Mathematics Commons^™

Rockin’ Rover On The Rainbow Road, Michael Kolta, Lawrence Burgee, Ying Yuan

Transformations

This paper presents a progressive series of age-appropriate lesson plans for grades K-12 that all use the same interdisciplinary activity to educate students about Science, Technology, Engineering, Art, and Mathematics (STEAM) simultaneously. Technology from Texas Instruments (TI) was employed including a TI Nspire graphing calculator that can run Python programs, a TI Innovator Hub, and a TI Rover. The TI Rover is a small, robotic car that has sensors and is controlled by the calculator via the Hub hardware interface. A Python program was developed that uses the color sensor in the Rover to detect the color on colored paper …

From Reluctance To Resilience: The Link Between Attitude And Growth Mindset In Calculus Students, Olivia Valente, Kathryn E. Pedings-Behling, Amy N. Langville

Journal of Educational Research and Practice

Many postsecondary students enter general education mathematics courses with negative attitudes, shaping their willingness to engage with the content. This study explores the relationship between students’ attitudes towards mathematics and their growth mindset, revealing effective strategies to enhance learning experiences, particularly for students who are reluctant learners. The research investigates two questions: (1) How do students’ Attitude Toward Mathematics Inventory (ATMI) scores and Growth Mindset Scale (GMS) scores relate? and (2) Do gender or course modality affect this relationship? This study addresses a gap in literature by examining how enjoyment, motivation, self-confidence, and perceived value connect with growth mindset. The …

The Effect Of Project-Based Learning Model On Entrepreneurship (Pjbl-E) With A Deep Learning Approach On Students' Problem-Solving And Cognitive Skills, Ricce Oktasari, Irwandi Irwandi, Siti Darwa Suryani

Jurnal Pendidikan Sains

This study aims to examine the effect of the Entrepreneurship-based Project Based Learning (PjBL-E) model integrated with a pedagogical Deep Learning approach on students’ problem-solving skills and cognitive learning outcomes in biology learning. The novelty of this study lies in the integration of entrepreneurship values and pedagogical deep learning principles into Project Based Learning to create contextual and meaningful learning experiences. Entrepreneurship integration encourages students to develop innovative products, identify real-world problems, and apply biological concepts in practical and socio-economic contexts. Meanwhile, the pedagogical Deep Learning approach promotes reflective thinking, conceptual understanding, critical analysis, and the ability to connect theory …

Course Portfolio: Elements Of Physics Phys 151, Evan A. Rich

UNL Faculty Course Portfolios

This course portfolio documents the instructional design, teaching methods, and ongoing assessment efforts for PHYS 151: Elements of Physics, an algebra-based introductory physics course at the University of Nebraska-Lincoln. The course serves a broad undergraduate population, including architecture, construction management, and life science majors. The portfolio describes the teaching framework that integrates pre-lecture video preparation, active in-class engagement through iClicker questions, and collaborative weekly recitation sections, all unified around a structured six-step problem-solving approach. A central concern of the course is building students’ self-efficacy in physics, particularly among those with math anxiety or limited preparation. Two assessments are reported: a …

Assessing The Effectiveness Of Tilt-Informed Assessments In Calculus I, Samuel Horelick

Inquiry: The Journal of the Virginia Community Colleges

Transparent Design in Learning and Teaching (TILT) is widely promoted as an evidence-based framework intended to clarify expectations, promote equity, and improve student learning. While prior research reports positive outcomes across many disciplines, less is known about how transparency functions in quantitative, problem-solving courses such as calculus, where students often value efficiency and autonomy. This study examines the effects of a TILT-informed assignment redesign in two sections of Calculus I at a Virginia Community College System institution. One section completed a traditional assignment, while the other completed an equivalent task redesigned to make the purpose, task, and evaluation criteria explicit. …

A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention, Salihah Ahmed E. Jaafari

Theses and Dissertations

Student retention and degree completion remain central challenges for higher-education institutions, with significant implications for student success, institutional effectiveness, and public accountability. While advances in predictive analytics have enabled earlier identification of students at risk of withdrawal, many commonly used machine learning approaches suffer from limited interpretability, constraining their practical usefulness for advising, intervention, and policy decision making. This dissertation addresses the problem of predicting student persistence by developing and evaluating optimization based, interpretable classification models within the Logical Analysis of Data (LAD) framework. Building on existing LAD formulations, this research introduces two novel pattern generation models, the Best Term …

Instructors' Lived Experiences Of Using Authentic Assessments In College Calculus Courses Across The United States: A Phenomenological Study, Christy Hart Kains

Doctoral Dissertations and Projects

The purpose of this transcendental phenomenological study was to describe the lived experiences of instructors with authentic assessments in college calculus courses across the United States. The theory guiding this study was Astin’s student involvement theory, which provided a framework to study the involvement of students in higher education. The central research question for this study was: What are the lived experiences of instructors who utilize authentic assessments in college calculus courses across the United States? This study used a qualitative design following the transcendental phenomenological approach of Moustakas. The sample included 12 instructors from two-year and four-year colleges in …

Does Sequence Matter? Impact Of Redesigning Sequential Calculus Course On Students’ Learning Outcomes, Chantal Levesque-Bristol Dr., Wonki Lee Dr., Emily M. Bonem, Benjamin C. Wiles, Jennifer D. Moss, Wilella D. Burgess, Weiling Li

International Journal of Teaching and Learning in Higher Education

As colleges and universities increasingly transform their STEM courses through the adoption of more active, student-centered pedagogies, there is a growing need to understand the impact of these educational innovations on student outcomes. This study is conducted in the context of a university-wide faculty development and course redesign project, IMPACT (Instruction Matters, Purdue Academic Course Transformation). IMPACT supports faculty in implementing student-centered pedagogical practices and creating equitable and inclusive learning environments. This study focuses on a sequence of two introductory calculus courses (Calculus 1 and Calculus 2, hereafter CALC 1 and CALC 2) that were transformed as part of the …

Student Conceptions Of Summation And Limits In The Definite Integral Following Quantitatively Focused Instruction, Caleb Daniel Holloway

2026 Scholarly Teaching Conference: Concurrent Session Papers

Recent studies have examined how students form productive conceptions of the definite integral and discussed techniques for promoting such conceptions. In this paper I present findings from interviews held with six students enrolled in second-semester calculus, four of whom had received quantitatively focused instruction on the definite integral. All six were chosen for their observed use of summation conceptions on definite integral problems, and here their conceptions are explored further. Additionally, we gain insight on their thinking regarding limits as related to the definite integral. The findings presented here add to our understanding of student thinking regarding the integral and …

Test Retakes In Introductory Math Courses, John Hird, Chris Mcclain

2026 Scholarly Teaching Conference: Poster Session Papers

In this poster, we describe the implementation of an exam retake model using specifications grading for math courses taken by non-STEM majors. This system was implemented by two faculty members over three years in two sequential courses. During that time, we tried several versions of allowed retakes, with varying restrictions on partial credit. Some of the challenges that we faced were scaling the system for use by different faculty members and with different courses, managing faculty workload on writing and grading multiple exams, and managing student expectations.

Content And Consequences: Impact Of Representation In Stem Higher Education Instructional Content On Marginalized Students, Nichole Ventura

Doctorate in Education

This qualitative study examined representation of historically marginalized students in STEM instructional content at the higher education level and its impact on their learning experiences. Despite growing diversity initiatives in STEM enrollment, curricular materials often fail to reflect the identities of underrepresented students. Using critical theory and interpretivist approaches, this research investigated how representation—or its absence—shapes students' sense of belonging, academic identity formation, and persistence. Through semi-structured interviews with undergraduate students from historically marginalized backgrounds, and purposeful sampling, this study captured the lived experiences of students engaging with STEM instructional materials. Interview protocols explored how students perceive their representation in …

Preparing Confident Elementary Mathematics Teachers: Addressing Anxiety, Building Fluency, And Strengthening Practice., Amber Diamond Pendleton

Electronic Theses and Dissertations

This dissertation, presented in three articles, examines how elementary preservice teachers (PSTs) experience and develop as mathematics learners and future educators when methods coursework deliberately integrates mathematical reasoning with affective supports. Collectively, the studies investigate how research-informed instructional design may help address mathematics anxiety (MA), mathematics teaching anxiety (MTA), procedural fluency, and instructional practice. The first article, written for practitioners and elementary mathematics teachers, illustrates how well-established instructional routines, such as number talks and student work analysis, can be facilitated to support procedural fluency in multiplication. Using classroom vignettes, this article highlights instructional moves that make structure visible, promote strategy …

The Calvin University Math Department History 1920-2020, Michael Stob

University Histories

No abstract provided.

The Other Side Of The Equation: De-Simplification, A Prerequisite For Calculus, Stephen L. Brown

ACMS Conference Proceedings 2005

No abstract provided.

Predictors Of Nursing Students' Stress, Anxiety, And Depression During The Covid-19 Pandemic In A Hispanic-Serving University In South Texas: A Cross-Sectional Study, Maria I. Diaz, Eleftherios Gkioulekas, Nancy Nadeau

School of Mathematical & Statistical Sciences Faculty Publications

Background: In nursing education, there have been several studies on the impact of the COVID-19 pandemic on the ability of nursing students to cope while in nursing school.

Purpose statement: The goal of this study is to assess undergraduate nursing students' support mechanisms as predictors of stress, anxiety, and depression during the COVID-19 pandemic within a Hispanic-serving institution in South Texas.

Methods: Across-sectional design was used in this study. An online survey using self-reported questionnaires was used to gather data from an undergraduate nursing student cohort during the Fall 2021 semester. Linear regression was used to identify the predictors of …

Culture And Context: How Frames Of Teaching And Of Learning Mathematics Form And Change For Graduate Student Instructors, Johan Benedict A. Cristobal

Department of Mathematics: Dissertations, Theses, and Student Research

Why do instructors teach the way that they do? This question is key in understanding how and why asset-based or deficit-based practices are enacted in the classroom. In consequence, this question also gives insight into how the environment where students learn is shaped. Mathematics education research, in particular, has been concerned with how instructors respond to students’ contributions in the classroom and how these ways of responding can (dis)empower students.

One way to answer this question is to understand how instructors frame their own teaching and their students’ learning. Frames are mental constructs which help individuals filter details, interpret information, …

Culture And Context: How Frames Of Teaching And Of Learning Mathematics Form And Change For Graduate Student Instructors, Johan Benedict Arroyo Cristobal

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Why do instructors teach the way that they do? This question is key in understanding how and why asset-based or deficit-based practices are enacted in the classroom. In consequence, this question also gives insight into how the environment where students learn is shaped. Mathematics education research, in particular, has been concerned with how instructors respond to students’ contributions in the classroom and how these ways of responding can (dis)empower students.

One way to answer this question is to understand how instructors frame their own teaching and their students’ learning. Frames are mental constructs which help individuals filter details, interpret information, …

Equity Vs. Excellence: Dichotomy Or Duo?, Nadjia I. Logans

Honors Program: Senior Projects (Public)

In this thesis, I investigate recent changes in mathematics education and how these developments connect to the principles of equity and excellence. I place a special focus on “active learning” methods. My methodology primarily consisted of interviews with educators, along with analyzing literature from math education researchers. I first define and explain the motivations behind active learning instruction methods. Next, I explore not only how instructors define equity and excellence but how educators perceive the role of the two principles within education. Finally, I challenge the pervasive media portrayal of equity and excellence as being mutually exclusive. Instead, I find …

Countering Deficit Narratives Through A Blackcrit Lens By Examining Case Studies Of Black College Mathematics Students’ Classroom Experiences, Akhenaton Wilbourn

All Dissertations

This dissertation examines the lived experiences of 11 Black college mathematics students at their predominantly white institution (PWI) through the lens of Black Critical Theory (BlackCrit) to counter deficit narratives about the racial achievement gap (RAG) in mathematics education courses. Deficit narratives often attribute disparities between Black and white students’ mathematical performance to assumed deficiencies in Black students’ abilities rather than systemic inequities, historical marginalization, and ongoing anti-Blackness in educational settings (Cobb & Russell, 2015; Kress, 2021). Using multiple case studies, this study explores how anti-Blackness manifests in mathematics classrooms, how students navigate tensions between multiculturalism, neoliberal educational policies, and …

Reinventing Mathematics Learning: An Exploration Of Undergraduate Mathematics Learning Post-Pandemic, Morgan R. Balesano

Honors Scholar Theses

In response to the COVID-19 pandemic, beginning in March 2020 nearly all secondary and undergraduate mathematics students were forced to adapt to new methods of learning and testing. As a result, the current experience for these mathematics students has changed vastly, as have the opinions and preferences of these students in terms of their learning. This study aims to identify instruction and testing resources and methods that students prefer and those that students find less beneficial in their current, post-pandemic educational experience. The past few years have seen a focus on the direct impacts of online learning during the pandemic, …

Ai Beliefs And Practices In Community College Classrooms, Julie Eng, Heather Umphlett, Jocelyn Gilchrist, Alicia Howell, Mary Ann Howell, Wendy Miller-Edwards, Laurel Pope

Inquiry: The Journal of the Virginia Community Colleges

The country, the Commonwealth of Virginia, and Virginia Community College System initiatives all promote generative AI within education. It is a topic of great concern and interest for higher education instructors, yet at the same time many faculty members feel uncertain about effectively integrating it into class material. To further add pressure to the AI explosion, community colleges particularly face a responsibility to prepare their students for success in this new AI-focused environment. In this article, seven faculty members from Camp Community College discuss the implications of generative AI programs, including subscriptions and chatbots, within their particular courses and how …

Number Talks To Promote Discourse In The Algebra 1 Classroom: A Number Talk Curriculum Development For A Unit On Quadratic Expressions, Lindsay C. Borger

Masters Theses/Capstone Projects

This project sought to develop a curriculum of Number Talks for use at the secondary level, specifically in an Algebra 1 class as a supplement to a unit on quadratic expressions. The project begins with a look at existing research on constructivism and social constructionism as well as the reforms in mathematics education informed by those learning theories. It then looks at calls for more discourse in the mathematics classroom as a part of these reform efforts, and the part Number Talks play in fostering discourse and mathematical thinking for students. The Number Talk curriculum includes a guide for implementing …

Patterns Within The Collatz Conjecture, Kiel Harrison

SACAD: Scholarly Activities

The Collatz Conjecture, also known as 3n+1, one of the most famous unsolved problems in mathematics, has been forever out of reach of being truly solved. However, through the application of traces, there is now a new pathway forward to working out a potential solution. This study shows how this pathway was found, and what steps need to be taken to follow it.

An In-Depth Analysis Of The Bellarmine University Student Athlete Experience, Mattingly E. Spalding

Undergraduate Theses

The goal of this thesis is to improve the student athlete experience at Bellarmine University through direct feedback from our current student athletes. By defining what parts of the student athlete experience they value most, Bellarmine can reflect on the support currently provided in these areas. Additionally, if it is concluded through the response that high valued areas are not being satisfied, Bellarmine can work to improve the support in these areas. Or, if there is abundant support in a low-valued area, Bellarmine could think to shift resources into a more needed concentration. Through the design sample, data was accumulated …

Stem Major Perspectives For Humanizing Undergraduate Mathematics Classes, Kelly Macarthur, Derek Williams, Bryce Hughes

Journal of Humanistic Mathematics

Using the eight dimensions of the rehumanizing framework [32] by Gutiérrez, built on a sociopolitical foundation, we report on research findings about what Latin* [41], Native American, LGBTQ+ and/or women science, technology, engineering, and mathematics (STEM) majors at two primarily white institutions (PWI) perceive as humanizing in their mathematics courses. In analysis of interviews with twenty students, we found that the core aspects of a humanized learning experience center relationality and a caring classroom environment. We then explore tensions that arose regarding the implementation of one teaching strategy reflecting the Cultures & Theirstories rehumanizing dimension, suggesting that implementation of such …

Developing Mathematical Maturity By Solving A Given Quadratic Equation, Armando A. Amador, Nieves Angulo, Juan B. Lacay

Publications and Research

This article explores the instructional challenges faced by mathematics educators when addressing students’ limited background knowledge and underdeveloped mathematical maturity, two critical barriers to success in college-level algebra. Using the quadratic equation 2x2+x−3=0, which is reducible over the field of rational numbers ℚ ⊂ ℝ, we analyze how diverse solution methods—factoring, completing the square, and the quadratic formula—can support learning. An additional strategy, “Slide and Divide,” was introduced to promote procedural fluency and conceptual flexibility. To gain insight into students’ evolving mathematical maturity, an online survey was conducted to students at various levels of mathematics. The survey captured their perspectives …

A Phenomenological Study Of Persistence For Black Women In Mathematics Doctoral Programs, Shushannah Marie Smith

Doctoral Dissertations and Projects

The purpose of this phenomenological study was to describe the doctoral persistence experiences of Black women mathematicians. Guided by McGee’s fragile and robust mathematical identity framework, the research design followed Moustakas’ qualitative transcendental phenomenological approach. The researcher explored the contributing factors to the phenomenon guided by the central research question, “What are the doctoral persistence experiences of Black women mathematicians?” The study involved 11 Black women participants who hold or were within one year of holding a doctoral degree in mathematics and were selected to ensure diversity and representativeness. Data collection encompassed three methods: a mathematical identity development timeline, one-on-one …

Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl

Journal of Humanistic Mathematics

According to a widely held view, mathematical proofs are essentially (indications of) formal derivations, and thus in principle mechanically checkable (this view is defended, for example, by Azzouni [3]). This should in particular hold for the kind of simple proof exercises typically given to students of mathematics learning to write proofs. If that is so, then automated proof checking should be an attractive option for math education at the undergraduate level. An opposing view would be that mathematical proofs are social objects and that what constitutes a mathematical proof can thus not be separated from the social context in which …

Quantitative Reasoning: What’S Math Got To Do With It?, Pamela Burdman

Numeracy

This keynote address explores the history and role of college math requirements with a focus on ensuring math courses serve to expand students’ horizons, rather than serve as gatekeepers. It discusses the advent of general education math courses, which brought more students into math departments, which ultimately contributed to broadening the scope of the courses to align with more students’ interests and majors, since their purpose was to advance quantitative reasoning, not mathematics skill per se. It also examines several practices to address calculus’ gatekeeping role: revising placement practices and prerequisites, redesigning courses, and updating instruction and assessment practices. Lastly, …

The Nature Of Undergraduate Calculus I Students' Participation In The Parallel Spaces Of Coursework And Peer-Led, Cooperative, Inquiry-Oriented Complementary Instruction, Karmen T. Yu

Theses, Dissertations and Culminating Projects

Calculus has long been known as a “gateway course” to STEM fields in postsecondary education. To moderate this gatekeeping effect, Montclair State University researchers developed a peer-led, inquiry-based instructional support (IBIS) to run parallel to Calculus classes. The design of the IBIS model was informed by an instructional approach called Complex Instruction (CI) and two other peer-led, cooperative learning models, Peer-Led Team Learning (PLTL) and Supplemental Instruction (SI). While the literature on peer-led models of cooperative learning confirms their effectiveness on undergraduate students’ academic outcomes in mathematics, this multiple-case study set out to address the following: What is the nature …