Education Commons^™

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 …

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.

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 …

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

Abstract Algebra

No abstract provided.

Dual Perspectives On Desargues' Theorem, Carl Lienert

Geometry

No abstract provided.

The Origin Of The Prime Number Theorem, Dominic Klyve

Number Theory

No abstract provided.

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 …

Deblurring Images, Jamie Mcmullen

WWU Honors College Senior Projects

Let the matrix B be a blurred version of a sharp image represented by the matrix X. Given B, we would like to recover X.

To accomplish this, we construct linear models of the blurring process that produced B from X. The idea is that we could then reverse the blurring to reproduce the original image.

For example, if the blurred image satisfies

B = CXR^T

for some invertible matrices C and R, then we could recover X as

X = C-¹B(R^T)^-1.

However, the blurring model …

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 …

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.

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

Topology

No abstract provided.

Nearness Without Distance, Nicholas A. Scoville

Topology

No abstract provided.

Determining The Determinant, Danny Otero

Linear Algebra

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 …

Using Three Fields Of Education Research To Frame The Development Of Digital Games, Michelle Zandieh, David Plaxco, Caro Williams-Peirce, Ashish Amresh

Ashish Amresh

No abstract provided.

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 …

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 …

Developmental Mathematics: A Quantitative Investigation Of Instructor Classification As Related To Student Success, Brittany A. Fish

Electronic Theses and Dissertations

The purpose of this quantitative study was to examine what type of predictive power exists between an instructor’s employment classification, student gender, student race, and first-generation status on a student’s academic success in developmental mathematics, as measured by final semester grades at a regionally comprehensive state university in Texas between fall 2013 and spring 2017. Data were collected from the institution under study and the sample population included 1932 unique student observations. The data collected in this study were analyzed through a binary logistic regression model to determine whether an instructor’s employment classification, student gender, student race, and first-generation status …

Secondary Mathematics Teachers’ Planned Approaches For Teaching Standard Deviation, Maryann E. Huey, Joe Champion, Stephanie Casey, Nicholas H. Wasserman

Mathematics Faculty Publications and Presentations

Research-based guidelines for learning variation exist (e.g., Franklin et al., 2007; Garfield, delMas, & Chance, 2007), but little is known about how teachers plan to teach standard deviation, or how these plans align with recent recommendations. In this article, we survey lesson plans designed by inservice and preservice secondary mathematical teachers. We report on the accuracy, technology usage, and visual representations in the lesson plans. We consider how many elements are used, the level of conceptual development, and the mathematical nature. Findings support differences between preservice and master’s level students in education, as well as a tendency by in-service teachers …

Start A Math Teacher Circle: Connect K-12 Teachers With Engaging, Approachable, And Meaningful Mathematical Problems, Tom Clark, Mike Janssen, Amanda Harsy, Dave Klanderman, Mandi Maxwell, Sharon Robbert

Faculty Work Comprehensive List

Many K-12 math teachers are not ready to teach from a conceptual and inquiry-oriented perspective because they have an algorithmic understanding of mathematics. One solution is to create a math teacher circle (MTC), which provides conceptual and inquiry-based learning activities and builds professionalism among the teachers. In this paper, we describe the origins of two such MTCs, highlighting the process of identifying leadership team members, submitting the grant proposal for seed money, and hosting launch events, intensive summer workshops, and monthly meetings during the academic year. We also share opportunities for professional development for college and university faculty, including research …

Supporting English Language Learners Inside The Mathematics Classroom: One Teacher’S Unique Perspective Working With Students During Their First Years In America, Amy Marie Fendrick

Research and Evaluation in Education, Technology, Art, and Design

Reflecting upon my personal experiences teaching mathematics to English Language Learners (ELL) in a public high school in Lincoln, Nebraska, this essay largely focuses on the time I spent as the only Accelerated Math teacher in my school building. From 2012 – 2017, I taught three different subjects at this high school: Advanced Algebra, Algebra, and Accelerated Math. This essay highlights why I chose to become a math and ELL teacher, as well as the challenges, issues, struggles, and successes I experienced during my time teaching. I focus on the challenges I faced teaching students who did not share my …

Learning Logic: A Mixed Methods Study To Examine The Effects Of Context Ordering On Reasoning About Conditionals, Christina W. Lommatsch

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Logical statements are prevalent in mathematics, the sciences, law, and many areas of everyday life. The most common logical statements are conditionals, which have the form “If H..., then C...,” where “H” is a hypothesis (or condition) to be satisfied and “C” is a conclusion to follow. Reasoning about conditionals is a skill that is only superficially understood by most individuals and depends on four main conditional contexts (e.g., intuitive, abstract, symbolic, or counterintuitive). The purpose of this study was to test a theory about the effects of context ordering on reasoning about conditionals. To test the theory, the researcher …

High Cognitive Demand Examples In Precalculus: Examining The Work And Knowledge Entailed In Enactment, Erica R. Miller

Department of Mathematics: Dissertations, Theses, and Student Research

Historically, pass rates in undergraduate precalculus courses have been dismally low and the teaching practices and knowledge of university instructors have been understudied. To help improve teaching effectiveness and student outcomes in undergraduate precalculus courses, I have studied the cognitive demand of enacted examples. The purpose of this dissertation is to examine the pedagogical work and mathematical knowledge entailed in the enactment of high cognitive demand examples in a three-part study. To answer my research questions, I conducted classroom observations as well as pre- and post-observation interviews with seven graduate student instructors at a large public R1 university in the …

Women In Science: A Course, Krystyna Krupinski

Senior Honors Projects

Ask any student to name five women who have made advancements in scientific fields and most likely they will not be able to name more than two. With a lack of courses highlighting women scientists’ achievements, this lack of knowledge is hardly surprising I am addressing this issue in my work. Through the researching of scientific advancements made by women, I have proposed a method to teach students about these scientists so names like Johnson, Franklin, and Curie become as commonplace as Einstein, Hawking, and Bohr. Frequently in science classes in middle schools and high schools, the focus is only …

Mathematical Surfaces And 3d Printing, Haily A. Slone, R. Duane Skaggs

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Forcing Number, Maximum Nullity, And Minimum Rank Theorems Concerning The Generalized Petersen Graph And Related Observations, Hobert J. Holbrook, R. Duane Skaggs

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Measuring A Rifle’S Recoil Using Wireless Dynamics Sensor System, Seth Baker, Ignacio Birriel

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.