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Approximate Solutions To The Allen-Cahn Equation Using The Finite Difference Method, Jamil Malik Villarreal

Theses and Dissertations

Seeking a deeper understanding of the world has been a driving factor in Applied Mathematics. From counting and measuring physical objects to developing equations and ratios that resemble patterns in nature, mathematics is used to interpret and explain the intricate structures that we observe everyday. The field of Applied Mathematics almost always involves setting up and then solving, or approximating solutions to, at least one partial differential equation that takes the physical and mathematical properties into consideration. This is the process of creating mathematical models. For this thesis, we will investigate approximate solutions to the Allen-Cahn equation whose analytic solution …

Impact Of Pro-Based Learning On Student Performance In Elementary Mathematics, Emmanuela Remy

Theses and Dissertations

Elementary school students have been underperforming in mathematics at the city, state, and national level. The National Education Goals, adopted by the United States Congress in 1989, did not achieve the two math goals (Goal #3 and Goal #5) by the year 2000 as outlined in the Goals 2000 Legislation. The 2019 National Assessment of Educational Progress (NAEP) results indicated that grade 4 students were not proficient in mathematics. This exploratory study, not only sought to address the two National Education math goals, but also investigated whether Pro-Based Learning (ProBL) was an effective pedagogical practice for elementary school students of …

The Impact Of Universally Accelerating Eighth Grade Mathematics Students In Heterogeneously Grouped Classrooms: An Interrupted Time Series, Patrick Walsh

Theses and Dissertations

Traditionally, students are scheduled to take Algebra I in their first year of high school mathematics in New York State. However, in many schools, the “top” students in a cohort have access to this course in eighth grade, tracking these high-achieving students ahead of their lower-achieving peers. In response, some schools have adopted the policy of “Algebra for all” in eighth grade – called universal acceleration. A perceived benefit to the policy of universal acceleration is ensuring equal access to a challenging curriculum for all students, regardless of race, socioeconomic status, or prior achievement- mitigating one of the perceived limitations …

Establishing Teaching Presence In Higher Education Online Mathematics Courses: A Phenomenological Study, Deltrye Eagle Holt

Theses and Dissertations

The purpose of this phenomenological study was to describe, based on the teaching presence component of the Community of Inquiry (CoI) theoretical framework, the lived experiences of mathematics instructors while establishing teaching presence in online higher education mathematics courses. Teaching presence, which is one of the three core elements of the community of inquiry (CoI) framework, is necessary for achieving learning outcomes and student satisfaction. The three main research questions were: 1. How do mathematics instructors establish teaching presence in online higher education mathematics courses? 2. How do mathematics instructors establish teaching presence in face-to-face higher education mathematics courses? 3. …

The Relationship Between Mathematics Teachers’ Perceptions Of Student Motivation And Their Use Of Instructional Strategies For At-Risk Math Students, Kayla Morris Couch

Theses and Dissertations

Student motivation in mathematics education can be affected by many variables, especially for at-risk students. Existing information is limited regarding teacher perceptions of their own pedagogy, instructional strategies, and at-risk student motivation in the area of mathematics for middle school and high school students. The purpose of this study was to analyze middle school and high school mathematics teachers’ perceptions of their own pedagogy, instructional strategies, and at-risk students’ motivation in mathematics. Deci and Ryan’s self-determination theory was the theoretical framework used to guide the current study, which focuses on psychological and instinctive needs of individuals. An explanatory, sequential mixed …

A Foundation For Understanding The Neurocognitive Processes That Underlie Mathematics Performance In Children, Christopher Anzalone

Theses and Dissertations

The current study investigated the prognostic utility of resting state EEG coherence in the prediction of standardized mathematics scores. Quantitative EEG analyses were performed for 60 school-aged children (ages 7 to 12 years) with and without math learning disabilities (MLD). Analyses assessing intrahemispheric coherence at rest were performed across the entire sample and several coherence networks were extracted.

Specifically, networks that included Brodmann area 40 (BA 40) -- a region of the brain heavily involved in the cognitive processes responsible for mathematics performance (Anderson, Betts, Ferris, & Fincham, 2011; Cohen, Dehaene, Chochon, Lehericy, & Naccache, 2000; Kroger, Nystrom, Cohen, & …

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 …

Developing Specialized Content Knowledge For Equitable Practice In Mathematics: Exploring A Constructivist Approach To Preservice Teacher Education, Jane Rector Wilkes

Theses and Dissertations

A successful teacher education program prepares preservice teachers to provide high quality mathematics education for all students. In order to effectively address the needs of diverse and historically underserved groups of students, future teachers need to have a deep understanding of both basic content knowledge and pedagogical content knowledge. The purpose of this study was to examine ways to support preservice teachers in improving procedural and conceptual content mastery, as well as the specialized content knowledge that they will need in order to feel empowered to teach their future students.

Based on the theoretical frameworks of two components of mathematical …

Feminist-Infused Participatory Action Research To Promote Female Students’ Self- Efficacy In Mathematics, Nicole Hreno

Theses and Dissertations

Prompted by the manifestations of decreased levels of mathematical self-efficacy among the female students in my district, the purpose of this study was to investigate the source of self-efficacy development that was most influential among our female students and engage in praxis to combat these gender inequities. Grounded in critical feminist theory, I engaged six teacher-researchers in participatory action research through qualitative methodologies. Using questionnaires to examine the worldviews of our female students, the emergent study was guided by these voices which were previously silenced. The interventions employed were a direct result of the females’ expressed mathematical experiences, leading us …

Effects Of Differentiating Instruction Through Tiered Lessons In Special Education Secondary Mathematics, Katlyn Lewis

Theses and Dissertations

This study examined the effects of differentiating instructing through tiered lessons to see if it would improve students' success in high school special education classes. The study was done in two Algebra II secondary special education classrooms including 17 students in total. There were 5 females and 12 males, all students were juniors in high school and aged 16 or 17 years old. All of the students were classified as either specific learning disabilities, other health impaired, or multiple disabilities including anxiety and depression. The students were enrolled in resources classes for all of their major academic subjects and inclusive …

The Effectiveness Of Growth Mindset Strategies On Off-Task Time In A Special Education Mathematics Classroom, Alisa Marie Ialacci

Theses and Dissertations

The purpose of this study was to investigate the effects of growth mindset strategies on off-task time and attitude in a special education classroom. This research was done using a two-group pretest-posttest design where students with IEPs will be compared to those who do not have IEPs. Student on-task time was monitored prior to the intervention to give a pre-assessment of each student's off-task time. During the intervention, the students' behaviors were observed for signs of improvement. Growth mindset strategies were implemented during each class as needed for improving the overall mood. Overall the results showed a decrease in off-task …

Effects Of Online Program Vs. Handheld Flashcards On Multiplication And Division Fact Knowledge Of 4th Grade Learners With Exceptional Needs, Lindsay M. Siegman

Theses and Dissertations

This study utilized a time series design to investigate the effects of a computer-based math fact program called Xtramath.org vs. the use of traditional handheld flashcards. Students were given a baseline assessment before beginning the school district's method for learning basic math facts: Xtramath.org. They were tested again after 6 weeks and then began to use traditional handheld flashcards. Students were tested again to compare the results. Eight 4th grade students (5 male and 3 female) with special needs were included in this study. These students attend school in a wealthy, suburban area with a predominantly white population.

Fluency in …

The Impact Of Intelligent Tutoring Software On Geometry Students, Simela Oueini

Theses and Dissertations

This purpose of this paper is to deepen the understanding for a problem of practice in the mathematics educators’ classroom of low retention of information thus leading to poor mathematics achievement. The identification of the problem of practice led to a development of a research focus examining the effects of using intelligent tutoring software in the mathematics classroom and the impact it has on mathematics achievement, student motivation as it relates to self-efficacy, student engagement and attitudes towards mathematics. Using a convergent mixed methods approach (Creswell, 2012), this paper elaborates on the research questions addressing “What effects does the integration …

The Relationship Between Mindset And Motivation In An Alternative School Mathematics Classroom, Jo Ellen Dowdy

Theses and Dissertations

The purpose of this action research study was to determine the impact of a Khan Academy growth mindset lesson plan on the motivation of at-risk ninth grade students in a mathematics classroom. Data were collected for quantitative analysis of students’ self- reporting of perceptions pertaining to mindset beliefs before and after a mindset intervention and perceptions about motivation in the mathematics classroom. Analysis revealed there was no relationship between mindset and motivation. A minimal decrease in fixed mathematical mindset was determined after a Khan Academy mindset intervention. Increases were found in students’ beliefs in the importance of math, the usefulness …

The Role Of Teaching Presence On Academic Achievement In Fully Online Asynchronous And Hybrid Undergraduate Mathematics Courses, Shaghayegh Azadi Setayesh

Theses and Dissertations

This study was designed to investigate how mathematics student perceptions of teaching presence differ by course delivery mode and student achievement. Online learning has had a steady growth in higher education, and mathematics courses are also offered in fully online and hybrid modes, but the research on online mathematics learning and academic achievement is limited. In order to contribute to the body of research in this field, the focus of this study was on teaching presence and academic achievement in two delivery modes: fully online asynchronous, and hybrid.

The Community of Inquiry was the theoretical framework of this study, where …

Teaching The Common Core State Standards (Ccss) Using Interdisciplinary Units: A Qualitative Case Study Of How Secondary Core Curriculum Teachers Implement The Ccss Using Interdisciplinary Units (Ius), Ella Jones Burch

Theses and Dissertations

The purpose of this qualitative case study was to explore how teachers understood and practiced using IUs to teach the core disciplines of the CCSS. The strategy of inquiry was a single case study in an urban high school where teachers of English, science, social studies, and math courses discussed IUs, and some teachers were observed using IUs. Data from public documents, teacher and student participant interviews, teacher classroom observations, a teacher survey, and field notes were analyzed and produced themes around the implementation of IUs.

The findings of this study indicate that teachers perceive how to conceptualize an IU, …

An Experimental Study On The Effects Of A Gamified Software Intervention In Mathematics Achievement Among Sixth Grade Students, Janice Watson

Theses and Dissertations

An Experimental Study on the Effects of a Gamified Software Intervention on Mathematics Achievement Among Sixth Grade Students. Janice Watson-Huggins, 2018: Applied Dissertation, Nova Southeastern University, Abraham S. Fischler College of Education. Keywords: Gamification: intrinsic motivation: extrinsic motivation: academic performance: mathematics: test scores: Edufocal©.

Children have been playing computer games for many years. Today's children are very technologically savvy compared to 10 years ago. However, no concrete research was done in the Caribbean and in Jamaica to be specific, that investigates the impact of gamification on student academic scores and motivation. Gamification is used to describe the use of …

The Impact Of Social And Academic Integration In Developmental Education, L. Marie Dionisi

Theses and Dissertations

The purpose of this study was to investigate academic and social integration among students in a developmental math course. A convenience sample was utilized in this study since many of the students either passed out or stopped out at the time the survey was distributed. The study used a survey consisting of the following six sections, background information/demographics, peer-group interactions, interactions with faculty, faculty concern for student development and teaching, academic and intellectual development, institutional and goal commitments.

The study found there was a positive response rate with interaction with faculty. In addition, many of the students were committed to …

Modeling Multimodal Failure Effects Of Complex Systems Using Polyweibull Distribution, Daniel A. Timme

Theses and Dissertations

The Department of Defense (DoD) enlists multiple complex systems across each of their departments. Between the aging systems going through an overhaul and emerging new systems, quality assurance to complete the mission and secure the nation‘s objectives is an absolute necessity. The U.S. Air Force‘s increased interest in Remotely Piloted Aircraft (RPA) and the Space Warfighting domain are current examples of complex systems that must maintain high reliability and sustainability in order to complete missions moving forward. DoD systems continue to grow in complexity with an increasing number of components and parts in more complex arrangements. Bathtub-shaped hazard functions arise …

The Effects Of Using A Whiteboard Interactively In A Middle School Mathematics Classroom, Joshua H. Schneider

Theses and Dissertations

The purpose of this study was to further examine the effects of using Interactive White Boards interactively versus as a glorified whiteboard. The experimental group consisted of seven eighth grade general education students and six eighth grade special education students. The experimental group was taught with lessons created to promote interactivity and student involvement and covered the five lessons in a unit on three-dimensional geometry. Baseline data was collected by using the mean of the students' recent test scores. The post-test was then compared to the students' baseline scores to show the effectiveness of the intervention. To further data analysis, …

Assessing Reading And Mathematics Achievement Of Students With Disabilities In A Suburban Middle School, Terri Melissa Toomer

Theses and Dissertations

Co-teaching classrooms consist of general and special education teachers working together to benefit students with disabilities (SWDs). Many parents and teachers believe the content knowledge provided by general educators in the regular education setting, combined with the instructional service delivery model (SDM) expertise of special educators, will result in the greatest academic growth for SWDs. However, it is not known if SWDs served in one SDM progress at a faster rate than SWDs served in another SWD. Therefore, the focus of this study was to compare the reading and mathematics achievement of male and female middle school SDWs in two …

Problem-Solving In An Early Childhood Mathematics Classroom, Lockey Plyler

Theses and Dissertations

Problem-solving occurs when mathematical tasks create opportunities that provide challenges for increasing students' mathematical understanding and development. This research study determined the influence of the launch-explore-summarize/extend problem-solving framework on second-grade student performance of place value tasks. The dissertation in practice measured problem-solving success. This action research study occurred at an elementary school in Columbia, South Carolina. The teacher-researcher determined appropriate problem-solving tasks and assessed students’ academic achievement and critical thinking skills. Following a mixed methods action research design, the researcher analyzed qualitative and quantitative data to determine the significance of the problem-solving framework. The data indicated significant student growth during …

Counseling Program Intervention For Improving African American Students’ Science, Technology, Engineering, And Mathematics Dual Enrollment Participation, Sonja L. Taylor

Theses and Dissertations

African Americans are underrepresented at all points in the STEM pipeline from K-12 coursework into professional careers. The reasons for this underrepresentation are varied and reflect a myriad of contributing factors based on early academic experiences, sociocultural influences, and the effects of standardized testing. The three-fold purpose of this study was to implement a counseling program to inform nine African American study participants about the dual enrollment opportunity at their high school, to gain perspective about the factors which shaped their STEM disposition, and to determine the effect of the program on their attitudes about dual enrollment participation. The study …

Differences In Spatial Visualization Ability And Vividness Of Spatial Imagery Between People With And Without Aphantasia, Anita Crowder

Theses and Dissertations

Mathematics education researchers have examined the relationship between visualization and mathematics for decades (e.g., Arcavi, 2003; Bishop, 1991; Duval, 1999; Fennema & Tartre, 1985; Presmeg, 1986). Studies have linked spatial visualization ability, such as measured in mental rotation tasks, directly to mathematics self-efficacy (Pajares & Kranzler, 1995; Weckbacher & Okamoto, 2014), which in turn influences mathematics achievement (Casey, Nuttall, & Pezaris, 1997). With the important role that spatial visualization plays in learning mathematics, the recent identification of congenital aphantasia (Zeman, Dewar, & Della Sala, 2015), which is the lack of mental imagery ability, has raised new questions for mathematics education …

The Effects Of Teaching Middle School Students Math Using The Gifted Supplementary Curriculum “Mawhiba” On Students’ Academic Achievement And Attitude Toward Math In Public Schools In Saudi Arabia, Ahmed M. Alreshidi

Theses and Dissertations

The purpose of this study was to investigate whether the use of a supplementary math curriculum, “Mawhiba,” that was designed for gifted students, would be appropriate for regular students in a mixed-abilities classroom. The researcher investigated the effects of implementing the Mawhiba enriched supplementary math curriculum on students’ achievements in mathematics and on students’ attitudes toward mathematics in Hail State, Saudi Arabia. The research design was an experimental randomized subject pretest, post-test, control group design. Two schools were chosen (a female middle school and a male middle school). The sample consisted of 121 students (60 males and 61 females). The …

Beyond Problem-Solving: Elementary Students’ Mathematical Dispositions When Faced With The Challenge Of Unsolved Problems, Jenna R. O'Dell

Theses and Dissertations

The goal of this study was to document the characteristics of students’ dispositions towards mathematics when they engaged in the exploration of parts of unsolved problems: Graceful Tree Conjecture and Collatz Conjecture. Ten students, Grades 4 and 5, from an after-school program in the Midwest participated in the study. I focused on the cognitive, affective, and conative aspects of their mathematical dispositions as they participated in 7 problem-solving sessions and two interviews.

With regard to cognitive aspects of the students’ dispositions, I focused on the students attempts to identify and justify patterns for labeling graphs. Overall, the unsolved problems were …

Exploring Bilingual Teachers' Beliefs About Academic Language Development In Mathematics Teaching: Implications For Bilingual Teachers' Professional Development, Viola Canales-Vela

Theses and Dissertations

The achievement of mathematics within Hispanic youth is of great concern across the nation. In order to improve student achievement in mathematics, the nature of a mathematics teacher’s complex belief system must be understood (McGee &Wang, 2014). The purpose of this exploratory qualitative study is to investigate the K-5 bilingual teachers’ beliefs about how to develop the academic language of mathematics in Spanish and English in the context of dual language programs at the elementary school level and bilingual teachers’ perceptions on the impact of professional development design for bilingual teachers to meet the needs of their students’ academic language …

The Effectiveness Of The Flipped Classroom For Students With Learning Disabilities In An Algebra I Resource Setting, Ashley Butterick

Theses and Dissertations

The purpose of this study was: (a) to examine the effectiveness of using the flipped classroom model to improve the academic scores of students with a specific learning disabilities (SLD), (b) to examine the effectiveness of using the flipped classroom to improve rates of homework completion by students with a SLD and (c) to evaluate student satisfaction and perception of the flipped classroom intervention. Five high school students, four males and one female, with a SLD participated in the study. A single subject ABAB design was used. During the baseline phases, students received Algebra I instruction through a traditional classroom …

The Effect Of Formal Pedagogical Training Of Mathematics Faculty On Community College Student Success And Retention, Douglas Neal Donohue

Theses and Dissertations

This study examined the correlation between the proportion of full time mathematics faculty with formal pedagogical training at eight Mississippi public community colleges named to the Aspen Foundation list of the top 150 community colleges in the United States and the proportion of developmental math students who successfully completed a college algebra course in their 1st year, the proportion of students who graduated within 4 years, and the proportion of 1st-time full-time students who returned for the 2nd year. After collecting data from 6 of the 8 colleges, a correlational analysis revealed no statistically significant relationships between the proportion of …

Making Sense Of School Reform: A Case Study Of Mathematics And Science Teachers' Sensemaking With One District's Differentiation And Detracking Initiatives, Katelyn Daplyn Skinner

Theses and Dissertations

The purpose of this case study was to examine how individual science and mathematics teachers within a particular high school made sense of a district differentiation effort. A focus on teachers' perceptions and interpretations of this effort was targeted through the theoretical framework of sensemaking. Two of the teachers were present for an initial detracking reform effort, which enabled the researcher to examine their sensemaking of both initiatives.

There were clear differences in the sense that teachers made of the differentiation initiative. Additionally, there were multiple factors that impacted teacher sensemaking; the district initiative was not one of these factors. …