Mathematics Commons^™

Exploring The Complex Relationship Between Engineering Students Math Experiences And Identity Formation, Jill Davishahl, Joseph Brobst, Elizabeth Litzler, Andrew Klein, Sura Alqudah

Division of Research and Economic Development Faculty & Staff Publications

This paper shares the experiences of a group of S-STEM scholarship students as they progressed through their first year of undergraduate mathematics education including a math placement exam, a math focused bridge program, and calculus course(s). In addition, connections between student experiences and their math identity development were investigated with the goal of better understanding math identity formation. The authors used a mixed-methods approach to explore the math-related experiences of 12 students over the first year of participation in an NSF-funded S-STEM program. Data includes answers to select survey questions and transcripts of student focus groups. First, each student case …

Improving College Students’ Views And Beliefs Relative To Mathematics: A Systematic Literature Review Followed By A Multiple Case Mixed Methods Exploration Of The Experiences That Underpin Community College Students’ Attitudes, Self-Efficacy, And Values In Mathematics, Marquita H. Sea

Theses and Dissertations

Mathematics is particularly important due to its relevance in our daily lives. It is a general requirement throughout schooling. Unfortunately, many students openly declare negative views/beliefs regarding math in their personal and academic lives. These in turn, negatively influence students’ achievement related behaviors and outcomes. First, a systematic literature review was conducted to determine what types of studies/initiatives have aimed to enhance students’ views/beliefs relative to mathematics, including domain general and specific perceptions of math as well as their judgements of who is successful in mathematics and if they themselves can be successful. Specifically, the review centered on the components …

Profiling Mathematical Procedural And Problem-Solving Skills Of Undergraduate Students Following A New Mathematics Curriculum, Fiona Faulkner, Mark Prendergast, Cormac Breen, Michael Carr

Articles

In 2010 a mathematics curriculum was introduced in Irish second level schools entitled ‘Project Maths’ (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). Report of the Project Maths implementation support group. https://www.education.ie/en/Publications/Policy-Reports/Report-of-the-Project-Maths-Implementation-Group.pdf]. This paper aims to examine the performance of 1st year undergraduate students’ procedural and problem solving skills after the introduction of PM. A diagnostic test was developed to determine students’ skills in each area and findings demonstrated that students perform statistically significantly …

Fourth Voices Conference On Teaching Stem With Song, Lawrence M. Lesser

Journal of Humanistic Mathematics

The fourth VOICES (Virtual Ongoing Interdisciplinary Collaborations on Educating with Song) conference will be held September 26, 2021, with its Sunday date especially targeting those whose teaching schedule precludes attendance on a weekday. This online-only conference explores the use of song to teach STEM content at the college or secondary school level and will include reviewed interactive sessions, video-posters, and discussions of interest to both practitioners and researchers.

The Math Games Seminar: A Mathematical Learning Community, Anthony Delegge, Ellen Ziliak

Journal of Humanistic Mathematics

Learning communities can be an effective means of engaging university students across disciplines. Games have always been a source of both enjoyment and interesting mathematics. Based on our own interest in games, and the deep, strategic discussions we found ourselves having with students when we played games with them, we decided to design a learning community around the mathematics of games. We hoped in particular that such a community could be a great pathway to introducing mathematical thinking to students not majoring in mathematics, and that they would gain a greater appreciation for our field. In this paper, we describe …

The French Connection: Borda, Condorcet And The Mathematics Of Voting Theory, Janet Heine Barnett

General Education and Liberal Studies

No abstract provided.

Qualitative Analysis Of Corequisite Instruction In A Quantitative Reasoning Course, Zachary Beamer

Inquiry: The Journal of the Virginia Community Colleges

In corequisite models of instruction, marginally prepared students are placed directly into college-level coursework, taught with a paired support course. Initial research suggests that such models yield significant improvements in the number of students passing credit-level mathematics when compared to previous models of prerequisite remediation. The present study employs qualitative methods to investigate methods of instruction at one community colleges to understand how instructors identify and respond to student needs. It concludes with recommendations for practice and highlights advantages of small format corequisite classes taught by the same instructor.

Coordinating Stem Core Courses For Student Success, Cristina Villalobos, Hyung Won Kim, Timothy J. Huber, Roger Knobel, Shaghayegh Setayesh, Lekshmi Sasidharan, Anahit Galstyan, Andras Balogh

School of Mathematical & Statistical Sciences Faculty Publications

Research indicates multi-section coordination improves the academic performance of students in STEM education. This paper describes the process of coordination in Precalculus, Calculus 1, and Calculus 2 courses undertaken by a large department that grew from the merger of two institutions through a pilot program, and a project grant. Components introduced in the project courses are documented, including collaborative problem-solving sessions, student learning assistants, Q&A sessions, and additional technology resources. Preliminary data is provided on the impacts of the initiative on student success. The study findings provide a template for coordination, faculty buy-in, and increased student engagement at similar institutions …

Developing Better Instruction, Better Instructors, And New Investigators, Clay Vander Kolk, Abigail Pyle

Celebration of Scholarship 2021

This research discusses how HAMTE and future educators collaborated to use the Principles to Action Professional Learning Toolkit in their classes and the tools they used to measure and gather conclusions about the development in the future teachers.

Stitching Dedekind Cuts To Construct The Real Numbers, Michael P. Saclolo

Analysis

No abstract provided.

An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

Numeracy

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole

Publications and Research

Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues.

A Relationship Built To Impact Instruction: Developing And Sustaining Productive Partnerships Between Mathematics Specialists And Principals, Nathan D. Potter, Hannah Adera Rooney, Melody Locher, Debra Kinsey

Journal of Mathematics and Science: Collaborative Explorations

How does the mathematics specialist provide a profound and lasting impact on instruction? We believe that a productive partnership between the principal and specialist, which we will call the principal-specialist relationship, is at the crux of the matter. When the principal-specialist relationship is built upon a foundation of a shared vision, clear roles, communication, and trust, both the teachers and students in the school benefit. We will explore the impact of the principal-specialist relationship on teacher success during the era of distance learning as necessitated by the COVID-19 pandemic. In order to explore how these ideas come alive in the …

Proctoring And Apps In College Algebra, Cynthia M. Shelton

Theses and Dissertations--Education Sciences

The pandemic forced more instructors and students to move to online learning. For the first time, many experienced a loosening of the reigns and were forced to allow students to submit non-proctored work. Many may have questioned what students really learned in the year 2020. Many college math course competencies emphasize procedures. Now that apps can do that for students, where does that leave math instructors? Additionally, online instruction has exploded over the last decade and has challenged the teaching of college mathematics. While online instruction opens the door to access, it does beg the question of whether students complete …

Characterizations Of Student, Instructor, And Textbook Discourse Related To Basis And Change Of Basis In Quantum Mechanics, Kaitlyn Stephens Serbin, Megan Wawro, Rebecah Storms

School of Mathematical & Statistical Sciences Faculty Publications

Communities develop social languages in which utterances take on culturally specific situated meanings. As physics students interact in their classroom, they can learn the broader physics community’s social language by co-constructing meanings with their instructors. We provide an exposition of a systematic and productive use of idiosyncratic, socially acquired language in two classroom communities that we consider to be subcultures of the broader community of physicists. We perform a discourse analysis on twelve quantum mechanics students, two instructors, and the course text related to statements about basis and change of basis within a spin-½ probability problem. We classify the utterances’ …

Adaptive Analytics: It’S About Time, Charles Dziuban, Colm Howlin, Patsy Moskal, Tammy Muhs, Connie Johnson, Rachel Griffin, Carissa Hamilton

Current Issues in Emerging eLearning

This article describes a cooperative research partnership among a large public university, a for-profit private institution and their common adaptive learning platform provider. The focus of this work explored adaptive analytics that uses data the investigators describe as metaphorical “digital learning dust” produced by the platform as a matter of course. The information configured itself into acquired knowledge, growth, baseline status and engagement. Two complimentary models evolved. The first, in the public university, captured end-of-course data for predicting success. The second approach, in the private university, formed the basis of a dynamic real-time data analytic algorithm. In both cases the …

Three Creativity-Fostering Projects Implemented In A Statistics Class, Margaret Adams

Journal of Humanistic Mathematics

Undergraduates in an introductory statistics class at a rural Southeastern college were assigned three creativity-fostering projects: statistics vocabulary crossword puzzle, word wall, and graffiti art poster. Given math anxiety, fear of failure, and lack of enthusiasm, it seemed imperative to spark interest and involvement. Rhodes 4P’s model (1961) served as the framework for this intrinsic case study involving 62 students. Independent thinking and research, peer collaboration, and use of art supplies within this model (person, press, process and product) generated remarkable learning outcomes. Grading rubrics focused on originality, quality and statistics content. Projects were classified into three qualitative categories ranging …

Tactivities: Fostering Creativity Through Tactile Learning Activities, Angie Hodge-Zickerman, Eric Stade, Cindy S. York, Janice Rech

Journal of Humanistic Mathematics

As mathematics teachers, we hope our students will approach problems with a spirit of creativity. One way to both model and encourage this spirit – and, at the same time, to keep ourselves from getting bored – is through creative approaches to problem design. In this paper, we discuss ``TACTivities'' – mathematical activities with a tactile component – as a creative outlet for those of us who teach mathematics, and as a resource for stimulating creative thinking in our students. We use examples, such as our ``derivative fridge magnets'' TACTivity, to illustrate the main ideas. We emphasize that TACTivities can …

Going Beyond Promoting: Preparing Students To Creatively Solve Future Problems, Kristin M. Arney, Kayla K. Blyman, Jennifer D. Cepeda, Scott A. Lynch, Michael J. Prokos, Scott Warnke

Journal of Humanistic Mathematics

While we cannot know what problems the future will bring, we can be almost certain that solving them will require creativity. In this article we describe how our course, a first-year undergraduate mathematics course, supports creative problem solving. Creative problem solving cannot be learned through a single experience, so we provide our students with a blend of experiences. We discuss how the course structure enables creative problem solving through class instruction, during class activities, during out of class assessments, and during in class assessments. We believe this course structure increases student comfort with solving open-ended and ill-defined problems similar to …

Does Your Course Effectively Promote Creativity? Introducing The Mathematical Problem Solving Creativity Rubric, Kayla K. Blyman, Kristin M. Arney, Bryan Adams, Tara A. Hudson

Journal of Humanistic Mathematics

As believers in the power of blending the creative with the quantitative, we design our courses with an eye towards developing creative problem solvers. However, when it comes time to evaluate our course's success in developing creative problem solvers we come away with a plethora of qualitative evidence and yet we are left hungry for the quantitative evidence we desire as mathematicians.

In this article we describe the development of the Mathematical Problem Solving Creativity Rubric and its pilot use in a freshman-level Mathematical Modeling and Introduction to Calculus course at the United States Military Academy. We not only come …

Cross-Cultural Comparisons: The Art Of Computing The Greatest Common Divisor, Mary K. Flagg

Number Theory

No abstract provided.

A Statistical Analysis Of The Unm Facets Design Identity & Beliefs Survey Data, Clarissa A. Sorensen-Unruh

Mathematics & Statistics ETDs

The NSF-funded FACETS (Formation of Accomplished Chemical Engineers for Transforming Society, NSF Award 1623105) grant aims to transform the undergraduate engineering experience in the Department of Chemical and Biological Engineering at the University of New Mexico to address attrition within engineering majors, especially among underserved populations (Brainard & Carlin, 1998). The UNM FACETS Design Identity & Beliefs survey, an assessment tool used as part of the research of the grant, generated the dataset used in this study. I performed several different statistical analyses on the dataset, including confirmatory factor analysis (CFA), principal component analysis (PCA), and cluster analysis. The …

Investigations Into Bolzano's Bounded Set Theorem, Dave Ruch

Analysis

No abstract provided.

Investigations Into D'Alembert's Definition Of Limit (Real Analysis Version), Dave Ruch

Analysis

No abstract provided.

A Recent Result About Random Metrics Explains Why All Of Us Have Similar Learning Potential, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the same class, after the same lesson, the amount of learned material often differs drastically, by a factor of ten. Does this mean that people have that different learning abilities? Not really: experiments show that among different students, learning abilities differ by no more than a factor of two. This fact have been successfully used in designing innovative teaching techniques, techniques that help students realize their full learning potential. In this paper, we deal with a different question: how to explain the above experimental result. It turns out that this result about learning abilities -- which are, due to …

College Students’ Images Of Mathematicians And Mathematical Careers, Katrina Piatek-Jimenez, Miranda Nouhan, Michaela Williams

Journal of Humanistic Mathematics

In this paper we report our findings of college students’ images of mathematicians and we reflect on different methodologies used to assess this information. The study reported in this paper was conducted in two stages. During the first stage, we asked 179 college students to “draw a mathematician” and also asked them to list five characteristics and five careers for a mathematician. In the second stage of the study, we conducted four focus group interviews with a total of twelve college students. During the focus group interviews, we showed the students 16 photos of real people and asked them to …

The Mobius Function And Mobius Inversion, Carl Lienert

Number Theory

No abstract provided.

Assessing Program Outcomes Of An M.Ed. Curriculum And Instruction Program: A Comparison Of Face-To-Face To Completely Online Deliverables, James A. Telese, Gregory Chamblee

Teaching and Learning Faculty Publications

Many mathematics education degree programs, especially at the graduate level, are now transitioning to an online format. There is a need to document how mathematics content and content pedagogy are assessed in an online environment. The objectives of this chapter are to document how a public higher education institution in Texas transitioned their master's degree program for mathematics teachers from a face-to-face program to an online program and how this transition impacted the assessment process related to the learning of content and pedagogical content knowledge.

The Wright Message, 2019-2020, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:
-- New Faculty
--Faculty Spotlight
--Around Wright Hall
--Retirement Announcement
--Alumni Spotlights
--News from the CTLM
--News from TEAM
--Student Spotlights
--Hari Shankar Lecture
--Donor Spotlight
--Teaching Award
--Contributions to an Account – Recognition
--Department Funds
--Contribution Form

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 …