avoidance. Females reported more self-regulatory behaviors in mathematics and less mathematics avoidance behaviors. In part two of the study, the investigator examined the measurement and structural model. In addition, the direct and indirect effects of mathematics self-efficacy on mathematics growth were analyzed. Results from this investigation showed no significant direct effect of mathematics self-efficacy on mathematics growth. However, there was a significant indirect effect of mathematics self-efficacy on mathematics growth with the following mediating variables: self-regulation in mathematics, mathematics avoidance, mathematics anxiety, and attitude toward mathematics. The indirect effect of mathematics self-efficacy on mathematics growth was small, and 5% of the variance in mathematics growth could be explained by the predictor variables. Though some of the data supported Bandura's (1977a, 1986, 1989) theory of self-efficacy, most of the findings do not support the theoretical framework. The findings from this investigation provide helpful information to the educators at the study's site. Further intervention studies in the areas of mathematics self-efficacy, self-regulation in mathematics, mathematics avoidance, mathematics (open full item for complete abstract)

EDD, Kent State University, 2023, College of Education, Health and Human Services / School of Foundations, Leadership and Administration

KELLERMANN, MARY K., JULY 2023 INTERPROFESSIONAL LEADERSHIP UNDERSTANDING THE WAYS TEACHERS ARE INFLUENCED IN THEIR CURRICULAR AND INSTRUCTIONAL DECISION-MAKING PROCESSES IN A FRESHMAN LEVEL MATHEMATICS CLASS (165 pp.) Co-Directors of Dissertation: Scott Courtney, Ph.D. Todd, Hawley, Ph. D. The purpose of this qualitative interpretive study was to understand the ways teachers were influenced in their curricular and instructional decision-making processes in a freshman level mathematics class. Understanding what influences teachers' decision-making processes, and how (the ways) these processes were influenced, may lead to improved practice and ultimately improved student learning. Data collection was from three purposefully selected participants at a Midwestern, midsize university and consisted of a two-part journal, questionnaire, and follow up interviews. The follow up interviews were after each data collection for a total of three interviews. The data were analyzed using Hatch's (2002) models of typological analysis, inductive analysis, and interpretive analysis. Codes, categories, and themes of the data were developed by using a thematic analysis by Braun and Clarke (2006). The key findings included what factors and how these factors influenced a teacher's curricular and instructional decision-making processes in a freshman level mathematics class. Many factors were found such as internal, external, constraints, positive, negative, coordinator position, piloting courses, and committee work. Implications of these findings may impact how teachers make decisions, decrease cognitive loads while teaching, influence teacher training and education, and may improve teacher practice and student learning.

Master of Arts, Wittenberg University, 2022, Education

Mathematical fluency is important to students' foundational math development. Based on Ohio's state math standards, students should be fluent with their multiplication facts by third grade. However, many fifth grade students are entering the classroom not meeting those standards. For many years, educators relied on procedural strategies to teach and assess numerical fluency. In recent years the theoretical approach to teaching shifted from procedural to a more conceptual method. This shift moves from rote memorization and timed-tests to more meaningful activities such as fluency games, rich problems, and number talks. The theoretical foundation for this study is constructivism and the interventions provided students opportunities to communicate and construct their own thinking. This action research reports the effect that providing multiple strategies for solving problems had on fifth-grade students' numerical fluency. A multi-methods design was used which included a Multiplication Fluency Assessment, a Beliefs Questionnaire, and student interviews. Overall students reported that they did not enjoy using models or find them beneficial, however many used models in their work. Students did show growth in their computational accuracy as well as in the strategies they used to solve problems.

Specialist in Education (Ed.S.), University of Dayton, 2022, School Psychology

Mathematics anxiety is a negative emotional response that results in stress and mathematics avoidance. The present study examined the predictive relationship of mathematics confidence and mathematics performance on mathematics anxiety in middle school students. Mathematics confidence and mathematics anxiety were assessed in (n = 60) 7th and 8th grade students in a suburban middle school. Mathematics performance was measured via the student's most recent mathematics benchmarking data point and their most recent mathematics quarter grade percentage. Results indicated that significant relationships exist between mathematics confidence, mathematics letter grade percentage, and mathematics anxiety, but no significant relationship exists between mathematics CBM benchmark score and mathematics anxiety. Furthermore, mathematics grade percentage explained for the most variance in mathematics anxiety. Implications for educators regarding mathematics anxiety in the schools are discussed.

PHD, Kent State University, 2014, College of Education, Health and Human Services / School of Teaching, Learning and Curriculum Studies

The purpose of this study was to explore elementary teachers’ interpretations of three of the Standards for Mathematical Practice in the Common Core State Standards. The research followed how these interpretations evolved during three types of professional learning experiences. The study also explored teachers’ beliefs about the supports that would be necessary to enact these standards successfully in a classroom, school, and district. A teacher development experiment was utilized for this qualitative study. Three teachers (two from grade five and one from grade one) were recruited from the same school district, and they participated in three individual interviews, two group discussions, and two videotaped lessons as they read and discussed the three chosen standards. Teachers’ comments were analyzed via an interpretive approach reflecting hermeneutic philosophy. Each teacher was considered a case; thus, the analysis focused on each teacher’s thinking as well as the similarities and differences among the teachers’ interpretations. The teachers were able to respond to tentative findings of the study, and adjustments to the analyses were made when appropriate. Findings indicated that teachers often interpret the text and intent of standards in very unique ways. These interpretations are influenced by past personal and professional experiences, opportunities to read and discuss standards with others, expectations set forth and support provided by administrators, and observations of student learning. Interpretations do not change quickly or without catalyst; rather, thinking evolves over extended periods of time when opportunities for professional learning and reflection are provided on a regular basis.

Master of Science, The Ohio State University, 2012, Mathematics

The purpose of this study was to show how mathematics can be used to analyze effects on sound. Our hope is that this may inspire student interest in mathematics. We analyzed five common industry standard effects. Research data was gathered using Mathematica and GarageBand software. Three versions of each effect were used to alter pure tone sound waves of ten different frequencies using GarageBand. Then using Mathematica's Fourier command, the frequency spectrum of each altered sound wave was generated. Through observation of each set of 30 frequency spectra, the most prominent and common pure tone components were determined. For each effect, Mathematica's Fit command was used to determine a best fit model of the magnitude of each component as a function of frequency. Our models provide descriptions of the effects that are consistent with the traditional descriptions of the industry standard effects in our study. If similar research is to be conducted, our recommendation is that more versions of each effect, a wider range of input frequencies, and a higher sampling rate would produce function models that are even more consistent with traditionally accepted effect descriptions. Furthermore, an understanding of the hardware and software design used to build effects on sound is highly recommended.

Doctor of Philosophy (PhD), Ohio University, 2010, Curriculum and Instruction Mathematics Education (Education)

This study investigated the attitudes toward mathematics of developmental students in six community colleges from a large Midwestern state in the United States. The perception of the students regarding mathematically intensive careers was also analyzed. A Web-based survey was conducted during the winter and spring of 2009. Two colleges were selected to represent each of the locale characterizations—rural, suburban, and urban. Student attitudes toward mathematics were measured using seven of the nine domains of the Fennema-Sherman Mathematics Attitude Scales (FSMAS). Three additional questions were used to gauge perceptions of mathematically intensive careers. These three questions elicited perception in terms of importance, reward, and the intention of pursuing a mathematically intensive career. The study found that generally community college developmental mathematics students showed fairly positive attitudes toward mathematics. The domains in which they showed highly positive attitudes were male domain and success; and slightly positive attitudes in teacher and usefulness. However, their attitudes were indifferent or mixed with regard to confidence, anxiety, and motivation. There was no statistically significant difference in the attitudes of developmental mathematics students in community colleges across locale or by gender. A statistically significant association was found among locale, socioeconomic status (using household income as a proxy), and ethnicity. Attendance status was the only demographic variable that statistically predicted perception of mathematically intensive careers. Full-time students are about 2.5 times more likely than part-time students to have a high perception of mathematically intensive careers. Other supplementary results were obtained as follows: Overall attitude positively correlates significantly with the perception of mathematically intensive careers. For urban males only, age positively correlates with perception of mathematic (open full item for complete abstract)

Doctor of Philosophy (Ph.D.), University of Dayton, 2013, Educational Leadership

Currently, many community colleges are struggling with poor student success rates in developmental math. Therefore, this qualitative study focused on employing best practices in developmental mathematics at an urban community college in Dayton, Ohio. Guiding the study were the following research questions: What are the best practices utilized by a group of developmental mathematics instructors at an urban community college? How do these instructors employ such practices to enhance student learning? Participants consisted of 20 developmental mathematics instructors from Sinclair Community College in Dayton, Ohio who had taught at least six developmental math classes over a two-year period and who self-reported success rates of at least 60% during that time. This study employed a pre-interview document and a face-to-face interview as the primary research instruments. Using the constant comparison method (Merriam, 2002a), the researcher constructed findings from both approaches regarding best practices in developmental math. Such practices included communication with students, the art of organization, collaborative learning, frequent low stake assessments, technology supplements, the use of mnemonics and memorable wording, and manipulatives, visuals and real-life applications. When addressing the topic of acceleration, the participants reported that this strategy is a proper fit for some students but not all. The following conclusions were based on the findings from this study. Effective communication should be established between developmental math instructors and students as well as among developmental math instructors. Developmental math faculty ought to work with their students in developing their organizational skills. Developmental math instructors should couple the implementation of frequent low stake assessments with student outreach. Collaborative learning can be beneficial to some developmental math students, but instructors must take into account t (open full item for complete abstract)

PHD, Kent State University, 2024, College of Education, Health and Human Services / School of Teaching, Learning and Curriculum Studies

This study explored the mathematical learning experiences of adult students enrolled in a community college developmental mathematics course during the Fall 2023 semester. The study's main objective was to identify the types of experiences that help adult students learn foundational mathematics. Another goal of the study was to provide empirical data to help design programs and strategies to assist students in being successful throughout their mathematical learning journey. This was an interpretive qualitative study that utilized responsive interviewing and artifact collection. Five participants were obtained through a pre-survey sent to 746 students enrolled in the lowest level course at a community college, Arithmetic/Pre-Algebra. This pre-survey collected general demographic and student information. The pre-survey also asked participants to rank their mathematics self-efficacy, growth mindset, and perceived care in the mathematics classroom. Finally, students took part – at varying levels of participation – in two interviews, artifact collection, and a post-survey. Through my analysis of the interview transcripts and shared artifacts, eight themes emerged. Five of the eight themes involve student perceptions and relate to 1) mathematics self- efficacy, growth mindset, and care diminish after elementary school; 2) low readiness for college-level mathematics; 3) the teaching environment and didactics implemented; 4) perceptions of the learning characteristics needed for success; 5) the absence of student barriers. The final three themes relate to the power of interactions, specifically, the power as it relates to 6) words, 7) actions, and 8) expectations. The study's findings provide implications for my teachings, my mathematics department, community colleges at large, and the field of mathematics education.

Honors Theses, Ohio Dominican University, 2023, Honors Theses

This paper describes the process of development and evaluation of an open educational resource (OER) e-module on the Central Limit Theorem written for an Introductory Statistics college-level course. The purpose of this project is two-fold. First, the e-module bridges the knowledge gap between introductory topics and Hypothesis Testing – one of the most challenging concepts in Statistics. Second, the project focuses on developing tools that allow instructors to analyze the effectiveness of the module and reveal student patterns of interaction with the platform. The overall goal of the project is to improve the quality of open educational resources, provide students/instructors with additional study materials in response to rising cost for textbooks and higher education, and provide more data for further research on student behavior while interacting with e-textbooks. The interactive e-module was developed using LaTeX markup language and Overleaf editor, uploaded to the XIMERA platform and tested on two sections of MTH 140, a college-level Statistics course. Once the experiment has been performed and the data collected, the results were analyzed using Python programming language. As a result of the study, some tools for analysis of user data have been developed, and an OER has been created.

Master of Mathematical Sciences, The Ohio State University, 2020, Mathematical Sciences

T his research focusses on the various forms of mathematics learning disorders that afflict many students from an early age, often adversely affecting not only their academic achievement, but their lives, and some of the tools and methods that are available to help overcome these afflictions. In closing, a case study illustrates how Learning Progressions may be used as a tool to help an adult, affected by math learning disorders most of her life overcome her math anxiety and start to enjoy learning mathematics.

Bachelor of Arts, Ohio University, 2020, Mathematics

T his research focusses on the various forms of mathematics learning disorders that afflict many students from an early age, often adversely affecting not only their academic achievement, but their lives, and some of the tools and methods that are available to help overcome these afflictions. In closing, a case study illustrates how Learning Progressions may be used as a tool to help an adult, affected by math learning disorders most of her life overcome her math anxiety and start to enjoy learning mathematics.

Doctor of Philosophy, University of Toledo, 2020, Curriculum and Instruction

This research examined how three middle school mathematics teachers who were supported by their district to use the Teaching Through Problem Solving approach interpreted and implemented the Standards for Mathematical practices (SMPs) developed by the Common Core State Standards (2010) and the Mathematics Teaching Practices (MTPs) developed by the National Council of Teachers of Mathematics (2014). Data sources included a pre and post-interview with each participant, one lesson plan from each participant, and one lesson observation for that lesson plan. Data analysis involved descriptive and interpretive components of qualitative methods to understand teachers' interpretation and implementation of SMPs and MTPs. Four themes emerged from this analysis: (1) Supporting teachers to use Teaching Through Problem Solving may help them in their implementation of the SMPs more than in their interpretations, (2) Teachers who use Teaching Through Problem Solving may understand and fully implement the MTPs, (3) Teachers who are supported to use Teaching Through Problem Solving may use Teaching For Problem Solving, and (4) Using Teaching For Problem Solving may result in partial implementation of the SMPs and MTPs.

Master of Mathematical Sciences, The Ohio State University, 2020, Mathematical Sciences

If one were to study mathematics without ever studying its history, they may be left with a rather skewed perception of how the discipline has developed. Vector algebra is a particularly good example of this. Students may be introduced to vectors as early as pre-calculus, and will certainly have become closely acquainted with them by integral and multivariable calculus. They are an essential means of representing and working with certain quantities -- velocity, force, etc. And so one may be led to believe that vectorial ideas must have been incorporated into mathematics long, long ago. However, the reality is quite different; it was actually not until the end of the nineteenth century that a vector system (or vector algebra or calculus) closely resembling our modern one was found, and not until the twentieth that it became widely used. The object of this thesis is to explore the interesting history behind this fact. We trace the widening of the idea of "quantity" from its conception in classical geometry and algebra to one that admits a vector. We explore early mathematical systems that dealt with vectorial ideas, especially W.R. Hamilton's quaternions. We explain how our modern vector system developed from this. The matters of how new ideas arise in mathematics and science, how such innovations are received, and how they evolve, are discussed both implicitly and explicitly.

PhD, University of Cincinnati, 2019, Education, Criminal Justice, and Human Services: Educational Studies

Despite calls for more equitable levels of mathematics achievement, students of economic disadvantage continue to achieve mathematics proficiency at lower rates than more well-to-do students. Built on Sirin's meta-analysis linking socioeconomic status to achievement and Ladson-Billings assertion that poorer students are more likely to rely on schools for academic supports, the study's guiding theoretical proposition suggested that schools with high proportions of economically disadvantaged students—high-level school dependency settings—may need to operate differently to support students' mathematics learning compared to low-level school dependency settings. The purpose of this mixed methods comparative case study was to better understand the relationship between school dependency and mathematics instruction and support practices in schools serving grades three through six in the U.S. state of Ohio. A sequential approach allowed for the examination a school's level of school dependency and mathematics practices in separate methodological phases. Each component was then combined to understand how mathematics practices differed in two types of contexts. The cluster analysis resulted in seven cluster profiles at four levels of school dependency. Two clusters representing maximum contrast for school dependency were selected for further investigation. From each cluster, two high-achieving school cases were selected for comparison to understand how they provided mathematics instruction and support to their students. The results of the cross-case analysis showed that the four cases employed practices related to departmental structure, core instructional materials, screening assessments and data use, and provision for a wide range of mathematics supports. Integrative analysis determined variation in these practices by school-dependency profile. High-level school-dependency schools, serving more students in need of intervention supports, used core material to en (open full item for complete abstract)

Doctor of Philosophy (PhD), Ohio University, 2018, Curriculum and Instruction Mathematics Education (Education)

When students engage in mathematical modeling, they use mathematics to solve open-ended, real- world problems. This process helps students to make connections and fosters their learning of mathematics itself. Engaging students in mathematical modeling, however, is not an easy task for teachers due to their lack of experience in such teaching. Hence, professional development is needed to advance mathematics teachers' capacity to enact mathematical modeling. This study examined the Mathematical Modeling and Spatial Reasoning (Modspar) professional development program, designed for high school mathematics teachers in Ohio. Two research questions were asked: (a) What is the nature of the professional development program? and (b) What did the participants learn as a result of participating in the program, and how did the program affect their teaching of modeling? To provide data sources for the research questions, (a) I interviewed each of 5 of the 28 participating teachers three times (once before the summer 2016 Modspar program and twice during the 2016–2017 school year), (b) I observed all of the activities enacted during the summer program and collected daily reflections from the 5 selected participants, and (c) I observed 4 of these participants enacting modeling in their classrooms twice during the 2016–2017 school year. For the first question, I examined the level of engagement and the type of modeling enacted during the summer program as all of the participating teachers completed the 20 institute activities: 8 involving modeling with algebra and 12 related to modeling with geometry. For the second question, I examined how the Modspar program advanced the 5 selected participants' knowledge and instruction of modeling. I coded the data thematically and constructed case reports. Results for the first question suggest that the algebra activities focused on mathematical modeling (i.e., using mathematics to solve real-world problems); whereas, the geometry a (open full item for complete abstract)

Master of Arts (MA), Bowling Green State University, 2016, Mathematics/Mathematics (Pure)

Graduate student instructors (GSIs) in mathematics are a vital part of undergraduate instruction and with the continued rise in university enrollment, they will continue be relied on. The major goal of this study is to better understand GSIs' classroom instruction. We coded and analyzed 34 first semester GSIs and nine mentor GSI video observations using an observation protocol refined for this study to identify their practices. This study is an initial investigation into the teaching practices of GSIs, contains professional development ideas and implications for future research.

Master of Mathematical Sciences, The Ohio State University, 2016, Mathematics

This project examines the impact of a mathematics course for prospective elementary teachers and a mathematics course for prospective middle school teachers on those enrolled in their respective courses using a pre-post test methodology. Prospective teachers were asked to take tests, designed by the Learning Mathematics for Teaching project, which claim to measure mathematical knowledge for teaching. Results indicate that the courses positively impacted the mathematical knowledge of prospective teachers. Examination of the results on clusters of items covering specific topics provides additional insight into how these courses are impacting prospective teachers and how they might be modified as a part of ongoing course improvement efforts.

EdD, University of Cincinnati, 2001, Education : Literacy

This study provides a rich narrative and a purposeful discussion and analysis of one group of first grade students' mathematics Discourse. It investigates the vocabulary they use, the importance they give to mathematical dialogue, and the broad discourse field in which they participate. The National Council of Teachers of Mathematics (1989, 1991, 2000) suggests that discourse in mathematics promotes, solidifies, and expands concept development. This research focuses on the voice of the students and their perspectives, coupled with research observations. The children discuss the language they use, demonstrate the social elements of the mathematics community in the classroom, and model their communication skills. Broad ranges of Discourse are evidenced as children intertwine beliefs and values with mathematical dialogue and social considerations. While many theorists speculate on what "should be" happening in classrooms, this study looks at what is actually happening in one classroom. If discourse is to become an active part of learning in the mathematics classroom, realistic expectations for language development and use create a base line for growth. Through description and analysis, this study seeks to provide a window into the reality of Discourse in mathematics. It sheds light on the kinds of mathematical identity that is represented in dialogue, and the impact of individual's attitudes, values, and behaviors in the social and academic context. It recognizes multi-layered elements in curriculum choices; the impact of classroom culture; the value of student motivation. It confirms that students do think mathematical language is an indicator of competence and social status, is probably an important tool for learning, and is an indicator of identity. Finally, the data illuminate the influence of teachers on young children, and the power of their abilities and attitudes toward communication and learning as they model and teach mathematical language in the classroom.