Education Commons^™

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.

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 …

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 …

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 …

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 …

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 …

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 …

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 …

Elementary/Middle School Pre-Service Teachers’ Understanding Of Variability And The Use Of Dynamical Statistical Software, Yaomingxin Lu

Research and Creative Activities Poster Day

A primary purpose of the study was to examine the effects of using dynamical statistical software (DSS) on prospective teachers’ (PSTs) understanding of statistical concepts, especially variability. Data were collected from PSTs enrolled in a probability and statistics course designed for prospective K-8 teachers. After initial analysis of the data using coding and classification schemes, we found the need to develop a more targeted framework to analyze students’ different levels of understanding. The variability framework (Garfield & Ben-Zvi, 2005) and the Structure of Observed Learning Outcomes (SOLO) taxonomy were then used in combination to develop a revised framework in order …

Project-Based And Problem-Based Instruction: A Literature Review, Sarah Angelle

Mahurin Honors College Capstone Experience/Thesis Projects

Science, technology, engineering, and mathematics (STEM) education has undergone great transformative reform during the last two decades with revised education standards calling for increased rigor to promote conceptual understanding of ideas and transferable 21st Century practices. Student-centered inquiry-based pedagogies like problem- and project-based instruction (PBI and PjBI) have begun to take root in K-12 STEM classrooms as an answer to the reform call. However, there is some disagreement of the specific characteristics of each pedagogy. There is also limited information regarding prevalence of these pedagogies in practice, their contextual patterns, degree to which they benefit all children, and the benefits/challenges …

Underachievement In Mathematics In The Early Childhood Classroom, Amy E. Lieberman

Education: Student Scholarship & Creative Works

No abstract provided.

The Impact Of Khan Academy Math Remediation On Ninth Grade Student Achievement, Sandra Kelly

Doctoral Dissertations and Projects

The purpose of this quasi-experimental study was to determine if using Khan Academy as math remediation for fifteen minutes per day during a ninth grade Math I class would significantly affect student math achievement as measured by the North Carolina READY Math I End-of-Course Assessment. This quantitative study conducted at two rural high schools in West Virginia used remediation theory to make a comparison against a control population with the independent variable being grade level instruction only or grade level instruction plus math remediation using Khan Academy. The participants in the study included 131 ninth grade high school students taking …

Investigating Secondary Students Beliefs About Mathematical Problem-Solving, Mark Prendergast, Cormac Breen, Aibhin Bray, Fiona Faulkner, Brian Carroll, Dominic Quinn

Articles

Many studies over the past thirty years have highlighted the important role of students’ beliefs for successful problem solving in mathematics. Given the recent emphasis afforded to problem solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing thirty item (five scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief …

On The Removal Of Motivation And Structural Barriers In The Classroom And Across The Mathematics Curriculum, Benjamin Wiles, Chantal Levesque-Bristol

IMPACT Presentations

Presentation at the research roundtable discussion at the 2018 Critical Issues in Math Education Workshop, Mathematical Sciences Research Institute, in Berkeley, CA.

Presents data on the ability of active learning methods to impact motivation and promote learning outcomes in mathematics courses.

Diagnostic Effects Of An Early Mastery Activity In College Algebra And Precalculus, Nathan Wakefield, Joe Champion, Jessalyn Bolkema, Douglas Dailey

Department of Mathematics: Faculty Publications

The purpose of this study was to investigate implementation of an early intervention mastery activity during the first two weeks of college algebra and precalculus courses at a large U.S. public university. Statistical modeling of (N = 935) students’ performance in the courses, including a logistic regression model of pass/fail course achievement with students’ high school rank, ACT Mathematics scores, and performance on the intervention as explanatory variables, suggested significant independent differences in course performance across performance levels on the early mastery activity. An evaluation of diagnostic validity for the model yielded a 19% false negative rate (predicted to …

The Great Escape, Caleb Kowalsk

Honors Expanded Learning Clubs

No abstract provided.

Course Portfolio For Math 407 Mathematics For High School Teaching: Refining Conceptual Understanding In A Mathematics Course For Pre-Service Teachers, Alexandra Seceleanu

UNL Faculty Course Portfolios

My intention in this portfolio is to present my approach to teaching an upper-level mathematics course for pre-service secondary level mathematics teachers. Several teaching strategies are discussed in the context of designing a coherent approach to this course, which emphasizes the need for conceptual reasoning above all other goals. These strategies are evaluated and assessed in connection to the learning outcomes using samples of student work from the course.

Also presented are samples of course materials that were used to lead students through an organized discussion of the relevant concepts. These materials convey some basic mathematical knowledge and therefore may …

Engaging Students In The Practice Of Statistics Through Undergraduate Research, Debra L. Hydorn

Mathematics

As statisticians, we engage in a variety of activities, some of which are regularly integrated into our undergraduate courses. However, the individual courses that comprise a mathematics or statistics degree program might not provide students with experiences in the broader range of activities that define the practice of statistics. To remedy this situation, faculty can consider developing and mentoring undergraduate research projects. This article briefly discusses the skills that comprise statistical practice along with some course and program options for helping students to develop these skills. Then, types of undergraduate research projects in statistics are described to help faculty generate …

The Effects Of Different Versions Of A Gateway Stem Course On Student Attitudes And Beliefs, Xiangming Wu, Jessica Deshler, Edgar Fuller

Faculty & Staff Scholarship

Background

Substantial research has been conducted focusing on student outcomes in mathematics courses in order to better understand the ways in which these outcomes depend on the underlying instructional methodologies found in the courses. From 2009 to 2014, the Mathematical Association of America (MAA) studied Calculus I instruction in United States (US) colleges and universities in the Characteristics of Successful Programs of College Calculus (CSPCC). One aspect of this study attempted to understand the impact of these courses on student experience.

Results

In this paper, we describe results from an examination of the effect of course structure on students’ attitudes …

Math Department Newsletter, 2017-2018, Mathematics Department

Mathematics Newsletter

No abstract provided.

Word-Level Neutrosophic Sentiment Similarity, Florentin Smarandache, Mihaela Colhon, Stefan Vladutescu, Xenis Negrea

Branch Mathematics and Statistics Faculty and Staff Publications

In the specialised literature, there are many approaches developed for capturing textual measures: textual similarity, textual readability and textual sentiment. This paper proposes a new sentiment similarity measures between pairs of words using a fuzzy-based approach in which words are considered single-valued neutrosophic sets. We build our study with the aid of the lexical resource SentiWordNet 3.0 as our intended scope is to design a new word-level similarity measure calculated by means of the sentiment scores of the involved words. Our study pays attention to the polysemous words because these words are a real challenge for any application that processes …

Neutrosophic Computing And Machine Learning, Vol. 1, Florentin Smarandache, Maikel Leyva-Vázquez

Branch Mathematics and Statistics Faculty and Staff Publications

La neutrosofía es una nueva rama de la filosofía la cual estudia el origen, naturaleza y alcance de las neutralidades, así como sus interacciones con diferentes espectros ideacionales: (A) es una idea, proposición, teoría, evento, concepto o entidad; anti (A) es el opuesto de (A); y (neut-A) significa ni (A) ni anti (A), es decir, la neutralidad entre los dos extremos. Etimológicamente neutron-sofía [Frances neutre < Latin neuter, neutral, y griego sophia, conocimiento] significa conocimiento de los pensamiento neutrales y comenzó en 1995. Su teoría fundamental afirma que toda idea < A > tiende a ser neutralizada, disminuida, balaceada por las ideas (no solo como Hegel planteó)- como un estado de equilibrio.

The Development Of Secondary Mathematics Teachers’ Pedagogical Identities In The Social Context Of Classroom Interactions, Hyung Won Kim

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Research demonstrates a disjuncture between the practices encouraged by teacher education programs and what teachers actually do in the classroom. It also informs us that the cognitive and social characteristics of individual teachers such as their attitudes, beliefs and knowledge contribute to their classroom practices. This qualitative study investigates how the teacher identity of mathematics teachers – the person’s sense of who he/she is as a mathematics teacher – is related to the disjuncture between encouraged and actual classroom practices. Specifically, the study looks into how mathematics teachers form their teaching practices in the social context of their classroom interactions, …