Mathematics Commons^™

Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez

Theses and Dissertations

This qualitative case study pursued to describe the different strategies Mexican American adult students in a local community college used to graph function transformations. Participants in the study were purposefully selected using a criterion sampling to ensure participants were atypical, above average students between the ages 18-22, and had a final course average of 89.5-100 in College Algebra. Three research questions were examined 1) In what ways do Mexican American adult college students graph a function transformation? 2) Which strategies do students implement when graphing a function transformation? Qualitative research methods using think aloud semi-structured interviews were used in this …

How An Instructor's Noticing For Equity Can Foster Students' Sense Of Belonging And Mathematical Confidence, Sthefania Espinosa

Theses and Dissertations

There are many aspects a teacher can notice inside the mathematics classroom, and the more a teacher notices, the more difficult it is to teach. In this study, I particularly focus on noticing for equity, which describes the role of the teacher in attending to students’ mathematical thinking through an equity lens that can allow the instructor to notice the aspects of classroom mathematical activity that can make students feel less or more empowered in their mathematical practices (van Es et al., 2017). There exists few research about how students perceive their instructor’s effort to promote equity and …

Figured Worlds Of Women Mathematics Education Scholars, Lili Zhou, Ricki L. Geller-Mckee, Brooke Max, Hyunyi Jung, Bima Sapkota, Jill Newton, Lindsay M. Keazer

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Drawing on the concept of figured worlds (Holland et al., 1998), this project focuses on addressing, responding to, and understanding the self within the figured world of the mathematics education community. Specifically, we examine a group of women with diverse backgrounds in terms of race, class, and cultural contexts, who are engaged in various roles as mathematics education scholars, including teachers, teacher educators, and researchers. Using a dialogical self approach, we facilitate both internal and external discourses, exploring personal histories, narratives, and the development of evolving identities. Our findings reveal that culture and social positions, such as gender, class, and …

Elementary Mathematics Curriculum: State Policy, Covid-19, And Teachers’ Control, Mona Baniahmadi, Bima Sapkota, Amy M. Olson

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In the U.S., state guidance to schools in response to the COVID-19 pandemic was politicized. We used state-level political affiliation to explore whether access to curricular resources differed pre-pandemic or during pandemic remote teaching and teachers' reported control over curricular resources during pandemic teaching. We found that pre-pandemic the percentage of teachers in Republican states reported higher levels of resources overall, and use of core and teacher-created curricular resources in particular. They also reported having greater control over their curricular decision-making during the pandemic. There were no state-level differences in teachers’ level of preparation for pandemic teaching, but teachers in …

Contextualizing The Mathematical Knowledge For Teaching Framework For Teachers Of Emergent Bilinguals, Luis Miguel Fernandez, Mayra Ortiz Galarza

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We are amid a rapid demographic shift, with Emergent Bilinguals (EBs) being the fastest growing K-12 student population. This has created an ambitious goal for teacher education programs as they must prepare mathematics pre-service teachers (PSTs) to assess the needs of EBs. As a response, this study conducted a qualitative analysis of 16 PSTs to propose a contextualized version of the Mathematical Knowledge for Teaching (MKT) framework as an emerging knowledge base of teaching that can be used to further guide the planning and enactment of teacher education programs in the mathematics education of EBs, specifically.

Developing Awareness Around Language Practices In The Elementary Bilingual Mathematics Classroom, Gladys Krause, Melissa Adams Corral, Luz A. Maldonado Rodríguez

Teaching and Learning Faculty Publications and Presentations

This study contributes to efforts to characterize teaching that is responsive to children’s mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students’ expression of their understanding using their own language practices, and on the literature surrounding children’s mathematical thinking, we present an example of a one-on-one interview and of the circulating portion of a mathematics class from a second grade classroom. We use these examples to foreground instructional practices, for researchers and practitioners, that highlight a shift from a simplified view of conveying mathematics as instruction in symbology and formal …

Mathematics Teachers’ Working With Cooperative Learning, Jaime Gomez

Theses and Dissertations

Teaching styles vary greatly amongst educators. One being extensively researched and highly discussed is the method of cooperative learning. Although many studies have shown the benefits of incorporating cooperative learning into classrooms, it has not been a widely used method of teaching in high school mathematics classrooms. This study explores some of the efforts that teachers, who utilize cooperative learning in their classrooms, make to implement cooperative learning lessons successfully. Furthermore, this study also explores the challenges these teachers have encountered when using cooperative learning. Data was collected qualitatively by interviews and surveys from six in-service high …

Navigating Mathematics Teacher Preparation During A Time Of Crisis, Zareen G. Rahman, Rani Satyam, Younggon Bae

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper we highlight the experience of a mathematics teacher educator (MTE) and their preservice teachers (PTs) in a middle school mathematics methods course during the 2020 shift to online instruction due to the COVID-19 pandemic. We believe it is valuable to report how the MTE reflected on their instructional decision-making in response to this massive transition to remote instruction. We also report that PTs needed support and guidance to employ new teaching practices they had learned in the methods course instead of reverting to familiar teaching methods.

Affect Graphing: Leveraging Graphical Representations In The Study Of Students’ Affect In Mathematics, V. Rani Satyam, Younggon Bae, John P. Smith Iii, Mariana Levin

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Affect (e.g., beliefs, attitudes, emotions) plays a crucial role in mathematics learning, but reliance on verbal and written responses (from surveys, interviews, etc.) limits students’ expression of their affective states. As a complement to existing methods that rely on verbal reports, we explore how graphing can be used to study affect during mathematical experiences. We analyze three studies that used graphing to represent, stimulate recall, and reflect on affect. In each, students were asked to draw their perception of an affective construct, such as confidence or intensity of emotion, against time. The studies differed in participant populations, target affect, timescales …

Latinx Students’ Mathematics Anxiety And Their Study Habits: Exploring Their Relationship At The Postsecondary Level, Luis M. Fernandez, Xiaohui Wang, Olga Ramirez, M. Cristina Villalobos

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Increasing Latinx students’ success in college-level mathematics calls for exploration on their mathematics anxiety as it relates to study habits. Using a sample of Latinx students in a Hispanic Serving Institution and their levels of mathematics anxiety, pairwise analyses revealed significant differences among subgroups. Moreover, regression analyses showed Latinx students’ study habits being predictive of mathematics anxiety. As a result, recommendations are provided that could alleviate mathematics anxiety and its effects on Latinx college students.

Factors That Influence Teachers' Utilization Of Siop Learning Strategies When Teaching English Language Learners, Courtney R. Stuart

Theses and Dissertations

Despite standardized certification tests and popular English Language Learner trainings, the strategies and methods used in two educators’ classes would not be identical. In this case-study we look to see what variables cause teachers to utilize certain strategies and how these variables affect the number of strategies used consistently when teaching ELLs. We study the effect of teachers’ language experiences, certifications, participation in SIOP trainings, education levels, perceived preparedness, and years spent in the classroom.

Using quantitative and qualitative data we conclude that dual-language fluency and professional advancements can lead to teachers using more ELL learning strategies in their classrooms, …

Characterizations Of Student, Instructor, And Textbook Discourse Related To Basis And Change Of Basis In Quantum Mechanics, Kaitlyn Stephens Serbin, Megan Wawro, Rebecah Storms

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Communities develop social languages in which utterances take on culturally specific situated meanings. As physics students interact in their classroom, they can learn the broader physics community’s social language by co-constructing meanings with their instructors. We provide an exposition of a systematic and productive use of idiosyncratic, socially acquired language in two classroom communities that we consider to be subcultures of the broader community of physicists. We perform a discourse analysis on twelve quantum mechanics students, two instructors, and the course text related to statements about basis and change of basis within a spin-½ probability problem. We classify the utterances’ …

Coordinating Stem Core Courses For Student Success, Cristina Villalobos, Hyung Won Kim, Timothy J. Huber, Roger Knobel, Shaghayegh Setayesh, Lekshmi Sasidharan, Anahit Galstyan, Andras Balogh

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Research indicates multi-section coordination improves the academic performance of students in STEM education. This paper describes the process of coordination in Precalculus, Calculus 1, and Calculus 2 courses undertaken by a large department that grew from the merger of two institutions through a pilot program, and a project grant. Components introduced in the project courses are documented, including collaborative problem-solving sessions, student learning assistants, Q&A sessions, and additional technology resources. Preliminary data is provided on the impacts of the initiative on student success. The study findings provide a template for coordination, faculty buy-in, and increased student engagement at similar institutions …

Surviving Mathematics, Nathalie M. Luna

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this essay written in an informal voice, the author shares the ups and downs of her experience in academia. She shares her motivation to study mathematics, her undergraduate experience in Puerto Rico, and her graduate experience in South Texas.

Assessing Program Outcomes Of An M.Ed. Curriculum And Instruction Program: A Comparison Of Face-To-Face To Completely Online Deliverables, James A. Telese, Gregory Chamblee

Teaching and Learning Faculty Publications and Presentations

Many mathematics education degree programs, especially at the graduate level, are now transitioning to an online format. There is a need to document how mathematics content and content pedagogy are assessed in an online environment. The objectives of this chapter are to document how a public higher education institution in Texas transitioned their master's degree program for mathematics teachers from a face-to-face program to an online program and how this transition impacted the assessment process related to the learning of content and pedagogical content knowledge.

“Diabesity” Among Latinos: A Culturally Relevant Mathematics Activity By A Mathematics Teacher Candidate, Olga Ramirez, Cherie Mccollough

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper summarizes a culturally relevant mathematics project conducted by a mentored secondary-level Latino teacher candidate (TC) as a requirement for an undergraduate mathematics project course at a south Texas university. The culturally relevant math project involved four secondary Latino students and their parents. The topic was “diabesity”; that is, diabetes and obesity among Latinos southern region in the United States of America with an emphasis on body mass index, proper diet, and exercise. Remarks by the faculty mentor and a faculty consultant about the TC work and reflections regarding this project are also included and provide perspectives on how …

Attitudes Toward Using And Teaching Confidence Intervals: A Latent Profile Analysis On Elementary Statistics Instructors, Hyung Won Kim, Woo Jin Kim, Aaron T. Wilson, Ho Kyoung Ko

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The use of confidence intervals (CIs) for making a statistical inference is gaining popularity in research communities. To evaluate college statistics instructors’ readiness to teach CIs, this study explores their attitudes toward teaching CIs in elementary statistics courses, and toward using CIs in inferential statistics. Data were collected with a survey that classifies instructors’ attitudes on the basis of three previously established pedagogical components: affective, cognitive, and behavioral. Based on the survey responses from 270 participants, we created three profiles (subgroups) via latent profile analysis, and identified each profile’s pattern of attitudes toward CIs and common characteristics of the instructors …

Connections Between Pre-Service Teachers’ Mathematical Dispositions And Self-Efficacy For Teaching Mathematics, Jasmine M. Cruz, Aaron T. Wilson, Xiaohui Wang

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Mathematical dispositions (MD) and self-efficacy for teaching mathematics (SEFTM) are important elements of teachers‟ beliefs that significantly influence their behaviors and educational practices in the classroom. This study looked at relationships between pre-service teachers‟ (PSTs) MD and their SEFTM in connection with other descriptors related to their progress through the teacher education program and prior mathematical experiences. Survey data were collected from 238 PSTs at a midsized university in the US. Results include the finding that PSTs‟ intended grade-level and subject approximately mirror their MD and SEFTM: those planning to be elementary school (generalist) teachers were slightly behind both middle …

The Development Of Secondary Mathematics Teachers’ Pedagogical Identities In The Social Context Of Classroom Interactions, Hyung Won Kim

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Research demonstrates a disjuncture between the practices encouraged by teacher education programs and what teachers actually do in the classroom. It also informs us that the cognitive and social characteristics of individual teachers such as their attitudes, beliefs and knowledge contribute to their classroom practices. This qualitative study investigates how the teacher identity of mathematics teachers – the person’s sense of who he/she is as a mathematics teacher – is related to the disjuncture between encouraged and actual classroom practices. Specifically, the study looks into how mathematics teachers form their teaching practices in the social context of their classroom interactions, …

Using Technology To Determine Factorability Or Non-Factorability Of Quadratic Algebraic Trinomials, John E. T. Bernard, Olga Ramirez, Cristina Villalobos

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper is aimed for mathematics educators who teach algebra, more specifically, the factoring of quadratic algebraic expressions, and who want to enhance student learning of this topic using technology in conjunction with the Middle Term Splitting Method (Donnell, 2010; MTSM 2016a; MTSM 2016b). We will use technology-based algebra and geometry connections to help determine factorability or nonfactorability of quadratic algebraic trinomials over the integers, over the real numbers, and over the complex numbers, both with clarity, certainty and with understanding by using two equations, one derived from the coefficients of the outer terms and the other from the middle …

A Study On Hispanic College Students' Mathematics Anxiety, Study Habits, And Academic Performances On Mathematics, Luis M. Fernandez

Theses and Dissertations - UTB/UTPA

Mathematics anxiety has been described as a feeling of apprehension, fear, tension, and discomfort when confronted with mathematics. Mathematics anxiety has also been shown to interfere with mathematics performance; therefore, for our research we investigated what portions of individuals seem to suffer higher levels of mathematics anxiety and to what extent they are affected by it. We also investigated the study habits of the students and how these affect their mathematics anxiety levels and overall mathematics performance. Our data was obtained from Hispanic undergraduate students (n=405) who took Elementary Algebra (Math 1300), Intermediate Algebra (Math 1334), College Algebra (Math 1340) …

Lessons Learned In Establishing Stem Student Cohorts At A Border University And The Effect On Student Retention And Success, Mikhail M. Bouniaev, Immanuel Edinbarough, Bill W. Elliott

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The University of Texas at Brownsville (UTB) serves more than 8,000 students in the Lower Rio Grande Valley area and broader Mexico region. UTB is a Hispanic-serving institution that attracts students from the surrounding areas, including the Mexico border region. The College of Science, Mathematics and Technology (CSMT) established a Science, Technology, Engineering, and Mathematics (STEM) cohort program to help the majority of students to earn a degree in a STEM field in the shortest possible time. The challenges and obstacles encountered during the planning and implementation phase of the STEM cohort program are discussed in this paper, as are …

On Equivalent Characterizations Of Convexity Of Functions, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.