Digital Commons Network^™

The Impact Of Physical Education On Students’ Performance Outcomes In Mathematics, Ryan Thomas Cox

Theses and Dissertations

Research studies have suggested that students who participate in daily physical activity and who are more physically fit may have improved academic achievement scores. However, pressures on school districts to improve students’ academic achievement in core course areas such as math, science, and English have put less emphasis on courses such as physical education. School districts around the country have eliminated and/or have lessened the amount of physical activity students receive during the school day. This study examined the impact of time of physical education and difference in 9th-grade students’ math achievement scores in their Algebra course and outcomes on …

Classifying Prime Character Degree Graphs, Sara Degroot

Student Presentations

In our work, we construct a family of graphs. We then classify whether or not each of these graphs occur as the prime character degree graph for some solvable group, with two notable exceptions. In this poster, we more closely investigate these two aforementioned graphs.

Designing An Experimental Apparatus For Rotational Mixing In Stokes Flow, William Bethard, Logan Hennes

Student Presentations

We report on the design, construction, and operation of a rotational mixing apparatus that magnetically rotates a thin metal rod interacting with tracers suspended in a high-viscosity fluid. The purpose of this apparatus is to achieve Stokes flow, defined as having a Reynolds number below 0.001, where viscous forces dominate over inertial forces in a fluid system. The apparatus, designed using 3D modeling software and constructed using additive manufacturing techniques, holds a rod at a fixed angle with a magnetic field and rotates the rod conically about a fixed point. Tracer trajectories within the fluid were tracked using a custom …

The Effects Of Stem And Non-Stem Mathematics Corequisite Courses On Student Success At Public Institutions In West Virginia, Vanessa S. Keadle

Theses, Dissertations and Capstones

This study explored the differences in student success outcomes between students enrolled in non-STEM and STEM corequisite mathematics courses at 18 postsecondary institutions across five academic years in West Virginia, using de-identified student data. The researcher analyzed this extant data to determine if student characteristics were predictors of success, as defined as passing the mathematics corequisite course, retention to the next semester, and earning a GPA of 2.0 or higher. The researcher also conducted analyses to understand if the differences in those outcomes between STEM and non-STEM courses were significant. This study identified statistically significant gaps in success for students …

Developing A Mathematics Common Assessment System: Using Data To Drive Instruction, Twianie Roberts

Teaching and Learning Faculty Research

There is an ongoing demand for school and district based educators to connect curriculum, instruction and assessment practices to monitor and increase student achievement. This paper describes the development of a Common Assessment system that connects curriculum, instruction and assessment. It can be implemented from a school based (teacher) or district based perspective. This model addresses the role of curriculum guides, instructional pacing, assessment system selection, test types, professional development and issues related to data disaggregation and dissemination. This model has implications for curriculum development, professional development, instruction and policy articulation.

On Loop Commutators, Quaternionic Automorphic Loops, And Related Topics, Mariah Kathleen Barnes

Electronic Theses and Dissertations

This dissertation deals with three topics inside loop and quasigroup theory. First, as a continuation of the project started by David Stanovský and Petr Vojtĕchovský, we study the commutator of congruences defined by Freese and McKenzie in order to create a more pleasing, equivalent definition of the commutator inside of loops. Moreover, we show that the commutator can be characterized by the generators of the inner mapping group of the loop. We then translate these results to characterize the commutator of two normal subloops of any loop.

Second, we study automorphic loops with the desire to find more examples of …

Local-Global Results On Discrete Structures, Alexander Lewis Stevens

Electronic Theses and Dissertations

Local-global arguments, or those which glean global insights from local information, are central ideas in many areas of mathematics and computer science. For instance, in computer science a greedy algorithm makes locally optimal choices that are guaranteed to be consistent with a globally optimal solution. On the mathematical end, global information on Riemannian manifolds is often implied by (local) curvature lower bounds. Discrete notions of graph curvature have recently emerged, allowing ideas pioneered in Riemannian geometry to be extended to the discrete setting. Bakry- Émery curvature has been one such successful notion of curvature. In this thesis we use combinatorial …

Banach Spaces On Topological Ramsey Structures, Cheng-Chih Ko

Electronic Theses and Dissertations

A Banach space T₁(d, θ) with a Tsirelson-type norm is constructed on the top of the topological Ramsey space T₁ defined by Dobrinen and Todorcevic [6]. Finite approximations of the isomorphic subtrees are utilised in constructing the norm. The subspace on each “branch” of the tree is shown to resemble the structure of an ℓ_∞ⁿ⁺¹ -space where the dimension corresponds to the number of terminal nodes on that branch. The Banach space T₁(d, θ) is isomorphic to (∑_n∊ℕ⊕ℓ_∞ⁿ⁺¹)_p , where d ∈ ℕ with d ≥ 2, …

Topics In Moufang Loops, Riley Britten

Electronic Theses and Dissertations

We will begin by discussing power graphs of Moufang loops. We are able to show that as in groups the directed power graph of a Moufang loop is uniquely determined by the undirected power graph. In the process of proving this result we define the generalized octonion loops, a variety of Moufang loops which behave analogously to the generalized quaternion groups. We proceed to investigate para-F quasigroups, a variety of quasigroups which we show are antilinear over Moufang loops. We briefly depart from the context of Moufang loops to discuss solvability in general loops. We then prove some results on …

Cache Code Math Mathematics Lesson Plans: Exponents And Repeats, Jody Clarke-Midura, Jessica Shumway, Kimberly Beck, Umar Shehzad, Mimi Recker

Instructional resources

This document entails four 5^th grade mathematics lesson plans. The lessons are intended to be implemented in conjunction with the computer lab activities found in “Integrated Lesson (CS and Math)”. The mathematics focus of these lessons is exponents as repeated multiplication, which is paired with the computer coding concepts of repeat loop blocks.

Seventh Grade Mathematics Results In A Standards-Based Learning Environment: Examining Teacher Collaboration And Leadership, Demetria C. Moon

Dissertations and Theses

The pressure on schools to improve student performance in middle school mathematics combined with the movement towards standards-based instruction leaves teachers searching for the most effective instructional practice and administration examining their role in improvement efforts. This study examines the effect on student achievement in middle school mathematics as a function of the quality of teacher collaboration interacting with administration presence during collaboration. This study used a quantitative research design in which seventh-grade mathematics teachers from two different middle schools in the same district with similar demographics taught the same standards-based unit of study and administered a common summative assessment …

Understanding Students' Perceptions Of Doing Mathematics: A Cultural Comparison, Gabriel T. Matney, Corrinne Fischer, Jack L. Jackson Ii

School of Inclusive Teacher Education Faculty Publications

Garnering different kinds of data from students about their perceptions of mathematics helps teachers, teacher leaders, districts and researchers better understand students' perceptions. In this study, we investigated and compared students’ perceptions of doing mathematics from samples of students from the United States, China, and Fiji. We administered the Draw Yourself Doing Mathematics instrument to students at three grade levels in China, Fiji, and the United States of America. Statistically significant differences among perceptions in the three countries and the three grade levels were observed. Student drawings were further analyzed for other qualitative components, including factors affecting the learning environment, …

Efficient Assessment Of Students’ Proportional Reasoning, Michele Carney, Katie Paulding, Joe Champion

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

Teachers need ways to efficiently assess students’ cognitive understanding. One promising approach involves easily adapted and administered item types that yield quantitative scores that can be interpreted in terms of whether or not students likely possess key understandings. This study illustrates an approach to analyzing response process validity evidence from item types for assessing two important aspects of proportional reasoning. Data include results from an interview protocol used with 33 middle school students to compare their responses to prototypical item types to their conceptions of composed unit and multiplicative comparison. The findings provide validity evidence in support of the score …

A Systematic Review Of Treatment Acceptability In Mathematics Instruction For Students With Learning Disabilities, Gena Nelson, Andrea Johnson, Mali Sawyer

Early and Special Education Faculty Publications and Presentations

Treatment acceptability is an aspect of social validity that refers to participants’ beliefs and perceptions about the intervention, such as the helpfulness of the strategies or the interventions’ efficacy to improve performance. The purpose of this study was to conduct a systematic review of treatment acceptability measures administered during mathematics interventions for students with learning disabilities (LD). We sought to identify the characteristics of the measures and the treatment acceptability outcomes. To be included in this review, studies had to (a) focus on testing the effectiveness of a mathematics intervention, (b) include preschool through 12th grade students who were diagnosed …

Assessing Teachers’ Pedagogical Practices And Students’ Learning Outcomes In Science And Mathematics Across Primary And Secondary School Level: A Nationwide Study (2018-21), Sadia Muzaffar Bhutta, Nusrat Fatima Rizvi

Institute for Educational Development, Karachi

No abstract provided.

Elementary Teachers’ Perspectives Of Direct Instruction With More Rigorous Mathematics Standards, Sharon Denise Taylor

Walden Dissertations and Doctoral Studies

AbstractMajestic County Schools (pseudonym), a large southeastern school district, has implemented changes in instruction to align with more rigorous state and national mathematics standards. The rigor of the new standards has led to changes in instruction to help students master the standards with evidence from the state-wide standardized test. Although the district has made curricular changes, over one-third of the students in Grades 3-5 at Flint Elementary are not mastering grade-level standards. This basic qualitative study focuses on one elementary school within the district. The purpose was to understand how teachers implement direct instruction (DI) strategies in the classroom to …

A Tale Of Four Departments: Interdisciplinary Faculty Learning Communities Informing Mathematics Education, Bryan D. Poole, Caroline Maher-Boulis, John Hearn, Jason Robinson, Patricia Mcclung, Amanda Jones

Journal of Mathematics and Science: Collaborative Explorations

As a result of the Curriculum Foundations Project and the SUMMIT-P consortium, faculty from four different departments at Lee University created a Faculty Learning Community (FLC) with the goal of improving students’ attitudes toward undergraduate mathematics courses, including students’ perception of the utility of mathematics in their lives and the feelings of anxiety that they experience in these courses. The interdisciplinary collaborations resulted in introducing novel activities and manipulatives in various mathematics courses (Introduction to Statistics, Concepts of Mathematics I and II, and Algebra for Calculus). This paper first describes the efforts of creating the inter-departmental FLC. Second, it discusses …

Discussion Of Educational Philosphy For Elementary Math Educators, Daniel Kurzweil

Open Educational Resources

No abstract provided.

Decision-Making Accuracy At The Classwide Level, Alexandra Payne

Legacy Theses & Dissertations (2009 - 2024)

This study was designed to evaluate decision-making accuracy at the classwide level within the context of classwide math intervention, where decisions are made regarding whether or not a class as a whole has met the predefined mastery criterion for a specific math skill. The current study examined decision accuracy when using existing classwide decision-making practices, in which one classwide data point is compared to the mastery criterion. In addition, the current study assessed the role of three variables: class size, decision rule used, and rate of classwide growth. As part of this study, an existing data set containing progress monitoring …

Mathematics Instructional Level As A Predictor Of Explicit Timing Fluency Intervention Success, Chasen Rain Dillon

Legacy Theses & Dissertations (2009 - 2024)

Various evidence-based mathematic interventions have been deemed effective in remediating skill deficits. However, despite recommendation of evidence-based intervention application within Response to Intervention (RTI) frameworks, little research has been done to differentiate intervention effectiveness, specifically Explicit Timing (ET), for students who present with varying skill proficiency prior to intervention implementation. The current study utilized secondary analysis of existing ET data that was supplemented with performance feedback as part of original intervention design (i.e. ET + Feedback). The purpose was to determine whether learning rates varied among students with differential baseline proficiency with the goal of determining proficiency’s relevance to treatment …

Lay It All On The Line: The Effect Of Teacher-Student Conferencing In Middle Grades Mathematics Classrooms, Natalie Ostrander

Doctor of Education Dissertations

Increasing math achievement continues to be a commonly talked about subject in the educational setting. This case study observes one classroom teacher who implemented teacher-student conferencing in middle grades mathematics classes. The purpose of this study was to reveal the perceived impact of teacher-student conferencing on student engagement and with student achievement. Through a qualitative approach, perceptual data were collected through teacher journaling, conference logs, observations, and an interview. Research occurred in one school district in southeastern North Carolina with middle grades students in sixth and eighth grades. After the qualitative data were collected by me, data were analyzed using …

Wittgenstein On Miscalculation And The Foundations Of Mathematics, Samuel J. Wheeler

Philosophy Faculty Publications

In Remarks on the Foundations of Mathematics, Wittgenstein notes that he has 'not yet made the role of miscalculating clear' and that 'the role of the proposition: "I must have miscalculated"...is really the key to an understanding of the "foundations" of mathematics.' In this paper, I hope to get clear on how this is the case. First, I will explain Wittgenstein's understanding of a 'foundation' for mathematics. Then, by showing how the proposition 'I must have miscalculated' differentiates mathematics from the physical sciences, we will see how this proposition is the key to understanding the foundations of mathematics.

Charter School, Kindergarten–6, Homeschool Parents’ Perceptions, Experiences, And Strategies For Mathematics Instruction, Wendy How Fayard

Walden Dissertations and Doctoral Studies

The research problem for this study was the lack of understanding regarding parents’ perceptions of and experiences with mathematics and instructional strategies for kindergarten through sixth-grade (K–6) students in a charter school, homeschool setting. Dewey’s theory of experience and education was the conceptual framework for the study. In this basic qualitative study, charter school homeschool parents’ perceptions about providing mathematic instruction for K–6 students, experiences with instructing K–6 students in mathematics, and choices and adjustments concerning mathematics teaching strategies were examined. Twelve participants took part in semistructured interviews on the Zoom platform. Their interview responses were analyzed qualitatively using coding …

Determining The Difficulty And Discrimination Parameters Of A Mathematics Performance-Based Assessment, Abraham Gyamfi, Douglas G. Wren

Educational Leadership & Workforce Development Faculty Publications

Performance-based assessment (PBA) is different from traditional testing methods in that PBA presents real-life problems for students to solve by integrating critical thinking with their content knowledge and skills. Implementing PBA regularly in mathematics classes is associated with improved student achievement and motivation to learn; however, there are concerns about the general lack of psychometric data to support the use of performance assessments. To address such concerns, this study applied item response theory to estimate the difficulty and discrimination indices of items that comprised a newly developed mathematics PBA. Data were collected by administering the PBA to 750 senior high …

Multicolor Ramsey And List Ramsey Numbers For Double Stars, Jake Ruotolo

Honors Undergraduate Theses

The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For a graph H, the k-color Ramsey number r(H; k) of H is the smallest integer n such that every k-edge-coloring of K_n contains a monochromatic copy of H. Despite active research for decades, very little is known about Ramsey numbers of graphs. This is especially true for r(H; k) when k is at least 3, also known as the multicolor Ramsey number of …

Local Finiteness And Automorphism Groups Of Low Complexity Subshifts, Ronnie Pavlov, Scott Schmieding

Mathematics: Faculty Scholarship

We prove that for any transitive subshift X with word complexity function c_n(X), if lim inf(log(c_n(X)/n)/(log log log n)) = 0, then the quotient group Aut(X, σ)/〈 σ〉 of the automorphism group of X by the subgroup generated by the shift σ is locally finite. We prove that significantly weaker upper bounds on c_n(X) imply the same conclusion if the gap conjecture from geometric group theory is true. Our proofs rely on a general upper bound for the number of automorphisms of X of range n in terms of word complexity, which may be …

Measure-Theoretically Mixing Subshifts With Low Complexity, Darren Creutz, Ronnie Pavlov, Shaun Rodock

Mathematics: Faculty Scholarship

We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any f : N → N with f (n)/n increasing and ∑ 1/f (n) < ∞, that there exists an extremely elevated staircase with word complexity p(n) = o(f (n)). This improves the previously lowest known complexity for mixing subshifts, resolving a conjecture of Ferenczi.

Math Department 2021-2022 Newsletter, Mathematics Department

Mathematics Newsletter

Welcome to our annual Mathematics Department Newsletter. As we are slowly coming out of the pandemic, we were able to resume many of our normal events.

Using An Interdisciplinary Case Study To Incorporate Quantitative Reasoning In Social Work, Nursing, And Mathematics, Elizabeth Post, Mischelle Stone, Lauren Cavner Williams, Mary Beaudry

Journal of Mathematics and Science: Collaborative Explorations

Through the national consortium, SUMMIT-P, Ferris State University faculty collaborated to develop and scaffold mathematics and quantitative reasoning across disciplines to reduce math anxiety. Participants in this collaborative group included faculty from social work, nursing, and mathematics who developed a case study on a Hurricane Katrina scenario that necessitated calculating the need for emergency shelter, water, food, and medicine, and as a response to the potential for a Malaria outbreak. This particular case study allowed faculty to use the lens of social justice to teach mathematical concepts and provided an avenue for nursing and social work students to engage in …

Connecting Weirdness And Wonder To Mathematics, Elizabeth Basile, Deborah H. Mcmurtrie, Bridget K. Coleman

South Carolina Association for Middle Level Education Journal

Middle school students are weird and wonderful. Why not bring some of that weirdness and wonder into the mathematics classroom? Effective teachers of mathematics can create a culture of engagement, curiosity, and collaboration in mathematics instruction by presenting “weird” problems (as opposed to word problems) and giving students opportunities to explore their wonderings. Inspired by “the bizarreness effect,” the problems presented here are infused with humor and designed to intrigue young adolescents.