Mathematics Commons^™

How (And Why) To Start A Math Circle At The County Jail, Aram Bingham

Journal of Humanistic Mathematics

Math circles are a common form of outreach usually run by professional mathematicians as enrichment for K-12 students or teachers. As a setting to stimulate interest and develop positive socialization around mathematical practice, a regular math circle can also be an effective bridge to higher education in carceral settings for both facilitators and participants. This article describes my journey through starting and running math circles in county jails, with a view towards the expansion of mathematics education as another tool for the dismantling of mass incarceration.

How Did Cauchy Prove His Integral Theorem? A Historical Reconstruction For Education Research, José Gerardo Piña-Aguirre, Rosa María Farfán Márquez

Journal of Humanistic Mathematics

In his article “Mémoire sur les Intégrales Définies, prises entre des limites imaginaires” of 1825, Cauchy proves that the integral of a complex function f defined on complex numbers is independent of the path of integration if the function f remains finite and continuous along the chosen path. In contemporary literature that analyzes the mathematics of Cauchy, the specific mathematical process that allowed Cauchy to prove this result is not explicitly presented. The purpose of this manuscript is to communicate a symbolic-algebraic derivation that justifies the narrative argument used by Cauchy to support his proof, thus hopefully filling this gap. …

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 …

Of Metaphors And Measurements: Cross-Disciplinary Learning In K-8 English Language Arts And Mathematics, Morgan Shiver, Janet Shiver

New Jersey English Journal

English Language Arts and mathematics may seem like an unlikely pair, but together, literature and math can foster meaningful cross-disciplinary learning. This article presents strategies for using literature in K-8 classrooms to meet both ELA and math standards, enhancing student engagement and comprehension.

Teaching Numeracy For Social Justice: Educational Equity, Esther Isabelle Wilder, Crystal C. Rodriguez, Caterina Shost, Eduardo Vianna, Frank Wang

Numeracy

The special collection, “Teaching Numeracy for Social Justice: Educational Equity,” focuses on how quantitative reasoning (QR) can function as a vehicle for equity, empowerment, and democratic participation. Building on a longstanding tradition that treats numeracy as inseparable from social justice, these contributions highlight how progressive pedagogies (e.g., active learning, authentic research, and equity-oriented assessment) have the potential to broaden access for students historically excluded from quantitative fields. The studies span a variety of conceptual frameworks, introductory and advanced quantitative instruction, and interdisciplinary applications, showcasing how inclusive QR practices can build confidence, agency, and real-world understanding. These articles demonstrate that when …

The Polymathematician, Leo Goldmakher

Journal of Math Circles

In loving memory of Bob Kaplan, the wisest and most inspiring seven-year-old I’ve ever met.

Second And Fifth Graders’ Changes In Strategies For Integer Addition, Mahtob Aqazade, Laura Bofferding

Faculty Publications – Mathematics

Research on integer addition often attributes students’ performance to their grade level while ignoring the role of prior whole number knowledge in influencing their learning difficulties. To explore whether these difficulties are related to their grade level or persistence in using rules based on their whole-number experiences, we first paired three second-grade students with three fifth-grade students who had similar integer addition strategies on their pretest. Then, we compared their strategy changes and performance after small-group sessions and whole-class activities around integer addition (i.e., instructional intervention). Although all pairs gained from the pretest to posttest, one fifth grader still relied …

Math Anxiety, Math Self-Concept And Math Self-Efficacy: A Study Of The Jingle-Jangle Fallacies, Marsha Natasha Durrant-Walker

Dissertations

Problem

The overlap and lack of clear distinction among the constructs of math anxiety, math self-concept, and math self-efficacy presents issues for research and practice. The literature reveals that math anxiety is closely linked to math self-concept (Klee et al., 2022). Additionally, math self-concept and math self-efficacy often overlap and are not easily distinguishable (Kranzler & Pajares, 1997; Pajares & Miller, 1994; Pajares & Urdan, 1996). Each of these constructs has been shown to play a critical role in student math achievement (Timmerman et al., 2016). -- When constructs are not defined or measured distinctly, inconsistencies may emerge in research …

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 …

Digital Technologies And Calculus: Students’ Peaks And Pits, Ricela Feliciano-Semidei, Kevin A. Palencia Infante, Alcibiades Bustillo-Zarate

Faculty Articles, Papers, and Other Scholarship

Understanding calculus students’ perspectives can provide valuable insights into their learning needs and help develop strategies to enhance persistence in STEM programs. Numerous studies have shown that the use of digital technologies (DT) influences student engagement, motivation, and mathematics achievement. In this project, we explored students’ perspectives on using DT in calculus. We interviewed eight calculus students from a midwestern doctorate-granting institution in the United States and used thematic analysis informed by the didactical tetrahedron, accounting for internal and external factors that may influence the teaching and learning process. Students reflected on their use of technology, identifying various benefits, including …

I Think, Therefore I Can: Self-Efficacy, Self-Regulation, And Sense Of Belonging In Introductory Physics, Danielle Christine Maldonado

Graduate Theses, Dissertations, and Problem Reports (ETD)

Cognitive and affective beliefs in physics classrooms are important indicators of student success beyond traditional measurements of academic performance. This body of work explores major beliefs and processes, including self-efficacy, self-regulation, and sense of belonging, as they relate to academic achievement among introductory undergraduate physics students. First, this dissertation explores the development of physics self-efficacy and physics sense of belonging, two highly correlated variables. This work identifies unique sources of physics self-efficacy and sense of belonging development from current and prior academic experiences, personality factors, and demographic variables. Then, relationships between early- semester self-efficacy and sense of belonging, mid-semester …

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.

The Effects Of Problem-Based Learning On Mathematical Creativity And Self-Efficacy Of High School Students, Margaret Remus

Graduate Research Theses & Dissertations

Mathematical creativity is recognized as an important component of mathematics education; however, there is limited understanding of how instructional approaches can effectively support this skill among high school students, particularly through problem-based learning (PBL). This study examined the effects of problem-based learning on mathematical creativity among high school students.

This study employed a mixed-methods approach using an alternating treatment design with two groups of participants. Group 1 received the PBL intervention followed by a control condition, while Group 2 received the control condition followed by the PBL intervention. Quantitative data were collected through a mathematical creativity test measuring flexibility, fluency, …

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 …

Fostering A Growth Mindset In Mathematics: Faculty And Student Experiences, Yolanda G. Rush

Theses and Dissertations

According to the Center for Community College Student Engagement (2019), many students attending two-year institutions need productive persistence strategies, including the development of a growth mindset. Although some growth mindset interventions have been effective in improving academic achievement among students (Boaler, 2016; Canning et al., 2024) and persistence (Lewis, 2019) among students, especially those with developmental needs (Suh et al., 2019) and those in mathematics, little is known about the experiences of students and teachers (i.e., students’ perceptions of teachers’ intentions and implementation) as teachers work to foster a growth mindset culture (Murphy et al., 2021). In this dissertation, I …

A Conceptual Framework For Cognitive Engagement And Human Agency In Ai-Mediated Learning, Sam Rhodes, Zuhal Yilmaz, Terrie Galanti, Younggon Bae, Victoria Delaney, Zareen Gul Aga, Stephen Hutt

School of Mathematical & Statistical Sciences Faculty Publications

The purpose of this chapter is to propose a conceptual framework that unpacks AI use in instructional practice across three interrelated dimensions: human agency, cognitive demand, and AI orchestration. We ground this work in historical perspectives on technology's mediating role in education. We then propose the conceptual framework and three characterizations of the use of AI in school instruction: cognitive load reducer, cognitive capacity builder, and cognitive companion. We then illustrate a worked example of each, including a curricular example and sample student prompts, and conclude with questions that educators might ask themselves as they consider if and how to …

Creating A Positive Learning Environment In A Math Course For Preservice Teachers, Kien H. Lim, Hilda Y. Sotelo

Departmental Papers (Math)

This study examines how a mathematics instructor cultivated a positive learning environment in a synchronous online course for 23 preservice teachers. Guided by self-determination theory, growth mindset, and mathematical caring, the course integrated high-cognitive-demand tasks, collaborative problem solving, flexible policies, and motivational supports. Data sources included reflection logs (Likert-scale items and open-ended responses) and a focus group; the instructor’s reflexive self-study informed result interpretation. Wilcoxon signed-rank tests indicated significant gains in students’ sense of inclusion and trust, though some instructor- related ratings declined late in the semester. Qualitative findings emphasized students’ appreciation for flexibility, encouragement, and growth-oriented feedback. Despite time …

An Exploratory Approach For Teaching Systems Of Linear Odes With Real Repeated Eigenvalues, Biyong Luo, Li Zhang

CODEE Journal

In this paper, we present a project that aims to pique students' interest and facilitate their engagement in learning. Students will be encouraged to take an active role in their learning of systems of linear ODEs with real repeated Eigenvalues. Through discussion and completion of a set of guided questions given in the project, students will gain a deeper understanding of the topic. Also, students will use the technology tool Bluffton App to draw solution trajectories in a phase plane, and then learn necessary skills for explaining the movements of the trajectories and their long term behaviors. This project may …

Analysis Of Solutions To Research Methods: Navigating The Infinite Content Of Mathematics, Jesus Navarro

Student Scholar Symposium

In the infinite realm of mathematical research, understanding and communicating complex concepts require structured and logical approaches. However, a variety of research methods are employed in mathematical studies; these may differ in approach, historical context, and other important considerations which can contribute to confusion and a lack of effective communication. The genesis of this research began with personal confusion during my research on "Counting the Uncountable: Life in a World Without Numbers", setting the stage for the central challenge: How do mathematicians explain their research? To answer this issue, we analyzed a variety of mathematical research articles to highlight their …

Predicting The Attitudes Towards Mathematical Modeling Of Primary Math Teachers: The Role Of Self-Efficacy And Motivation, Brenden Rawls

Doctoral Dissertations and Projects

The purpose of this non-experimental quantitative predictive correlational study was to investigate the extent to which efficacy for pedagogy in mathematics, efficacy for teaching mathematics content, effectance motivation in mathematics, years of experience, and access to statistics, data science, or mathematical modeling courses predict attitudes toward constructivist practices in mathematical modeling of Virginia primary school mathematics teachers. The goal of the research was to understand what affective characteristics support effective adoption Virginia's mathematics curriculum change. Higher levels of mathematics teacher self-efficacy have been associated with constructivist instructional practices and higher levels of student achievement. The sample included kindergarten through fifth-grade …

From Textbook To Classroom: Gaps In Mathematical Representation And Translation In Nepali Education, Deepak Basyal

Mathematics and Statistics

Translating real-world problem contexts into mathematical symbols is a key skill in curricula worldwide. This study examines Nepali students’ abilities to translate words into symbols and how Nepali textbooks from earlier grades support the development of these skills. To investigate this phenomenon, a sequential explanatory study was conducted with a test for 10th graders and an analysis of Grades 6—9 textbooks. Results show that students struggle to convert real-world contexts into mathematical symbols, while textbooks provide limited opportunities for practice. In particular, students have difficulty translating symbols back into real-world situations, suggesting a link between textbook opportunities and achievement. These …

Timss 2023 – Infographic: Future Pd Needs Of Maths Teachers, Jo Earp

Teacher infographics

The IEA’s Trends in International Mathematics and Science Study (TIMSS) is a global assessment measuring student achievement in years 4 and 8. Teachers from participating schools also complete a questionnaire. Today’s infographic looks at the topics that mathematics teachers reported needing professional development on in the future.

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 …

Connections On Manifolds: A Modern Approach To Classical Differential Geometry, Jed Allen Wilshire

Theses and Dissertations

The purpose of this thesis is to connect modern differential geometry concepts to the classical differential geometry study of surfaces, specifically spheres. This thesis will cover the topics of Riemannian manifolds, tangent spaces, vectors, vector fields, the connection of Levi-Civita, the Christoffel symbols, and Riemannian curvature. Each concept will be demonstrated on the well known unit sphere manifold.

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 …

Modeling Deep-Shallow Mindset Through Student-Instructor Interactions Within The Classroom, David Chan, Kaden Sadler, Charles Ibitamuno, Oyita Udiani, Rani Satyam, Miriah Dudley, Ajay Manohar, Indranil Sahoo, Yanjun Qian, Nick Wong

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Untitled Unmastered: Initial Conditions And Emergent Properties Of The Mathematics Classroom, Reginald L. Mcgee

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Infographic: Pisa Insights – Encouraging Mathematical Thinking, Dominique Russell

Teacher infographics

Each cycle of the global Programme for International Student Assessment (PISA) includes a teacher questionnaire. One questionnaire topic – encouraging mathematical thinking – can help foster critical thinking, enhance problem-solving skills and allow students to see the relevance and connectedness of mathematics in their lives.

Expanding Ode Examples: Introducing Gene Regulation Dynamics Through Hill Functions, Maila Hallare, Jane M. Santamore

CODEE Journal

Gene regulation is a fundamental biological process that controls gene expression. It can explain phenomena such as cell differentiation, circadian rhythms, disease progression, and metabolic control, among many others. Despite their importance in mathematical biology, gene regulation models are rarely featured in traditional ODE textbooks, which focus mainly on examples from engineering, physics, chemistry, and population biology. This article introduces gene regulation dynamics as a valuable addition to ODE curricula, presenting the models from a mathematical perspective and building on properties of the Hill function. These models deepen the understanding of biology-inspired ODE applications, provide accessible research opportunities for students, …