Science and Mathematics Education Commons^™

Solving For X: Centering Black Girls’ Experiences In Mathematics Education, Natasha A. Fortes

Graduate Doctoral Dissertations

Black girls can grow up, attend school, and move through their math classes without ever feeling seen as capable mathematical thinkers. Their teachers may not affirm their brilliance. Their voices may even go unheard. Math classes may not be a space where they can imagine themselves belonging. These experiences do not reflect ability. Instead, they reflect on the conditions in which they are expected to learn. This study centers the voices of Black girls and asks what they deserve from their mathematics education and instructors to develop a mathematics identity. The study is grounded in Black feminist traditions and draws …

Pre-Service Mathematics Teachers’ Perceptions Of Equity And Interactive Digital Tasks: Implications For Initial Teacher Education, Kate Roscioli, Liza Bondurant

Publications

Interactive digital tasks have the potential to aid mathematics educators in providing equitable mathematics learning experiences. However, research indicates that mathematics educators may not be aware of how interactive digital tasks can promote equitable teaching practices. This study reports on a design-based research project exploring pre-service teachers’ perceptions of equity and interactive digital tasks. Over three cycles of design, implementation, evaluation, and revision, 57 pre-service teachers participated; this article focuses on data from the third cycle, involving 25 pre-service teachers. Using lesson analyses grounded in the Equity-centered Transformative Technology Lesson Analysis Tool (EqT-tech LAT; Suh et al., 2022), we …

How Leadership Can Support Inquiry-Based Learning In Myp Mathematics, Paul A. Thompson

Graduate Teacher Education

This literature review examined the research question: “How can instructional leadership prepare IB MYP Mathematics teachers to implement inquiry-based learning (IBL) effectively?” The review defined IBL within the International Baccalaureate Middle Years Program (IB MYP), then explored how inquiry in the MYP was designed to promote better student outcomes in conceptual understandings, interdisciplinary learning, and real-life connections. The role of the MYP Coordinator (MYP), the pedagogical leader of this program, is central to answering the questions that focus on leadership. The literature also examined the benefits and barriers of implementing inquiry-based mathematics instruction. The findings suggested that effective IBL improves …

Examining Mathematics Identity And Student Capital In The United States And Norway: Comparative Insights From First-Generation College Students In First-Year Mathematics Courses, Margaret Ann Bolick

All Dissertations

First‑generation college students (FGCSs)—students whose parents did not complete a bachelor’s degree—are underrepresented in international research on first‑year mathematics course retention and are often compared to their continuing‑generation peers in ways that reinforce deficit narratives and skew perceptions of FGCSs. This study provides a descriptive comparison between FGCSs’ mathematics identity and forms of capital across the cultural contexts of Norway and the United States through four interconnected papers that address the overarching research question: How do cultural and educational contexts in Norway and the United States influence how FGCSs conceptualize and express forms of capital and mathematics identity in first-year …

The Math Teaching Atlas: Trails, Anchors, And Compass In Action, Ivan Z. Feng

Journal of Humanistic Mathematics

This paper advocates a shift grounded in mathematical reasoning: teach and write math through explicit routeways rather than narratives, anchor new ideas to familiar concepts on a roadmap, and use motivation and concrete examples as a compass and simulation for discovery.

Creating Art With The Generalized Pythagorean Theorem, Ángel Colín

Journal of Humanistic Mathematics

The Pythagorean Theorem and its generalizations have been widely studied. In this article we focus on one particular generalization that asserts that the area of a polygon with one side the hypotenuse of a right triangle is the sum of the areas of similar polygons whose corresponding sides are the other two sides [4]. Using this theorem together with interactive software or simply pencil and paper, we create some visually enticing artwork. This activity, we believe, can contribute positively to geometry teaching at all academic levels.

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

Journal of Humanistic Mathematics

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

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

Mathematics Dissertations

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

Rethinking Dfw In Gateway Mathematics: Preserved, Disrupted, And Dissipated Momentum Pathways To Student Retention, John Alan Nunnery, Charles Mathies

Educational Leadership & Workforce Development Faculty Publications

This study examines how disaggregated first-year mathematics outcomes, including failure, low-passing grades, course withdrawal, and no attempt at a credit-bearing mathematics course, are associated with second-year retention at a large, diverse, urban public university. The study extends academic momentum theory by positing and operationalizing preserved (marginal passing), disrupted (failure or withdrawal), and dissipated (non-enrollment) as qualitatively distinct momentum states rather than a single condition. Using a segmented binary logistic regression model with more than 26,000 first-time, full-time students across ten entry cohorts (2012–2021), we estimate differences in retention by mathematics outcome, course type, and cohort context. Results show a pronounced …

From Questions To Action: A Multi-Year Journey Toward Instructional Excellence In Middle School Mathematics, Courtney Baker, Johnna Bolyard, Deborah Crawford, Divya Varier

Journal of Mathematics and Science: Collaborative Explorations

This paper describes the evolution of a research-practice partnership (RPP) designed to understand the impact of data-informed decision making initiatives on supporting ambitious mathematics instruction and how middle-school based mathematics specialists facilitate those initiatives. While school-university partnerships have a history of designing, implementing, and studying instructional improvement efforts, the impact of such efforts on practice is not clear (Cai et al., 2017b; Denner et al., 2019; Henrick et al., 2016). Over the first three years of our partnership, we have collected data from a variety of sources and shared them in ongoing data conversations with a range of district-level collaborators. …

The Interplay Between Structure And Teacher Agency In The Detracking Of Algebra 1: A Qualitative Case Study, Kristine Norris

Dissertations

This single qualitative case study examined how detracking Algebra 1 at Mountainview High School (pseudonym) restructured the course’s rules and resources and how teachers exercised agency in response. Guided by Giddens’ structuration theory and Weis and Fine’s critical bifocality, the study explored how institutional structures both shape and are reshaped by teacher action within broader systems of inequality. Participants were seven Algebra 1 teachers involved in the first two years of detracking. Data was gathered using semi-structured interviews and analysis focused on two research questions: (1) In what ways did detracking alter the structures of Algebra 1 courses, and (2) …

Opportunities For Mathematical Thinking (Omt) In Fourth Grade Mathematics Textbooks., Lucas Wayne Elliott

Electronic Theses and Dissertations

Mathematical thinking is essential not only for students’ academic achievement but also for their ability to compete in a global workforce (Schoenfeld, 1992; Mullis & Martin, 2017). However, students in the United States continue to lag behind their international peers on assessments that measure mathematical thinking (Mullis et al., 2020; van Davier et al., 2024). These gaps emerge as early as elementary school, where the foundation for future academic success is established (Aunola et al., 2004; Locuniak & Jordan, 2008). Given the importance of mathematical thinking and the persistent disparities in student performance, this study examined how mathematical thinking is …

Mathematics Teachers' Perspectives On Computational Thinking: Insights Into Knowledge, Strategies, And Challenges, Hasan Djidu, Heri Retnawati, Haryanto Haryanto

The Qualitative Report

In this study we explored how mathematics teachers in Indonesia understood and implemented Computational Thinking Skills (CTS), as well as the challenges they encountered. While CTS—encompassing skills such as decomposition, pattern recognition, abstraction, and algorithmic thinking—had gained prominence in global education reform, its classroom-level integration remains uneven, especially in diverse school settings. Through semi-structured interviews with 11 mathematics teachers from primary and secondary schools across varied regions in Indonesia, including underserved and remote areas, we examined how CTS was conceptualized, practiced, and hindered in real-world teaching. Our thematic analysis revealed three key findings: (a) teachers demonstrated uneven familiarity with CTS, …

Predicting Secondary Mathematics-For-Teaching Knowledge Using Beliefs, Experience, And School Culture: A Hierarchical Regression Analysis, Adam R. Brulhardt

Theses and Dissertations

Research in recent decades has supported the notion that practice-based mathematical knowledge is crucial for effective teaching, playing an important role in enacting reform-oriented instruction required for improving student achievement. Despite its importance, teachers—especially novices—require more support in acquiring such knowledge, an ongoing challenge exacerbated by teacher shortages. The purpose of this quantitative study was to determine whether collaborative school culture (CSC) explained variance in knowledge of algebra for teaching (KAT) beyond variance explained by mathematics-related beliefs and years of teaching experience for U.S. secondary teachers. Measures within an online Qualtrics survey included the Beliefs About Mathematics and Teaching Scale …

Expansively Framing Mathematics And Computer Science Teaching With Digital Technology In Elementary Classrooms, Kimberly E. Beck, Jessica F. Shumway, Patrick Ocran, Jody Clarke-Midura, Mimi Recker

Publications

Expansive Framing (EF) is a theory and an instructional technique to facilitate connections between content and contexts. We employed EF as an approach to create a series of integrated mathematics and computer science (CS) lessons, using digital technology as a tool to leverage shared mathematical and computational ideas. We used deductive theoretical qualitative analysis of transcripts of classroom implementations to investigate how two fifth-grade teachers and one computer lab paraprofessional educator used EF during their teaching and what the EF approach looked like in practice. Findings suggested that educators engaged in EF principles when they were present in curricular materials, …

Rethinking “Key-Chain Swap” And Other Decontextualized Algorithm Teaching Practices For Rational Number Learners, Connor B. Desai

Education Dissertations

Mathematical literacy is critical in an increasingly data-driven society, yet many students struggle with rational number concepts due to the prevalence of decontextualized algorithmic instruction. This study investigates the impact of targeted professional development (PD) on sixth-grade teachers’ instructional strategies and their students’ rational number achievement. The research examines whether explicit, conceptually grounded teaching of rational number operations improves student understanding compared to traditional algorithm-based instruction. Using a mixed-methods approach, the study collected quantitative and qualitative data from students at two middle schools. The intervention was statistically significant at School A, where students in the intervention group demonstrated greater achievement …

Nurturing The Student Voice And Its Creative Power In Mathematics Teaching And Learning: Research With Students On Emotion, Imagination, And Understanding., Luis Adolfo Zambrano

Dissertations, Theses, and Capstone Projects

This research in mathematics education explores the teaching and learning of mathematics at the high school and community college levels, integrating diverse research methods to examine how educators can cultivate a dynamic, collaborative, and responsive classroom climate. Framed by K. Tobin and K. Alexakos’s authentic inquiry education research framework (2020), the methodology actively engages students as co-researchers, valuing their insights and experiences as integral to the learning process. This approach fosters a meaningful dialogue on managing emotional and cognitive challenges faced by students of mathematics while identifying strategies to support and enhance students’ innate imaginative and creative capacities.

Grounded in …

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

Department of Mathematics: Dissertations, Theses, and Student Research

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

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

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

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

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

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

High Ability, Hidden Gaps: Building Quantitative Reasoning Amongst Singapore’S Mathematically Literate, Rebecca M. Nichols

Numeracy

In Singapore, where primary and secondary students routinely top standardized worldwide mathematics examinations, a paradox emerges: when reaching university, many struggle to apply their skills critically in real-world contexts. This commentary examines the challenges and strategies involved in teaching quantitative reasoning (QR) to mathematically literate students in a top-ranking Singaporean university. While these students arrive well-trained in computation and procedural problem-solving, they often lack confidence and flexibility in ambiguous, data-driven decision-making. This article argues that fostering QR education is crucial not only for Singapore but for education globally, as QR skills underpin evidence-based reasoning within and across disciplines. Such an …

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

Honors Scholar Theses

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

A Model For Utilising Crises-Related Issues To Facilitate Transdisciplinary Outdoor Steam Education For Sustainability In Integrated Mathematics, Language Arts And Technology Classrooms, Musa Saimon, Zsolt Lavicza, Tony Houghton, Fredrick Mtenzi, Pablo Carranza

Institute for Educational Development, East Africa

STEAM (Science, Technology, Engineering, Arts and Mathematics) Education is one of the approaches that teachers adopt as they shift from content delivery focused teaching to skills development teaching. Also, effective STEAMING requires connection to issues outside the classroom (outdoor STEAM) and hence the coinage of the term Transdisciplinary Outdoor STEAM. However, research shows that teachers fail to design problems that match the framework of Transdisciplinary outdoor STEAM. In this study, we propose a model for using real-life crises such as Covid-19 or heatwaves or famine to support teachers in their effort to improve teaching practices in the 21st Century. The …

Knowing By Heart: Philosophical Dimensions Of Humanistic Mathematics Education, Catherine Henney

Theses and Dissertations

This project seeks to revive interest in late twentieth century humanistic mathematics education (HME) so that its principles might cross the boundary of higher education and settle in corners of the K-12 math education space. In particular, HME’s theme of teaching math humanistically directs attention to features and phenomena that bear strongly on students’ daily classroom experiences. Personhood, agency, inquiry, meaning, environment, feelings, relationships: these elements invite a more thorough meditation and philosophical analysis. Though it is a largely philosophical endeavor, this project is enlivened by classroom vignettes and case studies that bring practical relevance to HME’s core principles. Chapters …

Study Of Graduate Student Instructors’ Attempts To Incorporate And Reflect On Using Discourse Practices In Undergraduate Mathematics Courses, Katie Johnson Sprague

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

Within the last decade, the National Council of Teachers of Mathematics (NCTM) has made a call to action, asking educators to engage in effective teaching of mathematics which includes having classrooms rich in mathematical discourse (NCTM, 2014). In this nine-week dissertation study, three mathematics graduate student instructors (GSIs) teaching undergraduate students at a large midwestern university enacted discourse practices to promote mathematical discussions as part of a participatory action research study. The participants were video tapped teaching six times and attended four whole group meetings. The whole group meetings were used to discuss the practices, planning, and enactment of the …

Leveraging International Large-Scale Assessments: Insights From An Item-Writing Professional Development Program For High School Mathematics Teachers, Mark Lester B. Garcia, Catherine P. Vistro-Yu

Mathematics Faculty Publications

The Philippine Department of Education, despite seeing minimal improvements in the country’s score and rankings in the recent cycles of international large-scale assessments (ILSAs) such as TIMSS and PISA, maintained that it shall continue to participate in ILSAs to monitor the progress of educational effectiveness and benchmark with other countries by observing and adopting commendable practices. While legislators and other stakeholders push for increased financial resources in the education sector as part of the country’s preparations for upcoming ILSAs, one crucial aspect that is largely overlooked is teacher training. This paper presents a viable yet contentious way of upskilling teachers …

The Effects Of A Mediated Field Experience Methods Course On Pre-Service Elementary Mathematics Teachers' Beliefs, Valorie L. Zonnefeld, Luralyn M. Helming

Faculty Work Comprehensive List

A mediated field experience (MFE) mathematics methods course increased both pre-service elementary teachers’ (PSTs) self-efficacy for teaching mathematics and mathematical dispositions. The semester-long MFE with significant, structured teaching experiences was conducted onsite at an elementary school. Quantitative, pre- and post-surveys of mathematics teaching efficacy revealed statistically significant increases over the semester. A qualitative analysis of PSTs as sophomores and seniors further explored and supported this increase in PSTs’ self efficacy for teaching mathematics. Qualitative data also revealed interesting changes in mathematical dispositions and a shift in PSTs from a self-as-student perspective to a self-as-teacher focus.

Teachers' Experiences With Teaching For Social Justice In Tracked Middle School Mathematics Classes., Stephanie Jean White

Electronic Theses and Dissertations

Tracking is a longstanding structure in K-12 mathematics that decades of research has shown to be inequitable. Despites calls to detrack mathematics classes, most U.S. schools retain tracking. Mathematics educators have attempted to implement teaching pedagogies such as Teaching for Social Justice (TSJ) that promote equity in all mathematics classrooms, including tracked classes. This research used the Learning to Teach for Social Justice Belief (LTSJ-B) Scale with middle school mathematics teachers who have taught in tracked classes to measure their levels of commitment to TSJ. This research also employed case study methodology with three teachers and cross-case analysis using TSJ …

Mathematics Education Researchers’ Practices In Interdisciplinary Collaborations: Embracing Different Ways Of Knowing, Elizabeth Suazo-Flores, William S. Walker Iii, Signe E. Kastberg, Mahtob Aqazade, Hanan Alyami

Teaching, Leadership & Professional Practice Faculty Publications

Mathematics education researchers (MERs) use practices unique to the mathematics education discipline to conduct their work. MERs’ practices, i.e., ways of being, interacting, and operating, define the field of mathematics education, are initially learned in doctoral preparation programs, and are encouraged and sanctioned by conferences and publications. Disciplinary practices facilitate MERs’ interactions within mathematics education. When working in interdisciplinary groups, differences in disciplinary ways of being, interacting, and operating can create challenges with completing research and other work. Since MERs’ engagement in interdisciplinary collaborations is encouraged and can result in products contributing to the evolution of the mathematics education discipline, …

Secondary Math Teachers’ Responses To Errors In The Classroom, Richie Vicinanza

Honors College Theses

This study was conducted in an effort to find out how modern-day secondary math teachers respond to errors in their classrooms and the reasonings behind their responses. To fulfill the purpose of this study, various methods of research were used to gather information. Methods included looking into the scholarly sources surrounding the topic as well as a primary-conducted study in the field. Participants of this study were high school math teachers. The participants engaged in two semi-structured interviews (an initial and a debrief) as well as an observation that was conducted during one of their classes. Through the initial interview, …

Theorizing Mathematical Proof As Becoming: A Deleuzio-Guattarian Investigation, Joshua P. Case

Graduate Theses, Dissertations, and Problem Reports (ETD)

In this dissertation, I utilize the post-structural philosophy of Gilles Deleuze and Félix Guattari as a lens for investigating the proof process. Deleuze and Guattari were both post- structural philosophers who, like many in this tradition, troubled traditional notions related to stable identities, meaning, language, and mathematics. For Deleuze, sense and meaning is not the result of a sterile, transcendent effect or condition that is associated with propositions and states of affairs. Rather, it is the result of a material production that emerges from the world and that has independence from language and the mind. I apply this framework to …