Mathematics Commons^™

Conceptualizing And Interpreting Mean And Median With Future Teachers, Eryn M. Stehr, Ha Nguyen, Gregory Chamblee, Sharon Taylor

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Mathematical Education of Teachers II (METII), echoed by the American Statistical Association publication, Statistical Education of Teachers, recommended teacher preparation programs support future teachers in developing deep understandings of mean and median, such that middle grades teachers may use them to “summarize, describe, and compare distributions” (Conference Board of Mathematical Sciences, 2012, p. 44; Franklin et al., 2015). Georgia Standards of Excellence require statistical reasoning from students beginning as early as 6-7 years old, including interpretation of measures of center and statistical reasoning about best measures of center (Georgia Department of Education, 2015). This level of understanding and interpretation of …

An Alternative Approach To The Traditional Internship, Basil M. Conway, David Erikson, Christopher Parrish, Marilyn Strutchens, Jennifer Whitfield

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

This paper reports the benefits and challenges of incorporating a paired-placement model at four different post-secondary teacher preparation programs in secondary mathematics education. The paired-placement model places two secondary mathematics clinical teachers with one mentor (or cooperating) teacher during their internship experience. Benefits exhibited were increased collaboration, more knowledgeable cooperating teachers, increased sense of community, teaming, pedagogical risk-taking, increased reflective practice, established natural professional learning communities, Plan-Do-Study-Act Cycle (PDSA), and increased accountability. Challenges found through the PDSA cycle include personnel issues, number of days teaching, perceived classroom management preparation, preparing university supervisors, mentors, and teacher candidates, and support for collaboration …

K-2 Mathematicians & Writers: Professional Learning Communities For Developing Conceptual Understanding, Doris Santarone, Angel R. Abney, Sandra M. Webb

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

National Council of Teachers of Mathematics (NCTM) has long supported the use of children’s literature, writing, and manipulatives to improve conceptual understanding of mathematics (2000). In a professional learning community for K-2 teachers, professional development was designed and implemented on ways to incorporate literacy and manipulatives into a mathematics lesson. The teachers were charged with collaboratively planning lessons that included multiple components: the standard(s), a mathematics activity, manipulatives, a writing task, and children’s literature. As the data were analyzed, it became apparent that while most of the lessons were well connected, this did not happen for all of the lessons. …

Preparing Pre-Service Teachers To Present At A State Conference, Heidi Eisenreich

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

As mathematics teacher educators, we have a responsibility to prepare as many people as we can, to teach mathematics in ways that foster a deeper understanding of the content. We do this by teaching current and future teachers in college programs and providing professional development to in-service teachers. A less explored way is to prepare these “students” to present ideas they have learned to colleagues at their school, other schools in their district, and conferences. In this paper, I share my experience of helping students go through the process of preparing to present over the last two years at our …

Creative Writing In The Mathematics Classroom, William Lacefield, Laura Markert

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Creative writing in the mathematics classroom promotes mathematical applications in the real world, constructivist learning, embodied learning, transfer of mathematical ideas, and student engagement. When students are allowed to write about mathematical concepts creatively, they are able to take concepts that they have learned and put them into their world or even create a situation where the mathematical concept applies. Applying mathematical concepts to other environments helps learners transfer mathematical concepts. Learners are able to take the mathematics content and contextualize it outside of the classroom. Writing in mathematics also is a way for students to embody learning. Because writing …

Improving Student Achievement Through The Implementation Of A Classroom Performance System, Stacy Maria Artis

Theses and Dissertations

This applied dissertation was designed to implement and examine the impact of a classroom performance system (CPS) on student achievement for Grade 9 mathematics students. Seventy-five students in 4 Coordinate Algebra classes were observed during the regular school day for 9 weeks. The treatment group received CPS-based instruction, and the control group received traditional mathematics instruction without the use of a CPS. The teacher was the same for all classes.

Data from benchmark assessments as well as quarterly grade reports were compared for both groups. The findings of this study showed mixed results in relation to the impact of CPS-based …

New Types Of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/ Under-/ Off Set, Neutrosophic Refined Set, And Their Extension To Plithogenic Set/Logic/Probability, With Applications, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This international collective massive book, edited by Florentin Smarandache, has 716 pages, and represents the special issue on neutrosophic environment at SYMMETRY international journal (Scopus, Web of Science, IF: 2.143). The book contains 37 published papers, by 73 authors and coauthors, from 13 countries from around the world, in alphabetical order: China, Cuba, Ecuador, Egypt, India, Jordan, Korea, Malaysia, Pakistan, Romania, Saudi Arabia, United Kingdom, and United States of America.

Connections Between Pre-Service Teachers’ Mathematical Dispositions And Self-Efficacy For Teaching Mathematics, Jasmine M. Cruz, Aaron T. Wilson, Xiaohui Wang

School of Mathematical & Statistical Sciences Faculty Publications

Mathematical dispositions (MD) and self-efficacy for teaching mathematics (SEFTM) are important elements of teachers‟ beliefs that significantly influence their behaviors and educational practices in the classroom. This study looked at relationships between pre-service teachers‟ (PSTs) MD and their SEFTM in connection with other descriptors related to their progress through the teacher education program and prior mathematical experiences. Survey data were collected from 238 PSTs at a midsized university in the US. Results include the finding that PSTs‟ intended grade-level and subject approximately mirror their MD and SEFTM: those planning to be elementary school (generalist) teachers were slightly behind both middle …

Teaching With Technology: Using A Virtual Learning Community And Peer Mentoring To Create An Interdisciplinary Intervention, Rebecca Mazumdar, Nadia Benakli, Pamela Brown

Publications and Research

This paper describes the development and implementation of engaging and supportive experiences to promote student engagement, persistence and success at a commuter, open enrollment, public, minority serving institution. Project components included faculty development at the SENCER Summer Institute (SSI) 2016, attended by a team comprised of an academic administrator, full-time faculty from English and math, and part-time faculty in chemistry; creation of a virtual learning community of freshmen enrolled in chemistry, English, and math linked by the specific theme of the environmental impacts of deicing roads with salt and the overarching theme of the impacts of human activities on the …

Solutions For Fermi Questions, May 2019: Question 1: Graduation Speeches; Question 2: Fan Propulsion, Larry Weinstein

Physics Faculty Publications

[Introduction] How many person-hoursare spent listening to graduation speeches each year? How long is this in lifetimes?

Answer: Just about everyone graduates high school and goes to their graduation, usually with guests. Only about 30% of Americans (more than 10% and less than 100% graduate college, so we will ignore those graduates. Therefore we need to estimate the number of graduating high school seniors, the number of guests per senior, and the length of the graduation speeches.

The Near-Peer Mathematical Mentoring Cycle: Studying The Impact Of Outreach On High School Students’ Attitudes Toward Mathematics, Aaron T. Wilson, Sergey Grigorian

School of Mathematical & Statistical Sciences Faculty Publications

College students may be seen as near-peers to high school students and high school students are often able to see themselves in the college students who are but one step ahead. This nearness in maturity and educational level may place college students in a particularly powerful position when it comes to reaching out to high school students to promote higher education in math and science. In this study college students gave dynamic mathematics outreach presentations, MathShows, to minority and low-income high school students in a mid-sized public school district on the U.S. border with Mexico. The study investigated the impacts …

Find, Process, And Share: An Optimal Control In The Vidale-Wolfe Marketing Model, Michael C. Barg

CODEE Journal

The Vidale-Wolfe marketing model is a first-order, linear, non-homogeneous ordinary differential equation (ODE) where the forcing term is proportional to advertising expenditure. With an initial response in sales as the initial condition, the solution of the initial value problem is straightforward for a first undergraduate ODE course. The model serves as an excellent example of many relevant topics for those students whose interests lie in economics, finance, or marketing. Its inclusion in the curriculum is particularly rewarding at an institution without a physics program. The model is not new, but it was novel to us when a group of students …

Gizmos Computer Simulations In The Mathematics Classroom, Bethany L. Inman

Morehead State Theses and Dissertations

A capstone submitted in partial fulfillment of the requirements for the degree of Doctor of Education in the College of Education at Morehead State University by Bethany L. Inman on December 6, 2018

Euclidian Geometry: Proposed Lesson Plans To Teach Throughout A One Semester Course, Joseph Willert

Mathematics Undergraduate Theses

Overview We provide several engaging lesson plans that would aid in the teaching of geometry, specifically targeting Euclidian Geometry, towards students of high school age. The audience of this piece would be high school or college students who have not yet had an introduction to geometry, but have completed the standard mathematical courses leading up to this point (i.e. algebra, elementary math, etc.). This being the case the lessons and concepts realized in Chapter 1 target a basic understanding of what Euclidian Geometry is and the subsequent chapters aim specifically at underlying properties of a geometry. The main source of …

Teaching Differential Equations Without Computer Graphics Solutions Is A Crime, Beverly H. West

CODEE Journal

In the early 1980s computer graphics revolutionized the teaching of ordinary differential equations (ODEs). Yet the movement to teach and learn the qualitative methods that interactive graphics affords seems to have lost momentum. There still exist college courses, even at big universities, being taught without the immense power that computer graphics has brought to differential equations. The vast majority of ODEs that arise in mathematical models are nonlinear, and linearization only approximates solutions sufficiently near an equilibrium. Introductory courses need to include nonlinear DEs. Graphs of phase plane trajectories and time series solutions allow one to see and analyze the …

Experiences Using Inquiry-Oriented Instruction In Differential Equations, Keith Nabb

CODEE Journal

Student-centered instruction can be a challenging endeavor for teachers and students. This article reports on the use of the Inquiry-Oriented Differential Equations (IO-DE) curriculum (Rasmussen, 2002) in an undergraduate differential equations course. Examples of student work are shared with specific reference to research in mathematics education.

Dual Perspectives On Desargues' Theorem, Carl Lienert

Geometry

No abstract provided.

Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett

Abstract Algebra

No abstract provided.

The Origin Of The Prime Number Theorem, Dominic Klyve

Number Theory

No abstract provided.

The Effects Of Metacognitive Training On Algebra Students’ Calibration Accuracy, Achievement, And Mathematical Literacy, Deana J. Ford

Teaching & Learning Theses & Dissertations

This dissertation describes an empirical study that investigated how metacognitive training influenced lower achieving Algebra students’ calibration accuracy, achievement, and development of mathematics literacy. Multiple methods were used to collect and analyze the data. Close analysis of students’ work and classroom observations revealed that students that were exposed to the metacognitive training had significantly higher prediction accuracy and made gains in their understanding of the mathematics word problems than did students who did not receive the metacognitive training. Overall, however, both the intervention and comparison groups improved in their academic performance and became more mathematically literate and accurate in their …

How Design Features In Digital Math Games Support Learning And Mathematics Connections, Patricia S. Moyer-Packenham, Christina W. Lommatsch, Kristy Litster, Jill Ashby, Emma P. Bullock, Allison L. Roxburgh, Jessica F. Shumway, Emily Speed, Benjamin Covington, Christine Hartmann, Jody Clarke-Midura, Joel Skaria, Arla Westenskow, Beth L. Macdonald, Jurgen Symanzik, Kerry Jordan

Teacher Education and Leadership Faculty Publications

Current research shows that digital games can significantly enhance children’s learning. The purpose of this study was to examine how design features in 12 digital math games influenced children’s learning. The participants in this study were 193 children in Grades 2 through 6 (ages 8-12). During clinical interviews, children in the study completed pre-tests, interacted with digital math games, responded to questions about the digital math games, and completed post-tests. We recorded the interactions using two video perspectives that recorded children’s gameplay and responses to interviewers. We employed mixed methods to analyze the data and identify salient patterns in children’s …

The Effects Of Motivation, Technology And Satisfaction On Student Achievement In Face-To-Face And Online College Algebra Classes, Hanan Jamal Amro, Marie-Anne Mundy, Lori Kupczynski

TxDLA Journal of Digital Learning

Demand for online learning has increased in recent years due to the convenience of class delivery. However, some students appear to have difficulties with online education resulting in lack of completion. The study utilized a quantitative approach with archival data and survey design. The factors of demographics, motivation, technology, and satisfaction were compared for face-to-face and online students. MANCOVA tests were performed to analyze the data while controlling age and gender to uncover significant differences between the two groups. The sample and population for this study were predominantly Hispanic students.

Motivation and Technology were non-significant, but satisfaction was proven to …

Motherhood And Teaching: Radical Care, Ksenija Simic-Muller

Journal of Humanistic Mathematics

This essay is a personal reflection on how I leverage my positioning as a caregiver in my roles of a mathematician, teacher, and mother, to advance a vision for a more just and equitable society. I argue that care at home and in the classroom takes similar forms, and can be liberating instead of oppressive.

Nearness Without Distance, Nicholas A. Scoville

Topology

No abstract provided.

Determining The Determinant, Danny Otero

Linear Algebra

No abstract provided.

From Sets To Metric Spaces To Topological Spaces, Nicholas A. Scoville

Topology

No abstract provided.

Finding Meaning In A Multivariable World: A Conceptual Approach To An Algebra-Based Second Course In Statistics, Karen Mcgaughey, Beth Chance, Nathan L. Tintle, Soma Roy, Todd Swanson, Jill Vander Stoep

Faculty Work Comprehensive List

Although the teaching of the first course in statistics has improved dramatically in recent years, there has been less focus on a similarly conceptual-based second course aimed at non-majors. We present a curriculum for the second course, designed to expand statistical literacy across disciplines, which focuses on conceptual understanding of multivariable relationships through data visualization, study design, the role of confounding variables, reduction of unexplained variation, and simulation-based inference, rather than the mathematically-based discourse often used in the second course. Our curriculum uses a student-centered pedagogical approach, utilizing guided discovery activities based on real-world case studies, facilitated by student-focused technology …

The Bellringer Sequence: Investigating What And How Preservice Mathematics Teachers Learn Through Pedagogies Of Enactment, Mary A. Ochieng

Dissertations

This study examines preservice teacher learning through pedagogies of enactment—approaches to teacher education that allow preservice teachers to learn by doing what teachers do. Preservice teacher (PST) learning is examined through the implementation of the Bellringer Sequence (BRS), a pedagogy of enactment conceptualized in the study. The BRS is centered around bellringers—brief mathematical tasks implemented as students arrive for class. The BRS is a sequence of four activities centered on a bellringer: preparation (for teaching a bellringer) implementation (of the bellringer with peers), debriefing (discussing the implementation as colleagues), and written reflection (about the effectiveness of the bellringer).

Practice-based approaches …

Identifying Prevalent Mathematical Pathways To Engineering In South Carolina, Eliza Gallagher, Christy Brown, D. Andrew Brown, Kristin Kelly Frady, Patrick Bass, Michael A. Matthews, Thomas T. Peters, Robert J. Rabb, Ikhalfani Solan, Ronald W. Welch, Anand K. Gramopadhye

Faculty Publications

National data indicate that initial mathematics course placement in college is a strong predictor of persistence to degree in engineering, with students placed in calculus persisting at nearly twice the rate of those placed below calculus. Within the state of South Carolina, approximately 95% of engineering-intending students who initially place below calculus are from in-state. In order to make systemic change, we are first analyzing system-wide data to identify prevalent educational pathways within the state, and the mathematical milestones along those pathways taken by students in engineering and engineering-related fields. This paper reports preliminary analysis of that data to understand …

Meeting Real World Demands Of The Global Economy: An Employer's Perspective, Doreen Mcgunagle, Laura Zizka

Journal of Aviation/Aerospace Education & Research

Educational programs prepare students theoretically for the workplace, but many programs are still lacking in the real-world skills that the workplace requires. This is especially evident in Science, Technology, Engineering, and Math (STEM) education where today’s graduates hold a fundamental role in advancing science, medicine, sustainability, national security, and the economy, yet the programs to prepare them are falling short of employer expectations. At present, there is a lack of information on the necessary skills for workplace success that is specific to Airline, Aerospace, Defense (A&D) and related Industries’ STEM graduates. This paper attempts to fill this gap by offering …