Mathematics Commons^™

Fast-Track Ode: A Student-Centered, Game-Based Summer Differential Equations Course, Chamila D. Malagoda Gamage

CODEE Journal

This article describes a student-centered and game-based redesign of an Elementary Differential Equations course taught during a six-week summer session. In this compressed setting, students had to move through the standard course content quickly while still developing procedural fluency, conceptual understanding, and confidence with applications. To support these goals, the course used real-time feedback tools, collaborative problem solving, applications connected to students' fields, and mathematical games. The paper describes the course context, major activities, implementation details, and student feedback. Student responses suggest that the activities were well received and helped students stay engaged, participate regularly, prepare for exams, and see …

Developing A Learner-Centered Teaching Routine, Hyeeun Jang

Journal of Humanistic Mathematics

This paper shares my story of developing, from Fall 2022 to Spring 2025, a learner-centered teaching routine for my undergraduate mathematics courses. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a short end-of-class exit check, at times supported by quick visuals in Mathematica and, when useful, Python. Instead of relying on extended traditional lectures, the routine emphasizes collaborative problem solving and invites students to articulate and check their reasoning together. I used this routine mainly in my elementary statistics classes, but also in calculus and linear algebra. The evidence I …

Faith-Informed Instruction In Secondary Mathematics: A Hermeneutic Phenomenological Study Of Lutheran Church–Missouri Synod Teachers, Jonathan Balsman

Doctoral Dissertations and Projects

The purpose of this hermeneutic phenomenological study was to understand the phenomenon of faith-informed instruction as experienced by secondary mathematics teachers in Lutheran Church–Missouri Synod (LCMS) schools in the United States. The theory guiding this study was Vygotsky’s theory of social constructivism, which frames educators’ instructional and theological meaning-making as socially and contextually developed through collaborative, relational learning environments. The central research question guiding this study was: What are the lived experiences of LCMS secondary mathematics teachers as they practice faith-informed instruction? This study used a hermeneutic phenomenological design to interpret teacher meaning-making and reflective practice. Participants were selected using …

Differentiating And Accommodating Ocd And Anxiety In Mathematical Contexts, Madeline F. Gavares

Interdivisional Studies Summer Fellows

Students in mathematics classrooms may experience emotional and cognitive challenges that affect how they engage with coursework and assessments. While math anxiety has been widely documented, less attention has been given to how obsessive-compulsive disorder (OCD), particularly checking behaviors, may influence students’ experiences in math settings. This study explores how students who report math anxiety and those who report OCD symptoms describe their engagement with math tasks and test-taking. Drawing on survey and interview data from students and teachers, this study examines how these experiences are articulated and perceived in academic math contexts, rather than evaluating ability or outcomes. By …

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 …

Mississippi Early Childhood Math Resource Guide: Supporting Mathematical Development From Birth Through Age Eight, Melissa Luckett, Systems Change Lab, Mississippi State University, Social Science Research Center, Mississippi State University

Books

The Mississippi Early Childhood Math Resource Guide is a comprehensive, research-informed digital publication designed to support the development of foundational mathematical skills in children from birth through age eight. Developed by the Systems Change Lab at Mississippi State University's Social Science Research Center, the guide translates evidence-based early mathematics concepts into practical, accessible strategies for educators, families, and caregivers. 

Organized by developmental stages, the guide integrates learning domains, age-appropriate math skills, and everyday instructional practices to promote the use of "math talk" and embedded learning opportunities across settings. It incorporates activities, instructional strategies, and resources aligned to support both formal …

Statistical Investigation Project, Ahmad Almomani Ph.D.

School of Arts & Sciences

The assignment was developed by SUNY Geneseo Professor Ahmad Almomani for the course, MATH 242: Elements of Probability and Statistics in the spring 2026 semester.

The objective for this assignment is that students will apply statistical methods to analyze real-world data and communicate meaningful conclusions.

Math 242: Elements Of Probability And Statistics (Syllabus), Ahmad Almomani Ph.D.

School of Arts & Sciences

This syllabus was developed by SUNY Geneseo Professor Ahmad Almomani during the spring 2026 semester.

Course Objectives:

Upon successful completion of Math 242, R/Elements of Probability and Statistics, a student will be able to: 

• Organize, present and interpret statistical data, both numerically and graphically; 
• Use various methods to compute the probabilities of events; 
• Analyze and interpret statistical data using appropriate probability distributions, e.g. binomial and normal. 
• Apply central limit theorem to describe inferences; 
• Construct and interpret confidence intervals to estimate means, standard deviations and proportions for populations; 
• Perform parameter testing techniques, including single and multi-sample tests for means, standard deviations …

Demystifying Hardware Formal Verification For Undergraduate Education: A Risc-V Processor Case Study With Coursework Implementation, Riley A. Peters

Master's Theses

Hardware verification engineers apply formal methods to prove that a digital device always behaves according to its specification. This differs from traditional functional verification, in which engineers establish correctness by repeatedly sending test inputs to the device and comparing the outputs against a reference model. With the growing complexity of integrated circuits, the demand for digital verification engineers with formal methods experience has continued to increase. However, California Polytechnic State University: San Luis Obispo's current curriculum lacks dedicated material to prepare students for these roles.

This thesis seeks to address the lack of formal methods material through two efforts. First, …

Poems For A Calculus Class (After Reading Midlife Calculus And At The Dimensional Border), Kevin Farey

Journal of Humanistic Mathematics

This poetry folder is made up of two short trios. The first begins with “Methods,” a thirteen-line poem by Britt Kaufmann, and continues with two thirteen-line responses to it. The folder’s second half consists of three (non-thirteen-line) responses to a collection of thirteen-line-almost-sonnets by Philip Fried, who had in turn been inspired, during the pandemic, by Edwin Abbot’s Flatland.

Both Kaufmann and Fried are authors of previous JHM poetry folders. Poems from Kaufmann’s book Midlife Calculus appeared in the January 2025 issue and poems from Fried’s series At the Dimensional Border appeared in the July 2024 issue. In addition, …

Developing Collaboration And Community Through An Online Virtual Modality: Participatory Action Research, Jennifer Reed

Doctor of Education Dissertations

This action research study examined educators’ perceptions of collaboration and community within a virtual professional learning community and investigated how participation influenced collaborative actions over time. The study also compared the needs and goals of secondary and postsecondary educators participating in a shared VPLC model. Grounded in the Community of Inquiry and Online Collaborative Learning theoretical frameworks, this study addressed a growing need for effective, flexible professional learning structures that support collaboration across educational contexts. Data were collected from six educators, including three secondary and three postsecondary instructors, through pre- and post-administration of the Professional Learning Community Assessment–Revised, recorded virtual …

Using Provided Guided Notes In Coordinated Introductory First-Year Mathematics Courses, Jennifer L. Huber

Mathematics Dissertations

The goal of this study is to investigate how standardized guided notes shape instructional practices and student engagement in coordinated introductory first-year college mathematics courses at a large public university. The researcher explored three multi-section introductory mathematics courses with overlapping learning objectives. Each course required students to purchase a student workbook as part of the instructional materials for the class. The instructors taught primarily from the workbook containing guided notes created by a former coordinator of the course. The researcher used a mixed-methods approach. Instructors and students participated in surveys, class observations and provided class meeting notes. Instructors shared additional …

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 …

Growth Mindset In The Mathematics Classroom: Studying The Effects Of A Growth Mindset Intervention On High School Students In A Geometry Classroom, Katelyn Strauss

Mathematics Graduate Theses

Having a growth mindset is crucial to being successful in a mathematics classroom. However, many students believe themselves to be either “mathematics people” or “not mathematics people”. When students believe they are not a mathematics person, they are far less likely to engage in material where they face struggles, and thus they miss out on valuable learning. A review of the literature has show that students have been able to shift their mindset from fixed to growth through a series of interventions. I used a unit in Geometry to see how a growth mindset intervention would affect the mindset of …

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 …

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 …

Chatgpt As A Boundary Object Between In-School And Out-Of-School Mathematical Practices: The Case Of Numeracy Practices, Murad E. Jurdak

Journal of Humanistic Mathematics

This article explores the theoretical basis and practical potential of ChatGPT in bridging the gap between school-based and out-of-school mathematical practices. Drawing on Cultural Historical Activity Theory and the concept of boundary objects, we highlight how ChatGPT can serve as a boundary object to connect these two domains. Our analysis of ChatGPT-generated lesson plans designed to align with out-of-school practices reveals that the model had the greatest impact on the social and institutional relations component of the numeracy practices framework [6], while their impact was weakest in the values and beliefs component.

A Comparative Analysis Of Early Algebraic Thinking Activities From U.S. And Singapore Primary Textbooks, Christian Joel Hernandez

Theses and Dissertations

Many studies highlight the challenges students face when transitioning to algebra at the secondary level. Introducing algebraic concepts and fostering algebraic thinking at the primary level can help mitigate these difficulties. Prior to formal algebra instruction, early algebra can be cultivated as a mode of thinking known as algebraic thinking. Several international curricula, such as Singapore Math, incorporate early algebraic thinking into the early stages of schooling. Singapore Math, renowned for its high performance in international assessments, has been widely adopted by schools seeking to replicate its success.

This study compares two primary-level mathematics curricula—CCSSM-aligned textbooks and Singapore Math—specifically focusing …

The Implementation Of Stream In Mathematics Classrooms In Abu Dhabi Primary Schools: Prospects, Priorities, Processes, And Problems, Nadeia Rashed Alalawi

Dissertations

This study shed light on implementing science, technology, reading and writing, engineering, art, and mathematics (STREAM) in mathematics classrooms in Abu Dhabi primary schools. The study aimed to explore mathematics teachers’ views on the prospects, priorities, processes, and problems of the implementation of STREAM in their classrooms. The study employed qualitative methods to collect and analyze data to support the findings using interviews, classroom observations, and document analysis. Fifteen in-service mathematics teachers were interviewed to explore their views about the application of STREAM in their classrooms regarding prospects, priorities, processes, and problems (4 Ps). Then, three of them were observed …

The Value Of Adding Nothing: A Call For Reform-Oriented Polynomial Division, Jonathan Clark, Jeneva Clark

Journal of Humanistic Mathematics

The call to implement reform practices in schools reflects the historical turn away from the behaviorist theory of learning in education. Yet the praxis of this turn remains a significant challenge, particularly within mathematics classrooms where procedural memorization is emphasized. In this article, we show one means of how to advance our pursuit of meaningful mathematics into polynomial division. Building on the literature for reform-based division methods, an alternative to the long division algorithm will be explored that relies solely on adding zero and fundamental algebraic principles.

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, …

Struggling To Be Positive Problem Solvers – A Study On The Relationship Of Elementary Mathematical Self-Concept, Gender, Learner Identification, And Productive Struggle Trajectories On Constructed Response Questions When Being Taught With A Standardized Curriculum, Kali D. Rogers

LSU Doctoral Dissertations

Mathematical word problems are some of the most difficult problems for students to solve due to their complexity and relationship to real-world situations (Şahin et al., 2014; Verschaffel et al., 2020). With math being known for right-or-wrong answers, these open-ended questions cause much confusion and frustration, specifically for students of various subgroups. In the last several decades, educational teaching expectations have shifted from engaging, self-created learning to robotic and redundant curriculum expectations that induce a ‘teaching to the test’ environment (Shafiyeva, 2021). Mathematics is the powerhouse of where students can experience and succeed with productive struggle learning that teaches the …

Key Benefits Of Small Group Instruction For Diverse Learners, Lydia Mcevoy

Master's Theses

Utilizing a mixed method approach this research study investigated the effects of small group instruction on the learning of diverse learners. Informed by a preliminary literature review that supports the use of small-group instruction, the researcher conducted a small-scale action research project to focus on three diverse learners in a 1st-grade classroom over four weeks. One of the findings of this project shows that small group instruction helps promote social and emotional skills as students feel more comfortable interacting with peers in a small group rather than in a whole group. Another finding indicates that students feel more encouraged by …

The Perspectives Of Using Desmos For Students’ Conceptual Understanding And Procedural Fluency To Solve Linear Equations, Larmel Dimatulac Madrilejos

Theses and Dissertations

The study examines the perspectives of using the Desmos calculator of Algebra I students' conceptual understanding and procedural fluency to write, graph, and solve linear equations in Algebra I STAAR. While the students have continuously used technology for mathematics assessment, emergent bilingual students in South Texas still need help passing high-stakes testing. The framework of the study is grounded in the theory of mathematical education (knowledge of mathematics educators to teach), the theory of mathematical learning (understanding how students learn mathematics), and social constructivism. The study seeks ways to teach all students, mainly the minority, to learn …

Pre-Calculus: Thinking Deeply About Simple Things, Jacob Carter

Graduate Research Showcase

“Pre-Calculus: Thinking Deeply About Simple Things” is a research-based creative endeavor focused on designing a high-school pre-calculus course. This course aims to foster deep, meaningful thinking, as well as an appreciation of the values of diversity, equity, and inclusion in the math classroom. The course leverages students’ funds of knowledge to employ culturally responsive teaching methods to connect mathematical concepts to the students’ backgrounds, interests, and real-life situations. This course also integrates social-emotional learning to create an engaging and supportive learning environment for all students. By combining Peter Liljedahl’s “Building Thinking Classroom in Mathematics” approach with problem-based learning, the course …

Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise

Masters Theses (Archived)

The purpose of this study is to examine the impact of a social justice approach to mathematics instruction. While many students have math aversion, students in low socioeconomic communities exhibit this to a higher degree putting them at a disadvantage as they progress through their educational career. More than 3.4 million K-12 students in the United States come from families that earn less than the median income yet achieve scores in the top percentile (Wyner et al., 2007). This raises the question of why so many students in low-socioeconomic settings are not given rigorous content that will keep them competitive …

Building Community, Competency, And Creativity In Calculus 2: Summary Of A Pilot Year Of Project Implementation, Jennifer Beichman, Candice R. Price

Feminist Pedagogy

In light of the COVID-19 pandemic, instructional modes at our institution moved to fully online and remote, then fully online but on campus, and back to in-person learning in fall 2021. To combat perceived issues in student engagement, we piloted using group projects in place of exams at the natural content break points in Calculus 2.

Using Gamification To Foster Student Resilience And Motivation To Learn, And Using Games To Teach Significance Testing Concepts In The Statistics Classroom, Todd Partridge

All Graduate Theses and Dissertations, Fall 2023 to Present

Two studies are outlined in this dissertation.

In the first study, elements of Super Mario Bros. videos games were used to change the way college students in a beginners’ statistics course were graded on their work. This was part of an effort to help students remain optimistic in the face of challenging coursework and even failure on assignments and tests. The study shows that the changes made to the grading structure did help students to keep trying and to use the materials given to them by their professor until they achieved their desired grade in the course, and suggests ways …