RUME 28
2026
Alexandria, Virginia
Number of pages: 1506
Number of papers: 274
- Aditya P. Adiredja
- Brian P Katz (BK)
- Kathleen Melhuish
- Keith Gallagher
2026
Alexandria, Virginia
Number of pages: 1506
Number of papers: 274
Mathematics uses standard logic, in which the truth value of the conditional ‘if A then B’ is completely determined by the truth values of A and B. Specifically, when A is false, ‘if A then B’ is, by definition, true. This makes the mathematical conditional out of line with natural language, where research using truth table tasks shows that conditionals are often considered irrelevant in false-antecedent cases. What does this mean for mathematics undergraduates? Do they interpret conditionals according to standard logic, or do their responses align with everyday interpretations? Do they make consistent interpretations, or do these vary by content? This report contributes a first investigation of this issue.
This study examines how precalculus students reason about rate and point as multiplicative objects in the contexts of linear equations and approximation. To capture students’ developing conceptions, I introduce a framework distinguishing three levels of abstracted ratio: generalized ratio, unit rate, and interiorized ratio. Findings show that although students progressed toward interiorized reasoning, their understanding was fragile when working with non-integer or symbolic values. They also struggled to coordinate slope with a reference point, which limited their ability to interpret points as records of covariation. Geometric approaches to linear approximation highlighted these conceptual difficulties more clearly than symbolic tangent line equations, underscoring the need for instructional support that fosters covariational reasoning.
Mathematicians’ community values and norms play a vital role in shaping approaches to practice, including with respect to definitions. Mathematicians have suggested that in their instruction they portray norms related to the value of clear communication more than those related to freedom in their use of definitions, but limited work has examined what students take from instruction. Here, we examine survey responses from proof-based linear and abstract algebra courses taught by the same instructor. Results include widespread recognition of definitions’ role in supporting arguments and facilitating unambiguous communication as well as some support for mathematical doers’ agency in creating and using definitions, suggesting it is possible to portray this freedom in instruction.
We explore prospective intermediate and secondary school teachers’ strategies for supporting students in coding and troubleshooting errors while working in Scratch ©. Participants were asked to create an imagined dialogue that addressed student-generated “starter” code, which included bugs, in order to explore the probability of different sums of two dice rolls and present these sums as a graph. Our analysis shows that participants attended to different possible student difficulties with the coding, yet few of them attended to the given starter code as an instance of student thinking when suggesting viable resolutions or ways forward. Instead, participants tended to introduce their own approaches and trajectories for how to advance the code. We suggest that while participants demonstrated useful teaching strategies to support student-characters, their attention was focused on advancing any code, rather than building with or on ideas presented by the student-characters.
The mathematics community has a variety of standard norms of practice by which it operates, which are guided by collective values, including in the context of definitions. However, these norms and values are not always shared with students in instruction. Here we examine teaching practices that linear and abstract algebra students perceived as influencing their understanding of norms around mathematical definitions. Teaching practices in linear algebra tended to align more with instructor-centered actions whereas teaching practices in abstract algebra tended to align more with student-centered activities. Implications include the impact of homework and classroom activities on students’ perceptions, as well as the long-term use of activities seeming to be more salient in students’ perceptions of influential activities.
In the United States, students in the K-12 system are often adversely affected by a so-called “race to calculus” that we believe to be caused, in part, by the emphasis on analysis found in the mathematics curriculum at both the undergraduate and graduate levels. This originates partially from a historical need for calculus in industry, a need which is no longer as prevalent as it once was. Here, we examine the curricula at 100 of the top graduate and undergraduate programs in the United States and the prevalence of a variety of topics in these programs, including calculus, analysis, linear algebra, abstract algebra, geometry, and statistics. As expected, analysis was much more prevalent than any other advanced topic. We discuss reasons for this prevalence and how such prevalence should be mitigated in the future.
The ACT UP Math project was a multi-institutional research practice partnership (RPP) formed to engage students, faculty, and administrators in collective equity-oriented work for critical change in undergraduate mathematics programs. Through careful critique of our own decisions and results, we identify opportunities with which we could have embraced greater criticality, especially in relation to disrupting our own white comfort. In doing so, we aim to provide guidance on better practices to enact when engaging in critical work. We orient ourselves to this critique with (critical) love, engaging with love for ourselves with the goal of growth as researchers, love for the research we do with the goal of growth for our field, and love for the research participants with whom we partnered with the goal of learning from one another.
Dual enrollment (DE) students have simultaneous roles as both high school and college students. DE programs have been utilized to enhance students’ access to higher education and post-secondary success. While many studies have focused on the effects of DE programs through quantitative, outcome-oriented frameworks, few studies utilized sociocultural, qualitative approaches to examine DE students’ perspectives on their experiences by centering their own voices. Our qualitative case study addresses this need by exploring how three high school students taking a DE Calculus course describe their experiences with college calculus instruction. Student views about the affordances and limitations of college instruction emerged as themes in our study, which have critical implications for undergraduate mathematics education.
In this report we address the longstanding problem of the perceived relevance of upper division math courses for prospective secondary school teachers. Through a multi-year design-based research approach we are reimaging a Dynamical Systems and Modeling course and investigating ways to make the course more relevant to prospective teachers. In this work we report on the impact of these efforts on students’ relational understanding of why a particular function is a horizontal shift to the left of another function, a high school topic that is often only instrumentally taught and understood. Analysis of beginning and mid-semester assessments indicate significant growth in our students’ ability to provide meaningful explanations. We also report on students’ perspectives on classroom activities that influenced their reasoning.
Researchers have recognized Adding Up Pieces (e.g., Jones, 2013) to be a critical interpretation when applying definite integrals to problems in physics and other domains. At the same time, researchers have not investigated as closely students’ moment-to-moment reasoning when constructing pieces of an approximation and how that reasoning might vary across situations. We interviewed 11 students enrolled in calculus-based physics courses using tasks that asked for approximations, not definite integrals. Individual students approached approximations in more than one way––depending on the problem situation and how it was presented––and they did not always make connections among their different approaches. Based on this observation, we conjecture that approximation in service of Riemann sums is a good candidate for a coordination class (e.g., diSessa, 2002; diSessa & Wagner, 2005). We summarize the theory, present the case of one student, and draw out implications for research and instruction.
One’s sense of belonging, or their sense of feeling like an accepted member of an academic community, has been identified as a major contributor to women’s decisions to stick with or leave their STEM major. Prior work has examined ways in which pedagogical practices such as providing opportunities for students to engage in active learning in undergraduate courses might influence women’s sense of belonging in STEM. However, the focus had been on students’ perceptions of the practices themselves rather than the person enacting those practices – the instructor. With this study, I explore ways in which women describe the role their instructor plays in supporting their sense of belonging in an active learning Calculus course. Women’s survey responses suggest several ways in which their instructor supported their sense of belonging by portraying care both through their enactment of active learning as well as other pedagogical and personal attributes.
This report examines how group roles and instructional practices shaped student participation in an inquiry-oriented undergraduate mathematics course. Using classroom video with thematic analysis and equity analytics, findings indicate alignment with the four pillars of Inquiry-Based Mathematics Education (IBME). The role responsible for reporting to the class (called reporter) most clearly influenced participation, while other roles were taken up more fluidly as students responded to the needs of the group’s mathematical exploration. An important observation is that calling on reporters in a male-dominant classroom may constrain who speaks publicly, even within an intentional design for equity. Overall, the results suggest that IBME design fosters collaborative learning while also highlighting opportunities for future research on how group roles and instructional practices can be refined to support equitable participation.
This is part of a larger APOS-grounded study where we investigate students’ reasoning about and between multiple components of multivariable differential calculus. We report on the different reasoning of the strongest interview participants from two sections taught by the same instructor. One section used the locally linear approach; the other was taught traditionally. The locally linear approach leverages the geometric understanding of the point-slopes equation of a plane to help students develop key ideas for the differential calculus of two-variable functions. We used semi-structured interviews to investigate students’ understanding of multiple components of differential calculus and the relations established between those components. In this report, our analysis focuses on the relations that two high-performing students established between the components of plane and vertical change. Findings suggest that the locally linear approach may help students obtain a deeper understanding of vertical change on a plane than traditional instruction.
There has been a call to emphasize how mathematics can be used to tackle social issues in ways that create a more just world. Such efforts can take the form of an explicit topic, entire course, or as a call-to-action impacting communities in various manners. This study analyzed course reflections of 15 mathematics majors enrolled in a Teaching Math for Social Justice course. We used open coding and constant comparison analysis to analyze pre-class and post-class reflections to understand the ways that students conceptualized the notion of “justice”. Eight themes emerged from the data, with notable differences between the ways students described justice before and after the course, with students’ conceptualizations demonstrating change or becoming solidified after completion of the course. These findings contribute to the larger body of research that continues to investigate how mathematics students engage with incorporating social justice contexts into mathematics teaching and learning.
Meanings for the definite integral are most productive when rooted in quantitative reasoning. However, little is known about how instruction may effectively support these meanings. This study examines the discourse actions of one instructor who intended to promote students’ quantitative reasoning in a lesson exploring ideas foundational to the definite integral. We draw upon video data of the instructor’s conversations with three undergraduate students who were working together during class. We analyzed whether his conversational turns could promote quantitative reasoning and characterized them according to a discourse action typology. Results suggest most of his discourse actions did opportune quantitative reasoning and that different types of discourse actions had the potential to elicit quantitative reasoning in distinct ways. We also identify two additional discourse actions not in the original typology. We conclude with implications for practice and suggestions for future research.
What does it mean to engage in equity work and critical transformation efforts? We asked mathematicians who were part of research-practice partnerships addressing inequities in their departments to create or find an image to represent what it meant to them to engage in critical transformation work. We interviewed them about their images, and categorized images in overlapping domains of the processes of critical transformation efforts, emotions, and relative positioning of members. Many participants illustrated and voiced the process of building community, which often included an inclusive power dynamic and positive and productive feelings. Images without both community and inclusivity present instead centered loneliness and discouragement. A key implication for engaging in critical transformation efforts includes the need to center building inclusive communities.
“Rigor” is often used as a benchmark to determine whether mathematical work is sufficiently high-quality, and, thus, has significant bearing on students’ course success and continuation in STEM majors. However, judgements about what constitute rigor are deeply subjective and may function as a vehicle for social bias. To interrogate possible connections between disciplinary standards and exclusionary gatekeeping, we analyze references to rigor by members of an “elite” mathematics department’s equity-oriented change community. Our findings exhibit how participants’ perceptions of rigor unveil a culture of power operating in undergraduate mathematics. We conclude with implications for research and practice.
Active-learning-based instructional practices are well-established in undergraduate mathematics. What it means to align assessment with those active learning methods is an emerging area of research and development. Here we present student experiences of “active assessment,” assessment strategies grounded in the values and practices of active learning. As part of a larger study, we gathered undergraduate student responses to survey and semi-structured focus group interview questions about their experiences with various active assessments. Their instructors all were part of a year-long Assessment Community of Practice focused on active assessment. In this paper, we focus on student-identified benefits of active assessments, as well as student perceptions about how the assessments were equitable or potentially inequitable. We conclude with suggestions for instructors and discussion of considerations for moving forward.
This study investigates the symbolic forms pre-service teachers (PSTs) drew upon while mathematizing a real-world laundry task. Drawing from Sherin’s (2001) framework of symbolic forms we analyzed how two PSTs, Mia and Ava, coordinated mathematical symbols templates with conceptual reasoning to model when clothes should be washed based on bacterial load thresholds. Our analysis identifies both singleton forms: threshold and exponentially growing, and networks of forms: rate, contributing factors and exponential growth with a threshold. We end with implications for research on student cognition during modeling.
Students often struggle to interpret the multiplicative structure within integrals––what we call the “product layer” (f(x)∙dx)––when reasoning about applied problems. In this study, we analyze the reasoning of Melinda, an undergraduate in a calculus-based physics course, as she works on two tasks: estimating the total force on a tank wall (water pressure) and the total voltage across a capacitor (electricity). Using conceptual blending theory, we examine how Melinda connects symbolic, mathematical, and physical ideas when setting up integrals. Melinda frequently interprets integration as summation of small pieces or as area under a curve but struggles to coordinate multiplicative relationships among varying quantities (e.g., pressure x area, current x time). These findings suggest that challenges with product layer reasoning persist across contexts, highlighting the need for instruction that explicitly supports blended multiplicative reasoning.
This study examined the professional identity development of six mathematics graduate students by exploring how they enacted and constructed meanings around five role identities: teacher, researcher, mathematician, mentor, and peer. Drawing on role identity theory, I highlighted the socially mediated nature of identity formation and the ways it was shaped by program structures, departmental cultures, and disciplinary expectations. Findings indicated that while graduate students identified the roles of teacher and researcher as most central to becoming mathematics faculty, the program offered more formalized opportunities for teaching than for research, suggesting an imbalance in preparation. This work contributes to understanding the liminal space between graduate student and professor, where multiple roles are navigated. The study points to the need for graduate programs to intentionally design structures that expand opportunities for development as researchers, mentoring, and community building.
This multiple case study explores the affordances and limitations of four data sources: a validated math anxiety (MA) scale, written narratives about one’s relationship with mathematics, semi-structured interviews, and recorded classroom observations. Analysis of three preservice elementary teachers revealed that each data source provides a unique and valuable perspective. Our findings demonstrate the need for researchers to leverage a diverse range of data sources to develop a more robust understanding of each individual’s MA experiences, their MA triggers, responses to these triggers, and how these things may change over time.
Bold problem solving (BPS) describes an orientation towards mathematical problem-solving involving risk taking, inventiveness, and independence. Research establishing BPS is promising but requires more validity work to better position the construct. This study does so, exploring the factor structure of the BPS orientation scale, examining how BPS relates to risk taking, math identity and agency, and investigating if gendered differences in BPS orientations persist with more flexible gender measures than those used in earlier studies. Electronic survey data from 204 students enrolled in calculus or above at a single university were collected and analyzed using statistical methods. Results suggest that the BPS orientation scale has one dimension, but the measure can be improved. Risk taking and math identity have strong unique relationships to BPS. Gendered differences in BPS largely were non-existent using more flexible gender measures. Collectively, this work helps further the structural and external validity of BPS.
In this study, we leverage the Conceptions of Derivative (CoD) framework (Author et al., 2025) to analyze eight U.S. college calculus instructors’ instructional tasks for introducing derivatives. During four task-oriented interviews, each instructor proposed up to eight tasks for introducing derivatives with inquiry in their calculus I courses. Based on Zandieh's (2000) process-object model, the CoD framework was used to reveal derivative conceptions that instructors were targeting in their tasks. We identified four components of derivative conceptions targeted in the tasks: contextual framing, epistemological approaches (limit-based, infinitesimal/differential-based, and instrumental/rule-based), mathematical representations, and process-object layers. While pure contextual frames and limit-based approaches dominated early instruction of derivatives for these instructors, some targeted physics and biology contexts as well as infinitesimal/differential-based and rule-based epistemologies. We discuss implications for research on calculus teaching.
Although research has shown benefits of inquiry-oriented (IO) instruction for student learning, it has also been reported not to benefit all students equally. In this report, we illustrate how UDL can serve as a generative framework for (re)designing IO instruction in such a way that attends to the individual needs and strengths of students, working toward creating an equitable learning environment. We will also share UDL-aligned teaching practices for IO classrooms, including those fostering relationship-building, multimodal participation, and equitable assessment.
The increasing use of online videos in mathematics education has led to a need to understand what makes them captivating. This study applied Dietiker’s mathematical story framework to online mathematics instructional videos (OMIVs), specifically analyzing several videos from a popular YouTube channel. Using a qualitative case study approach, we identified the central role of questions from a narrative lens and observed four open question types and three types of their closure. Findings also show how different question types may relate to the plot’s characteristics and enrich the plot. This study is an initial exploration of mathematical stories in the context of OMIVs, providing new perspectives that would hopefully inspire further research and practical application in math education.
Graduate Teaching Assistants (GTAs) play a critical role in undergraduate mathematics, often serving as instructors of record with limited preparation for teaching. This paper examines the case of Anthony, a College Algebra GTA participating in a semester-long professional development seminar focused on anticipating student strategies, planning purposeful questions, and reflecting on teaching. Across three observations, Anthony’s lessons shifted from lecture-heavy explanations to student-centered problem solving, supported by targeted guiding questions. Monitoring charts from Anthony’s planning and post-lesson debriefs revealed how his instructional decisions were shaped by prior beliefs about student-centered learning and contextual pressures such as pacing demands and coordinator feedback. This case study provides insight into the tensions GTAs face in balancing explanation and inquiry and illustrates how professional development can support incremental shifts toward more student-centered mathematics instruction.
Increasingly, institutions of higher education utilize undergraduate Learning Assistants (LAs) to support students’ learning in introductory calculus courses. Prior research has shown a promising impact of the LAs on students’ success and retention. However, little is known about students’ perceptions of LAs’ roles or whether academic factors influence these perceptions. In this mixed-methods study, we analyzed 411 Calculus I students’ survey responses. The results of statistical analysis indicate that, regardless of course performance or prior Calculus experience, students generally perceive LAs positively, with students who seek additional learning resources having even more favorable perceptions of LAs. Additionally, a natural language processing (NLP) technique– topic modeling—revealed two themes: Investigating Procedural Activities and Conceptually Framing Results through Collaboration. Findings support LAs’ role in fostering meaningful engagement for a range of students and demonstrate the value of NLP in educational research, offering insights for LA support of active learning in Calculus courses.
The enculturation of mathematics students into the mathematical norms of proof can be a source of epistemic injustice when personal, social, and cultural norms are in tension with those held by the mathematics community. This injustice can be addressed through students’ conscious appropriation of these norms, and I argue that queer readings, a form of critical textual analysis originating in queer theory, offers relevant analytical tools for this appropriation. In this paper, I present findings from a study on queer readings of mathematical proof and illustrate how our queer appropriations of mathematical norms resulted in an epistemically just interaction with proof and invited queer joy into the proof reading process.
Because many mathematics instructors rely on lectures as their primary mode of instruction, change efforts should engage with and build on instructors’ existing values and practices rather than attempt to replace them. We report on the first year of our project, where we take a collaborative approach to improve instruction surrounding definitions through activity design and implementation. Constructing narrative cases, we explored how our collaboration aided participants in navigating alignments and tensions between their professional obligations and their activity. We found our collaboration succeeded in guiding our participants, but it required careful examination of reasons as to why instructors may not institute instructional change.
Deciding to pursue graduate study is a pivotal step in students’ academic and professional trajectories. However, limited research exists on the motivations to apply to mathematics graduate programs. To address this gap, we analyzed 74 personal statements, in which applicants articulate their motivations, goals, and experiences, submitted as part of applications to master’s and doctoral programs in mathematics and statistics at a mid-sized research-intensive university (2015–2024). Using qualitative coding with AI-assisted analysis, five key themes emerged: pursuit of knowledge, research aspirations, career advancement, growth as a teacher, and appreciation of mathematics. Most applicants expressed multiple, overlapping motivations, often linking professional goals to disciplinary growth and research. A distinctive finding was the prominence of appreciation of mathematics, where applicants described joy and fascination with the subject as central to their decision-making. These results expand understanding of mathematics graduate decision-making and carry implications for recruitment, advising, and program design.
Ontology—the recognition or erasure of ways of being—is a justice issue in mathematics, intersecting with race, gender, sexuality, and disability. Despite growing scholarship on liberatory ontologies in mathematics education, little is known about how such paradigms might be enacted in postsecondary contexts, or how trans mathematics-doers experience ontological tensions uniquely. We address this gap by analyzing a mathematical representation of trans experience created by a transfeminine, graduate student of color in mathematics, and the ontological tensions it draws from us as trans mathematician-researchers. Our findings identify ontological erasure, disembodiment, and categorization as features of mathematics that conflict with trans ways of being. We propose ontological possibilities for postsecondary mathematics that affirm trans and other marginalized realities, and invite further exploration of postsecondary mathematics as a site for ontological justice.
This study explores how undergraduate students develop reasoning about the relationship between a matrix and its null space through progressive mathematization within an inquiry-oriented linear algebra context. Using a playful hallway map task, students engaged in a paired teaching experiment to investigate how modifying the number of rooms and hallways affects the dimension of the null space. We drew on a river journey metaphor to examine students’ movement along and between shores of contextual or formal symbolic reasoning. Findings reveal a dynamic interplay between contextual reasoning and formal symbolic representations, as students moved fluidly between the realistic hallway context and matrix-based interpretations. Through successive horizontal and vertical mathematization, students gradually developed reasoning that approached a reinvention of the rank-nullity theorem. The results highlight the complexity of this journey and suggest further research into providing supports for instruction.
Discursive interactions have been of great interest to researchers studying students' sense of belonging in the classroom. The study of discourse helps us understand positions of authority and agency, as well as creating a common language to describe expected social roles in student-teacher and student-student interactions (storylines). Positioning theory provides the groundwork for understanding how our beliefs about social roles influence how we express ourselves. In each of these areas, verbal communication is typically studied directly, with nonverbal communication used as confirmatory or add-on illustrations. This study centers nonverbal communication, using empirical data from an observation of a higher education mathematics classroom over two class sessions. We seek to identify how the instructor’s use of classroom space and body movement demonstrates the assignment and shifting of power structures, as well as the enactment of storylines.
This study investigates mechanisms of equity in active learning by examining student networks in an Inquiry-Oriented Linear Algebra (IOLA) classroom through social network analysis (SNA). Drawing from the sociopolitical perspective on equity, particularly the dimension of power, the research analyzes how race/ethnicity and gender shape student nominations of peers. Data were collected from an IOLA class of 64 students at a Southeastern U.S. university, using discussion board “shout-outs” and replies to track social networks. Findings reveal strong patterns of racial and gender homophily and highlight that women of color occupied disproportionately central positions within the network. While these positions suggest potential empowerment, they may also reflect additional labor on women of color to sustain visibility and influence. The study underscores the need to frame equity in active learning not as inherent but as contingent on power dynamics, solidarity, and segregation within mathematics learning communities.
Textbooks remain central in undergraduate STEM education, yet little is known about how readers distribute attention across the diverse elements of extended mathematical texts. This study investigates how mathematics majors, non-mathematics STEM faculty, and non-math majors read a four-page excerpt from a standard calculus textbook. Using eye-tracking, we compared participants’ attention to expository prose, worked examples, figures, and a highlighted formula. Exploratory analyses suggested differences between the groups’ distributions of attention. However, a compositional data analysis did not reveal statistically significant group-level differences. These findings point to the importance of disciplinary literacy frameworks in interpreting attention patterns and raise questions about how readers’ identities shape engagement with mathematics texts.
To examine the forms of reasoning novice statistics students employed when reasoning about sampling distributions, I used Charles S. Peirce’s three classic forms of inferential reasoning— deduction, induction, and abduction—defined by case, rule, and result. In this paper, I report on a subset of these findings by describing and comparing the reasoning of seven undergraduate students. I engaged each student in a statistical task that I designed to investigate their reasoning in a repeated sampling environment when given a population with an unknown parameter. Findings indicate that abductive reasoning was powerful in making inferences from sample data to the unknown population.
This study explores how linear algebra students reason with a novel coordinate system, the COSLA system. As part of a larger study, individual clinical interviews were conducted with three students, and their work was analyzed through the ReNaming and ReLocating framework (Author; 2023, 2024). Findings include various approaches in interpreting n-tuples and vector notations and different ways to reason about a displacement vector. The study also presents challenges students may face with non-Cartesian systems and suggests future implications for teaching change of basis.
We report on a qualitative case study of a college algebra student, Ava, who participated in a series of online task-based interviews involving graphs of different dynamic situations. Our analysis focused on the nature of Ava’s graph reasoning and coordinate system conceptions within and across these tasks. During Ava’s interviews, she primarily demonstrated Variation and Covariation graph reasoning while conceiving of the coordinate system quantitatively. Yet, she also had an expectation that her graphs would represent the motion of the objects in the dynamic situations or the motion of the traces in the graphs themselves. Ava’s Motion graph reasoning amid her quantitative conceptions of coordinate systems demonstrates overlap between quantitative and physical conceptions. Her case speaks to the richness of students’ conceptions of graphs; even when they conceive of quantitative coordinate systems, they can also expect a graph trace to resemble the motion of an object.
This study uses narrative inquiry to explore undergraduate students’ experiences learning mathematical proof and engaging with proof culture. Drawing on interviews and journey plots from five students at Hispanic-serving institutions, we constructed interpretive narratives to examine how their stories reinforced or resisted mathematical master narratives, such as mathematics being done in isolation or requiring innate ability. Students’ journeys revealed moments of joy and triumph, as well as loneliness and frustration. While elements of their stories reinforced master narratives—such as feeling isolated—others emphasized the effort required to develop proof skills, countering the narrative that mathematical ability is innate. Our findings highlight how learning environments and instructional practices influence students’ engagement with proof and their perceptions of who belongs in mathematics. By analyzing how students navigate proof culture, this work contributes to efforts to make mathematics more inclusive and to better understand the cultural narratives that impact students’ mathematical development.
We implemented a semester-long professional development workshop series, training Calculus I and II instructors to implement active learning and equitable teaching practices. The workshops actively engaged instructors in approximations of practice (Grossman et al., 2009) in which they learned to enact various teaching practices like designing tasks; eliciting, noticing, and responding to evidence of student thinking; orchestrating class discussions; fostering inclusive social norms; and equitably managing student participation. After they participated in the workshops, we interviewed the instructors about their decisions to implement the teaching practices from the approximations of practice in their teaching. We analyzed the instructors’ resources, orientations, and goals that informed their decision to enact those practices.
This study examines changes in self-regulated learning (SRL) skills among undergraduate Calculus I and II students, without explicit interventions. Using pre- and post-surveys aligned with Zimmerman’s SRL model, we identified both improvement and decline across items assessing various SRL practices. Calculus II students showed significant improvements in planning, self-control, and information management, which appear to be supported by student maturity, conceptual course content, and collaborative instruction. In contrast, Calculus I students exhibited a decline in performance-phase strategies, reflecting challenges from large lectures, formulaic content, and first-year adjustment. The researchers’ hypotheses on potential reasons for the observed results were corroborated by the course instructor and teaching assistants. However, more research is needed to understand these patterns and their underlying causes. Our findings suggest that while some SRL skills may develop naturally in more advanced contexts, first-year students may require targeted support to become more effective learners.
Proportional reasoning is a central concept for students to learn, yet they often struggle when solving proportionality-type problems. While prior work has examined students’ solution strategies, little attention has been given to the meanings of equivalence that support proportional and multiplicative reasoning. This study investigates how students reason about equivalence in measurement contexts with tasks adapted from Authors (year). Using task-based clinical interviews with four preservice secondary teachers, we analyzed responses to tasks involving relationships such as “1 lunar cycle = 28 days.” Focusing on one participant, we identified the use of two ways of reasoning about equivalence which proved productive for her. Findings highlight the critical role of descriptive reasoning for connecting quantities and magnitudes in proportional situations. We argue for expanding research on equivalence in measurement-based proportional contexts.
To study what shapes instructors’ use of student-centered active teaching methods, we examined multiple influences across the faculty career span, using survey data from over 600 mathematics faculty. We present a path model that incorporates factors from graduate teaching experience and job choice to professional development, departmental norms, and involvement in student- oriented scholarly and professional activities. We adapt Adelman’s concept of momentum to interpret results and highlight the role of early decision-making and professional environments that reinforce teaching-focused choices in shaping faculty teaching practices.
This study examines how institutions navigate praxeological uncertainty when implementing Modeling Life, a mathematical modeling curriculum for life sciences students. Using the Anthropological Theory of the Didactic, we analyzed implementation across five institutions where didactic transposition processes remain under active negotiation. We identify four interconnected patterns: positioning uncertainty, epistemological conflicts, human resource demands, and systematic adaptations. These findings illustrate how novel mathematical organizations whose requirements exceed existing institutional conditions both generate and are shaped by institutional adaptation processes during ongoing curricular development.
Undergraduate students’ views on proof provide insight into how they engage with mathematical practices, yet little is known about the values and goals they associate with proof. We surveyed 32 students at two Hispanic-Serving Institutions and identified themes related to values and goals of the proof community across three domains: the proof itself, the utility of proof, and the prover. Students’ perspectives often echoed mathematicians’ values such as rigor and explanatory power, but also emphasized less-documented dimensions, including creativity, problem solving, and educational aims. By highlighting both alignment and extension of disciplinary norms, these findings suggest ways to better support students’ participation in proof-based mathematics.
Mathematics graduate teaching assistants (MGTAs) are central to undergraduate instruction, yet their professional development (PD) is often limited. The Engaged Learning & Intentional Teaching Experiences PD program is a multi-institutional effort to strengthen MGTA PD around active learning, equity, and inclusion. To examine how such initiatives can be enacted and sustained, we studied departmental culture at two participating universities (Beta and Gamma) using Bolman and Deal’s (2017) Four Frames model, focusing on the structural and symbolic dimensions. Interviews with nine departmental leaders revealed five cross-cutting categories shaping MGTA involvement. Findings highlight how sustainable change requires alignment between structures (e.g., coordination, PD requirements) and symbols (e.g., values for equity and active learning). At Beta University, mathematics coordination structures reinforced symbolic commitments, embedding MGTAs in active learning reforms. At Gamma University, symbolic commitments appeared stronger but lacked structural reinforcement.
Developing reflective practitioners can lead to and sustain new practices in undergraduate mathematics. In this study, we used Cultural Historical Activity Theory (CHAT) to examine relationships between objects, tools, and outcomes from a Networked Improvement Community (NIC) seeking to critically transform introductory mathematics. By examining interviews and observer field notes, we found three pathways that connected NIC members’ individual and collective goals (objects), NIC activities and resources (tools), and NIC members’ perspectives on teaching and students (outcomes). We found that sometimes objects, mediated by tools, led to outcomes, but not always. Although the transformation that NIC members envisioned was not realized, the experience shaped their thinking about teaching and students in impactful ways such that “You can’t unring the bell.”
In the past decade, teacher professional development has gained popularity as a tool for preparing graduate student instructors. Research demonstrates the immediate positive impacts of this training for both the undergraduate students the graduate students teach and the graduate students’ own professional teacher identity development. However, much less is known about its long-term impact. For this study, we interviewed eleven former graduate student instructors who participated in such a training program and now have a position in higher education with teaching responsibilities. We leverage Lankveld et al.’s (2016) framework of psychological processes and contextual factors for teacher identity development to explore their sense of competence as mathematics educators as they transition into their new higher education contexts. Findings suggest that a sense of connectedness to new peers and past training experiences supports productive comparison and reflective practice that promotes identity growth in new academic environments.
Syllabi contain information about an instructor’s teaching and have been used as a measure of change in response to professional development. Syllabus scores have been linked to more widely used and resource intensive measures of change, including observations and surveys. We used the theory of planned behavior to examine the relationship between syllabus scores and self reported teaching practices and tested for changes in these measures in response to professional development. We found syllabi scores can approximate instructor teaching intentions, which seemed to manifest in their use of teaching practices. Instructor’s teaching intentions changed in response to PD, but their teaching practices did not. These findings are consistent with the theory of planned behavior, indicating that intentions change before behaviors, which supports the use of syllabi as a measure of change that can be economically deployed and detect nascent changes in teaching practices.
Students’ conceptions play a large role in how they learn math. When students experience challenges, or epistemological obstacles, they may struggle to adapt their ideas that previously served them well. Little research has been done regarding interactions between co-occurring epistemological obstacles. This report utilizes a proposed adjacency matrix methodology for analyzing the co-occurrence of epistemological obstacles. Our results show that students’ difficulty noticing hidden quantification had strong thematic connections to two other challenges: quantifying the negation and transforming logical implications into related forms.
As coursework extends beyond arithmetic, students encounter forms of equivalence beyond numerical equality. This study examines how college students characterize equivalence in mathematics generally, and specifically for equations and expressions. Responses from 198 students were analyzed and coded as numerical or non-numerical. Across questions, most responses appealed to numerical criteria, treating equivalence as equality to a single number, with higher prevalence of non-numerical criteria correlating with higher-level courses. We observed multiple variants of both numerical and non-numerical criteria, including converting algebraic expressions to numbers to justify equivalence. Findings highlight the need for educators to support students in distinguishing types of equivalence and their associated criteria.
Transformational reasoning is a powerful form of reasoning that can be leveraged during collaborative mathematical activity. However, little research has been done to investigate how transformational reasoning supports collaboration, if at all. Using Brown’s (2025) framework for identifying verbalized transformational reasoning and Staats’ (2021) poetic structure methodology, the present study sought to investigate how transformational reasoning supported students to collaborate. The results demonstrate that students spent the bulk of their time collaborating on a collective solution by warranting the operation(s) they envisioned transforming the objects.
Self-regulated learning (SRL) skills have been linked to academic success, particularly in developmental mathematics courses. This study investigates student SRL strategies in a developmental College Algebra course, taught using Inquiry-Based Learning (IBL) and supplemented with ALEKS. While SRL strategies have been investigated in a variety of contexts, research is lacking in IBL courses with ALEKS support. Data were collected from seventy-four students using open-ended surveys, which were used to answer the research question: What SRL strategies do students use in an IBL with ALEKS course? This was answered in three learning contexts: in-class, ALEKS time, and outside studying. Findings indicate that seeking social assistance and seeking information, especially from ALEKS were the most reported strategies, followed by note-taking and practicing problems. However, very few students reported using SRL strategies related to goal-setting and planning. This suggests that students may need more support in developing SRL strategies, such as through interventions.
This paper explores findings from a quasi-experimental study, focusing on implementation and impacts of an innovative corequisite mathematics intervention. Conducted in a large U.S. community college, the study is evaluating the impacts of a novel statistics corequisite course on student outcomes compared to the business-as-usual statistics corequisite course. Preliminary analyses show positive student outcomes in courses using the curriculum. Whether and to what extent key implementation fidelity factors likely drive those outcomes is investigated. These factors include use of a contextualized curriculum designed to be relevant to students, incorporating student collaboration in online and in person classes, and addressing the social-emotional and academic needs of students. Understanding the impact of these factors on student outcomes has implications for the design of corequisite mathematics coursework that supports students’ success. While not ready for the proposal, the final paper will also include whether the treatment impact varies by level of implementation.
This exploratory study examines the nature of students’ cognition during high demand mathematics tasks when an AI tool is available. Using video and screen recordings from 20 undergraduates, we analyze students’ cognitive demand on a task involving a nonroutine roller coaster application of domain and range. Our findings show wide variability in how students approach the task, how and how often they elected to use ChatGPT (half chose to use it, half did not), and the levels of cognitive demand that students exhibit in their solutions and thinking. Students that solve the task with high demand tend to grapple with its nonroutine aspects and challenge AI output, while students that solve with low demand give decontextualized prompts, struggle to use AI output, and/or trust AI despite hallucinations. We discuss implications that undergraduate mathematics researchers and educators might consider to preserve opportunities for students to experience high demand problem solving.
In this report, we seek to add to the literature about the use of computational tools and techniques to enrich student’s mathematical reasoning in combinatorics by contrasting novice and experienced programmers in their exploration of combinatorial tasks in the context of Python. Drawing upon Lockwood’s model of combinatorial thinking, we present data from interviews with students who were engaging with a set of modules in Python designed to help students solve counting problems. We contrast pairs of students who had different levels of prior experience with coding, and we highlight aspects of the experienced coders’ solution that reflects ways in which their experience with coding arose in their combinatorial solution.
Mathematics textbooks demand specialized forms of literacy, yet little research has examined how readers actually move through them. Drawing on the concepts of agency and didactical disciplinary literacy, this paper explores how readers allocate attention across textbook components and the reasons they give for doing so. We also propose an “attention continuum” in which shifting patterns of engagement represent agentive choices. These findings highlight how textbook reading intertwines literacy practices, disciplinary positioning, and agency, offering new insight into mathematics learning.
Research-based assessments (RBAs) are widely used to evaluate student learning in STEM, yet most provide only total scores. We illustrate the value of moving beyond overall performance by applying a cognitive diagnostic (CD) model to student responses on the Precalculus Concept Assessment (PCA) and the Calculus Concept Inventory (CCI). Using 1,366 pre/post responses collected through the LASSO platform, we modeled five key calculus skills: prerequisites, limits, derivatives, applications of derivatives, and introductory integration. Traditional analyses revealed small but statistically significant score increases (d = 0.09 for PCA; d = 0.26 for CCI). CD modeling also showed limited shifts in skill proficiency profiles: students who lacked prerequisite skills did not gain those skills. These results underscore how CDs provide finer-grained evidence than total scores and motivate the development of a Calculus Cognitive Diagnostic to support timely instructional interventions.
Through analysis of 7 mathematicians’ perspectives teaching proof-based linear algebra, we found that participants wanted to offer benefits to students during class which were analogous to the benefits documented in previous research that mathematicians have when attending and giving mathematics lectures at professional events (e.g., conferences, symposia, or workshops). Findings suggest that mathematicians may see attending mathematics lectures as an authentic mathematical practice in ways that education researchers have not previously attended to.
This study explores student-generated memes submitted as a part of a Calculus II homework assignment. Drawing on a twofold theoretical perspective that combines Bini et al.’s (2023) heuristic model for the creation of a mathematical meme and Bolman and Deal’s (2008) Four Frames framework of an organizational culture, we analyzed 32 memes and corresponding reflections. We found that via memes, students reflect on and communicate their struggles with Calculus and draw connections between Calculus concepts. Memes also became a vehicle for reflecting and shaping the classroom culture, offering students an opportunity to “laugh back” at the course authority. Together, these findings illustrate how memes can serve as reflective artifacts that capture both cognitive and socio-cultural dimensions of learning. We argue that meme-based assignments hold promise for fostering higher-order thinking, humanizing instruction, and promoting engagement in a challenging Calculus course.
In this study we examine how faculty members grade optimization problems from calculus. Eight faculty members were interviewed and asked to grade three student solutions for three different optimization problems. In addition, faculty members also discussed their grading philosophies and practices for both optimization problems and in general. We used open thematic analysis to analyze all faculty interviews and two major themes of reflection of understanding and key steps in optimization solutions emerged from the data. These themes that was supported by faculty were further analyzed for the interplay between them. In addition, we delve deeper into reflection of understanding using Skemp’s instrumental and relational understanding to establish when faculty assessed good student understanding of optimization problems. Our results provide insight into how mathematics faculty grade student solutions for optimization problems, how they emphasize student understanding, and offer possible insights into the variations in scores we observed in this study.
This study examines undergraduate student motivation in an inquiry-oriented linear algebra course using expectancy-value theory (EVT). While EVT has more frequently been applied in K–12 settings, its use in undergraduate mathematics remains limited. Through interviews with four students, this study explores how components of EVT—expectation for success, attainment value, intrinsic value, utility value, and cost—relate to students’ engagement. Findings show that the expectancy-value theory can be helpful in making sense of the motivations of undergraduate students. Students were motivated in different ways, with many citing their key influences as collaboration, real-world applications, and classroom expectations that promote a novel definition of success. Inquiry-oriented instruction appeared to support positive motivational outcomes by normalizing struggle and promoting group-based problem solving. This suggests EVT is a useful framework for understanding motivations in undergraduate mathematics, particularly in the context of inquiry-oriented instruction.
Research in combinatorics education highlights the importance of examining how students think about counting problems to gain deeper insight into their conceptualizations. Such an examination involves attending to students’ interpretations of counting problems, particularly the subjective elements that influence their combinatorial thinking. Subjective combinatorics has recently been introduced to account for these elements in how students interpret counting problems and engage in counting activity. This paper refines the construct and demonstrates its usefulness as a lens for analyzing students’ engagement with counting problems through an examination of student work on a set-partition task.
Spring 2020 marked the start of a national pandemic response teaching (PRT) period as colleges and universities responded to the public health emergency and associated upheavals and restrictions. Instructional practices and delivery modalities changed during this period, but there have been lingering questions about any lasting impact on pedagogy. In 2025, we conducted a national survey, following up with instructors of undergraduate chemistry, mathematics, and physics courses who had reported on their teaching in 2019, to explore this question. This paper focuses on questions about modality of instruction, distribution of class time between lecture and more active practices, and a set of other common instructional practices. In general, we find an aggregate return to pre-PRT practices, although there has been uptake of certain auxiliary digital practices (e.g., online office hours).
General theories of analogy dictate that connections can be made between virtually any two domains, thus suggesting an extremely large number of analogies that one might observe. Unsurprisingly, some analogies are of course more useful than others. How then do students come to observe “useful” analogies? Multi-constraint theory is one such avenue for exploring questions such as these. In this contributed report, I adopt a multi-constraint approach to parsing students’ analogical reasoning with the goal of uncovering how certain choices are made when developing ring-theoretic analogies to group-theoretic structures. Analysis revealed that the participants exhibited variations in emphasis of analogical constraints during their reasoning in three ways: (a) adhering to basic structure, (b) adhering to conceptual structure, and (c) flouting constraints to advance exploration. Implications for the teaching and learning of abstract algebra and curriculum development are discussed.
This study examined the role of students’ graphical, covariational, and proportional (GCP) reasoning skills in predicting performance in introductory STEM courses. Specifically, it investigates whether GCP proficiency predicts overall course performance. Data from 382 students revealed significant course-level differences, F(2, 379) = 10.27, p < .001. Students in Introductory Chemistry for Engineers scored highest (EMM = 59.0), significantly outperforming peers in Biology (EMM = 49.5) and Chemistry (EMM = 43.9). GCP scores were moderately correlated with course performance (r = .56). Mixed-effects modeling confirmed that GCP scores were a strong predictor of final performance (β = 0.025, p < .001), even when accounting for variation across majors. This study has implications for STEM instructors. Assessments should be designed to evaluate students' application of knowledge, problem-solving skills, and ability to formulate coherent arguments. This would give a more comprehensive picture of a student's academic potential that goes beyond memory recall.
In mathematics, the teaching and use of “tricks,” known formally as mathematical mnemonics, is commonplace. However, little research has focused on this topic, particularly in university mathematics tutoring. In this study, we investigated when and why undergraduate mathematics tutors implemented mathematical mnemonics in their tutoring practice. Video recordings of online tutoring sessions were collected from eight tutors working at an R1 university in the United States. Of the eight, five were observed using mathematical mnemonics in their tutoring practice. Our results show that these tutors used mathematical mnemonics for three reasons: in response to a student committing an error or demonstrating a misconception, as a response that represents how the tutor reasons about the topic, and as part of a predeveloped curriculum script. We argue that each of these reasons is an implicit attempt by the tutor to reshape a student’s concept image of the topic under consideration.
This study investigates how a first-year undergraduate mathematics student engaged with a set of digital interactive figures to explore properties of stochastic matrices and Markov chains. Using the frameworks of instrumental genesis and Vergnaud’s theory of conceptual fields, we analyzed the student’s interaction in terms of their observations and conjectures, two key stages in our Observation, Conjecture, Proof, Theorem (OCPT) pedagogical model. Through task- based interview data, we identified elements of the student’s emerging conjecturing scheme, including rules-of-action and theorems-in-action that illustrate their process of sensemaking and experimentation. We argue that this scheme development evidences the student’s instrumentation of the figures into a functional instrument for mathematical reasoning.
The topic of topology is an important and unique course in advanced mathematics that carries two simultaneous complexities: logical proof and spatial reasoning. While proof and problem-solving are two areas that are well documented in mathematics education research, topology itself is a fairly rare topic to appear in the literature of mathematics education written in English. To address the gap in the literature, this paper analyzes a study in which two students attempt a topology question in order to understand their problem-solving techniques and how they leverage their various forms of thinking. We networked the theories of Tall’s Three Worlds of Mathematical Thinking and Cognitive Blending to describe the participants’ behaviors. The results showed that students leveraged a blend of their thinking to progress through the proof.
The purpose of this report is to identify specific content topics and assessment or reassessment behaviors to classify students’ performance in a College Algebra course using alternative grading. Our data consist of students’ individual standard mastery marks, reassessment frequency, standards reassessed, and final letter grades (which were primarily based on the number of standards mastered in the course). Our analysis involved constructing logistic models and a random forest to identify predictor variables that reduced the Akaike Information Criterion (AIC) and the mean Gini Index. Our results describe two content standards and reassessment behaviors whose attributes were central to our classification models, which can inform the instruction or revision of traditional- and alternative grading-based College Algebra courses.
In the developmental mathematics education literature, course failure typically leads only to attrition from the course sequence. That is, an overlooked, and not well-understood, experience in developmental mathematics, is course repetition. In this quantitative study, I aimed to investigate the incidence and impact of developmental mathematics course repetition. Specifically, I aimed to document how experiences with course repetition contributed to students’ course taking patterns within and beyond developmental mathematics. Findings indicate that the consequences of experiences with developmental mathematics course repetition are significant and far reaching, influencing longer-term academic outcomes including program retention and degree attainment. The need for further investigation, particularly using qualitative methods to understand how and why observed relationships in a student’s mathematics/academic trajectory operate and function, is well supported by the quantitative results of this study.
We made a short sequence of interactive tasks in which a student must estimate the total amount of water in a pool, given the water rate (gals/min) at a handful of moments. Through working on these tasks in a small teaching experiment, an undergraduate who had not seen calculus learned to conceptualize the area under a linearly increasing water rate graph as representing the total accumulated volume of water. From this we developed a learning trajectory, highlighting requisite and developing concepts, actions, and teacher-researcher interactions that were key to his learning. His learning trajectory, which entailed imagery of lower and upper Riemann sums, reveals ways to learn key calculus concepts while maintaining the relationship between rate and amount quantities as a central, rather than an easily jettisoned, part of students’ understanding of ‘area under a curve’.
The success of any educational change requires the support of instructors, and at the introductory undergraduate mathematics level, up to 30% of those courses are taught by graduate teaching assistants (GTAs). Research has shown the prevalence and importance of covariational reasoning at the precalculus/calculus level, and this study examines how GTAs interpret and respond to students’ attempts at graphing via covariational reasoning. Through engaging in a version of Carlson et al.’s (2002) Bottle Problem, and then watching and responding to two precalculus students’ video responses to the problem, 11 GTAs had the opportunity to express their teacher decision making around student thinking. I analyzed their responses using Herbst et al.’s (2023) categories of perception teachers use when considering framed student contributions: normativity, serviceability, and responsiveness. The results indicate that GTAs primarily focus on (non)-serviceable and (non)-normative aspects of students’ work. I detail these results and discuss implications for GTA training.
Students in a college algebra course completed reflective metacognition journal assignments about their studying and performance in the course. This paper is a thematic analysis of the qualitative data collected from those journal assignments and surveys about the effects of the journal assignments on their studying and performance in the course. We investigate how the journal assignments affected the study strategies they used in college algebra and what students learned about themselves as learners through these reflective assignments. Findings indicate that metacognition journals were effective in supporting students in reflecting and changing their study habits. Qualitative analysis is used to describe students’ reflection and changes to study habits after engaging with journals embedded in a mathematics course.
This study investigates students’ mathematical reasoning when determining the period of the sum of two cosine functions through exploratory teaching interviews. Two undergraduate students engaged with Desmos applets to explore the sum of two cosine functions. The analysis revealed output-oriented reasoning that focuses on identifying input values where function output repeats, and alignment-oriented reasoning that focuses on where the period of the sum function aligns with the periods of individual trigonometric functions to determine the period of a sum of two trigonometric functions.
Mathematics and mathematics education are implicated in broader societal inequities. These inequities can manifest in racialized and gendered classroom experiences and are perpetuated by the very practices students are encouraged to employ. While some scholarship in undergraduate mathematics describes possibilities for using mathematics toward social justice, this area has been largely limited to algebra, statistics and calculus, leaving proof unexplored despite its critical role within K-16 mathematics. The aim of this study was to develop an instructional theory for how students can productively discuss and debate sociopolitical issues through practicing competencies from proof-based mathematics. I report data from the first cycle of a constructivist teaching experiment with two undergraduates designed to help them use logic to support their sensemaking about prisons and abolition. Ultimately, students’ successful activity attending to definitions and identifying assumptions in a geometric context supported their ability to identify commonplace assumptions about prisons.
Given ever-declining numbers of undergraduate students choosing to major in mathematics, research in undergraduate mathematics education seeking to understand the motivations and perceptions of math majors is more important than ever before. Of particular interest in this report are community college mathematics majors-they make up a significant proportion of math majors in any given year and yet research on recruitment and retention in STEM fields that has been done has been nearly exclusively conducted with students at four-year colleges. We report findings from in-depth interviews with eight community college math majors regarding their motivations to major in mathematics. We then examine the ways in which such motivations interact with institutional and departmental structures traditionally noted to influence persistence in STEM majors. Implications are discussed for improving math major retention and advancing the field’s understanding of the influence of collegiate context on perceptions of mathematical culture.
Students seeking careers in STEM will increasingly be required to develop proficiency with computational tools. As such, many students will be at least incentivized, if not required, to learn to program early on in their undergraduate careers. We hypothesize that, though many opportunities exist in which students can learn programming skills, providing undergraduate students with opportunities to program in the context of mathematics courses will be advantageous for students. We report on interviews conducted with students as they learned to program in the MATLAB language, undergraduate mathematics problems. We discuss how a student’s mathematical knowledge mediated his programming practices.
Mathematics graduate teaching assistants (MGTAs) often teach or support undergraduate courses and can have a significant impact on learners’ experiences in mathematics. However, professional development (PD) programs rarely provide MGTAs with supportive, extended opportunities to learn about, enact, reflect on, and grow in evidence-based teaching practices. We designed a multi-year PD program for MGTAs focused on engaging students in mathematics and enacting equity-focused practices. We analyzed multiple sources of data to investigate shifts in MGTAs’ teaching practices using principles of the PD. Applying the Theory of Planned Behavior, we describe the growth of two participating MGTAs. Both participants set and sustained intentions, modified their behaviors to align with their intentions to support engaging group work and empower women, respectively, and experienced positive shifts in their attitude and perceived behavioral control. Key implications include the importance of opportunities for MGTAs to reflect on their intentions and teaching practices in long-term PD.
As part of a project developing and researching the use of team-worthy lessons in discrete mathematics in two- and four-year colleges, we conducted a study of three instructors and their 105 students. Classroom observations indicated that the use of team-worthy lessons changed the structure of classroom activity from primarily didactic lecture to at least 75% student-centered activity (e.g., group work, student presentation). However, a change in observed structure is only evidence of an affordance, not of students’ experience of it or how it might have been productive for students. After each team-worthy lesson, students completed surveys about what went well (and not). Analysis of student responses used a framework based on social learning theory. Here we present results about students’ self-reported experiences in terms of agency, authority, creativity, and self-efficacy.
The experiences of multilingual women in U.S. mathematics Ph.D. programs are shaped by intersections of language, race, gender, and nationality. This narrative inquiry examines the identity formation of three women from Korea, Colombia, and Mexico, employing a combined framework of intersectionality and Phenomenological Variant of Ecological Systems Theory (PVEST). Findings identify three distinct pathways: the carryover of prior gendered invalidation, leading to impostor syndrome despite high commitment; context-dependent coping across bilingual ecologies; and the consolidation of an advocacy identity in a more protective environment. Theoretically, the study extends PVEST to Asian and Latin populations and clarifies a dual-function coping mechanism where strategies can be both adaptive and costly. Findings call for strengthening protective factors and identity-inclusive instructional designs in mathematics education to support this growing student population.
In this contributed report, we share results from a study focused on the verbal communication acts of four undergraduate mathematics instructors while they are setting up group tasks. All four instructors teach at the same large eastern university and are experienced with active learning instructional practices. We found that two of the four instructors engaged in numerous verbal communication acts that assigned rights and duties to themselves as instructors and to their students. The other two instructors assigned only a few rights and duties to themselves or to students. We describe patterns in instructors’ assignment of rights and duties, as well as how instructors' verbal communication acts shaped the classroom learning environment. Finally, we suggest how verbal communication acts focused on assigning rights and duties may relate to opportunities to learn, and propose considerations for supporting students’ participation in group work in active learning undergraduate mathematics classrooms.
How do undergraduate students with reading difficulties engage in mathematics – a symbolically dense, text-heavy subject? This study analyzes reflections from seven undergraduate STEM students with dyslexia on their approaches to mathematical learning and problem-solving. Our findings indicate that students experienced multiple dyslexia-related cognitive challenges, including processing, organizing, and manipulating conceptual information. To combat these challenges, students reported strategies to structure information visually and minimize the cognitive burden of the tasks. These results offer an initial account of how students with dyslexia approach and experience undergraduate mathematics.
This study examines gender-inclusive practices within a graduate chapter of the Association for Women in Mathematics (AWM). Using an ethnographic approach, I explore how AWM navigated their inclusive practices. Results revealed that inclusion was viewed as both a logistical necessity and a strategic move toward equity, fostering community building and identifying male allies. Additionally, tensions such as maintaining women-centered spaces and replicating gendered labor divisions also arose. AWM’s efforts reflect both an aspirational reimagining of gender dynamics and the persistent realities of societal gender inequities. These findings contribute to understanding how gender-inclusive social structures can both challenge and reproduce dominant gender norms.
The objective of a counting problem is to determine the cardinality of a set of outcomes, but there is never a singular, unique way to conceive of those outcomes. I report on data of combinatorics experts solving a counting problem whose numerical solution is 2^6, a standard expression to see in combinatorics, but whose set of outcomes is not standard. I demonstrate four distinct models that the participants used to conceive of the outcomes, and how each of those led to different ways of explaining the solution. I argue that these differences among experts reflect the challenging nature of articulating what the set of outcomes for a counting problem is, and how to approach a solution using this set. These data may inform how counting could be presented to learners when adopting a wide view on the multiple possible sets of outcomes for any given problem.
Using a mixed methods approach, we investigate students’ facility using Taylor series expansions in the context of the electric dipole. Eight students participated in one-on-one teaching-learning interviews, during which audio and video data were recorded while they completed a written activity. We show that while physics students at this level are very familiar with the procedural aspects of Taylor series expansions, they may not recognize several common cues to use them to simplify functions. We find that sketching out the exact function and an approximation of it can help students learn to associate these common cues with Taylor series. In addition, we probe students’ conceptions of the meaning of the expansion point and find that one difficulty in choosing an expansion point in a physics context is associating that ‘point’ with a spatial location. We conclude with recommendations for physics and calculus instructors.
In this sequential explanatory mixed methods study, I examined Black and Latina female students’ sense of belonging in gateway mathematics at a diverse, open-access minority-serving institution. Using frameworks of intersectionality, sense of belonging, and authorizing student perspectives, I explored how students’ identities shaped their experiences in college algebra and precalculus. I surveyed 1,136 students (pre-survey) and 639 students (post-survey) using an adapted Math Sense of Belonging Scale and analyzed data using ANOVA and ANCOVA. Results showed that mathematics affinity and expected grades were stronger predictors of belonging than race or gender. From the qualitative data, I identified six positive and six negative factors influencing belonging, including professors’ mathematical microaffirmations and microaggressions, perception of caring faculty, peer collaboration, peer connections, mathematics self-efficacy, and perceptions of class diversity. These findings highlight the importance of caring faculty, collaborative learning, and peer support in fostering belonging in racially diverse mathematics classrooms.
This phenomenological case study examines evidence of undergraduate students’ metacognitive reasoning while completing proof construction tasks. Two pairs of undergraduate mathematics majors participated in task-based video recorded interviews where they were presented with contextual scenarios and asked to prove or disprove a related mathematical statement using think-aloud protocols. Participants then took part in stimulated recall interviews where they were shown video clips from their task completion and asked to reflect on their thought processes. This contributed report explores each student’s access of metacognitive knowledge and the subsequent actions they took during these proof tasks.
In this theoretical report, we present a conceptual framework that details inservice teachers’ emergent utility perspectives towards advanced mathematics and their advanced mathematics coursework. We leverage a river journey metaphor to help illustrate aspects of our conceptual framework. Along the river are utility points that refer to opportunities for teachers to reflect on the usefulness and relevance of advanced mathematics content in relation to its impact on their teaching. Then, we provide examples of both preservice and inservice teachers from extant literature and an initial study conducted in a real analysis course to highlight the four main components of the conceptual framework. We end with implications for designers aligned with the instructional design theory of Realistic Mathematics Education for creating courses for secondary mathematics teachers.
Researchers studying derivative conceptions often use Zandieh’s (2000) framework, which emphasizes graphical, symbolic, verbal, and physical representations within three process-object layers of ratio, limit, and function. While foundational and aligned with traditional calculus instruction, recent literature on derivative teaching reveals additional conceptions. I present the Conceptions of Derivative (CoD) framework, which expands Zandieh’s work to offer a more comprehensive perspective on contextual and cognitive processes when thinking about derivatives. The framework provides researchers with a comprehensive lens, while offering instructors awareness and language for intentional targeting of derivative conceptions based on their students’ conceptual needs.
Research in math education calls upon “love” more and more, but rarely with careful theoretical development. Hence we offer a theory of “critical love” here, drawing upon pedagogy scholarship, activist writing, and queer theory. Critical love calls us beyond a superficiality of knowing in our minds to a deeper knowing in our beings and actions. We elucidate the theory by identifying its essential components, organized along four horizontal frames: change, power, connection, and practice. We conclude with implications of critical love as an orientation in mathematics classrooms, teacher professional development, and pedagogy research.
We examine how 2 approaches to coordinating quantitative meanings for rates, proportional relationships, and variation can support reasoning about 2 aspects essential for instantaneous rates of change and derivatives. First, rates are single measures and, second, rates of change remain approximately constant as changes in 2 variables tend to 0. The first approach––based on coordinating unit rates, multiple batches, and chunky variation––has dominated research on rates. The second approach––based on coordinating measurement rates, variable parts, and smooth variation––has been largely overlooked. We argue that approaching instantaneous rates of change and derivatives through unit rates is inherently tied to chunky covariational reasoning and that approaching these same topics through measurement rates fits well with smooth covariational reasoning and should be investigated in future empirical research.
Research on students’ and teachers’ quantitative reasoning continues to underscore its importance for their learning and development. This importance requires that researchers continue to make strides in identifying salient and important ways of reasoning quantitatively. In this paper, we delineate four forms of quantitative reasoning to characterize both students’ images of situations and their graphing meanings related to those images. Specifically, we differentiate between students conceiving quantities’ changes via states reasoning, transformational reasoning, and gross or quantified covariational reasoning. We connect these forms of reasoning to their meanings for graphs when attempting to represent those quantities.
Introductory college mathematics courses remain significant barriers to persistence in STEM, especially for students from historically marginalized backgrounds. While recent reforms have emphasized pedagogical changes, relatively little attention has been paid to the social and emotional dynamics of these classrooms. Drawing on work from K-12 education, we argue that relational dimensions of teaching, such as care and cultural responsiveness, are essential for supporting equitable student success in undergraduate mathematics. This paper introduces a conceptual framework for understanding caring relations in college mathematics instruction, using insights from research on warm demander pedagogy and sociocultural theories of learning. The framework centers on the instructor’s dual role in challenging students intellectually while supporting them relationally. We offer this as a tool to guide research and professional development, aiming to expand how we define and study effective instruction in ways that humanize and affirm all students.
With the rising popularity of generative artificial intelligence, particularly large language models (LLMs), it is imperative to understand how students are leveraging these rapidly evolving tools in their learning. Although researchers have begun to address issues of academic integrity, acceptance, and adoption, few conceptual frameworks exist for analyzing how students interact with LLMs in the context of mathematics problem solving. This paper introduces the MATH-AI framework, a synthesis of theories on metacognition, student agency, trust in automation, and human processing and regulation to examine how AI mediates math problem solving and potentially reconfigures the learning process. A case study of two students is provided to demonstrate the framework’s application and illustrate distinct patterns of trust, processing, and self-regulation during AI-mediated mathematics problem solving. These cases highlight the potential risks and opportunities associated with LLM use and provide a foundation for future empirical studies and development of subject-specific AI guidelines.
In this theoretical paper, we build on prior frameworks on teacher knowledge and affect to propose a holistic framework for the competencies required for teaching modeling—a framework that integrates teacher competencies from both the cognitive and affective domains. We illustrate elements of the framework through the case of one secondary teacher’s work from a modeling-focused professional development program. Finally, we describe implications of our framework for researchers and educational stakeholders.
We draw on poststructuralism to interrogate assumptions of what counts as “normal” in proof. Guided by post-qualitative inquiry, we share moments from an unstructured interview with an undergraduate student, Sherine, alongside research literature to question two dominant proof norms: depersonalization and the absence of the problem-solving process. Our interrogations reveal how proof norms potentially reinforce messages that exclude relationality, storytelling, and emotional connection from the proof process, as well as newcomers to proof who benefit from seeing the nonlinear process of problem-solving. We argue for broadening what gets recognized as legitimate proof, where proofs can be both formal and personal, polished and messy, logical and human.
Work in first-year calculus has clearly shown the power that “differentials” afford for first-year calculus learning, but it also speaks of the need to build ideas of limits. While some researchers have loosely described informal differentials and limits within the same paradigm, their actual conceptual definitions and relationships have not always been explicitly constructed. Continued progress in this area could benefit from theoretical consideration of: (a) providing clearer intuitive definitions for differentials inside a limits-based approach to calculus, and (b) defining more exactly the relationships between differentials and limits. We provide here a theoretical framework for building a simultaneous differentials-and-limits approach to first-year calculus.
This theoretical report integrates insights from various lines of research to posit an argument that early logic instruction for proof-based mathematics should use set-based conditions for the truth of conditional statements rather than the widely used truth table definition. We claim the truth table definition poses unnecessary barriers for students, in part because it does not adequately express mathematical practice. In contrast, the set-based meaning seems highly productive and may better support students in reasoning about conditionals as objects, which our experiments suggest is a highly propitious development for learners
Evidence-based instructional practices (EBIPs) are widely recognized as effective, yet their use in undergraduate mathematics remains sparse. While prior work has explained why faculty adopt EBIPs, less attention has been given to what happens after that decision – namely, how instructors implement these practices, why they use some approaches over others, and what shapes their persistence. In this theoretical report, I review literature on individual and contextual factors influencing EBIP use and identify limitations in existing models of instructional decision-making. I then propose a revised model that integrates Lattuca and Pollard’s (2016) framework with Schoenfeld’s (2010) resources-orientations-goals (ROG) theory. The model emphasizes the context-dependent nature of mathematics faculty’s EBIP use and centers implementation as the site where persistence is shaped. Using data from one case study, I illustrate how the model can trace the full cycle of EBIP engagement from adoption, to enactment, to the experiences that influence continued use.
Mathematics is frequently presented as a universal and objective discipline. Yet these claims of universality are culturally framed by whiteness and limit the possibilities for relational and ethics-driven approaches to mathematics that align with Indigenous knowledge systems. This theoretical report synthesizes insights from Indigenous perspectives, anticolonial theory, and critical mathematics education to critically examine the colonial underpinnings of mathematics. Leveraging these insights, we present a three dimensional framework for anticolonial praxis addressing axiology, epistemology, and ontology, and seed an illustrative curricular possibility. We conclude with a call to action, urging instructors and researchers to negotiate the complexities of actualizing anticolonial praxis in institutions governed by colonial traditions.
Active learning has become a widely cited cornerstone of undergraduate education reform; yet the construct remains conceptually ambiguous, leading to challenges in research synthesis, instructional implementation, and policy alignment. This paper synthesizes literature across mathematics and STEM education to trace this ambiguity to the conflation of three distinct but interconnected facets: dimensions of engagement, strategies for implementation, and outcomes of learning. To address this gap, I propose a theoretical framework that disentangles and defines these facets, providing analytic clarity for both researchers and practitioners. By situating this framework within ontological, epistemological, and axiological perspectives, the paper illuminates how differing research traditions conceptualize, investigate, and value active learning. This reframing enables systemic inquiry into how strategies activate specific engagement dimensions to produce desired outcomes in diverse contexts, informing instructional design. The framework thus offers researchers, practitioners, and policymakers a roadmap for advancing both scholarship and meaningful reform in undergraduate mathematics education.
In this theoretical report, we argue that unit transformation graphs are an appropriate and useful tool for modeling students’ solutions to transformation geometry problems. Developed by mathematics education researchers working from a Piagetian theoretical perspective, unit transformation graphs explicate the mental actions that students use in solving problems, along with the objects (or units) on which they are acting. This theoretical report contributes to an understanding of how unit transformation graphs can be extended, beyond their current use, to model student reasoning in a new mathematical domain. We illustrate the potential efficacy of unit transformations in modeling students’ solutions to transformation geometry problems with two researcher-generated solutions to a transformation geometry problem, and we call for future empirical research to model students’ solutions to transformation problems with UTGs.
This paper uses a conceptual analysis of histories of algebra to identify a kind of reasoning, combinatorial reasoning, that was essential to the solution of polynomial equations. Historically, mathematicians increased reliance on combinatorial reasoning in the solution of polynomial equations co-occurred with the rise of symbolic algebra. Algebraic symbols were often the context in, and on, which they engaged in combinatorial reasoning. Combinatorial reasoning, however, is often in the background of proofs or arguments—present but not framed as an essential kind of reasoning that could be developed to understand the proofs or arguments. The purpose of foregrounding this reasoning in this paper is to argue that it can serve as a conceptual foundation for designing coherent algebra curricula across grades 9-16—curricula that allow students and teachers to see deeper connections between school and abstract algebra.
In this theoretical report, we argue for a need to extend the theoretical boundaries of Mathematical Knowledge for Teaching (MKT) beyond its historical applications. Our motivation is the longstanding concern regarding the ability of Calculus as a service course to effectively scaffold non-math-major students’ ways of knowing mathematics to support them in transitioning to their primary discipline, particularly in Engineering. We extend the theoretical boundaries of MKT to encompass the knowledge needed to connect Calculus to its ways of use within Engineering in a way that is perceptible and comprehensible to students. Finally, we distinguish this form of MKT from existing work in MKT, and we demonstrate its utility in advancing our understanding of the knowledge required to improving Calculus instruction.
Supporting students’ collaborative work requires more than simply placing them in groups; instructors must actively shape participation and discourse through scaffolding. Group scaffolding refers to the set of instructional strategies that help students coordinate, distribute responsibility, and build shared understanding in groups. Despite its relevance for undergraduate active learning environments, existing theories have tended to isolate central elements, including teacher guidance of student reasoning, discourse moves shaping participation, and classroom norms structuring collaboration. In this paper, we analyze episodes of instruction by mathematics graduate teaching assistants (MGTAs) to motivate a unified theory of group scaffolding. Our framework integrates four interdependent dimensions: (a) norms setting, (b) task and material design, (c) discourse moves, and (d) access distribution. We argue that this theory both advances research on collaborative learning in undergraduate mathematics and informs professional development efforts that prepare instructors to foster more equitable and effective group work.
Mathematical structure refers to the characteristics, topology, and relationships within and between mathematical concepts invariant to external contexts and interpretations which instantiate the concept. Research on mathematical structure is typically guided by the post-positivist and interpretivist research paradigms, which respectively emphasize the impact of human observations and interpretations on mathematical concepts, both of which are external to the intrinsic structure of mathematical concepts. This report proposes a shift to complexity theory, a research paradigm standard to modern physics and engineering which emphasizes physically necessary mathematical principles over observation and interpretation, to faithfully study structure intrinsic to mathematics itself. I propose the Tornado Theory as a theoretical framework emerging from the tenets of complexity theory and current mathematics education literature which could guide future research on mathematical structure. Finally, potential analytical techniques for the Tornado Theory based on network- and information-theoretic principles are introduced.
Participation in undergraduate mathematics courses is viewed as an important metric for assessing student learning and motivation, especially in active learning classrooms. However, engagement has been understood through a narrow lens, which overlooks the way students—especially students of color—engage with mathematics courses and positions them as disengaged. In this theoretical report, we introduce the idea of culturally meaningful participation in undergraduate mathematics to capture the organic ways that students of color draw upon cultural resources to create spaces for engagement in or with their mathematics courses. We draw upon Yosso’s Community Cultural Wealth Framework and the notion of Ong’s STEM counterspace to support our theorizing. We argue that CME recognizes the assets that students bring to support their engagement with mathematics and also illuminates how these assets are drawn upon. We argue that CME has the potential to support broader anti-deficit efforts in undergraduate mathematics education.
Although students’ epistemological frameworks have been extensively studied in introductory undergraduate courses and lecture-based advanced mathematics courses, there has been less work on students’ epistemological frameworks in advanced student-centered courses. The purpose of this case study is to examine the beliefs held about mathematics learning of nine students in a flipped real analysis course using Schommer et al.’s (1992) mathematical epistemological framework as a theoretical perspective. The findings suggest that while there were minimal differences in beliefs when grouping students by major or final course grade; overall, the typical participant’s epistemological framework was grounded in effort, a desire for understanding, and belief that there must be at least some reliance on their instructor and peers to provide instruction and support their learning in the course.
Graphs are essential across STEM fields, yet students often lack opportunities to develop graphing competencies. One challenge is that the ways graphs are used vary across disciplines. This study develops a framework for characterizing graphs in undergraduate STEM contexts by examining features such as coordinate systems, reference frames, and the objects of interpretation. Preliminary analyses of STEM resources highlight differences—such as spatial versus quantitative coordinate systems—and similarities that can inform cross-disciplinary instruction. Our goal is to support more coherent approaches to graphing instruction, preparing students to interpret and construct graphs in ways that align with disciplinary practices.
Although research on persistence and attrition in the undergraduate mathematics major remains limited, existing studies point to structural, curricular, and identity-related barriers that shape student trajectories. This autoethnographic study extends that conversation by exploring the lived experience of a first-generation, low-income undergraduate math major in the United States, using digital journaling to explore persistence, barriers, and systems of support. Guided by Tinto’s theory of student departure, the study highlights the impacts of financial uncertainty, faculty interactions, and institutional and social demands on students’ academic integration, sense of belonging, and self-image as a mathematician. Persistence emerges as an act of resistance. This study contributes to the literature on equity in undergraduate mathematics education by highlighting the complex interaction between identity and institutional structures. In doing so, the study offers insights for the creation of inclusive advising and pathways that support the success of students from disadvantaged backgrounds in mathematics.
This study used a survey containing two open-ended questions and a ranked choice question. I investigated undergraduate students’ mathematical convictions relating to whether they experienced a lack of conviction. Students were asked about their proclivities when an instructor presents a proof to the class. Preliminary findings show that few students experienced a lack of conviction with either theorems or proofs. For theorems, a lack of understanding was often cited. For proofs, students cited doubts about the rigor of those proof types such as picture proofs. Students’ proclivities seemed to show that their focus was on understanding a proof’s content. Further evidence provided by follow-up interviews corroborated this interpretation and that students may in fact reflect on matters of conviction in mathematical settings.
Double integration is challenging for many students. It involves the interrelationship between three variables x, y, z within an object in 3D space expressed in both algebraic and graphical representations. When the integral domain is not a rectangular region, values of x and y along its boundaries may become dependent. However, how students perceive interdependency of variables and what mental actions are involved in double integration have not been fully explored. To answer these questions, multivariational reasoning framework is used in this study to analyze students’ cognitive activities. Interview data collected from a university-level calculus enrichment course is analyzed to explore student’s reasoning. The findings suggest that students demonstrate several mental actions of multivariational reasoning when performing double integration over different regions. They also suggest some possible directions of extending the theoretical framework of multivariational reasoning to adapt some specific concepts such as range and change of variables in double integration.
One equity-oriented Networked Improvement Community (NIC) aimed to interrogate their use of “rigor” and its potential ramifications for the undergraduate mathematics program. In this preliminary report, we use critical discourse analysis on journal and interview data from this NIC to uncover how overloaded the word “rigor” is in mathematical spaces. These preliminary results reveal that rigor is conflated with difficulty, deep understanding, and other notions associated with teaching and learning mathematics. Findings suggest that there is a need to clarify and agree upon what we mean when we say “rigor” within our mathematical circles. We end with discussion and implications for practice.
In this preliminary study, we examine the beliefs of graduate teaching assistants and investigate how seemingly identity-neutral beliefs may reinforce deficit narratives in precalculus and calculus courses. Drawing on the Attributions of Mathematical Excellence (Jacobson et al., 2022), we report the analysis of one participant’s attributional beliefs and how they may explicitly and subtly reify deficit discourses. Our findings underscore the need for critical conversations about instructor beliefs regarding success and struggle in undergraduate pre/calculus. We recommend training programs provide graduate teaching assistants the opportunity to engage in reflective dialogue to identify opportunities to disrupt harmful narratives in undergraduate mathematics education.
Kinematics graphs offer potential for developing relationships between derivates and antiderivatives, but students experience challenges with recognizing the meaning of the area under a velocity graph as change in position. We designed a series of playful math tasks offering structured exploration, in which students worked in virtual environments to develop relationships between speed, time, and distance in tabular and graphical formats. Preliminary analysis suggests that students can use rate reasoning to develop accumulated distance under constant velocity graphs, which then can be developed under linear graphs via Riemann sums.
Embedded tutor (ET) programs have increased significantly in recent years to respond to new state requirements to phase out remedial math courses and increased need for tutoring support brought about by the COVID-19 pandemic. Despite this increase, ETs have remained understudied. ETs can face limitations in the classroom when instructors are underprepared to integrate ETs into their lessons. In particular, instructors can be unaware of the physical limitations ETs encounter in their practice, which can prevent them from delivering needed support to students. To better understand how ETs develop their practice this study uses the construct of teacher noticing to analyze interviews with an ET as they reflect on video recordings of their instruction. Findings demonstrate how an ET identified and addressed classroom features that limited their access to students. This study presents implications for faculty to ensure the presence of a collaborative work relationship between ETs, Instructors, and faculty.
Equivalence is a central concept of mathematics and is a fixture in the K-16 curriculum. Though equivalence has been very well-studied overall, very little is known about how students reason with formal equivalence relations in advanced mathematics. Recent research has demonstrated that one component of productive reasoning about equivalence relations entails the ability to flexibly move between viewing equivalence from both an elementwise (local) perspective and a set-oriented (global) perspective. Building on this work, we report on a pilot study intended to aid the development of a conceptual analysis of equivalence in advanced mathematics - in which we seek to refine the notion of a global perspective on equivalence. In this preliminary report, by showcasing excerpts from task-based clinical interviews with two advanced mathematics students, we propose ‘indifference’ as a beneficial way of reasoning about equivalence from a global perspective.
This preliminary research report examines how undergraduate elementary preservice teachers (PSTs) reason about area and volume measurements prior to receiving instruction in mathematics content course in algebra, geometry, and measurement topics. This is a pilot study for a larger project. The preliminary analysis results from the pre-assessment data of 27 PSTs indicate that they lack productive reasoning about area measurements and their conversions, and they also employ direct linear dimensions conversion strategies on the volume task. This highlights the need for instructional unit to focus explicitly on developing PSTs’ productive reasoning about area and volume measurements.
In this preliminary report, we present results of examining the collaborative process used by teams of students, teachers, authors, and researchers to develop novel interactive questions for free, open calculus and linear algebra textbooks. Of concern is student agency as both a temporally-based social process and an ecological phenomenon as collaborators understand and construct the role of student. Discursive practices of the collaborators contributed to student positioning. In some cases, this resulted in an absence of student voice in the development of content, while in others, student agency yielded meaningful pedagogical changes in the development of questions.
Mathematical writing is often portrayed as objective and authorless, yet prior work shows that mathematicians’ writing contains nonobjective and authority-related features (Burton & Morgan, 2000). We build on this foundation by analyzing 51,325 single-authored mathematics papers from arXiv, focusing on proofs and surrounding narratives. Using curated dictionaries of hedges and evaluative adjectives and mathematics-specific rules, we document their frequency and explore whether gender and publishing output of the author relate to their use. Preliminary results indicate that both features appear to vary with author characteristics. These findings suggest that linguistic choices in mathematics are tied to identity and status, complicating the myth of purely objective discourse.
The student perspective provides valuable information into what students find to be difficult when reading proof. Such information can be used to productively support students as they face these difficulties. In this preliminary report, we investigate what students report as contributing factors of how difficult a proof is to understand. For this report, we focus on data regarding two proofs from the introduction to proof setting. Our findings indicate that the density and width of a proof are key contributors towards the difficulty rating given to the proofs.
In the spring of 2025, introductory Physics, Calculus, and Chemistry instructors were surveyed about their usage of active learning techniques and use of Research Based Instructional Strategies. Using open-source large language models running on consumer hardware, responses to open ended survey items data were analyzed to better understand the usage of specific strategies during and after the Pandemic Response Teaching period resulting from the COVID-19 pandemic, as well as for reasons how and why instructors adopted, maintained, or stopped RBIS. While the large language models were able to apply qualitative codes to the data, their effectiveness was significantly varied based on the dataset, initial prompt, large language model used, code specificity, and code prevalence.
This study investigates how marginalized students experienced affirmation of their mathematical identities in first-year calculus. Thematic analysis revealed thirteen forms of identity affirmation, clustered into internal (understanding and utility) and external (peer instruction, community, instructor recognition) categories. While understanding and utility were universally affirming, most affirmations were socially mediated. Findings highlight the critical role of community and instructional practices in shaping identity, suggesting that affirming environments are essential for supporting persistence in STEM.
Understanding departmental teaching culture has been recognized as a useful starting point for implementing instructional and institutional change. However, there is a lack of consistency in the literature with respect to how teaching culture is operationally defined and systematically measured. In order to begin addressing this gap, we highlight findings from a series of focus groups conducted within a math department in the Southeastern United States. Utilizing Reinholz and Apkarian’s (2018) Four Frames model, we characterize the department’s culture through the four interrelated frames of structures, symbols, people, and power. These frames provide a snapshot of the unique math departmental teaching culture, which can be leveraged not only to assess the effectiveness of future change initiatives, but also to individualize such change initiatives to meet the unique needs of the department.
Integrals can be conceptualized with an infinitesimal or limit definition, and holding a certain conceptualization may change how someone frames and solves an integral problem. We present excerpts from two different interview studies where we asked second-semester calculus-based intro physics students integral questions. Student utterances and differing answers to these selected questions led us to define two conceptual resources concerning infinitesimals, which correspond to the different definitions of integration. This work highlights subtle differences in students’ interpretation of integration and areas for future study
Preliminary findings from a study exploring student understanding of vector products are presented. We discuss multiple-choice and free-response data from 118 students who completed four dot product magnitude tasks across two semesters of introductory physics instruction. Each semester had a physics-free dot product along with a physics context relevant to the content of each course (mechanical work and electric flux). Performance ranged from 28% to 59% and students do not always answer consistently between pairs of tasks. Coding of explanations revealed four main computational strategies used by students along with two more conceptual reasoning categories. The most common strategy was students using a trigonometric definition of the dot product with varied results depending on the context.
We present a preliminary report on community college students’ perspectives of classroom environments in college algebra. Drawing on nine student interviews from four states, we developed and calibrated a coding framework of 34 codes organized into nine categories. Our analysis highlights three broad dimensions of classroom experience: individual factors, relational dynamics, and structural or contextual elements. Students emphasized the role of supportive and responsive instruction, including instructors who re-explained concepts, offered second chances, and adapted to diverse learning needs. They also described participation structures that shaped collaboration with peers, as well as classroom climates that encouraged or at times discouraged active engagement. Beyond their current experiences, students voiced aspirations for more inclusive and collaborative practices. These early findings provide insight into how community college students experience college algebra and point toward future directions for exploring diversity, equity, and inclusion in mathematics classrooms.
This report describes a preliminary investigation into how multivariate calculus students understand trigonometric functions. Trigonometric functions are an essential component of understanding single-variable calculus which in turn is generalized into multivariable calculus. Therefore, an understanding of trigonometry is not only expected but an important component for success in multivariable calculus courses. Replicating a Weber (2005) study investigating trigonometry students’ understanding of trigonometric functions, we surveyed multivariate calculus students to see how they understand trigonometric functions. Similarly, we leveraged the idea of procepts (Gray & Tall, 1994) to aid in interpreting students’ descriptions of trigonometric concepts and properties.
The limit is a key calculus concept, but research has clearly shown how important differential-based reasoning is, as well. Thus, calculus education would benefit from paradigms that construct both in a way that they can coherently co-exist. In this preliminary report, we discuss a small piece of a larger project meant to build one possible paradigm. Here, we describe a single quantities-based task that is meant to develop both limits and differentials together, in the same activity. We also provide preliminary results on two pairs of students’ emerging understanding.
We examine the presence of calculus concepts and skills in the portions of a standard textbook that are generally covered in the second and third courses of a typical introductory calculus-based physics course. Using the Calculus Concept Framework (Sofronas 2011) three researchers independently coded calculus concepts and skills in eighteen chapters of a calculus-based physics textbook covering electricity and magnetism, geometrical and physical optics, and modern physics. Along with prior work on the first twelve chapters covering mechanics, this analysis suggests that the calculus content is uneven and not well aligned with prerequisites.
Creating and bringing a sheet of notes to a math exam can help students perform better and feel less anxious, but not all note sheets are equally helpful. This study explores how undergraduate students prepare and use exam note sheets in an intermediate algebra course. We surveyed 119 students about how they created and used their exam note sheet and how they perceived the usefulness of their sheet. We also collected students’ note sheets and exam scores. Preliminary analyses revealed that most students spent less than two hours preparing their note sheet. Most students felt the note sheet helped them study for and perform well on the exam and lessened their anxiety. Forthcoming analysis will explore relationships between students’ exam performance and features and use of their sheet. Findings can be used to develop guidance for students on how to more effectively prepare and use exam note sheets.
This proposal reports on the impact of a course designed to prepare first-year students for success in Precalculus. The course, Approaches to College Mathematics (ACM), was developed as a prerequisite course in response to one university’s high failure rate in Precalculus. In addition to a carefully designed yet flexible curriculum that aims to have students explore familiar topics in fresh ways, the course focuses on growth objectives meant to help students transition to their first semester as a college student. Institutional data and survey data from both students and instructors were collected. Preliminary results show that the overall failure rate in Precalculus decreased the semester after ACM was implemented. Additionally, a high percentage of students in ACM reported feeling that ACM was the right placement for them. Finally, ACM grades and the ACM instructors’ sense of their students’ mathematical confidence significantly predicted grades in Precalculus.
Providers of teaching-focused professional development (TPD) for novice college mathematics instructors (e.g. graduate students) are a critical part of undergraduate education. A challenge remains in capturing and communicating the work done by Providers, including program-level efforts to changes local TPD. Doing so would allow other departments to “scale across” and adapt their own local TPD productively. This preliminary study used a four frames of change model (people, power, symbols, structure) with two dimensions (process and product) to document 10 mathematics TPD program change journeys. Inductive and thematic coding of survey responses and interviews allowed researchers to identify interactions between key change elements. Preliminary findings illustrate certain interactions (e.g. people and power) were more prevalent in successful TPD change efforts than others. The findings provide a means for understanding changes at the appropriate granularity for trans-local use by other departments.
The shift to proof-based mathematics in university programs often takes place in an introduction to proof (ITP) course. Literature exists describing the nature of these courses and some of the difficulties students experience in the course, but we know little about students’ goal, beliefs, and conceptions of proof at the beginning of an ITP course (David & Zazkis, 2020; Bleiler-Baxter & Pair, 2017). Seven students were interviewed during the first two weeks of their ITP course. These same students are participating in a longitudinal study examining how ITP students’ goals, beliefs, and engagement patterns evolve during an ITP course. Students were uniformly capable of providing a description of proof compatible with those commonly used in ITP courses, though students’ ability to construct proof was varied. Students could identify components of proof writing that were different from other writing (e.g. the use of the word “or”). Students’ goal orientations were seen to be malleable at the beginning of the semester, with most students adopting a learning goal orientation (Dweck & Leggett, 1988).
This analytic autoethnography preliminary report examines how early-career mathematics teacher educators (MTEs) make decisions about if and how to use generative AI (GenAI) in alignment with their values. Using reflective journals and group discussions, with Value-Sensitive Design, our analysis highlights three themes in GenAI use: preserving autonomy and creativity, protecting human elements of our job while viewing GenAI as a supplemental tool, and managing institutional pressures. This work highlights values-based perspectives informing the broader understanding of MTE GenAI decision making.
Learning to construct and critique proofs is central to advanced mathematics but challenging for students and. This paper reports on an NSF-funded project to build HaLLMos, an AI model that helps students learn to write mathematical proofs. HaLLMos uses a constitutional approach along with expert-guided feedback to generate responses to students’ proof efforts. Guided by Schoenfeld’s Goals–Orientations–Resources framework and perspectives on proof as discourse, we are investigating the tool’s alignment with constitutional principles, as well as student and faculty perespectives on HaLLMos’ value. Preliminary data from interviews and system logs suggest that HaLLMos supports students’ independence while also preparing them to participate in mathematical conversations. Findings suggest HaLLMos can expand resources for students and faculty while raising new questions about how AI generated feedback can support students’ mathematical interactions and ultimately their sense of belonging in mathematics.
The concept of difference, and its representation as distance within a graphical representation pervades Calculus. Indeed, difference expressions represent change, the very foundation of the subject. Yet, students may often default to a takeaway conception of subtraction, which may be incompatible with viewing subtraction as finding change. Other ways of conceiving of subtraction may support additional ideas in Calculus, related to translating functions, finding areas and volumes, or indexing terms of a sequence. In this preliminary report, we investigate the prevalence of various conceptions of subtraction in the study of Calculus through a textbook analysis of Stewart’s Calculus: Early Transcendentals. We report our findings from our analysis and future directions for research.
In mathematics classrooms, equity has been researched, defined, and reported by those who have the ability and authority (professional organizations, instructors, state and federal educational agencies, local administrators, universities, and teaching faculty). However, the students who are susceptible to these definitions have not been asked for their perspectives of what equity would look like or what would remove the inequities they experience in their mathematics classes. Our goal is to center community college students’ experiences with and definitions of equity as they reflect on their mathematics’ learning journey, significant moments that shaped their engagement in mathematics, how they thought about equity, and whether and how they had experienced equity or inequities specifically in College Algebra. We found that participants’ understandings and definitions of equity varied significantly, as did their experiences in mathematics classes. Additionally, we found that participants situated their understanding of equity in features of their identities.
We present results from a pilot study conducted to inform possible directions for further investigation focused on a specific community of practice: an informal summer mathematics program for mathematically talented students. While the program is attended by high school students, they take undergraduate level proof-based courses and engage in research at a level comparable to a research experience for undergraduates. Journals and interviews were used to investigate aspects of the program using Wenger's Communities of Practice theoretical framework, which describes social characteristics of a community of practice in terms of mutual engagement, joint enterprise, and shared repertoire. Suggestions for feedback from the reader and audience are included.
We present a preliminary local instructional theory of students’ embodied guided reinvention of the bijectivity theorem of invertible functions. We leveraged the design principles of Realistic Mathematics Education (Freudenthal, 1991) and Embodied Design (Abrahamson et al., 2020). We present our task sequence, describe implementation in a classroom, and provide an analysis of student reasoning. We discuss our plans for reimplementation and implications for teaching.
Large language models (LLMs) such as ChatGPT are increasingly used in higher education, raising questions about how they influence student learning. While unstructured use often leads to shallow engagement, carefully designed AI tutors may foster deeper reasoning. This study examines student engagement with an AI tutor in a multivariable calculus course, drawing on the ICAP framework. The focal task asked students to use dot products and vector reasoning to estimate storm velocity from radar data. Preliminary results suggest that while the AI tutor frequently posed prompts aligned with constructive engagement, student responses were most often active, reflecting a “completionist” approach to problem solving. Constructive reasoning was difficult to sustain, and tutor follow-up was sometimes limited. These findings highlight both the promise and the complexity of designing AI tutors to elicit and maintain constructive mathematical engagement.
We report on an extension of previous findings from a project aimed at improving equitable group work in the context of undergraduate proof-based courses through designing and implementing group-worthy tasks. This quantitative method study reports on three group-worthy tasks implemented in two topology courses. We investigated how student interactions in small groups reflect participatory equity when relating to perceived academic status along with differences in participation patterns between the two classes. Results are indicative of the tasks having the effect of balancing talk turns regardless of status, disrupting status hierarchy, or neither; similar to what has been reported previously. These findings suggest that implementation of group-worthy tasks is not sufficient to ensure equitable participation in small groups and that normalized groupwork has no impact on the effectiveness of the utilized tasks.
Spatial reasoning and cognitive demand are both critical for mathematical learning, yet they are rarely examined together. This study analyzes 178 tasks from the graph theory chapter of Discrete Mathematics: An Open Introduction to explore how these dimensions present themselves and how they interact. Most tasks were of high cognitive demand and required spatial reasoning, especially spatial relations and visualization. Notably, spatial reasoning did not consistently appear as cognitive demand increased in tasks. These findings suggest that while spatial reasoning is crucial for success in discrete math, selecting high-level tasks alone is insufficient to foster it. Instead, these findings point to the need for careful task selection, pre-college preparation, and in-class scaffolding to equip students with the spatial skills necessary for success in discrete mathematics and beyond.
This study presents a task-based content analysis of homework problems from a year-long, calculus-based physics sequence designed for life science students. Using a codebook created by adapting ideas from the Calculus Content Framework (CCF), we coded each homework task for the types of mathematical reasoning required, including derivatives, integrals, manipulating algebraic expressions, geometric reasoning, arithmetic calculation, and graph interpretation. Across the year, we found that manipulating algebraic expressions, arithmetic calculation, and geometric concepts appeared more frequently than calculus procedures such as derivatives or integrals. These findings align with prior work suggesting that algebraic skills and modeling are more central than calculus topics like derivatives or integrals in many physics tasks. As a preliminary study, this work invites feedback on how to build toward broader analyses, such as alignment with modeling-first calculus courses, with the long-term goal of better supporting students in navigating mathematics across disciplinary boundaries.
For decades, women have consistently earned fewer than 30% of PhDs in mathematics in the United States each year. Advancement through a doctoral mathematics program can be viewed as a process of integration into the communities of practice within the department, and a student’s persistence (or attrition) is influenced by experiences that enhance or inhibit their participation in the activities of each community. In this preliminary report, I discuss the experiences of six women in a doctoral program and their participation in the coursework, research, and graduate teaching communities of practice in their departments. In contrast to past studies that propose that these communities of practice are mutually exclusive, my participants’ accounts illustrate some overlap between them.
Students pursuing science, technology, engineering, and mathematics (STEM) degrees require some proficiency in Calculus. The Fundamental Theorem of Calculus is arguably the most important theorem taught in a Calculus I course, yet it is not covered until the last weeks of the semester in a traditional three-part Calculus sequence. As a result, students tend not to hold deep conceptual understandings around integration, and the conceptions that they do hold are procedurally based. This paper illustrates the disconnection between student conceptions around integration (primarily area-based) and the general emphasis (from mathematics education literature) on accumulation. In addition, our work highlights how course learning objectives may drive a primarily area-based interpretation of integration. Our preliminary findings from interview data with Calculus III students confirm prior research, suggesting that students hold strong procedural and area-based conceptions, rather than accumulation conceptions.
We present a preliminary linguistic analysis of how proofs are organized. In particular, we performed a Theme analysis—an analysis from systemic functional linguistics (SFL) that identifies the starting points of messages at the level of independent clauses—on proofs from undergraduate textbooks. Theme analysis is one of the ways in which SFL studies the textual metafunction, that is, how texts are organized to relate to their context. Our preliminary results show that the main marked (i.e., unusual) Theme constructions in our dataset are: (a) beginning clauses with Adjuncts, and (b) beginning clause complexes with dependent clauses. Further, we found that textual elements (e.g., thus, so, since, if) were common as part of multiple Theme constructions.
Abstract Algebra is often cited as being a difficult course for undergraduate students because it is more abstract than computationally based courses such as Calculus. But what does it mean for something to be “abstract”? I conducted a grounded theory analysis of student survey data from an Introduction to Abstract Algebra course to explore how students define abstraction. The data show that students’ personal definitions of abstraction go beyond conceptions of abstraction discussed in the literature, and the concept of abstraction acts as a mathematical artifact that influences the way students view abstract algebra concepts. Preliminary analysis also suggest that students’ definitions of abstraction differed depending on their major area of study, indicating that abstraction is a boundary object whose definitions and uses vary depending on context.
Noticing is the first step to reflective teaching. Mathematics graduate teachers (MGTs) used ‘brief-but-vivid’ classroom accounts to reflect on teaching, documenting weekly moments and discussing them in facilitated groups. Two major themes emerged: (1) Collaborative Learning and Shared Reflection, where peer interaction fostered camaraderie, accountability, and co-construction of professional knowledge; and (2) Capturing Fleeting Moments, emphasizing subtle classroom dynamics, student behavior, and practical strategies. Participants focused more on pedagogy than content, highlighting early instructors’ priorities. Findings demonstrate that socially mediated reflection shapes teaching identity, informs instructional decisions, and links individual noticing to collective learning, with implications for designing more effective teaching professional development.
This poster provides an overview of an in-progress yearlong multiple case study that explores the quantitative literacy practices of a group of undergraduates at Trinity University.
Near-peer mentors (NPMs) — undergraduate students who support peers’ learning in STEM classrooms — have been shown to improve student success, retention, and engagement. However, less is known about how these mentors enact such impacts within the classroom. This ongoing study investigates NPM practices in lower-division mathematics courses at a mid-sized public university, focusing on the positions, acts, and storylines that shape NPM-student interactions. Data sources include classroom observations, student and NPM focus groups, and course success metrics in two developmental mathematics courses. Positioning theory provides a lens to analyze the dynamics of classroom interactions, while Bloom’s taxonomy categorizes the cognitive levels of NPM questioning and facilitation. Findings will contribute to a deeper understanding of how peer mentorship structures shape learning environments and inform the design and training of NPM programs in introductory mathematics.
The rapid integration of artificial intelligence (AI) into higher education has introduced new opportunities and challenges for student learning. This study, conducted at Timberline University (TU) during the Fall 2025 semester, examines how AI tools influence metacognition, study habits, and academic performance. Using a mixed-methods design, the research analyzes quantitative and qualitative data from student surveys, focus groups, and instructor feedback to identify patterns of AI use and their relationship to learning behaviors. The study explores how students engage with AI in ways that affect reasoning, persistence, and self-regulation. In particular, it investigates how AI supports or shapes metacognitive processes, including students’ ability to plan, monitor, and evaluate their own learning strategies, recognize gaps in understanding, and adjust approaches to problem-solving. Additionally, the study examines the impact of AI on study habits, such as time management, task prioritization, note-taking strategies, and the development of consistent, effective practice routines. By highlighting the interplay between AI use, metacognition, and study habits, findings aim to clarify how AI supports or hinders the development of key cognitive and academic skills, and to provide insights into how AI can be effectively integrated to promote self-directed learning, reflective thinking, and long-term academic success.
Students’ intuitive reasonings of the limit of a function at a point play a role in their overall conceptual understanding of the limit concept. Some researchers have defined intuitive limit views as students’ understanding of the limit concept based on their everyday experiences (e.g., Adiredja, 2014; Adiredja et al., 2020; Rathnayake & Jayakody, 2023). In this study, I characterize limit views that are based primarily on reasonings with less emphasis on mathematizing those ideas as intuitive. Research shows that intuitive views are closely linked to students' graphical reasoning (Adamoah & Strayer, 2025). Building on the findings of Adamoah and Strayer (2025), this study explored how students’ intuitive understandings of limits are connected with graphical representations. The results of this study highlight an instructional approach to help overcome what past research identified as students’ misconceptions about the difference between limit as x→a of f(x) and f(a) (Bezuidenhout, 2001; Denbel, 2014; Fernández, 2004). Specifically, I addressed the research question: How do students’ intuitive limit views influence their reasoning with and use of graphical representations in calculus? In this study, I found that students’ intuitive limit views were linked with the graphical representational approach in two ways: (1) viewing limits with graphical representation as an object and (2) viewing limits with graphical representation as a tool. Graphical representation as an object implies students’ belief that “it shows me” and graphical representation as a tool implies students’ belief that “I’m using it to show”. Below was Jake’s explanation of how the graph with removable discontinuity showed and helped him to distinguish limit as x→2 of f(x) and f(2). The results of this study offer calculus instructors ways to integrate and effectively use graphical representations either as an object or as a tool to help deepen students’ understanding of limits in general.
Recent research shows that inquiry-oriented (IO) instruction can reproduce existing hierarchies, privileging dominant voices and marginalizing others. Our project explores what IO instruction can feel like when it creates a more affirming space, especially for students from historically excluded groups. Using poetic transcription, we share the experience of the first author, a trans undergraduate student, in an IO Calculus 2 course. The poem offers a hopeful story, illustrating how IO instruction can nurture belonging and joy in mathematics.
In this poster, we outline an analytic perspective for understanding students' development of practice-linked identities (Nasir, 2011) as a construct to study undergraduate students' personal connections to contextual practices in mathematics classrooms. This analytic perspective captures clarified criteria for researchers to consider. In the poster presentation, we will offer examples and non-examples from our data with Calculus I undergraduate students.
In this poster proposal we ask the question "what do mathematicians view as their role in instruction and what do the view as the students responsibility?" We present the preliminary analysis from our data and share our future study directions.
This project explores the impact of undergraduate-led mathematics workshops designed to engage middle school students in problem-solving and mathematical reasoning. The initiative brings together faculty mentors and STEM undergraduates to develop and teach sessions based on topics from the American Mathematics Competition (AMC). The study examines how participation in these workshops enhances undergraduates’ skills in communication, leadership, and research, while also assessing the learning outcomes of middle school participants through pre- and post-assessments. By positioning undergraduates as instructors and researchers, the program promotes a deeper understanding of mathematics, strengthens teaching and research competencies, and fosters community engagement in STEM education. This model offers a scalable framework for integrating outreach, experiential learning, and research in undergraduate mathematics education.
To address growing concerns in teacher preparedness and competence, researchers have shifted from Mathematical Knowledge for Teaching (MKT) (Ball et al., 2008) to Statistical Knowledge for Teaching (SKT) (Groth, 2013), since statistics requires its own specialized skillset. As such, there is a need to consider frameworks that utilize statistics specific knowledge when addressing teacher capabilities in a statistics unit or classroom. Studies have supported that pedagogical content knowledge for statistics, combined with subject matter knowledge is associated with student learning outcomes (Callingham et al., 2016). The main research question is: How can we observe SKT in real time in mathematics classrooms? Answering this question can explore the specific practices teachers employ during instruction. These practices differentiate the knowledge needed to teach mathematics from those needed to teach statistics. The goal of the project would be to develop an observational protocol embedded with an SKT theory to help teachers improve their teaching of statistics. One way to do this may be to observe how teachers operate in a routine day to see how they transition through various practices, and then assess their degree of attainment of various skills.
Preservice elementary school teachers tend to struggle with having a conceptual understanding of strategies of multiplication and division. Thereby, finding it difficult to effectively explain those strategies to their students. This activity explored various strategies of multiplication and division through worked-out examples using an inquiry-based approach. The strategies for multiplication include modeling with base 10 blocks, area or box method, partial products, lattice method and the traditional method. The strategies for division include modeling with base 10 blocks, box method, repeated subtraction (or partial quotients), grid method and the traditional method. The worked-out examples include writing prompts to encourage self-explanation on step-by-step approach of how to use a particular strategy. Using this method, students worked in pairs to identify patterns and review step-by-step procedures of solved mathematical problems in the classroom. After reviewing worked-out examples, students were able to solve problems using the alternative strategies effectively and efficiently. Implementing the use of worked-out examples and inquiry-based approach provided students with a powerful step-by-step detailed explanation of how problems were solved.
This study examined students’ mathematics self-efficacy (MSE, students’ beliefs about their ability to successfully do mathematics) in collegiate calculus using a semi-structured interview and examining both global and local MSE. Results show students did report that calculus affected their MSE, with half reporting their MSE was lower for calculus than for previous mathematics courses though four students also reported higher MSE. Participants reported reasons for changes to their MSE included difficulty of the exams, pace of the courses, and differences in teaching style. For local MSE, participants were generally confident on the problems, reporting the highest confidence in finding a procedural derivative using the product rule and the lowest confidence on using the first derivative test. Results have implications for our knowledge of MSE, a relatively stable belief that can still change under certain conditions (Bandura, 1997; Byars-Winston, et al., 2017; Friedel et al., 2010).
The emergence of quantitative reasoning—conceiving situations in terms of measurable attributes and relationships between those attributes (Carlson et al., 2002; Karagöz Akar et al., 2022; Thompson, 2011; Thompson & Carlson, 2017)—as critical for K-16 students’ mathematical development has generated a need for exploring its role in preparing future teachers. Also related to supporting K-16 students’ mathematical development is the act of decentering, which involves a teacher putting aside their own ways of thinking for the purpose of discerning and building a model of their students’ thinking (Baş-Ader & Carlson, 2022; Carlson et al., 2022; Ellis, 2022; Hackenberg et al., 2024; Silverman & Thompson, 2008; Teuscher et al., 2016). Notably, researchers have recently illustrated an important link between teachers’ decentering and quantitative reasoning capacities (Tallman & Frank, 2020; Tallman et al., 2024). In this poster, we explore secondary mathematic pre-service teachers’ (PSTs’) decentering actions and their quantitative reasoning. Specifically, we draw on clinical interview data to illustrate relationships between the PSTs’ enacted meanings and the ways in which they appraise secondary students’ solutions and reasoning.
When higher education rapidly shifted online in 2020, STEM instructors encountered fundamental challenges including academic integrity concerns, inequitable access to technology, insufficient training, unclear communication, and emotional strain. This poster draws on open-ended responses from 934 chemistry, mathematics, and physics instructors to investigate the pandemic-era challenges they described and the capacities they believed were lacking. Guided by resilience theory (Holling, 1973; Norris et al., 2008), we view these reflections not as a record of crisis, but as insight into what is required for instructional readiness. Resilience in this context is more than the ability to move courses online quickly; it is the extent to which this transition does not compromise academic integrity, dismantle professional communities, widen inequity, or encroach on learning. Preliminary analysis reveals recurring challenges related to technology, assessment, communication, equity, and isolation. These reflections can inform a framework for crisis-readiness in STEM departments.
This study examines how Open Educational Resources (OER) and interactive technologies influence learning in an undergraduate mathematics content course for elementary education majors. Using the Scholarship of Teaching and Learning (SoTL) framework, it investigates whether H5P and GeoGebra–based modules enhance engagement, motivation, and self-directed learning compared to a traditional publisher’s homework platform. Fifteen weekly modules were embedded in the university Learning Management System, and student outcomes were evaluated through final exams and surveys measuring perceptions of learning, feedback, and pacing. While exam performance showed no statistically significant differences, students reported higher engagement, appreciated the ability to work at their own pace, and valued immediate feedback. Qualitative feedback emphasized greater motivation and enjoyment in completing assignments. This study demonstrates how SoTL-guided research can systematically evaluate teaching innovations and highlights the potential of OER and interactive technologies to improve learning experiences across undergraduate mathematics courses.
Since 2003, the Mathematical Association of America’s (MAA’s) National Research Experience for Undergraduates Program (NREUP) has provided opportunities for racially minoritized students to collaborate with faculty in the mathematical sciences on summer research projects at a diverse range of institutions. Through a rigorous and accessible research experience, NREUP’s goals are to increase undergraduate degree completion rates and ignite students’ interest in obtaining graduate degrees and embarking upon careers in the mathematical sciences. In this poster presentation, we will share results of our evaluative study aimed at understanding the nature of former participants’ experiences in and the impact of the program. We conducted individual interviews with 18 randomly selected former students who participated in various NREUPs during the summers of 2019-2024. Results indicate gains in knowledge about the research process, the benefits of having formal and informal mentors to learn more about discipline-based opportunities, and the advantages of collaborating with undergraduate and graduate student peers. Students also praised the structure of the program and expressed that it led to increased confidence as emerging scholars within the mathematical sciences. Given this, we highlight potential avenues for future RUME work that consider different programmatic structures and mentoring approaches associated with NREUPs. In all, our study extends prior work regarding undergraduate research experiences by following up with participants from racially minoritized groups who participated in NREUPs.
Problems are an important component of mathematics education. Exploring the language used within problems allows us to investigate typical ways we pose mathematical problems – that might help us infer what information is (and is not) conveyed by the specific verb stem (e.g., imperative) used in a problem. Building on a conceptualization of two common mathematical problem types, SOLVE and EVALUATE (Author(s), 2025), this poster reports findings from a K-16 textbook analysis that aimed to identify linguistic features associated with each type of problem. Results include a list of specific verb stems associated with each problem type, as well as verb stems that may have been either. Other linguistic features, such as two-verb structures or plurality, may also differentiate the two. These results inform various ways we might clarify the nature of a mathematical problem by choices around the language we choose to use in posing it.
Academic disciplinary conferences are critical sites of professional and intellectual development, yet motivations for attending—and barriers to participation—remain under-researched. This study investigates how members of the undergraduate mathematics education research community perceive the SIGMAA on RUME Annual Conference, focusing on intellectual and social dimensions of belonging. A survey distributed at the 2025 conference and via the RUME listserv collected 165 responses about participants’ backgrounds, initial and current reasons for attending, and barriers to participation. The most frequently selected “most important” reasons for attending were being part of a warm, welcoming community (41%), feeling the conference is an intellectual home (38%), and networking (34%). Ninety-one respondents reported at least one barrier, most commonly lack of belonging, financial constraints, topic relevance, imposter syndrome, and workload conflicts. Results highlight SIGMAA-RUME’s role as both intellectual and social community, and the ways in which these aspects can present barriers to participation.
This study investigated growth mindset as a bridge between teacher cognition and student experience in mathematics. A descriptive correlational research design was used for this study. The sample size included seven teachers and 181 first year students from the mathematics education unit. Implicit Theory of Intelligence Scale; Student Opinion Scale and General Self-Efficacy Scale were used to collect data. The collected data were analyzed using descriptive statistics and regression analysis. The findings of the study showed a Mean of 3.73 and SD of 1.04 were obtained, thus indicating that the majority of the teachers leaned towards the growth mindset belief. The result of the regression analysis revealed that teachers' belief accounted for some variations in students' growth mindset, motivation and confidence. Students are therefore encouraged to seek out faculty with growth mindset attributes as they are more inclined to creating a supportive learning environment.
Addressing the needs of freshmen who fail college Precalculus or its placement exam, Institution State University (ISU) began offering an Approaches to College Mathematics (ACM) course in Fall 2024. ACM lessons are designed to engage and support students while attending to their struggles with mathematics. One common struggle is interpreting graphs. Responding to research on benefits of integrated STEM lessons and surveys showing that many ACM students are prospective biology majors, the ACM team designed an integrated math/biology lesson where students analyze graphs from ISU’s introductory biology text. In this paper we report on the first iteration of our design experiment on this lesson and analyze student work for evidence of integrated reasoning and static or emergent shape thinking (Moore & Thompson, 2015). We describe features of students’ engagement with the lesson and reasoning about these graphs. We discuss how differences between math and biology textbook graphs highlight students’ struggles.
Change can be transformative when it aligns with a department’s cultural norms and faculty’s shared vision. Informed by the literature on sustainable change, the Foundational Course Transformation Academy (FCTA), a team-based initiative from (Institution) Learning in collaboration with the Department of Mathematics, is redesigning the Calculus I course to create learning environments that are better for students and instructors. In phase 1, the FCTA team established community norms, reviewed literature, and developed a shared, value-based vision. After aligning their proposals with the literature, stakeholder feedback, and institutional data, they crafted several transformational goals. In phase 2, the team is applying the backward design framework to define course competencies and learning outcomes, and to develop instructional material that reflects those goals. The final phase will focus on implementation, assessment, and sustainability. By attending this poster, participants will gain insight into our change process and effective, sustainable redesign strategies.
This study investigated how eleven first-generation STEM students enacted their assets to persist through their calculus journey. Using Yosso’s (2005) community cultural wealth framework as a basis, this study expands on such framework to explain the process on how assets are enacted during calculus. Through interpretative phenomenological analysis, findings from participants’ interviews show certain content challenges within the course but also assets that stem from family or aspirations to support their persistence. These initial findings give insights on how to view students’ calculus journey as a multidimensional process that centers on their assets rather than viewing their experience in a situated academic setting.
University students who choose STEM majors often do not complete their degrees in STEM. This study examines how attending peer tutoring for mathematics courses impacts STEM retention. We employed an explanatory sequential mixed methods design. Our first quantitative phase examined the statistical correlation between tutoring visits and STEM persistence. These results informed the second qualitative phase which consisted of interviews with seven STEM majors who attended tutoring. We found a statistically significant positive correlation between tutoring visits and persistence, and that the odds of persisting in STEM increases by 10.92% for each additional visit to the MLSC per math course. All seven of the interviewees reported positive experiences in their math courses and several mentioned the impact of the social aspect of the tutoring center.
Many large research universities offer calculus in a large lecture format, supplemented by recitations. Merit recitations, which offer extended time, smaller class size, and trained graduate student facilitators, were offered as an alternative to undergraduate students enrolling in Calculus I. This qualitative study explores students' decision to enroll in Merit, their learning experiences, and mathematics self-efficacy. We used Bandura's sources of information to code end-of-semester focus groups with Merit students in order to create personas of students choosing to enroll in a Merit calculus recitation. Personas can illustrate user's motivations and needs, providing insight into aspects of the student experience for recitation designers. We created two personas and discuss their similarities and differences in terms of mathematical self-efficacy, parental influences, and aspects of the classroom environment that facilitated their ability to ask for and receive help.
We explore mathematicians’ views on intuitive knowledge specific to the teaching and learning of abstract algebra. More specifically, we narrow in on the views of seven mathematicians as they discussed what the word intuitive means, what abstract algebra concepts they find intuitive or not intuitive for themselves and learners, and how those concepts became intuitive for them. Our findings highlight (a) the criteria mathematicians used to determine if a concept was intuitive or not, and (b) the varied approaches that they took to develop an intuitive feel for some of the most difficult abstract algebra concepts. These findings contribute to the fields’ understanding of intuitive knowledge as we compile defining criteria for “intuitive” and undocumented methods used to develop an intuitive feel for abstract algebra concepts. We also provide future directions for research.
This study investigates the potential developmental nature of Thompson and Carlson’s (2017) levels of covariational reasoning. Through task-based clinical interviews with Calculus I students, we explore how engagement with non-normative graphing tasks can promote the development of students’ covariational reasoning. Findings reveal that some students experience perturbations when interpreting their self-constructed graphs. We focus on characterizing one students' mathematical activity as she consistently worked to revise her perturbations which ultimately led to her accommodating her graphing scheme through four distinct phases. We take this as preliminary evidence there might be a developmental progression among the levels of covariational reasoning and that students' work interpreting their self-constructed graphs can might be a mechanism for the development of covariational reasoning.
In this poster presentation, we share how one prospective secondary mathematics teacher designed a task that centered a local socio-ecological issue. In a secondary mathematics methods course, students were asked to engage in an activity called "Mathematizing Your World", in which they explore their local environment and reflect on the mathematics around them. This poster presents how one student's background knowledge about a local invasive species led them to design a lesson on proportional reasoning rooted in their local environment.
Mathematics Education researchers aim to collectively explore a multitude of phenomena related to the teaching and learning of mathematics and disseminate the products of their research to those who might be positioned to leverage its insights to improve students’ learning. The research reported in this paper addresses the need to understand how and for what purpose college mathematics faculty and instructors apply insights from this literature. I applied a survey and clinical interview design to explore the perspectives and considerations of instructors regarding the utility of this literature along with perceived facilitations or hindrances to accessing and applying its insights. Informed by the elements of schemes of usage from the Documentational Approach to Didactics, my thematic analysis of the data revealed several convergent themes related to mathematics instructors’ perceptions and application of the mathematics education literature. I present these themes and discuss their implications for improving the content and dissemination practices of scholarly products to address the barriers practitioners experience in accessing, applying, and learning from the insights reported in the literature related to the teaching and learning of mathematics.
We define a peer assisted learning model called a Guided Study Group (GSG) and seek to create, implement, and evaluate a training program for undergraduate GSG leaders at a mathematics learning center. The creation, implementation, and evaluation of the training was informed by the theoretical lens of Communities of Practice. Fifteen GSG leaders took part in the training at the beginning of the Fall 2025 semester. This poster presents a case study of preliminary data from one particular GSG leader who was successful in making the students active members of the problem-solving process, encouraging students to work together, and noticing common misconceptions which were then addressed as a whole group.
We focus on teaching practices that support active learning and group collaboration in a professional development program (PD) for mathematics graduate teaching assistants (MGTAs). In doing so, we hope that MGTAs adopt such teaching practices in order to improve the experiences of their students. We analyzed over 1000 undergraduate surveys corresponding to a cohort of 12 MGTAs in our PD program. We completed two statistical analyses by comparing means and standard deviations for this cohort between the winter and spring terms: (1) in their first academic year, (2) and in their second academic year. In both analyses, we found statistically significant improvements from the winter to spring terms in scores related to student engagement and belonging, in addition to other evidence-based teaching practices. Ongoing research is investigating the extent to which experiences improved for different subpopulations of students within MGTAs’ classrooms.
Prospective secondary mathematics and statistics teachers (PSTs) should have opportunities to analyze student work and construct “second-order models” of student thinking—that is, PSTs’ conceptions of students’ thinking informed by their observations and knowledge for teaching. We report findings from a qualitative analysis of group discussions in a curriculum course where PSTs constructed second-order models in response to hypothetical students’ statements about sampling distributions. The analysis revealed productive engagement with key statistical ideas and evidence of elaborate forms of second-order model-building while also revealing opportunities to more comprehensively attend to the features of the sampling distribution concept. Additionally, this work contributes to existing literature documenting PSTs' understandings of the sampling distribution concept. More broadly, our work suggests that engaging PSTs in second-order model-building can help teacher educators surface and address underemphasized statistical ideas, supporting deeper content knowledge for teaching.
Although proof-based courses are predominately taught through lecture, many instructors have begun to incorporate more inquiry-oriented learning in their courses, providing space for small-group and whole-class work in addition to individual proving. There is little known regarding how these different contexts foster mathematical creativity. In this study, I investigate how students report experiencing creativity in an introduction-to-proof course taught through collaborative, inquiry-oriented methods. I give specific attention to how students reported experiencing creativity in individual, small group, and whole-class contexts. Student responses to an open-ended end-of-course reflection prompt were first analyzed inductively to identify the contexts students described feeling creative. Across the seven responses, five students specifically identified small group work, three students identified whole class work, and three students identified individual work as contexts in which they experienced creativity throughout the course. I provide an in-depth analysis of each of these contexts to report how students experienced creativity.
In this poster, we explore the role of computing in students’ mathematical reasoning and how students engage with coding modules while solving combinatorics problems. While analyzing paired students’ classroom work, we noticed that students pointed out different aspects of their code in their explanation of how they solved the problems. We seek to answer the following research question: What aspects of the code did students attend to as they used code as a representation in solving combinatorial problems, and how did they leverage these aspects of code? We draw on Lockwood’s model (2013) of combinatorial thinking in connecting aspects of code that represent counting process and sets of outcomes. We found that some of the ways that the code was used to represent their listing process, to represent their counting process, and using the output of the code as a representation.
In the context of the political nature of the world today, it is more important than ever to amplify the voices of individuals with historically marginalized identities. Mathematics classrooms in particular are largely white-male dominated at the undergraduate level; for students that do not identify this way, feelings of danger tend to emerge in a space meant to be collaborative and safe. Hearing these students’ perspectives is the first step toward looking closely at problems of discrimination occurring in our classrooms and identifying what is working to combat it and what remains broken. This poster tells the stories of Latina women in STEM and how they navigate racialized and gendered experiences while also negotiating the different facets of their identity. I also present encouragement for future researchers and Latina girls with STEM aspirations.
All faculty members teaching a coordinated precalculus course collaborated on a rubric development and scoring program to address the need for grading consistency across all sections. The course learning outcomes include students solving multi-step applied problems and clearly communicating their solutions, so the course had a large amount of written work to be graded. Developing the ability of faculty members to write task-specific rubrics and implement them consistently is of important practical concern. The literature indicates that achieving grading consistency can be challenging but enhanced by using task-specific rubrics and rater training. We implemented a structured rubric development and scoring program on four rounds of scoring student solutions (n = 147) to assessment tasks. The literature indicates that faculty time constraints can be a barrier to implementation. However, the literature does not seem to adequately address how, after an initial investment, rubric use can become routine. We seek to investigate the following research question: after instructors invest time in rubric development and training, how does the time needed for rubric implementation change?
We report on a student support program in college algebra, designed by combining principles of co-requisite support and Peer Led Team Learning. The program provided just-in-time support to strengthen pre-requisite skills via small group collaborative learning facilitated by undergraduate peers. Students whose placement test scores were below the requirement for college algebra were invited to participate. Findings suggest that the program is effective in supporting student success in college algebra (grades of C or better) and in setting students up for success in subsequent calculus sequence courses. In particular, program students were statistically as likely to receive a C or higher as those who placed directly into college algebra. We share additional details and seek discussion about research into other aspects of the program as well as what research opportunities might exist if this program were expanded to other courses in the calculus sequence (e.g., pre-calculus and first-semester calculus).
Lecture-based instruction prevails as the primary pedagogical approach used to teach undergraduate proof-based courses; thus, mathematics education researchers should investigate ways to improve the lecture rather than replace lectures (Melhuish et al., 2022). Mathematicians around the world utilize the “chalk talk” approach when teaching undergraduate mathematics (Artemeva and Fox, 2011), essentially describing the process verbally while referencing the formal mathematics they write on the board. Instructors and students have observed positive impacts of the use of guided notes during mathematics classroom lectures (Cardetti et al., 2010; Krapf and Pfefforkorn, 2022). Course coordination has been successfully implemented in mathematics programs to standardize student experience (Regier et al., 2024), to meet legislative needs (Jensen-Vallin, 2013), and to shift the pedagogical approach across multiple sections of the same course (Golnabi et al., 2020; Rahman et al., 2021). The goal of this study is to examine the use of guided notes in coordinated courses.
Modeling plays an important role in helping students make sense of and analyze complex biological systems, which is essential for those in life sciences or health professions. This study investigates undergraduate students’ covariational reasoning (CR) when engaging in tasks requiring movement across multiple representations, such as developing a trajectory from a time series and, conversely, developing a time series from a trajectory. A trajectory illustrates how two variables change in a space formed by those variables, while a time series demonstrates how a variable changes as a function of time. Covariational reasoning refers to an understanding of how two quantities interact with one another, and is foundational to reasoning with multiple quantities, comprehending the concept of function, and modeling dynamic events. Building on our previous work, we focus on how students reason through multiple representational shifts and how their CR manifests across tasks. Ten task-based think-aloud interviews were conducted with students who had completed a life science modeling course at a research-intensive university in the southwestern region of the United States. Interview data were deductively coded using Thompson and Carlson’s (2017) six levels of CR, followed by reflexive thematic analysis (Braun & Clarke, 2006). Preliminary findings elucidate the dynamic and flexible nature of CR, as students shifted between reasoning levels depending on task demands. We present three empirical cases to illustrate the various CR pathways and show how classroom norms and teacher expectations may shape students’ conceptions of what counts as “correct.”
To attend graduate school in mathematics, students must undergo a complex, often difficult application process. We examined mathematics major’s perceived barriers to applying to graduate school through the lens of the highest degree earned within their social network. Data was collected using a 57-item survey sent to mathematics majors across the U.S. and we received responses from 181 institutions. Kruskal-Wallis tests reveal that the level of education within a mathematics major’s social network can impact the extent to which they perceive some aspects of the graduate school application process as obstacles to applying. We found students whose social networks that contains graduate degrees are less intimidated by the application process due to their social capital. This benefits those who know someone with a graduate degree, as they can rely on them and/or their social network for knowledge on obtaining proper application materials or preparing for life as graduate student.
Students often first encounter orthogonal projection in linear algebra as a procedural formula, leading to disconnects between geometric intuition, vector decomposition, and symbolic manipulation. At the pre-pilot stage, this poster introduces a preliminary classroom design leveraging Principal Component Analysis (PCA) technique as a visual means and data-driven context to bridge these gaps. Students engage with 3D and 2D PCA figures, coordinating image, vector, and symbolic reasoning through guided tasks such as vector decomposition and dot product computations. Grounded in Multiple External Representations (MERs) theory and constructivism, the approach emphasizes representational fluency and conceptual reasoning. Targeted prompts and alignment rubrics address recurring misconceptions, including “along” vs. “onto” and PCA vs. regression. The expected outcome is improved conceptual understanding of orthogonal projection and a portable instructional toolkit for instructors. This poster prepares for pilot implementation and future data collection. Pilot results will guide further refinement and broader adoption of this instructional approach in undergraduate linear algebra courses.
Undergraduate students rely on the use of variables and algebraic manipulation when solving problems in a calculus context. However, students often treat variables as symbols to be manipulated rather than as quantities to be related (e.g., LaRue & Infante, 2015; White & Mitchelmore,1996). While mathematics education research in algebra (e.g., Booth, 1989; Küchemann, 1981; Lucariello et al., 2014) studied students’ interpretation and manipulation of variables, more research is needed to understand how these processes manifest specifically among calculus students (e.g., LaRue & Infante, 2015; White & Mitchelmore,1996). This poster will address aspects of this need.
Recent interest in alternative grading practices has prompted exploration of methods that prioritize learning, feedback, and iteration over traditional points-based assessments. Outcomes-based testing (OBT) is one alternative grading approach, allowing students multiple attempts on clearly defined outcomes without penalty. This quantitative and qualitative study examined student perceptions of OBT in undergraduate linear algebra at a medium-sized public engineering institution. Data were collected through pre- and post-semester surveys across four sections of the course taught by two instructors. A thematic analysis of qualitative data, combined with quantitative results, explored perceived benefits and drawbacks and what grades represent to students. Findings indicate students view OBT as supporting deeper learning and self-regulation, reducing stress, and providing fairer, more accurate grades. However, student experience varied based on frequency of reattempting outcomes, with greater benefits for students who used fewer reattempts. Implications for improving OBT implementation and promoting equity in student learning will be discussed.
To explore the role of context in adult learner’s problem solving, we designed two tasks with similar mathematical structure but set in different real-world contexts. The goal was to consider in what ways adult learners approached these similarly structured mathematical tasks, and in what ways the contexts of the scenarios influenced their problem-solving. Because we aimed to elicit connections to prior experiences, we conducted clinical interviews with two adult learners using missing value proportion tasks. We analyzed (1) how they solved each task, (2) how they thought about the similarities and differences across the two tasks, and (3) how they reflected on their solving processes. We found 5 different ways of solving in terms of the main ratio the student leveraged and how they leveraged the ratio. We found context played a role in solving, with participants reflecting on prior experiences both in math classrooms and in their personal life.
Active learning is increasingly central in undergraduate mathematics, yet less is known about how students experience these environments. This study examined student perceptions of an active-learning model used in Calculus I recitations at a medium-sized university. Using open-ended end-of-semester survey responses from 238 students across two semesters, we conducted an inductive thematic analysis to identify what students would keep and what they would alter if they were the instructor. Twenty-three themes emerged across five categories. Overall, students mentioned more elements to keep than to change, indicating generally positive perceptions. Group work was the most frequently cited strength, with students valuing collaboration and peer explanations. Other strengths included worksheets, teacher-led problem solving, and structured openings and wrap-ups. Suggested improvements focused on refining, rather than removing, assignment-related aspects such as worksheet clarity, appropriate difficulty, and group work facilitation. Findings provide student-driven, actionable recommendations for enhancing active-learning recitations in introductory mathematics.
The Midweek Math Training (MMT) program is a weekly peer-led practice exam sessions students can voluntarily attend. Math anxious students often avoid working practice problems, particularly practice exam problems (Jenifer, Levine, and Beilock, 2023). In this study we are looking into the connectiion between Calculus students’ reported math anxiety and relationship with math with use or disuse of MMT.
In the chemistry curriculum, physical chemistry stands out as one of the most challenging given its reliance on calculus, particularly when using quantum mechanics to describe atomic and molecular structure. Though there is literature in chemistry education research that investigates students' conceptions of quantum chemistry, few of these studies focus on students' use of mathematics in this context. To this end, we interviewed graduate students (N = 23) about the "particle-in-a-box", one of the first quantum models discussed in physical chemistry. Preliminary analysis investigates phenomenographical categories of students' problem-solving strategies and their affective responses to the problem-solving task.
Beginning in 2021, a three-course Indigenous Math sequence has been developed at Turtle Mountain College as part of the Secondary Math Education bachelor’s program. Studying the development of these courses will afford opportunities to further strengthen the courses and program as well as offer insights to support any math faculty interested in integrating more Indigenous ways of knowing and being into any undergraduate math class. Under the umbrella of an Indigenous research paradigm, a process tracing method will be applied as a retrospective analysis on the development of the Indigenous Math courses. Identifying moments of decision, struggle, and overcoming demonstrates one way to increase Indigenous math content in any math course/program.
Given that Calculus 1 in the United States is often linked to declines in students' enjoyment and persistence, we examined course coordination as an opportunity to improve student experiences and outcomes. We conducted a review of the literature on coordination, identifying 62 articles that reference coordination, of which 23 report on student outcomes. Coordination is defined as a system that synchronizes content under designated leadership and ongoing collaboration. Most outcome papers reported decreased fail rates or improved pass rates, while several others reported improvements in student belonging and persistence. These findings were particularly clear when coordination aligned instructors around research-based instructional practices and embedded classroom support.
This study extends previous work on community college students’ conceptions of smartness in mathematics by examining how instructors’ implicit beliefs align with or diverge from students’ perspectives. The study takes place at a Southern California Hispanic-Serving Institution (SCHSI), a comprehensive two-year community college. The study involved 103 student responses to the prompt “What does it mean to be smart in math at SCHSI?” and interviews with five instructors who participated in equity-focused professional development. Student responses were thematically coded and mapped across two axes, process to outcome and dominant to counternarrative conceptions of smartness. Instructor interviews, analyzed using the same framework, revealed tensions between desired equitable practices and persistent procedural tendencies. For example, instructors described valuing conceptual understanding and student agency, yet often defaulted to practices reinforcing dominant narratives. Findings highlight how instructors’ implicit conceptions of smartness may reproduce or disrupt inequitable narratives, underscoring opportunities for professional learning that explicitly engages notions of smartness in mathematics.
This poster introduces the Undergraduate Mathematics Classroom Assessment Questionnaire (UMCAQ), a novel instrument designed to capture student perspectives on equity and inclusivity in mathematics learning environments. Unlike traditional observation-based measures, UMCAQ centers student voices to reveal patterns that influence classroom climate and participation. We describe the development process, validation efforts, and key findings from pilot studies, highlighting how UMCAQ can inform both research and practice.
Many undergraduate mathematics students struggle not only with content but also with the metacognitive skills needed to monitor, regulate, and direct their learning. The Thinking Project (TTP) is a metacognitive support initiative implemented in multiple sections of an Applied Calculus course at a large R1 university. TTP fosters students’ metacognitive awareness through structured, web-based activities embedded throughout the course. These activities encourage self-reflection, increase awareness of course content, academic progress, and learning goals, and are accessible and easy to complete. To investigate the impact of TTP, the Metacognitive Awareness Inventory (MAI) is being administered at the beginning and end of the semester, and qualitative feedback is being collected to explore students’ perceptions of the activities. This poster presents the project’s theoretical rationale, design, and ongoing data collection process, highlighting a research-informed approach for examining how structured, course-embedded activities can support metacognitive growth in undergraduate mathematics.
This study examines how peer mentoring influences novice graduate student instructors (GSIs) of precalculus in developing their teaching practices. We explore the motivations and participation of a group of five novice GSIs and their peer mentor to understand how mentoring interventions shape engagement and reflection. Survey feedback revealed that while novices valued community and shared experience, they did not always recognize teaching reflection and teaching-focused professional development as central goals of mentoring. In response, we implemented a more intentional, practice-oriented approach that emphasized collaborative lesson design and pedagogical discussion. Following this intervention, participants demonstrated greater engagement in lesson planning and deeper reflection during post-observation discussions. These findings suggest that explicitly framing mentoring as a space for collaborative instructional growth can strengthen novice GSIs’ professional development and teaching practices. The project also fostered the mentor's own growth as a facilitator and researcher. More broadly, this work illustrates how peer mentoring can serve as a theory-informed and sustainable model of professional development that bridges the worlds of mathematics and mathematics education.
Over the last few decades graphical and numerical methods have gained importance to study differential equations. One central skill when studying the long-term behaviors of models described by differential equations is the ability to navigate between time series and phase plane trajectories. Building on previous research that described how students mainly used smooth or chunky continuous reasoning when building these graphs, we investigated how students justify the use of either of these levels of reasoning. We gave students one (smooth) time series and two possible corresponding trajectories, one smooth and one chunky. While all students said that the smooth trajectory best corresponded to the given time series, the reasonings invoked varied greatly. We will present and discuss the different types of arguments invoked by the students as well as implications for practice.
Despite the fact that the Polar Coordinate System has affordances for graphing circular and rotational phenomena that the Cartesian Coordinate System simply does not have, students spend too little time engaged with it. The time they do spend is dominated by procedural tasks that deny them experiences that would enable them to appreciate its power. This poster presents design research in progress that seeks to discern the elements of an enactive educational ecosystem for emergent learning that enables learners to graph and reason within the PCS. Coordinated material and embodied interactions are emerging in preliminary findings that are enabling learners to make sense of the PCS by moving between it and the CCS as they coordinate the same varying quantities across those two worlds. The phenomenology of these interactions and the interactions themselves have implications for the design of experiences that enable learners to develop robust conceptions of the PCS.
This study aims to better understand student learning experiences reported in reflective portfolio assignments. Our study context is a quantitative reasoning course geared toward elementary education majors and STEM majors in which we collected end-of-semester portfolios. We are interested in how portfolios reveal students’ self-regulated learning (SRL), which includes processes of self-motivation beliefs, self-control, and self-reaction. Thematic analysis of student writing revealed experiences relevant to these processes such as mindset shifts, a sense of creativity, and productive struggle. Insights gained from this study can provide us with information about the impact of teaching practices on student experiences from varying backgrounds, as well as the benefits of reflective assignments.
This study examines the opportunities and challenges in developing a shared, online developmental math course recognized across Montana Tribal Colleges and Universities (TCUs). Using a qualitative case study, the research examines the perspectives of faculty, staff, and administrators, institutional readiness, and perceived cultural responsiveness. Findings are showing strong interest in a unified, certificate-based model that promotes equitable access, supports collaboration, and integrates Indigenous values. The study contributes to ongoing discussions on culturally responsive and sustainable mathematics pathways at TCUs.
Initial results are presented for students’ perceptions of instructor actions and their intentions in an undergraduate math context, highlighting the variability in student perceptions. Video-recorded classroom observations were conducted throughout the Fall 2025 semester in an interactive undergraduate precalculus class. Seven focal students were asked to reflect on select clips from these observations during early- and late-semester interviews. These clips centered on student-instructor interactions (sometimes involving the student being interviewed), and the students were asked (among other things) about their perceptions of relevant instructor actions and what they believe the instructor intended with these actions. Current analysis of these interview transcripts show that students can have varied interpretations of which instructor actions are significant or what the instructor’s intentions are with particular actions. Further analysis looks to explore how these varied perceptions of instructor actions in the classroom may relate to students’ larger views of themselves as “doers of math.”
While previous studies have examined college algebra students’ experiences and undergraduate belonging in mathematics, limited research explores how community college students understand diversity, equity, and inclusion. In this poster, we focus specifically on students’ understanding of equity and present preliminary findings from a Q methodology analysis of 25 participants from eight community colleges across the U.S. A total of four semi-structured interviews were planned for each participant. The first three interviews have been completed and the fourth is currently in progress. The third interview included a Q-sort activity using 33 statements representing diverse perspectives on equity in mathematics. Using the KADE desktop application for a Q-sort analysis, we identified four distinct factors (Needs, Success, Race, and Equality) that represent how students conceptualize equity in college algebra classrooms. Subsequent analyses will focus on how students’ experiences and backgrounds influence these themes.
Few studies have determined how students understand dynamic systems using iterative algebra. Our study addresses this gap in research through investigating how students—who mostly do not have a calculus background—make sense of the mathematics and science behind a climate system using iterative algebra. We used the Sci-Math sensemaking framework as a tool to analyze the types of mathematics and science sensemaking students engaged in while working with a mathematical model of climate. In an undergraduate college algebra classroom, students were tasked to develop and interpret recursive equations representing the dynamics of the North Atlantic Current. Using the Sci-Math Sensemaking Framework, the sensemaking processes of three different groups of students were studied while working on the mathematical climate model activity. The results suggest that students, with primarily no calculus background, can engage in interdisciplinary sensemaking of a dynamic system. This provides promise for teaching more students dynamic systems through iterative algebra.
Didactic lecture remains the dominant pedagogy in introductory undergraduate STEM courses. Alternatives, such as group work, are often met with barriers such as course enrollment (class size) and classroom setup. In our study, we investigate whether changes in course enrollment and classroom setup relate to changes in the amount of time instructors dedicate to group work. Data was gathered, via survey, from instructors teaching undergraduate introductory STEM courses in 2019, and again from the same instructors in 2025. These instructors were categorized based on whether their course enrollment increased, decreased, or remained the same, and pairwise t-tests were conducted on each groups' 2019 and 2025 reports of group work usage. Our analysis indicates that there are no significant differences in the amount of time spent doing group work (between 2019 and 2025) regardless of whether, and how, their class size changed.
Initial college mathematics placement of Science Technology Engineering and Mathematics (STEM) majors may be linked to the direction and duration of their college studies. This study aims to explore how preparation for tertiary mathematics may influence STEM majors’ initial mathematics placement. For this study, we consider mathematics preparation to consist of secondary mathematics courses and college preparation advice. Mathematics course sequences for secondary school students may be accelerated. This practice can be advantageous for some students yet push others too quickly through the mathematics curriculum. Additionally, potential STEM majors may receive advice from their secondary community; however, the community may prioritize high school calculus for its perceived role in college admissions. This sequential mixed methods study addresses the question of how undergraduate STEM majors’ high school mathematics experiences and college preparation are connected to their initial college mathematics placement.
Dispositions include an individual’s behavioral, cognitive, and affective tendencies. Productive dispositions and a growth mindset lead to better learning outcomes, while unproductive dispositions result in avoidance, anxiety, and lack of confidence. Supporting the development of productive dispositions is therefore critical for improving students’ mathematical knowledge and achievement. This three-year study examines pre-service elementary teachers’ (PSETs’) mathematical dispositions during their first mathematics content course, focusing on four key constructs: mindset, self-efficacy, anxiety, and avoidance. We focus on PSETs as this population is reported to exhibit unproductive mathematical dispositions, which may negatively influence their learning of mathematics, their future teaching, and their students’ attitudes toward math. Data were collected via pre- and post-semester surveys, including validated scales for math anxiety, self-efficacy, growth mindset, and content knowledge in all three years. During the second and third years, students completed targeted in-class interventions guided by their instructors. Additionally, a subset of students (volunteers) participated in an eye-tracking study at the beginning and end of each semester. Eye-tracking technology was used to assess implicit visual behaviors during arithmetic tasks, offering insights into math-related anxiety and avoidance. Quantitative results revealed that students in the intervention semester showed a significantly greater decrease in math anxiety and significant gains in growth-oriented mindset and math content knowledge. Preliminary eye-tracking data suggest that students with higher math anxiety exhibit lower fixation rates and durations during arithmetic tasks, indicating potential visual avoidance. These findings underscore the importance of targeted interventions to reduce math anxiety and foster productive dispositions among future educators.
This poster will share preliminary results from a study regarding mathematical modeling in nonformal learning environments for preservice K-8 teachers (PSTs) in an elementary mathematics content course. Students participated in a field trip that involved visiting a farm to bake bread, estimate areas of fields, and engage in various profit estimation activities. Data include an interview with the farm owner and interviews with students. These data were analyzed using reflexive thematic analysis to generate themes regarding (a) connections between school mathematics and activities outside of school and (b) PSTs’ perceptions of mathematics and its contexts and the purposes of learning mathematics. The resulting themes will inform activity revisions and research design in future semesters.
Students at a Tribal College or University (TCU) can be said to have a “home and family culture that does not fully resonate with that of school and the wider society (Bishop, 1991).” Frequently, attempts to improve math education for these students look at improving access to better math instruction in order to increase achievement. This is the “dominant axis of equity (Gutiérrez, 2012).” Is it possible that using the critical axis, identity to power, math instruction can help TCU students leverage their cultural identities?
This research involves mathematicians and mathematics education researchers co-developing knowledge for teaching via their collaborations in Lesson Study within undergraduate geometry courses. We describe how we incorporated considerations of Responsibility, Relationships, Relevance, Responsiveness, and Rigor in our development of an observation instrument. The poster will present the current form of the protocol as well as highlights of our learning from creating it.
Inquiry-oriented (IO) instruction is grounded in constructivist theories, which provide the foundation for realizing its transformative potential in supporting students’ cognitive growth. However, given the dynamic nature of IO environments and learners, there is a need to delve more into the different ways learning can occur in this space to engage in thoughtful classroom design. This poster explores a researcher’s relationship with data to recognize the material world that facilitates learning in an IO classroom. New materialist and post-representationist approaches were employed while engaging with two sessions of a video-taped IO class to evoke new wonderings about IO instruction. The poster presentation will share observations from the IO class sessions. Instead of presenting “traditional” qualitative research findings, these observations will be accompanied by wonderings that could inspire reformulation of theories for IO classrooms.
Calculus is a foundational course supporting many STEM majors, making it important to investigate the nature of students’ experience in calculus, changes in motivational processes and beliefs occurring across calculus coursework, and the role of such changes in predicting students’ intention to remain in STEM. The present study seeks to conduct such an investigation through longitudinal analysis of the utility value, complexity, and general and task-based self-efficacy beliefs of students in a first-semester calculus course. Across four time-points implemented consistently after completion of common course exams, we examine growth trajectories in these motivational and efficacy beliefs and their contribution to students’ belonging perceptions and anxiety in mathematics and their intention to major and remain in a STEM discipline. Additionally, we consider the nature of change in students’ beliefs over time, explore patterns and associations with student characteristics, and consider the prediction of students’ academic achievement based on these motivational trajectories.
Investigations have been conducted into how students conceptualize exponents and logarithms, utilizing APOS theory, particularly regarding how students justify exponent rules. The thesis by Williams (2011) presents a list of codes to identify the conceptions that students hold regarding logarithms. However, a gap in the literature remains on how students justify the corresponding logarithm rules. In this poster, I compare the thinking of two students to extend her work.
Mentoring and coordination are central to supporting graduate student instructors (GSIs) as they learn to teach foundational mathematics courses within complex collegiate systems. In the context of professional development sessions for eight faculty members who are foundational math course coordinators, we present a system dynamics model built using Vensim software (Mohaghar et al., 2017). This model simulates how mentoring structures, coordinator orientations, and institutional policies interact to shape instructor belonging and the use of active learning (AL) strategies over time. The model comprises 12 interacting variables connected through three key feedback loops: the Mentoring Loop, Humanistic Growth Orientation Loop, and Exclusion Brake. These loops represent dynamic pathways through which mentoring fosters AL, belonging reinforces growth-oriented coordination, and institutional pressures can either suppress or sustain support. Variables such as Shared Time, Recognition Events, Course Resource Rationales, and Barriers to AL function as policy levers that influence the system’s long-term behavior. Rather than isolating individual factors, the model provides a generative framework for examining how coordinator orientation, structural design, and cultural signaling co-produce inclusive learning environments that can support sustained instructional growth in coordinated mathematics courses.
Following the rapid introduction of generative artificial intelligence (GenAI) tools such as ChatGPT, universities have an increased incentive to define expectations for AI use. This study analyzes 14 instructor-written GenAI policies from a university mathematics department. Using inductive thematic analysis, we examine how calculus-sequence and proof-based courses frame GenAI in relation to learning, integrity, and reliability. Most policies took a moderate stance, allowing conceptual use but prohibiting AI-generated solutions to homework, while a few were fully restrictive or open. Instructors more frequently mentioned learning and metacognition than academic integrity or unreliability. Policies did occasionally possess contradictory language, banning GenAI while requiring citation, suggesting ongoing ambiguity. Clarifying such tensions and supporting students in ethical, informed use remain central challenges as disciplinary norms continue to develop.
Mathematical equations are a key part of undergraduate science instruction. Students who can engage in blended sensemaking (make connections between mathematical equations and the scientific phenomenon they represent) are better able to solve novel or complex quantitative problems in science. However, little research has explored the impact of task on students’ blended sensemaking. This study analyzed student discourse while students were working on different tasks involving mathematical equations representing population growth (e.g., developing mathematical equations, modifying mathematical equations, problem solving) to identify the number of instances and the level of blended sensemaking. Students engaged in more instances of blended sensemaking when asked to develop and then modify a mathematical equation compared to solving a problem using a mathematical equation and then modifying the equation. During modification tasks, students tended to engage in higher level of blended sensemaking. These findings have implications for instructional design in both science and mathematics classes.
This poster explores an investigation of undergraduate students’ experiences with proof-based courses, focusing on what they perceive as supportive or unsupportive to their learning. Although there has been some focus on the challenges students have with proof comprehension or production, relatively little is known about their experiences with proofs. We interviewed five students who finished at least three proofs classes and asked what helped them out or didn’t. They pointed out a few big problems: grading felt confusing, the language rules were too strict, and there was less chance to work together. This suggests that making grading expectations clearer and giving students more ways to collaborate can make a real difference. To answer our research question, we used a thematic analysis to identify what students noted as helpful or not in relation to their experience in their proof-based course. This poster shows some simple changes that can help more students feel like they really belong in proof-based math.
Texts have an interpersonal function that establishes relationships between authors, readers, and the content of the texts, and, thus, can be exclusionary. However, little research has critically analyzed how postsecondary mathematics textbooks may deny readers mathematical authority. We present an analysis of 40 books in the Graduate Texts in Mathematics series, exploring how power is implicated in authors’ use of pronouns. Using theories of power evasiveness, we illustrate how authors use inclusive language while simultaneously constraining the reader’s mathematical agency. While inclusive language is important for readers to be seen as full members of the mathematics community, our analysis signifies a need to reconstitute mathematical talk and writing in ways that ascribe more agency to emerging mathematicians.
So-called “Gatekeeper Courses” such as Calculus I and Precalculus often serve as an impediment to student aspirations, with negative impacts on university retention and equity goals, particularly within STEM degree programs. Particularly given challenges that students are experiencing post covid-19, interventions that improve success rates in initial mathematics classes thus have substantial value for university policymakers. This poster presents data examining the outcomes of two mathematics support options for entering undergraduates: an intensive summer “Bootcamp” immediately prior to the start of the Fall semester, and “Companion Courses” which run throughout the semester and attempt to provide just-in-time math practice, both supervised by faculty members and implemented by Undergraduate Learning Assistants. Data indicate that these two support structures have the potential to improve student outcomes, providing a possible option to raise student retention and reduce the impact of initial mathematics courses as a gatekeeper.
Inquiry-Based Learning (IBL) is a type of learning model, where students are given investigative tasks that promote the engagement of students in the creation of important mathematical concepts. However, IBL is more practitioner focused without a consistent definition, so how IBL gets implemented in the classroom may differ across instructors. The research questions are: (1) What are the differences in the implementation of IBL by instructors? (1a) What is the frequency of activities and questions students and instructors engage in? (1b) What are the differences of the levels of inquiry in the classroom? This project uses classroom observations of five sections of college algebra to see how IBL is being implemented. Classes differed in their IBL implementation in a variety of ways, such as the percentage of groupwork and lecturing, the frequency and type of questions, the mathematics being completed, and the ways the instructors elicited and utilized student contributions.
Many examinations in mathematics given to students often focus on the students being able to perform procedures or otherwise require little conceptual understanding to solve, even if the question was not designed as such. In contrast, a concept assessment or concept inventory is an assessment dedicated to assessing conceptual knowledge within a given subject area. For calculus, Epstein's Calculus Concept Inventory was such an early concept assessment, but it has been critiqued for its lack of research as a foundation as well as its lack of validity. This research is part of a larger research project aiming to create an improved and modular concept assessment for calculus, with this section in particular focused on derivatives. The project is still in its early stages, with the current task being to develop the questions based around what the research says about student understanding derivatives.
Attitudes toward mathematics play a critical role in shaping students’ learning experiences, academic performance, and long-term engagement with the subject. In the context of community college education, where students often face diverse academic and personal challenges, understanding these attitudes becomes especially important. Focusing on the first of four interviews, this study explored students’ affective connection to mathematics and how their experiences in college algebra classes at community colleges impact their relationship with mathematics. Preliminary findings identified college algebra students’ affective relationship with mathematics, observations about learning mathematics, and beliefs about the nature of mathematics.
Animation-based graphing tasks, when carefully designed, can support students’ covariational reasoning. To support such reasoning, researchers have recommended avoiding contexts in which students are coordinating changes in time with changes in another quantity. In this poster, I examined Calculus 1 students’ level of covariational reasoning as they engaged with distance-time graphing tasks with normative and non-normative axes (i.e., time on the vertical axis). Consistent with prior empirical reports, I found that students engaged in limited forms of covariational reasoning on distance-time tasks with normative axes. However, all 12 students engaged in covariational reasoning on the time-distance tasks (non-normative axes). I discuss implications for curriculum design and research on covariational reasoning.
The research in undergraduate mathematics education (RUME) community has amassed insights into features of high-quality learning opportunities for students and what instructors need to know and do to create such opportunities. What does it look like if we leverage what is known from that literature to consider the question: How do we use RUME findings to design and study leader development for the mathematics education community? We focus on leaders who function as Stewards, whose broad and deep knowledge enables them to serve as innovators and custodians of teaching-focused professional development. Building on prior work on leadership for instructor professional learning, in this theoretical exploration we consider the design of authentic group-worthy tasks for professional learning (e.g., tasks relevant to the work of teaching and leadership in post-secondary mathematics) and what is necessary for those who offer such learning to know and do.
Classroom Observation Protocol in Undergraduate STEM (COPUS) and Toolkit for Assessing Mathematics Instructors – Observation Protocol (TAMI-OP) are observation protocols created as part of a broader effort to examine practices within active learning STEM courses. They seek to describe and categorize instructor and student actions across time. While these tools are typically utilized as a means of professional development and in evaluation processes, less is known about how they can function as analytic tools within the research process. From our analysis, we show that COPUS and TAMI-OP can both be valuable research tools, but each has strengths that highlight distinct aspects of classroom interactions. Our work illustrates how these observation protocols can be appropriately adapted as research tools and how each provides different perspectives on active learning in undergraduate mathematics classrooms.
Prerequisite mathematics courses often function as gatekeepers, contributing to high attrition and delayed degree progress. This study investigates whether integrating active learning and written instructor feedback can improve outcomes in such courses. Grounded in research connecting interactive engagement and constructive feedback to student understanding and persistence (Bressoud & Rasmussen, 2015; Cirillo et al., 2024; Grove & Good, 2020; Vroom et al., 2022), the redesign replaced portions of lecture with structured, in-class problem solving and increased individualized written feedback on student work. Institutional D/F/W (drop/fail/withdraw) rates from semesters before and after implementation will be analyzed to examine potential changes in student success. The study aims to determine whether combining active learning with more frequent descriptive feedback can foster greater persistence and achievement in collegiate prerequisite mathematics. This work contributes to ongoing discussions about designing undergraduate learning environments that are equitable, feedback-rich spaces that help students do mathematics versus simply watch mathematics.
Physical models are frequently used in elementary mathematics classrooms to support students’ understanding of multiplication. These models are discrete, and many represent multiplication as repeated addition, area or an array. Thompson and Saldanha (2003, p. 104) found that “thinking about multiplication as repeated addition leads to severe difficulties in later grades” and Hurst (2015, p. 11) suggested that “multiplication as scaling…is a key aspect of thinking that needs to be developed.” McLoughlin and Droujkova (2013) developed a diagrammatic definition of multiplication using parallel lines to scale the length of one segment by the length of a different segment. We developed the SunRule, an interactive device that harnesses parallel rays of the sun to perform multiplication. Beams of light cast shadows from gnomons onto a measuring plane; by varying the tilt and height different multipliers, multiplicands, and products can be generated.
This study examines how instructional modality relates to academic performance and motivation among undergraduate mathematics students. Four modalities were considered: Face-to-Face (F2F), Hybrid (H), Online Synchronous (OS), and Online Asynchronous (OA). Data were collected through an anonymous survey administered at the tutoring center of a majority Hispanic institution, with responses from students enrolled in courses ranging from college algebra to ordinary differential equations. A total of 249 responses were collected, including Likert-scale questions about how course modality affects their motivation to participate in class, the impact of their final grade due to the course modality, and their final letter grade for each class and modality. The data were analyzed using SPSS to compare means and 95% confidence intervals of the survey scores across the four modalities. The findings suggest that environments that promote active interaction, such as F2F and H, enhance students’ achievement and motivation when it comes to the mathematics classroom. These results align with Kundu et al. (2023), who found that hybrid learning promotes satisfaction and engagement of mathematics students.
Gender has long been studied within math education, evolving from deficit and assimilationist models, positioning girls' lower participation as a problem to be fixed, to feminist and sociocultural frameworks that conceptualize gender as relational and interesting with other axes of identity (Leder, 2019). Examining how it has been theorized, operationalized, and represented in RUME proceedings sheds light on the field’s evolving commitments to equity and inclusion. This gap motivates our landscape analysis of RUME proceedings from 2018 to 2024 to map how gender is being operationalized. This paper presents four categories of papers: Core, Peripheral, Non-Focal and Unrelated. Findings and trends of the less than 25% of papers identified as Core or Peripheral will be shared.
Undergraduate quantum mechanics students often have to transition between abstract quantum concepts and their complex mathematical formalism counterparts. As quantum mechanics typically requires students to have an in-depth mathematical understanding before introducing physical concepts, understanding how students perceive and understand mathematical formalism is critical. This study examines students’ perceptions of mathematical treatment in an upper-level undergraduate quantum mechanics course, with a focus on how mathematical reasoning influences their understanding of physics and experimental phenomena. Through a series of semi-structured interviews, student responses were coded and analyzed, revealing a range of emotions, from appreciation and confidence in mathematical precision to frustration with abstraction and a perceived lack of physical grounding. Findings suggest that students’ sense of ownership of mathematical tools correlates with their ability to conceptually bridge quantum measurement and experimental practice. The analysis emphasizes the pedagogical significance of explicitly linking symbolic operations to interpretive and experimental contexts.
Struggling with mathematics can be done productively. In this poster, I share a brief literature review and theoretical background for productive struggle. Next, I share the results of applying the Productive Struggle framework (Warshauer, 2015a; 2015b) to one participant’s data from a teaching experiment with an undergraduate developmental mathematics student. Finally, I propose potential extensions to the Productive Struggle framework. I provide examples of unexpected teacher response categories that contributed to the participant's productive struggle and share an additional ending for a struggle.
The call to rehumanize mathematics can be answered with joy and play; yet many studies incorporating these concepts into mathematics limit themselves to early education settings. This study examines the potential for joy and play in a doctoral-level Abstract Algebra seminar, revealing characteristics that can foster a joyful secondary and post-secondary mathematics classroom. Using a mixed-methods concept-mapping analysis, researcher-participants identified preliminary themes of structured flexibility, safety, exploration, and community. By identifying these characteristics, the researcher-participants demonstrate that joy and play can enhance the teaching and learning of undergraduate and graduate mathematics.
This study examines the instructor moves used in an inquiry-based university mathematics course for prospective secondary mathematics teachers. Thematic analysis techniques were used to analyze transcriptions from classroom video recordings across three 80-minute class sessions for instructor moves facilitating groups of students engaged in tasks on functions. Open coding of instructor moves identified the following codes: Promoting, Probing, Redirecting, Revoicing, Mathematically Precise Speech, Relating to Other Concepts, or Vague/Non-Response. Effectiveness of instructor moves was analyzed based on changes in student discourse on functions before and after each episode of instructor moves. Preliminary results suggest that the effectiveness of using a particular instructor move may be dependent upon the state of student discourse at the time of use. Findings also suggest that the shifts in student discourse after each IME also may indicate enhanced conceptual understandings of functions.
Zero’s introduction into mathematics sparked a new understanding of our number system even though we now perceive it as very subtle and obvious. Zero has grown to become important in many fields of mathematics including calculus. Researchers have suggested that students' and teachers’ understanding of zero is limited or incomplete (Seidelmann, 2004). In this study, I consider the many conceptions of zero that calculus students hold and how they employ those conceptions differently based on tasks types and context. Four calculus classes will participate in a digital survey aimed at uncovering their conceptions of zero and how they operationalize those conceptions. A subset of those students representing diverse conceptions of zero will participate in follow-up interviews that expand upon the topics found in the survey. I will conduct a thematic analysis with a series of a priori frameworks from existing literature as a guide to establish students’ conceptions of zero.
This study uses topological analysis to examine Calculus I students’ mindsets through coded reflections from successful students. Mindset combinations were modeled as simplicial complexes representing productive, non-productive, and mixed patterns. Students encountering Calculus first at the university level showed more productive mindset structures than those with prior high school experience. Findings suggest that prior exposure shapes how students experience Calculus and point to benefits of instruction that accounts for these differences.
We examine how undergraduate students navigate proof writing through two complementary “images of activity”: puzzle-piece (“chunky”) assembly and flow (“smooth”) throughlines, and how students transition between them while producing a final, coherent proof write-up. Adapting the chunky/smooth covariational lens (Castillo-Garsow, Johnson, & Moore) from modeling to writing proofs, we examine what episode types arise during student proofwriting, what triggers students’ commitment to and transition between these two images, and how these ideas are visible (or not) in the finished proof. This mixed-method research is conducted using exploratory 40-60 minute think-aloud interviews in which students work two multi-route proof tasks, with a follow-up survey to examine participants’ beliefs about proofwriting and elements of a good proof. Participants are sampled across upper division undergraduate proof-based courses. Results aim to characterize commitment triggers and stalls and to inform instruction that scaffolds productive shifts in proofwriting.
This exploratory study centers on investigating second-semester calculus students’ understanding of series convergence using both scripting and non-scripting-based tasks on series convergence, across two interview sessions, and examining how these tasks elicit student understanding. The research question focuses on the affordances of these tasks when examining students’ concept image and concept definition of series convergence alongside the formal definition of series convergence. Each participant either completed a set of non-scripting tasks within the first interview session followed by a scripting task during the second session or vice versa. Data analysis included the use of a priori codes identified from the literature and identifying emergent codes and themes. Findings reveal how participants relate series and partial sums suggesting the nature of potential conflict factors regarding students’ understanding of series convergence. This exploratory work provides support for scripting as a research tool and as a viable assessment on student learning of series.
There is a vast underrepresentation of contexts of Indigenous learners and from the contexts of TCUs. Further exacerbating this underrepresentation is the general lack of presence of research in developmental mathematics education in mathematics education research spaces. Research in undergraduate mathematics education focusing on developmental math and research on mathematics education in TCU contexts are each severely lacking. Research at the intersection, developmental mathematics education in TCU contexts, is scant if not nonexistent. In order to advance knowledge in these areas, there is a need to highlight the work being done at TCUs. This project provides snapshot of current contexts for developmental mathematics education and mathematics pathways in TCU contexts, with a particular focus on developmental mathematics and math pathways, consisting of: a literature review that provides an analysis of trends in the literature pertinent to mathematics education at TCUs, targeting trends and needs in research and practice in the areas of developmental math and math pathways; a landscape analysis consisting of summary of qualitative and quantitative data on mathematics programs, in particular developmental math and math pathways at TCUs; and a Promising Practices report summarizing innovative and promising practices in developmental math and mathematics pathways as shared by TCU math faculty participating in the project.
Historically, research in mathematics education has explored how students’ prior knowledge and learning experiences shape outcomes in subsequent coursework. This poster explores differences between student outcomes, specifically final course grades on a 4.0 GPA scale, through their choice of prerequisite course. We compared the final course grades of students in Elementary Mathematics for Teachers (EMT) entering from two different prerequisite pathways, Quantitative Literacy (QL) and College Algebra (CA), using institutional course-tracking data from the past two academic years (Fall 2023 to Spring 2025). Descriptive and inferential analyses revealed a statistically significant difference in final course grades, suggesting a link between knowledge acquired in prerequisites and outcomes in subsequent mathematics courses. Future work will extend this analysis by incorporating additional contextual variables to identify potential sources of student performance variation.
Mathematics self-concept and interest are key predictors of student achievement and career choices. While prior studies demonstrated the relationship between these constructs and classroom climate, they predominantly rely on Eurocentric sociocultural theories such as Moos’s framework, Bronfenbrenner’s ecological systems theory, Vygotsky’s sociocultural theory, and the four phase model of interest development. This study proposes a humanizing framework that integrates these theories with the African philosophy of Ubuntu, which emphasizes interconnectedness and shared humanity. In education, Ubuntu pedagogy fosters democratic, respectful, and co-learning environments. The hypothesized model described in this study illustrates how Ubuntu enriches the explanatory power of existing theories to better understand the influence of classroom climate on mathematics self-concept and interest. This framework offers new directions for undergraduate mathematics classroom practice and curriculum design. Future research will use mixed methods to test the hypothesized model
In this poster, we analyze and present a researcher-instructor collaboration with mathematicians to identify features of activities that would increase mathematicians use of active learning pedagogy in a proof-based linear algebra course. We use data generated from these interactions to identify and consider different instructors’ openness to interlocutor pairs: student-student and instructor-student in discussion-based mathematics. We then consider their conflicting obligations when contemplating the implementation of discussion inside of the classroom, and the reasons that peer-peer discussion may be more viable outside of class.
This poster highlights my investigation of alignment between an instructor’s and students’ perspectives on students’ self-efficacy levels and sources for using proving techniques in an Introduction-to-Proofs (ITP) course. This study is guided by Bandura’s self-efficacy theory (1977) and builds on Klassen’s and Lynch’s study (2007) that investigated alignment of perspectives on Grade 8 and 9 students with learning disabilities’ self-efficacy levels and sources. Data collection is ongoing during the Fall 2025 semester by observing and recording classroom sessions and conducting three rounds of interviews with six students and two rounds of interviews with the instructor. Each interview consists of three phases that ask questions about each participant’s perspective on students’ self-efficacy levels and sources relating to using proving techniques. This poster will highlight preliminary results regarding the alignment of the instructor’s and students’ perspectives on the students’ self-efficacy levels and sources related to using proving techniques throughout the ITP course.
Concept maps are used across many disciplines but are less frequently utilized in mathematics. In this study, we investigate how mathematics students engage with the idea of the derivative when tasked with creating a concept map. These concept maps are analyzed with an established method – a scoring system. Our findings suggest that current approaches to analyzing concept maps make them an ineffective tool for deeply understanding student reasoning about the derivative.
Mathematical skills are often considered essential for success in engineering. In this preliminary work, we examine the written work of environmental engineering students on their midterm exams in a class on small water systems. Using an adapted version of Carlson and Bloom's Multidimensional Problem-Solving Framework, we identified the problem-solving phase in which students committed errors on their exams. Preliminary analysis of these data suggest that the engineering students in our sample possessed the necessary mathematical skills necessary to solve problems related to the design of small water systems, but their ability to solve these problems successfully was inhibited by gaps in their understanding of engineering content.
At a time when statistics and data science continue to grow in popularity, graduate teaching assistants (GTAs) are relied upon often to teach introductory undergraduate statistics courses. However, GTA preparation for these roles is inconsistent across institutions and little research has been done to understand GTAs’ knowledge for teaching statistics. Using a combination of the Technological, Pedagogical, and Content Knowledge model (TPACK; Mishra & Koehler, 2006), Ball et al.’s (2008) domains of mathematical knowledge for teaching, and Groth’s (2007) model of statistical knowledge for teaching, we explore two interviews with Norman, a GTA with prior experience working in an introductory statistics course, as he demonstrates his teaching practice in a series of scripting tasks. We highlight areas where the use of scripting tasks made Norman’s knowledge for teaching visible and discuss the potential for using scripting tasks to engage statistics GTAs in thinking about students’ alternative conceptions in statistics.
The authors redesigned their Mathematics for Elementary School Teachers course sequence to use alternative grading practices. The goal of these changes was to decrease DFW rates and to improve equitable access to mathematical ideas. We discuss the nature of the assessments used, the implications for course content, and technological innovations for further adoption. We analyze the grade distributions, and some focus group interviews with students.
We conducted a pilot study that explored the integration of computational thinking (CT) in the teaching and learning of statistics. Participants were undergraduate college students enrolled in an elementary statistics course addressed to students with various majors (Group 1), and in a mathematics course addressed to future early childhood and elementary education teachers (Group 2). The statistics curriculum for Group 2 students included only descriptive statistics. Both groups of students completed a project containing the following: title and research question, data collection/ dataset description, descriptive statistics and/or inferential statistics, visual representations, analysis and interpretation, CT reflection, references, data source documentation. Data was analyzed across the CT core components: i) decomposition- dividing problems into manageable parts; ii) pattern recognition – identifying patterns, trends, correlations; iii) abstraction – simplifying the problem, focusing on essential variables or characteristics; iv) algorithm design – constructing an algorithm or a sequence of computational steps. Both groups scored high on decomposition. Some of the projects from Group 2 demonstrated strong pattern recognition. The projects from Group 1 achieved higher scores in abstraction and algorithm design. Overall, Group 1 reflections showed stronger CT integration. The CT integration in statistics is promising, but we need to account for its variability across educational contexts, including learners and curricula.
Technology is commonly used in mathematics education to communicate ideas and support understanding of complex concepts. Drijvers (2012) describes students’ use of technology as either doing mathematics or learning mathematics, with the latter including practicing skills and developing conceptual understanding. Roschelle et al. (2017) expand on this by considering productive and transformative perspectives of students’ purpose to situate to describe the broader literature on educational technology. In this poster presentation, we use this framework to understand calculus students’ engagement with dynamic graphing software (Desmos) in a calculus context. We found the framework useful for capturing how students interacted with the technology, and how that was related to their thinking.
This poster presents results of a study designed to identify barriers to success for students enrolled in first year mathematics courses at a private university in the northeastern United States. The author presents results of pre- and post-surveys looking at students' experiences in both their prior and college mathematics courses. Responses will be analyzed along with student grades and attendance data, to attempt to identify common factors in students who are successful and in those who are unsuccessful in their first year math courses.
This multi-year project created a series of engaging, accessible proofs paired with their original authors’ biographies. The proofs and biographies were designed for Introduction to Proof (ITP) courses as a means to broaden the mathematical stories students encounter and challenge narrow stereotypes of “who does mathematics.” Exploratory analyses from nine ITP sections examined the effects of pre-survey scores, gender, and curriculum exposure on post-survey scores for logic and sense of belonging. Data collection is ongoing, but preliminary results show that higher pre-survey scores predict greater post-survey gains in logic (3.57 points per SD) and sense of belonging (5.34 points per SD), with women predicted to score 1.87 points higher on logic.
Access to graduate education in the U.S. depends not only on academic ability but also on informal knowledge passed through family networks. This study surveys 519 undergraduate mathematics students across 181 institutions to examine how family education levels shape familiarity with the graduate application process. Chi-square analyses show that students from families with graduate degrees report greater awareness of key elements—such as financial aid, personal statements, and the GRE—while first-generation graduate students were less familiar and more often from lower-income backgrounds. This consistent trend reveals how inherited educational capital creates structural advantages. These findings highlight the need for early advising, transparent funding guidance, and mentorship programs to support students lacking familial experience with graduate education.
Many first-year college students often face significant challenges, dealing with hard courses like college-level mathematics, requiring more effective learning strategies. To support students, we design educational materials that integrate three dimensions of learning: metacognition, resource awareness, and social learning. These materials include reflective journals, searches for university resources, and collaborative assignments and encourage students to develop their own learning styles and make connections with their peers. Our central research questions are: (1) What is the effectiveness of the proposed activities for metacognitive, social learning, and resource awareness skills? (2) What learning strategies do students develop through these proposed activities? These materials were implemented in a general education calculus course using a mixed method approach combining surveys and semi-structured clinical interviews. Data analysis is ongoing. During the poster presentation we will share the implementation framework and new findings regarding its effectiveness.
Bijection is a foundational concept in undergraduate mathematics, yet little is known about how students construct and reason with bijections in combinatorial settings. This study investigates how undergraduate students’ ways of understanding and reasoning about bijections support their combinatorial thinking and vice versa using a small-group teaching experiment. By the conference, I expect to share emerging findings about students’ bijective reasoning.
A persistent goal in mathematics education at the undergraduate level is improving the calculus experience for non-mathematics majors. Recent calls from disciplinary experts in the life sciences have expressed the importance of mathematics to biology (Steen, 2005). Many institutions have responded by offering a course like biocalculus, where calculus concepts are shown to apply to examples from biology. However, the content is not meeting the needs of life scientists (Cozzens & Roberts, 2020, p. 87). In this study, we consider a modeling-first approach to mathematics, developed specifically for life science majors, which we take to be the result of a didactic transposition of quantitative biology into an introductory course (Bosch et al., 2021). Using the developer’s retrospective account of conceiving and implementing the course, we report on an analysis of the conditions and circumstances that shaped its creation.
Graduate mathematics teaching assistants (GMTAs) play a key role in undergraduate instruction but often begin with limited teaching experience. While they are experts in their content area, this expertise alone is insufficient for effective teaching. This study examines how participation in a graduate teaching seminar shapes GMTAs’ Mathematical Knowledge for Teaching (MKT), the kind of knowledge that blends mathematical understanding with insight into how students think and learn mathematics. Using a mixed-methods case study design, we analyzed a semester-long seminar for thirteen beginning GMTAs at a large public university. Data sources included seminar observations, interviews, course materials, and pre- and post-assessments using a modified MKT instrument. Findings indicate that GMTAs enter with highly variable MKT and that structured seminars can strengthen this knowledge by fostering reflection, discussion, and legitimate peripheral participation. Building on this work, we will pursue a design-based research project to iteratively refine the seminar curriculum and further investigate how structured support shapes GMTAs’ growth in MKT.
PRIME (Preparing Responsive and Inclusive Instruction for Meaningful Mathematical Experiences) is a professional development initiative aimed at empowering Graduate Teaching Assistants (GTAs) to deliver inclusive and responsive instruction in gateway math courses with historically high DFW (drop, fail, withdraw) rates. The program addresses disparities in student success that disproportionately affect marginalized student populations. By equipping GTAs with evidence-based pedagogical strategies and fostering a deeper understanding of a sense of belonging’s impact on students’ success, PRIME aims to build a more equitable mathematical learning environment. This poster will share the program’s design, key pedagogical interventions, and initial implementation data. It will also explore the role of GTAs in mitigating systemic inequities in undergraduate STEM education, and how a collaboration between a university’s central teaching and learning office and math department can support graduate students, faculty and undergraduates.
The Mathematical Knowledge for Teaching (MKT) framework is one of the foundational models to explore professional knowledge of mathematics teachers. Although MKT was originally developed for the elementary level, the knowledge required in teaching contexts has made the framework applicable across various levels. Over time, the framework has been utilized for higher grades. This review asks: What patterns emerge regarding the theoretical frameworks utilized, methods employed, purposes, and participant selection in MKT studies focused on university-level teaching? This report presents themes and identifies gaps in MKT studies in undergraduate contexts.
Graduate teaching assistants (TAs) play a pivotal role in undergraduate mathematics education, yet few pedagogical resources are designed specifically for this audience. This project addresses that gap by using artificial intelligence to adapt discourse-based case studies originally developed for secondary mathematics teachers into calculus-specific vignettes for TA training. The resulting “Calculus Transcripts” simulate authentic instructional challenges—such as navigating authority, eliciting student reasoning, and fostering discussion in recitation settings—while preserving the integrity of evidence-based pedagogical principles. This poster will share the adaptation process, examples of the AI-generated transcripts, and reflections from pilot implementation in a semester-long TA training course. Preliminary findings suggest that, while the AI-generated materials required refinement to better represent authentic student reasoning, they show promise as a scalable approach to developing research-informed professional development resources that bridge K–12 and undergraduate mathematics teaching communities.
This study examines how Middle Eastern/North African (MENA) undergraduate students negotiate their mathematical identities in relation to cultural and familial ideologies. Although research in mathematics education has shown that identity shapes how learners engage with mathematics, few studies have explored how such ideologies influence students’ perceptions of the subject. Qualitative interviews asked students about their relationships with mathematics and cultural factors that shaped them. Findings indicate that participants experienced familial and cultural pressures to excel in mathematics and pursue STEM fields, often linking mathematical success to socioeconomic stability. Over time, many shifted from obligation to appreciation as they connected mathematics to their majors or family narratives, reflecting evolving mathematical identities. Overall, this study highlights cultural and familial influences that shape MENA students’ engagement with mathematics and underscores the importance of examining how identity development is mediated by social and cultural meanings.
Although statistics graduate teaching assistants (GTAs) face the difficult task of teaching undergraduate students with a broad range of backgrounds, they often do so with little to no preparation in statistics teaching. There are resources developed for mathematics GTAs; however, there is a lack of resources that can support statistics GTAs in addressing the disciplinary need of teaching and learning statistics. To address this challenge, we developed four modules for Learning to teach Equitably with Authentic Data based on a design-based approach. These modules build on existing frameworks of teaching mathematics and recommendations for teaching undergraduate statistics. The poster will include descriptions of each module and problems of practice that emerged when GTAs participated in modules at two GTA communities.
Generative artificial intelligence (AI) and data science have become increasingly important in mathematics education. For this poster, we will explore the use of custom agents to generate a set of AI students that can be leveraged in training pre-service teachers to notice students’ mathematical thinking. In this proposal, we present the results of study where preservice teachers engaged with the AI student students to gain experience with statistics content and practice noticing and responding to students.
With the goal of enhancing student equity in undergraduate general education terminal mathematics courses, Homp et al. (in progress) implemented inclusive instructional strategies, namely, biographical writing assignments on current, historically minoritized mathematicians. This study explores student artifacts to analyze changes in the students' sense of belonging. A pre- and post-survey adapted from Hazari et al. (2020) revealed a statistically significant increase in students’ sense of belonging within the broader mathematical community. Using Gutiérrez’s (2012) framework for equity in mathematics education—comprising the dimensions of access, achievement, identity, and power— Early in the semester, students primarily focused on mathematicians’ achievements, but later writings included a focus on the identities of the mathematicians. This suggests the instructional tasks described here, which are relatively simple and inexpensive to implement, can have a significant impact on improving mathematical identity for students in a general education mathematics course.
According to Gentner (1983), an analogy maps a source domain (the unfamiliar) to a target domain (the familiar). Thus, the objective of an analogy is to capture the essence of the concept and demonstrate that idea in a familiar setting. In our poster, we will introduce an example of a carefully constructed analogy and how it can be a useful tool for beginners that are still gaining intuition in unfamiliar concepts. Comfortability in college algebra skills are the only assumed prior knowledge. The topic in question is introducing a specific numerical method for solving linear variable-coefficient ordinary differential equations (ODEs) in a two-point boundary value problem (target) by utilizing an analogy involving a cube of varying density restricted to a ruler (source). Along with the poster itself, we include portable manipulatives that represent physical aspects in the source domain such as cube, ruler, small tape measure, thumbtacks, etc. Additionally, the details and actions from the source domain are mapped and explained in terms and steps from the target domain. Through our analogy, we introduce an approachable Realistic Mathematics Education (RME) example with visual and interactive components and, ideally, creates a fun and memorable learning experience (Antonides & Battista, 2022; Gravemeijer, 1999; Lakoff & Núñez, 2000; Nathan, 2021). Thus, with the support of RME and embodied learning, the goal of our poster is to demonstrate the resourcefulness of analogies as a teaching tool and the notion of translating complex mathematical concepts into unconventional context.
There is considerable research on effective professional development (PD) in both undergraduate and K-12 educational settings; however, there is less research on how the characteristics of PD can influence teacher uptake and retention of PD resources and lessons. We report on preliminary findings of a survey of 157 K-12 STEM teachers who participated in large-scale research-based PD. The survey used Likert-style prompts reflecting the main priorities of math education PD. Through Factor Analysis, we identified new categories of administrative support, resources and materials, community, classroom practices, and facilitation that best described the experiences of these participants. We found that while the PDs served different communities and had different goals, these factors show important attributes of PD across projects. While K-12 schools have different contexts, nuances, and challenges than undergraduate teaching spaces, these survey results may provide guidance when designing, implementing, and conducting research in undergraduate communities.
The development of instructional practices, skills, and pedagogical content knowledge is a key aspect of training Graduate Teaching Assistants (GTAs). Current work, like the CoMinDS resource, shared at RUME conferences, aims to understand and support GTAs as they develop these professional teaching practices. This study was conducted in a GTA seminar for an inquiry based precalculus course to investigate the impact of guided reflection, alongside video recording, on graduate teachers’ pedagogy and how it supports decentering. We observed and recorded novice GTA lessons and had them complete guided self reflection forms immediately after teaching a lesson, and then while they watched the recording of the lesson. They then met with a co-instructor for the seminar to discuss their noticings, areas of improvement, and areas of successful student-centered teaching practices. This poster will provide examples of the conversations had between the co-instructor and GTAs after 2 different observations to show the change in pedagogical approaches from the GTAs. This study supports the findings that self reflective teaching and video recordings help teachers change their teaching practices to be less teacher-centered and more student-centered.
Students’ written mathematical communication is a critical competence emphasized worldwide, serving as an essential part of mathematics. In the context of non-proof writing in courses like Calculus and Algebra for undergraduate students, American and Indian students’ writing has visible differences. For high schoolers, such differences have been associated with showing work versus showing thinking (Nachowitz, 2019). In this study, we analyzed students’ cognitive monitoring acts (Garofalo et al., 1985) while answering descriptive and problem-solving tasks. We further analyzed its relationship with the familiarity of the task (Boesen et al., 2010) in an exam-setting. This study has the potential to provide a viable range of cognitive monitoring acts (Garofalo et al., 1985) among Indian and American students’ written responses. The observation, if found viable, can be studied further for implications for assessment.
Harel (2024) published a theoretical framework epistemological justification which manifests itself when asking questions on why and how a piece of mathematical knowledge was created. We aim to build a model using the framework of epistemological justification to examine students in a second linear algebra course. We hope to add insight as to when epistemological justification manifests in proof based linear algebra students as well as attempt to determine what instructional decisions promote epistemological justification. This research will continue to add to the conversation around proof based linear algebra which has been less explored and give further insight into students thinking about linear algebra proofs.
In this poster, I share a literature review describing the current state of research on the experiences of Dalit students and teachers in mathematical spaces and in higher education spaces in India, to motivate my work for my dissertation. Dalits in India are historically positioned as the lowest group of caste community in caste hierarchy. They have been subjected to severe forms of segregation by the so-called upper castes, with brahmins being on top of the hierarchy, controlling power, property and educational access. At present, there is hardly any research that discusses the caste questions in mathematics education, and no work that discusses Dalit mathematics teachers’ practices in and out of the classrooms that support Dalit students across grades. I aim to bridge this gap through my dissertation by studying how Dalit university mathematics teachers and students build solidarity and support each other in and out of the classroom to counter the brahmanical supremacy in mathematics spaces.
This study explores the factors influencing the attitudes of multilingual undergraduates’ attitudes toward mathematics. Drawing from interviews with five Hispanic undergraduates who learned English as an additional language, we adopt a multidimensional definition of mathematics attitudes that encompasses cognitive, affective, and behavioral components. Findings reveal that personal drive, teacher support, and bilingual identity significantly shape students’ mathematics attitudes. The study highlights the need for asset-based pedagogical approaches that leverage students’ linguistic and cultural resources to promote equitable mathematics learning.