Mathematics Commons^™

Algebraic Topics For Future Middle School Teachers, Leonard Van Wyk

Department of Mathematics and Statistics - Faculty Scholarship

This text contains algebraic concepts relevant to the middle school mathematics curriculum. Topics include the basics of number theory, functions, linear systems, matrices, and polynomials.

Ai Beliefs And Practices In Community College Classrooms, Julie Eng, Heather Umphlett, Jocelyn Gilchrist, Alicia Howell, Mary Ann Howell, Wendy Miller-Edwards, Laurel Pope

Inquiry: The Journal of the Virginia Community Colleges

The country, the Commonwealth of Virginia, and Virginia Community College System initiatives all promote generative AI within education. It is a topic of great concern and interest for higher education instructors, yet at the same time many faculty members feel uncertain about effectively integrating it into class material. To further add pressure to the AI explosion, community colleges particularly face a responsibility to prepare their students for success in this new AI-focused environment. In this article, seven faculty members from Camp Community College discuss the implications of generative AI programs, including subscriptions and chatbots, within their particular courses and how …

Number Talks To Promote Discourse In The Algebra 1 Classroom: A Number Talk Curriculum Development For A Unit On Quadratic Expressions, Lindsay C. Borger

Masters Theses/Capstone Projects

This project sought to develop a curriculum of Number Talks for use at the secondary level, specifically in an Algebra 1 class as a supplement to a unit on quadratic expressions. The project begins with a look at existing research on constructivism and social constructionism as well as the reforms in mathematics education informed by those learning theories. It then looks at calls for more discourse in the mathematics classroom as a part of these reform efforts, and the part Number Talks play in fostering discourse and mathematical thinking for students. The Number Talk curriculum includes a guide for implementing …

Patterns Within The Collatz Conjecture, Kiel Harrison

SACAD: Scholarly Activities

The Collatz Conjecture, also known as 3n+1, one of the most famous unsolved problems in mathematics, has been forever out of reach of being truly solved. However, through the application of traces, there is now a new pathway forward to working out a potential solution. This study shows how this pathway was found, and what steps need to be taken to follow it.

Navigating Geometry With Interactive Lessons: A Collection Of Resources In Geogebra That Address Frequently Held Misconceptions, Sara Vance

Honors Program: Senior Projects (Public)

Nearly every high school student in the United States is required to take a geometry class, and for many, it’s unlike any math class they’ve taken before. Additionally, there are certain topics with which past and present geometry students alike tend to struggle. This project was created to address these issues; my goal is that these materials will help students better understand these topics and clear up their frequently held misconceptions about geometry. This project was supported by interviews I conducted with veteran high school geometry teachers with over 75 years of teaching math between them.

This collection of interactive …

An In-Depth Analysis Of The Bellarmine University Student Athlete Experience, Mattingly E. Spalding

Undergraduate Theses

The goal of this thesis is to improve the student athlete experience at Bellarmine University through direct feedback from our current student athletes. By defining what parts of the student athlete experience they value most, Bellarmine can reflect on the support currently provided in these areas. Additionally, if it is concluded through the response that high valued areas are not being satisfied, Bellarmine can work to improve the support in these areas. Or, if there is abundant support in a low-valued area, Bellarmine could think to shift resources into a more needed concentration. Through the design sample, data was accumulated …

Best Strategies For Bilingual Education: How Can We Explain Their Success?, Claudia Cabrera, Olga Kosheleva, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

When designing AI-based tools for education, it is important to take into account the experience of human teachers. In this, it is necessary to distinguish between the education features that are justified by the general features of the corresponding education task -- these features should be taken into account in AI-based learning as well -- and features which are specific for traditional non-AI teaching. In this paper, on the important example of bilingual education, we show that several empirically successful teaching strategies can be explained in the general context -- and thus, should be implemented in AI-based teaching as well.

The Effects Of Functional Moves In Teacher Questioning On Students’ Contextualization Of Mathematical Word Problem Solving, Yi-Jung Lee

Curriculum and Instruction Faculty Publications and Presentations

Posing purposeful questions is one of the most effective teaching practices (NCTM in Principles to actions: Ensuring mathematics success for all. National Council of Teachers of Mathematics, 2014). Although the types and functions of teacher questioning have been abundantly studied, research on the role of teacher questioning in students’ contextualization process as they solve word problems is rather scarce. This study was conducted to investigate the function of six elementary preservice teachers’ questioning, its impact on students’ contextualization, as well as the successes and difficulties of enacting questioning. The collected data were analyzed using thematic analysis. The findings indicated that …

What Happened When I Took Calculus For The First Time At Age 47, Britt Kaufmann

Journal of Humanistic Mathematics

These five poems are inspired by being in high school math classes and could be used in the classroom for cross-curricular enrichment.

Revisiting The Hidden Symmetries Of The Multiplication Table, Zoheir Barka

Journal of Humanistic Mathematics

In previous work, we have explored some of the symmetries hidden in the multiplication tables of natural numbers and integers. In this article, we dive deeper into the hidden symmetries within the distribution of positive and negative integers. We also share various ideas to explore these symmetries in a classroom setting, encouraging active engagement and deeper understanding among students.

Ethnomathematics Projects For Projective Geometry In Distance Learning, Wen-Haw Chen, Ja'faruddin Arsyad Ide

Journal of Humanistic Mathematics

This article reports on an ethnomathematics project we developed and implemented in an online learning environment to connect with students’ cultural backgrounds and to highlight the links between their environment, culture, and mathematics. The project is based on Simple House Theory, a framework that involves the application of projective geometry in the design of traditional houses and building numbers. Our results show that this approach fostered active participation and engagement despite the standard constraints and challenges of distance learning.

Engaging Mathematicians One Step At A Time: Math Trails, Mary L. Dalton, Jennifer Yantz

Journal of Humanistic Mathematics

Mathematics is present in everything we see and do. Sometimes we look past it, looking for some mathematical mystery when the beauty of mathematics is evident in the most obvious ways. One way to engage students to notice connections to mathematics in these everyday objects and events is to direct them in a guided math trail. A math trail is an activity where participants follow a map or guide to various locations while they are encouraged to take notice of connections to mathematical patterns and concepts in the objects around them. An important benefit is that going on a math …

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

Journal of Humanistic Mathematics

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

An Unlikely Duo: Injecting Art Projects In The Lower-Division Mathematics Classroom, Douglas T. Pfeffer, Christina Durón

Journal of Humanistic Mathematics

Too often society has sterilized mathematics to the point that many view it as drab and deplete of aesthetic intrigue---in higher education, this is particularly true of students in the lower-division classroom. In this paper, we propose the use of art projects as a novel way to alter this perspective. Art projects function as a hands-on, active way to invite students to both identify connections between math and various non-mathematical disciplines as well as view math as overall more intriguing, inviting, and interesting. This paper details our implementation and discusses anonymously solicited survey data that highlights our successes.

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. …

Math Is _______: A Study On Prospective Teachers' Perceptions Of Math And Teaching Math, Kayla Mead, Katherine Baker

Journal of Humanistic Mathematics

In this project, we examined one cohort of twenty-eight college students and their perceptions of mathematics at the beginning and end of a semester-long mathematics content course for K-8 prospective teachers (PTs). More specifically, our study explored PTs’ perceptions of what mathematics is and what mathematics teaching is, and how and why those perceptions might change over the semester-long mathematics course. PTs’ perceptions were captured through open-ended surveys and follow-up interviews. Our intention was to better understand the reasonings for changes in perceptions during the course to support teacher educators in their work of preparing prospective teachers.

Stem Major Perspectives For Humanizing Undergraduate Mathematics Classes, Kelly Macarthur, Derek Williams, Bryce Hughes

Journal of Humanistic Mathematics

Using the eight dimensions of the rehumanizing framework [32] by Gutiérrez, built on a sociopolitical foundation, we report on research findings about what Latin* [41], Native American, LGBTQ+ and/or women science, technology, engineering, and mathematics (STEM) majors at two primarily white institutions (PWI) perceive as humanizing in their mathematics courses. In analysis of interviews with twenty students, we found that the core aspects of a humanized learning experience center relationality and a caring classroom environment. We then explore tensions that arose regarding the implementation of one teaching strategy reflecting the Cultures & Theirstories rehumanizing dimension, suggesting that implementation of such …

Comparing Two Psychometric Approaches: The Case Of Item Analysis For A Classroom Test In Mathematics, Mark Lester B. Garcia, Kevin Carl P. Santos, Catherine P. Vistro-Yu

Mathematics Faculty Publications

Multiple-choice and constructed-response item formats are widely used in Philippine classrooms where tests are primarily summative. Conducting item analysis provides teachers the professional possibility to independently improve their test items while also allowing them to make informed decisions about test improvement and ensure that their assessments provide meaningful scores. Comparisons of item analysis approaches have been extensively used in standardized tests but not so much in small-scale testing such as classroom assessments. Hence, this research reports an empirical study where a summative test for classroom use is analyzed using psychometric techniques from the Classical Test Theory (CTT) and the Item …

Image Of Mathematics: A Case Study Of Two Women's Early Mathematics Experiences, Lili Zhou, Elizabeth Suazo-Flores, Bima Sapkota, Rose Mbewe, Jill Newton

School of Mathematical & Statistical Sciences Faculty Publications

People often view mathematics as abstract, cold, and irrelevant to real life, and their school experiences likely influence such views. In this case study, we investigated the mathematics experiences of two women who participated in an afterschool girls-only STEM club 30 years ago when they were in fifth and sixth grades. We explored how the participants' early in- and out-of-school experiences informed their images of mathematics. We collected data through a survey, focus group interviews, and individual interviews. We employed oral history methods in interviews to grant participants a significant degree of freedom to retrospectively recount and reconstruct their experiences. …

Examining Student Understanding Of Series Convergence Using Script Writing, Eduardo Torres Manzanarez

Mathematics Dissertations - Archive

This exploratory study investigates second-semester calculus students’ understanding of series convergence using both nonscripting and scripting-based tasks. Researchers recognize that students encounter difficulties with learning series, including series convergence, and that there is a need for more meaningful tasks that aid students’ learning of series. Script writing, used mainly with prospective mathematics teachers, can be used to explore mathematical understandings. Thus, this study examines how script writing, in the form of a scripting task, elicits students’ understanding of series convergence in contrast to nonscripting-based tasks to determine the potential of script writing in assessing this student understanding. We examine students’ …

Developing Mathematical Maturity By Solving A Given Quadratic Equation, Armando A. Amador, Nieves Angulo, Juan B. Lacay

Publications and Research

This article explores the instructional challenges faced by mathematics educators when addressing students’ limited background knowledge and underdeveloped mathematical maturity, two critical barriers to success in college-level algebra. Using the quadratic equation 2x2+x−3=0, which is reducible over the field of rational numbers ℚ ⊂ ℝ, we analyze how diverse solution methods—factoring, completing the square, and the quadratic formula—can support learning. An additional strategy, “Slide and Divide,” was introduced to promote procedural fluency and conceptual flexibility. To gain insight into students’ evolving mathematical maturity, an online survey was conducted to students at various levels of mathematics. The survey captured their perspectives …

A Novel Format For Math Circles: Circles With No Center, Frederick A. Peck, Ian P. Renga, Nick Grener, David R. Erickson, Matt B. Roscoe, Ke Wu

Journal of Math Circles

This paper shares a novel format for Math Circles, which we call “circles with no center.” Circles with no center do not have a traditional facilitator. The problem or activity is novel to everyone in the room. All members engage in mathematical inquiry, and everyone takes responsibility for running the gathering. The “no center” format has benefits for participants and organizers. For participants, the format offers more freedom and more responsibility. For organizers, the format is easier to organize, more fun, and involves less pressure. Our assessment of a 3-day retreat for teachers suggests participants may prefer a circle with …

Mathematics In Amusement Parks, Kacey Laumann

Honors Projects

This project focuses specifically on the Walt Disney World Park, Magic Kingdom. I started by collecting data through the MyDisneyExperience app. By recording the data, I was then able to create polynomial functions to the fifth the degree. Each attraction received a function which allowed me to predict the wait times for that attraction. Then, by graphing the functions and analyzing the graph using calculus the “best time” and “worst time” to go to the attraction were found. After the analysis the information is used to build a unique schedule for a guest. Then the guest receives this schedule after …

Teachers’ Perceptions On The Impact And Effectiveness Of Certification Programs In Preparing And Retaining Educators, Teresa De Jesus Padilla

Theses and Dissertations

Mathematics is integral to STEM fields, making math critically important for the stability and development of the nation. As a result, mathematics teachers have a crucial role in our society. A role whose importance needs the necessary support to accomplish its numerous responsibilities. However, research indicates that certification routes—traditional and alternative—often fail to adequately prepare math teachers for the challenges they face, leading to high turnover rates. This study explores the impact of these certification routes on teachers’ abilities to support student achievement, address diverse learning needs, and manage additional duties. Surveying secondary math teachers in the Rio Grande Valley, …

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

Theses and Dissertations

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

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

Shevtsov: Teaching Modeling To First-Year Life Science Students: The Ucsc Experience, Martin H. Weissman

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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

Dissertations

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

A Phenomenological Study Of Persistence For Black Women In Mathematics Doctoral Programs, Shushannah Marie Smith

Doctoral Dissertations and Projects

The purpose of this phenomenological study was to describe the doctoral persistence experiences of Black women mathematicians. Guided by McGee’s fragile and robust mathematical identity framework, the research design followed Moustakas’ qualitative transcendental phenomenological approach. The researcher explored the contributing factors to the phenomenon guided by the central research question, “What are the doctoral persistence experiences of Black women mathematicians?” The study involved 11 Black women participants who hold or were within one year of holding a doctoral degree in mathematics and were selected to ensure diversity and representativeness. Data collection encompassed three methods: a mathematical identity development timeline, one-on-one …

Exploring The Roles Of Genetics, Gender, Nurturing, And Learning Methods In Mathematical Skills Development, Laura Alinani, Jana Shyti

Honors Projects

This research explores the multifaceted factors influencing the development of mathematical competence through a combination of cognitive, psychological, and sociocultural frameworks. The study aims to address how genetic predispositions, nurturing environments, teaching methods, and societal influences interact to shape mathematical abilities. Using insights from genetic research, cognitive psychology, and education theory, we analyze the role of effective teaching methods, such as active knowledge construction and differentiated instruction, in fostering mathematical skills. The study also examines how societal biases, particularly gender stereotypes, impact students' confidence and interest in math. The findings highlight the importance of promoting gender-inclusive practices and early exposure …

Predicting Students' Academic Performance Via Machine Learning Algorithms: An Empirical Review And Practical Application, Edmund F. Agyemang, Joseph A. Mensah, Obu-Amoah Ampomah, Louis Agyekum, Justice Akuoko-Frimpong, Amma Quansah, Oluwaferanmi M. Akinlosotu

School of Mathematical & Statistical Sciences Faculty Publications

Predicting academic outcomes is complex and influenced by factors like socioeconomic background, motivation, and learning style. Machine Learning (ML) algorithms have become increasingly important due to their ability to analyze large data volumes and identify prediction patterns. Results show ML’s success in predicting academic performance, though effectiveness varies by dataset, algorithm choice, and training features. There is no consensus on the most effective ML method for predicting student performance with broad applicability. Among the five algorithms evaluated in this study, the Random Forest Classifier emerged as the best model, achieving the highest G-Mean and accuracy of 0.9243 and 85.42% respectively. …