Mathematics Commons^™

Developing A Learner-Centered Teaching Routine, Hyeeun Jang

Journal of Humanistic Mathematics

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

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

Doctoral Dissertations and Projects

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

The Effect Of Emotional Intelligence And Logical-Mathematical Intelligence On Students’ Mathematical Problem-Solving Ability, Zulkyfli Siduppa, Sutji Rochaminah, Muh Hasbi, Dasa Ismaimuza

Jurnal Pendidikan Sains

Mathematical problem-solving ability is an essential competency in mathematics education because it supports students’ reasoning, critical thinking, and decision-making skills. This study aimed to examine the influence of emotional intelligence and logical-mathematical intelligence on the mathematical problem-solving ability of Grade XII students at SMA Negeri 1 Tolitoli. The study employed a quantitative survey design involving 143 students from the Mathematics and Natural Sciences (MIPA) program during the 2023/2024 academic year. Data were collected using an emotional intelligence questionnaire, a logical-mathematical intelligence questionnaire, and a mathematical problem-solving test on algebraic function limits. All instruments were validated and demonstrated satisfactory reliability, with …

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

Books

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

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

Conceptualizing A Responsive Design Pedagogy To Support Teachers' Responsiveness To Students' Mathematical Ideas Through Making, Denish Ogweno Akuom

Theses, Dissertations and Culminating Projects

This study develops Responsive Design Pedagogy (RDP), a conceptual and analytic model of teacher responsiveness in design-based environments, to account for how responsiveness emerges through interactions among students, tools, and tasks. Although responsiveness has been widely studied in mathematics education, limited attention has been given to responsiveness within mathematical design activity and to how teachers attend to the multiple modes through which students express their mathematical ideas. Addressing these gaps, this qualitative study examined one teacher’s enactment of responsiveness in a Learning-by-Design classroom where students designed and used 3D-printed mathematical tools. Data sources included classroom video, student design artifacts, teacher …

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 …

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, …

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, …

Teaching Mathematics For Labour Emancipation: An Autoethnography Of A Math Teacher In Mykonos, Dimitris T. Maris, Konstantinos P. Christou

Journal of Humanistic Mathematics

A wealthy society does not necessarily ensure a good education for its students, just as it does not guarantee wealth for its workers. In this paper we visit a junior high school mathematics classroom on the Greek island of Mykonos, where a significant number of students are employed. In this context, we explore how a mathematics teacher, inspired by social justice mathematics, can empower students in their work environments. We adopt an autoethnographic approach in our narrative, presenting the process of designing and implementing specific mathematical activities aimed at revealing the issue of labour exploitation in the touristic Greek islands. …

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 …

Building Communities Of Care For Equity, Justice, And Culturally Responsive Practice In Mathematics Education, Nicole Fletcher, B Waid

Journal of Humanistic Mathematics

Teaching is widely considered one of the “caring professions,” but conceptualizations of care and how care is put into practice in education are not universal. In this article, we draw from a range of perspectives on care that integrate supportive interpersonal relationships, high expectations, and culturally relevant theories of critical care, as well as Queer Theory and Disability Justice, to explore the application of these ideas in mathematics education. We identify key elements for building communities of care in mathematics education contexts: co-constructing community agreements, redefining participation, shifting traditional power structures, collaborative problem solving, and building networks of care beyond …

Longitudinal Investigation Of Early Mathematical Achievement And Classroom Strategic Diversity: A Replication And Extension Study, Douglas H. Clements, Yixiao Dong, Crystal A. Day-Hess, Julie Sarama

Early Childhood Special Education: Faculty Scholarship

Developing solution strategies, effortful procedures that students employ to solve a specific problem, is an important mathematical goal. Studies have documented intraindividual strategy variability and its significance for learning, but only some have addressed the interindividual strategic diversity across students within a classroom. This study analyzed classroom strategy diversity using assessments of 527 kindergartens to 2nd-grade students. Latent growth modeling analysis revealed that the best fit was a spline model featuring two phases of linear growth with different growth rates (i.e., one in Kindergarten, the other from Kindergarten spring to second grade). A growth mixture modeling analysis demonstrated that only …

Tasks For Learning Trigonometry, Sydnee Andreasen

All Graduate Reports and Creative Projects, Fall 2023 to Present

Many studies have been done using task-based learning within different mathematics courses. Within the field of trigonometry, task-based learning is lacking. The following research aimed to create engaging, mathematically rich tasks that meet the standards for the current trigonometry course at Utah State University and align with the State of Utah Core Standards for 7th through 12th grades. Four lessons were selected and developed based on the alignment of standards, the relevance to the remainder of the trigonometry course, and the relevance to courses beyond trigonometry. The four lessons that were chosen and developed were related to trigonometric ratios, graphing …

“Don’T Call On Me!”: Mediating Preservice Elementary Teachers’ Mathematics Anxiety In A Problem-Based Classroom, Christina Koehne, Wenyen Huang, Nataly Chesky

Excelsior: Leadership in Teaching and Learning

This study aims to understand the ways in which problem-based teaching in a mathematics content course can alleviate pre-service elementary school teachers' mathematics anxiety. The significance of this work is to help increase the content and pedagogical knowledge of mathematics education, as outlined in STEM policies. Using a mixed method approach, the teachers-researchers explore what methods, procedures, and other perhaps unknown variables, helped pre-service elementary teachers decrease their mathematics anxiety during two mathematics content courses. The findings illuminate five major themes the authors discuss, which are illustrated by rich descriptions of students’ narratives and interviews. Given the importance of mathematics …

Facilitating Mathematics And Computer Science Connections: A Cross-Curricular Approach, Kimberly E. Beck, Jessica F. Shumway, Umar Shehzad, Jody Clarke-Midura, Mimi Recker

Publications

In the United States, school curricula are often created and taught with distinct boundaries between disciplines. This division between curricular areas may serve as a hindrance to students' long-term learning and their ability to generalize. In contrast, cross-curricular pedagogy provides a way for students to think beyond the classroom walls and make important connections across disciplines. The purpose of this paper is a theoretical reflection on our use of Expansive Framing in our design of lessons across learning environments within the school. We provide a narrative account of our early work in using this theoretical framework to co-plan and enact …

Prospective Teachers' Conceptions Of Area, Betsy Mcneal, Sayonita Ghosh Hajra, Michael Battista, Ayse Ozturk

Teaching & Learning Faculty Publications

This study explored 10 prospective teachers’ (PTs’) understanding of the area of a rectangular region using square and non-square rectangular area-units. In an hour-long interview, each PT was first asked to explain how they would find the area of a given rectangular region in terms of a non-square notecard. For several PTs, this task prompted discussion of a square unit defined by the edge of the notecard. In a second task, PTs were presented with a rectangular array of squares and were asked to explain to a fictional child why multiplying length times width does not count the top left …

Book Review: Algebra The Beautiful: An Ode To Math’S Least-Loved Subject By G. Arnell Williams, Judith V. Grabiner

Journal of Humanistic Mathematics

In his book Algebra the Beautiful, G. Darnell Williams has undertaken a challenging job – to show the importance, deep structure, intellectual connections, and sheer beauty of classroom algebra. This review describes some of the questions the book raises, the historical and cultural context it provides, and the intellectual apparatus it deploys.

Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur

Journal of Humanistic Mathematics

Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …

The Nothing That Really Matters, Szilárd Svitek

Journal of Humanistic Mathematics

Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, that of natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state …

Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos

Journal of Humanistic Mathematics

We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …

The Fractal Geometry Of Mathematics Classrooms: Navigating Classroom Environments In Factory-Model Schools, Cacey L. Wells

Journal of Humanistic Mathematics

Mathematics education has a diverse and complex history. After decades of national reform, mathematics classrooms today are still in desperate need of change. This article examines the current state of factory-model schooling through the lens of Mandelbrot's The Fractal Geometry of Nature in order to rethink pedagogic practices.

Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder

Department of Mathematics: Faculty Publications

In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …

Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder

Department of Mathematics: Faculty Publications

In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …

The Problem Of Words: Learning To Teach Mathematics When Numbers And Languages Mix, Gladys Krause

Journal of Humanistic Mathematics

In this piece I propose a perspective shift, from a simplified view of mathematics story problems to a more academically rigorous perspective that integrates mathematical proficiency and language practices crucial for educating bilingual students. The data presented in this article provide a window into what preparing bilingual pre-service teachers to teach mathematics might involve. I discuss issues that arise in the context of preparing Spanish-English bilingual pre-service teachers in a way that can inform their practice in linguistically and culturally diverse classrooms.

Mindfully Navigating The Wind And Water: Defining The Currents Of Metaphors That Interfere With Excellence In Mathematics Education, Rob Blom, Olivia Lu, Chunlei Lu

Journal of Humanistic Mathematics

We bring to the forefront of educational thought a specific attitude toward the COVID-19 crisis that harnesses the symbolism of wind and water to navigate the cultural storm interfering upon our mathematical and pedagogical craft. The purpose of our paper is to open up space for opportunities in mathematics education using integral mindfulness as the rudder to readjust our bearings. More specifically, through conceptual analyses and making explicit the currents of change, disorder, and technology, we can apply discernment to these metaphors that intersect our pedagogy to re-align efforts and attitudes toward an integrated (aperspectival) culture of mathematics education. Through …

Middle School Students Generating Mathematical Problems From A Real-Life Situation, David Coffland, Ying Xie

Journal of Humanistic Mathematics

In this study, we examined the effect of different presentation formats of a realistic situation on students’ mathematical problem-posing behavior. We divided thirty-six middle school students into two groups, gave them a pretest, and then showed them a realistic, problem-posing situation in Artifact or Video format. We used Silver’s core dimensions of creativity, namely fluency, flexibility, and originality, to measure participants’ problem-posing activity. The results for the fluency measures showed that the Artifact group wrote more questions than the Video group but the same number of mathematics problems. The Video group posed problems in more mathematical domains than the Artifact …