Digital Commons Network^™

Good Teachers Borrow, Great Teachers Steal: A Case Study In Borrowing For A Teaching Project, Mike May, Rebecca Segal, Victor Piercey, Tao Chen

Journal of Mathematics and Science: Collaborative Explorations

Very few great ideas in teaching are without ancestors or descendants. This paper presents a case study in how one particular pedagogical project, the work at Saint Louis University as part of the National Science Foundation supported SUMMIT-P consortium, borrowed from other sources. The particular project was an interdisciplinary collaboration to make mathematics education more effective for business students. The various borrowings are treated in roughly chronological order from initial inspiration through planned adoption and adaptation of the work of others to the addition of features that only became available mid-project. The kinds of sources include a particular business calculus …

Characteristics Of Critical Friendship That Transform Professional Identity, Signe E. Kastberg, Melva R. Grant

Teaching & Learning Faculty Publications

We met at CASTLE 2018, two trained mathematics teacher educators (MTEs), interested in mathematics, and teaching elementary mathematics methods to preservice teachers (PTs). Melva’s self-study research, focused on improving her online methods course, was approaching its second year and her second critical friend had lost interest in continuing. Melva invited Signe to be her critical friend (Schuck & Russell, 2005) and Signe agreed. Explicit expectations of our critical friendship included weekly meetings. Our critical friendship seemed to follow an expected trajectory for, “supporting/coaching the transformation of another’s teaching” (Stolle, et al., 2019, p. 20). However, there were implicit ways our …

The Knapsack Subproblem Of The Algorithm To Compute The Erdos-Selfridge Function, Brianna Sorenson

Undergraduate Honors Thesis Collection

This thesis summarizes the methodology of a new algorithm to compute the Erdos-Selfridge function which uses a wheel sieve, shows that a knapsack algorithm can be used to minimize the work needed to compute these values by selecting a subset of rings for use in the wheel, and compares the results of several different knapsack algorithms in this particular scenario.

Understanding The Effects Of Mathematics Professional Development On Teachers’ Perceptions Of Mathematics, Mike Flynn

Walden Dissertations and Doctoral Studies

Negative mathematics perceptions may affect how teachers teach the subject, how much time they spend on the subject, and how well they teach it. The problem that grounded this study was that although anecdotal evidence showed that teachers’ experience with professional development (PD) courses in mathematics teaching improved their perceptions of mathematics, there was a lack of data regarding how PD affects changes in teachers’ perceptions. The study purpose was to gain a deeper understanding of what elements of a PD course have the greatest effect on improving teachers’ perceptions of mathematics. Piaget’s constructivist and Vygotsky’s socio-constructivism theories made up …

Curricular Change In Institutional Context: A Profile Of The Summit-P Institutions, Mary D.R. Beisiegel, Suzanne I. Dorée

Journal of Mathematics and Science: Collaborative Explorations

There is a national call to improve the mathematics curricula in the first two undergraduate years to improve student success and engagement. But curricular change happens in an institutional context: Who are the students, and what do they need to succeed? What is the climate for change? Does the department regularly revise its courses and curriculum? Is it common for different departments to collaborate on curricular change? What supports or obstacles does the department, college, or university have for changing the curriculum? Who are the institutional stakeholders, and what practices build their buy-in? In the SUMMIT-P project, nine different institutions …

Demographic Differences In Post-Secondary Outcomes Following Participation In The Diagnostic Assessment And Achievement Of College Skills Intervention, Jana Vanderslice-Barr

Legacy Theses & Dissertations (2009 - 2024)

The majority of high school seniors are unprepared for post-secondary coursework in mathematics and reading (National Assessment of Educational Progress, 2019). Research shows traditional methods for bolstering college readiness skills to be ineffective, unnecessary for the majority of students, and associated with negative outcomes (Jaggars & Stacey, 2014). Another approach to enhancing college readiness is to offer newly enrolled college students the opportunity to assess their level of readiness, and take steps to become better prepared on their own. The Diagnostic Assessment and Achievement of College Skills (DAACS) system was developed with this purpose in mind. The DAACS is intended …

Creating Project-Based Math Curricula: A Narrative Inquiry, Marcie Hull

West Chester University Doctoral Projects

This study is a narrative inquiry about the participant’s experiences, in three individual case studies, involving teachers of high school mathematics engaged in the creation of a project-based learning curriculum, in a one-to-one laptop school. The researcher analyzed data from field notes, digital artifacts, and teacher interviews to document how math teachers are creating curriculum in an inquiry-driven, project-based, technology-infused instructional model. Findings from restorying and the analysis of three-dimensional space —regarding teacher lore —reveal themes about math teacher curriculum conflicts in skill-building, application of iterative design thinking, and structures inherent to project-based learning. Rich, thick description of the cases, …

Teacher Support Of Co- And Socially-Shared Regulation Of Learning In Middle School Mathematics Classrooms, Melissa Quackenbush, Linda Bol

Educational Leadership & Workforce Development Faculty Publications

Social influences on classroom learning have a long research tradition and are critical components of self-regulated learning theories. More recently, researchers have explored the social influences of self-regulated learning in cooperative learning contexts. In these settings, co-regulation of learning and socially-shared regulation of learning strategies have been aligned with self-regulated learning theory. However, without specific training or structure, teachers are not likely to explicitly integrate SRL strategies into their teaching. We use case studies to better understand how Zimmerman's theory of self-regulated learning (2008) and Hadwin's conceptual framework of socially-shared regulation of learning (2018) emerge from teachers' support of student-centered …

Mathematics Teachers’ Preparedness To Teach In A Virtual Classroom: Focus On Covid-19 Impact On Education, Jemimah Wangui Ng'ang'a

Master of Education

Virtual classroom is a “web-based online environment that delivers course materials to learners and provides collaboration and interaction” (Subramaniam & Kandasamy, 2011, p.1) opportunity as well as support the learners’ independent study. Virtual classroom facilitates virtual learning in a virtual learning environment (VLE). In the recent times virtual learning has become inevitable especially considering the situation where learners are supposed to be home for a longer period than usual. This has been evident with the outbreak of corona virus COVID-19, by the beginning of the year 2020 the disease had spread to other parts of the world thus paralyzing a …

New Challenges In Neutrosophic Theory And Applications, Florentin Smarandache, Stefan Vladutescu, Miihaela Colhon, Wadei Al-Omeri, Saeid Jafari, Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of …

Math 3100 - Mathematical Thinking: Communication And Proof - Week 1 Outline, Laura J. Wallace, Cory Johnson, Shawn Mcmurran, Min-Lin Lo

Q2S Enhancing Pedagogy

As a group, we hope through this FLC project to develop a course that promotes departmental SLOs, as well as University learning outcomes for a writing-intensive course. We focused on our new foundational course (MATH 3100 Mathematical Thinking: Communication and Proof). This course, designated as a writing-intensive course, introduces students to disciplinary ways of thinking and communicating in mathematics with emphasis on the construction of valid mathematical arguments, critiques of arguments, and structure of professional mathematical writing including typesetting. We would like to develop a library of useful materials that faculty members can adapt in their classrooms in order to …

Math 3100: Communication And Proof - Assessment, Shawn Mcmurran, Min-Lin Lo, Corrine Johnson, Laura Wallace

Q2S Enhancing Pedagogy

As a group, we hope through this FLC project to develop a course that promotes departmental SLOs, as well as University learning outcomes for a writing-intensive course. We focused on our new foundational course (MATH 3100 Mathematical Thinking: Communication and Proof). This course, designated as a writing-intensive course, introduces students to disciplinary ways of thinking and communicating in mathematics with emphasis on the construction of valid mathematical arguments, critiques of arguments, and structure of professional mathematical writing including typesetting. We would like to develop a library of useful materials that faculty members can adapt in their classrooms in order to …

Geometry Of Linear Subspace Arrangements With Connections To Matroid Theory, William Trok

Theses and Dissertations--Mathematics

This dissertation is devoted to the study of the geometric properties of subspace configurations, with an emphasis on configurations of points. One distinguishing feature is the widespread use of techniques from Matroid Theory and Combinatorial Optimization. In part we generalize a theorem of Edmond's about partitions of matroids in independent subsets. We then apply this to establish a conjectured bound on the Castelnuovo-Mumford regularity of a set of fat points.

We then study how the dimension of an ideal of point changes when intersected with a generic fat subspace. In particular we introduce the concept of a ``very unexpected hypersurface'' …

Saudi Mathematics Teachers’ Beliefs And Attitude Towards Teaching Mathematics, Theyab Alhallafi Ghaythah Hamdan

Student Works (2020-2029)

Mathematics is one of the major educational subjects in schools because of its overwhelming relevance and application to human life and progress. Mathematics is central to human development and mastery of the planet earth and beyond particularly in this age of computer and information technology. Teaching Mathematics is an endeavor that dated back three (3) millennia. For centuries, teaching and Mathematics teachers have been subjected to various forms of scholarly investigations. This study examines teachers’ beliefs and attitudes and their impacts on the way they teach the subject of mathematics in their respective schools across the Kingdom of Saudi Arabia. …

Curving Towards Bézout: An Examination Of Plane Curves And Their Intersection, Camron Alexander Robey Cohen

Honors Papers

One area of interest in studying plane curves is intersection. Namely, given two plane curves, we are interested in understanding how they intersect. In this paper, we will build the machinery necessary to describe this intersection. Our discussion will include developing algebraic tools, describing how two curves intersect at a given point, and accounting for points at infinity by way of projective space. With all these tools, we will prove Bézout’s theorem, a robust description of the intersection between two curves relating the degrees of the defining polynomials to the number of points in the intersection.

Scottish National Assessments: National Report For Academic Year 2018 To 2019, Australian Council For Educational Research (Acer)

Assessment and Reporting

No abstract provided.

Test Anxiety And Mathematics Teaching Strategies In Youth Mathematics, Daniel Linder

Williams Honors College, Honors Research Projects

This literature review analyzes the power of a math aversion, as well as the test anxiety that often coexists. Through the psychology of motivation, researchers have been able to establish correlation between motivation and test anxiety. In addition, research highlights the way in which instruction impacts students perception of mathematics. The review analyzes instructional techniques and how changing of instructional techniques can improve perception of mathematics.

Use Of Calculators In High School Mathematics, Alex Mcdaniel

Williams Honors College, Honors Research Projects

For many collegiate level mathematics courses at universities across the country, students are not allowed to use calculators. This is often a huge adjustment for students who have spent their entire high school career using calculators. Whether it is graphing or simple arithmetic, students relied on calculators in high school, but for college, the tool of a calculator may not be available for them. This leads to a multitude of questions: Should calculators be used in high school? Do calculators help students learn or are they simply a tool to get answers? Are calculators beneficial in some courses, but not …

Effective Response To Intervention In Middle School, Angela Mechelle Ellison

Electronic Theses and Dissertations

This applied mixed methods program evaluation sought to increase student proficiency in mathematics at a rural middle school in central Mississippi. The program focused on improving student achievement through effective professional development. Quantitative and qualitative data was used to gage the program’s effectiveness. Research supporting an effective Response to Intervention Model, professional learning communities, and teacher development was cited and used to construct the program’s implementation framework.

Predicting Stag And Hare Hunting Behaviors Using Hidden Markov Model, Rex Bringula, Ma. Mercedes T. Rodrigo

Department of Information Systems & Computer Science Faculty Publications

In this paper, we used Hidden Markov Model (HMM) to describe the gaming behaviors of students and whether they will exhibit “stag” or “hare” hunting behavior in a mobile game for mathematics learning. We found that there is a 99% probability that the students will stay either as stag or hare hunters. Our results also suggest that they would choose arithmetic problems involving addition. These game behaviors are not beneficial to learning because they are only exhibiting mathematical skills they already know. The results of the study show that stag and hare hunters have unique traits that separate the one …

The Ubiquity Of Phi In Human Culture & The Natural World, Jennifer Bressler

Masters Essays

No abstract provided.

Intersections Of Deleted Digits Cantor Sets With Gaussian Integer Bases, Vincent T. Shaw

Browse all Theses and Dissertations

In this paper, the intersections of deleted digits Cantor sets and their fractal dimensions were analyzed. Previously, it had been shown that for any dimension between 0 and the dimension of the given deleted digits Cantor set of the real number line, a translate of the set could be constructed such that the intersection of the set with the translate would have this dimension. Here, we consider deleted digits Cantor sets of the complex plane with Gaussian integer bases and show that the result still holds.

Full Issue

Journal of Mathematics and Science: Collaborative Explorations

No abstract provided.

Perspective On Coarse-Graining, Cognitive Load, And Materials Simulation, Eric Jankowski, Nealee Ellyson, Jenny W. Fothergill, Michael M. Henry, Mitchell H. Leibowitz, Evan D. Miller, Mone't Alberts, Jamie D. Guevara, Chris D. Jones, Mia Klopfenstein, Kendra K. Noneman, Rachel Singleton, Matthew L. Jones

Materials Science and Engineering Faculty Publications and Presentations

The predictive capabilities of computational materials science today derive from overlapping advances in simulation tools, modeling techniques, and best practices. We outline this ecosystem of molecular simulations by explaining how important contributions in each of these areas have fed into each other. The combined output of these tools, techniques, and practices is the ability for researchers to advance understanding by efficiently combining simple models with powerful software. As specific examples, we show how the prediction of organic photovoltaic morphologies have improved by orders of magnitude over the last decade, and how the processing of reacting epoxy thermosets can now be …

Course Portfolio For Math 309: Introduction To Mathematical Proofs - A Peer Review Of Teaching Project Benchmark Portfolio, Josh Brummer

UNL Faculty Course Portfolios

In this course portfolio, I examine dimensions of an active learning curriculum developed for a sophomore-level undergraduate course serving as an introduction to mathematical proofs. Prominent course goals include developing effective practices for communicating mathematics using formal language, learning to read, comprehend, and evaluate the validity of mathematical proofs, and practicing to write rigorous and concise mathematical proofs. I explore a new piece of collaborative annotation software called Perusall to help students read and understand mathematics together, and I analyze mastery level grading scales across exams throughout the semester. The portfolio also contains information about the structure and syllabus for …

The Relationship Between Professional Development, Instruction, And Student Achievement In Elementary Mathematics, Linsey Sims

Walden Dissertations and Doctoral Studies

Many school districts acknowledge professional development (PD) as an approach that can change teaching practices and improve student achievement. Because elementary teachers often struggle to provide instruction for mathematical proficiency, the purpose of this quantitative study was to examine the strength of the relationships among teacher participation in math PD courses, Texas Teacher Evaluation and Support System (T-TESS) implementation scores, and student achievement. The theoretical framework for the study is based on Guskey’s model of teacher change. The research questions pertained to the strength of the relationship between the following pairs of variables: (a) teacher participation in math PD and …

Middle-School Mathematics Teachers' Use Of Formative Assessment Data, Shawana T. Green

Walden Dissertations and Doctoral Studies

A school district located in the southeastern United States uses benchmark tests as formative assessment to provide teachers with data to differentiate their instruction to meet the individual needs of students in their classrooms. Despite this effort, student achievement in mathematics in this school district has not improved. The purpose of this study was to gain an understanding of how middle-grade mathematics teachers used the benchmark results as formative data to guide instruction and meet student needs. The conceptual framework that grounded this study was the model of formative assessment developed by Black and Wiliam. For this basic qualitative study, …

Middle School Principal Perceptions Of Instructional Coaching Effectiveness On Mathematics Teacher Performance, Jaimie Carin Foster

Walden Dissertations and Doctoral Studies

In middle schools in central Pennsylvania, instructional coaching has increased as a job-embedded professional development to support teachers in increasing their capacity and performance. The local problem was middle school principals were unsure of the effectiveness of their instructional coach on mathematics teacher capacity and performance. The purpose of this study was to explore middle school principal perceptions of the effect of instructional coaching on mathematics teacher performance. This study was guided by the social constructivist framework, which considers learning a unique sense-making experience filled with opportunities for self-reflection and growth. The research question focused on how middle school principals …

Mymathlab And Nontraditional Students' Attitudes Toward Technology In Mathematics, Lisa Sherry Olsen

Walden Dissertations and Doctoral Studies

Nontraditional students, who often do not have a background in computer usage, are a growing population in higher education. These students are often ill prepared for success in mathematics courses due to attitudes toward mathematics and the use of technology in the learning process. Researchers have looked into the needs of nontraditional students in academic settings but have not focused on nontraditional students' use of adaptive learning components, such as Pearson's MyMathLab (MML), in blended classrooms. The purpose of this sequential explanatory mixed-methods study was to explore the difference in nontraditional students' attitudes toward math and the use of technology …

Middle School Teachers’ Use Of Technology To Transform Mathematics Instruction, Camille Georgia James

Walden Dissertations and Doctoral Studies

AbstractIncorporating technology into instructional practices is needed to cultivate learners who are digitally competent to function in a society in which technology keeps evolving. The problem that exists at the study site is that although technology is available, it is primarily being used to enhance learning rather than transform learning. Transforming the teaching- learning process, requires the use of technology to modify and redefine learning. Therefore, the purpose of the study was to explore the extent to which middle school mathematics teachers in a PreK–8 independent day school in Denver, Colorado use digital technology as a transformative learning tool in …