UMD Theses and Dissertations
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Item EXPLORING THE IMPACT OF A COMPUTATIONAL THINKING MODULE FOR MATHEMATICS AND SCIENCE METHODS COURSES(2024) Moon, Peter; Walkoe, Janet; Education Policy, and Leadership; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Computational thinking (CT) has great potential for enhancing mathematics and science lessons in K-12 education. Numerous studies demonstrate that under the right circumstances, CT integration in math and science can improve student learning and promote deeper understanding. However, teacher education currently does not include preparation for using CT in the classroom on a widespread scale. Instead, most current CT courses or professional development (PD) opportunities for teachers are taught by a local CT researcher who can only reach a limited number of teachers. This qualitative three-article dissertation summarizes the development, implementation, and effects of a five-lesson module on CT designed to be integrated within a math & science methods course or a similar course for teachers. The goal of this module is to provide learning about CT within most teacher education programs without substantially affecting that program’s requirements for teachers (i.e., adding a new course). In Study 1, “Module Implementation in a Mathematics and Science Methods Course,” I describe the module activities, the CT knowledge of the teacher candidates who participated in the study, and how that knowledge evolved. I argue that participants’ understanding of CT expanded from a limited scope to a wide variety of practices and skills, and that the experience-first design helped them build knowledge of CT as distinct from knowledge of their discipline. In Study 2, “Use of CT Knowledge as Classroom Teachers,” I discuss sets of interviews with two teachers who had previously participated in the CT module in different years, analyzing commonalities and differences in their organization and use of CT knowledge. I argue that the Preparation for Future Learning (PFL) (Bransford & Schwartz, 1999) perspective is particularly important when considering the impact of the CT module. In Study 3, “A Faculty Workshop on CT Implementation with Mathematics and Science Methods Courses,” I discuss the effects of a summer workshop with methods instructors from universities throughout Maryland, noting different perspectives around what “counts” as a CT activity, and two implementation profiles for CT that instructors used that fall. I argue that the PFL perspective is important to consider for methods instructors’ CT integration.Item INHIBITION IS KEY: A COGNITIVE APPROACH TO SUCCESSFUL WORD PROBLEM SOLVING(2024) Jaffe, Joshua Benjamin; Bolger, Donald J; Human Development; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Numerical competency and reading comprehension skills are necessary, but insufficient for word problem success. Depending on the word problem structure, successful problem solving may require inhibiting the seemingly obvious and correct answer. Inhibitory control plays a significant role in processing and solving word problems. Through classroom practices and textbook problems, I argue that individuals form associations between relational terminology and specific mathematical operations (“more” for addition and “less” for subtraction), and the notion that all numerical values in a problem must be used to produce an answer. In this study, I proposed an inhibitory performance-based model that posits two approaches to problem solving: (a) a successful approach where solvers inhibit mathematical associations and form appropriate set schemas to conceptualize semantic relations, and (b) an association approach where solvers do not inhibit associations and therefore may have an inaccurate understanding of the semantic relations. To test the model, data were analyzed from 105 undergraduate students at the University of Maryland. The study consisted of four sections: cognitive skills, word problems, domain-specific inhibitory control tasks, and a semi-structured interview. The word problem section included problems that were both consistent and inconsistent with an individual’s operational and numerical associations. Overall, the quantitative results identified that participants performed significantly worse on inconsistent problems. Further, the data suggest that failure to correctly answer inconsistent problems may be due to inhibitory control rather than other cognitive skills. The qualitative data indicated that a vast majority of participants believed in both mathematical associations and remembered classroom experiences that may have contributed to these beliefs. While inhibitory control has been suggested to play a significant role in word problem performance, this is one of the first studies to explicitly examine the relationship through domain-specific inhibitory control tasks and an interview. These results guide a path for future research to examine how individuals develop mathematical associations and for interventions to dissuade their usage.Item MATHEMATICS INSTRUCTION IN JUVENILE CORRECTIONAL FACILITIES DURING COVID-19(2023) Ross Benedick, Amanda; Taboada Barber, Ana; Special Education; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Students with disabilities are overrepresented in correctional settings in the United States and there is a dearth of information in the professional literature about the adequacy of instruction for these youth. Moreover, during the recent COVID-19 pandemic (2020-2022), access to education was abridged for many youth including those in juvenile correctional facilities (JCFs). This dissertation addresses the adequacy of academic instruction in juvenile corrections with a specific focus on mathematics instruction for youth receiving special education services. After an introduction to the topic in this first chapter, Chapter II presents a systematic review of academic and vocational interventions in juvenile correctional facilities (JCFs). Chapter III presents a descriptive study of special education mathematics teachers in JCF. Among other things the survey attempted to provide a snapshot of curriculum choices, instructional contexts, instructional adaptations for students with disabilities, and barriers to instruction for students during the initial weeks (March 20, 2020, through July 31, 2020) of the COVID-19 pandemic. The survey was framed by the existing literature on evidence- based mathematical curriculum and instructional approaches found to be successful in traditional secondary school settings. Results showed that the 31 respondents infrequently used state and locally based curriculum, frequently incorporated the use of student calculators when teaching, and found only a few barriers to teaching during the initial weeks of COVID-19 pandemic.Chapter IV provides suggestions to practitioners working in JCFs in preparation for any future health emergency. While directed at special education mathematics teachers and administrators in these facilities, other practitioners who work in JCFs could benefit from these tips. Proactive planning is a theme present in all the suggestions created in response to the concerns and needs presented by both administrators and teachers working in JCF at the start of the COVID-19 pandemic. Chapter V summarizes and synthesizes information from the systematic literature review, the empirical study presented in Chapter III, and the suggestions for practitioners presented in Chapter IV. The final chapter also discusses implications that flow from the elements of the dissertation and suggests areas for future research.Item This is the Remix: A Math Teacher's Reflective Journey Through Fine-Tuning Her Culturally Relevant Teaching(2023) Ivy, Kelly Kristina; Brantlinger, Andrew M.; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)While many educational institutions have updated their strategic plans mandating culturally responsive teaching (CRT) or culturally relevant pedagogy (CRP), mathematics teachers are reluctant to embrace CRT/CRP, approaching the teaching and learning of mathematics from deficit paradigms that reflect the pedagogy of poverty. Culturally responsive mathematics teaching (CRMT) is necessary because it promises to promote meaningfulness for, accessibility to, and high levels of engagement with school mathematics for Black, Latinx, and other historically marginalized students. However, to date, there have been numerous theoretical arguments for, but few empirical examples of CRMT, and, as a result, many mathematics teachers are uncomfortable employing CRMT. This qualitative case study examines how an experienced and highly regarded Black urban middle school mathematics teacher (Ms. Collier) understands the theoretical and empirical literature on CRP and how she changes her teaching during and after implementing a CRP curriculum unit with her Black and Latinx students. In the context of this study, I offer Ms. Collier’s journey of embracing CRMT by “remixing” her mindset as a mathematics teacher by reading and discussing CRP and CRMT literature and then remixing her curriculum and instruction in response to her “remixed” understandings. In sum, using frameworks such as Culturally Relevant Pedagogy, Culturally Responsive Mathematics Teaching, and Teacher Change Theory, I explored Ms. Collier’s theory-to-practice applications of CRT. The dissertation results are organized into two parts corresponding with different study phases. Part 1 focused on Ms. Collier’s fine-tuned understanding of CRP, and Part 2 focused on Ms. Collier’s perspectives on her experiences implementing CRMT with her Black and Latinx students. Data were collected from four sources: conversations, semi-structured interviews, written reflections, and memos. Key findings indicate that Ms. Collier was, in fact, a Dreamkeeper, understanding Ladson-Billings’ foundational CRP tenets of Academic Achievement, Cultural Competence, and Critical Consciousness. Findings also crystallized two new tenets of CRP I advance that are present but not explicitly named in the literature: Classroom Domain and Teacher Mindset. In addition, salient themes demonstrating each domain of Teacher Change Theory emerged, with Ms. Collier experiencing a meaningful change in perspective: It's about the curriculum AND who the person is. With this study, I challenge the idea of reducing CRP to a set of practices. My stance is that CRP is more so a process of being for the teacher because this body of work studies the more significant issue of mathematics education for Black and Latinx students. As a mathematics teacher who understands the many stereotypes and stigmas that Black and Latinx students face in the learning and doing of mathematics, Ms. Collier expressed a clear awareness of the impact that culturally relevant instructional and relational practices could have on her Black and Latinx students.Item Rupturing antiblackness in mathematics education research: Blackquantcrit as theory, methodology, & praxis(2023) Turner, Blake O'Neal; Liu, Rossina Zamora RZ; Education Policy, and Leadership; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Antiblackness and white supremacy are embedded in mathematics education, which is (re)produced and justified through epistemic violence in research. Research on the “achievement gap” is one well-known example of epistemic violence in mathematics education research where antiblackness is encoded into statistical archives. These quantitative master narratives position Black doers and learners as mathematically illiterate and normalize ideological discourses about Black inferiority, impacting research, policy, and praxis. Thus, this manuscript-style dissertation aligns with calls to advance mathematics education research, policy, and practice toward liberation for Black learners. The three studies in this dissertation employ two distinct but complementary theoretical frameworks, Black Critical Theory (BlackCrit) and Quantitative Critical Theory (QuantCrit), to advance our understanding of supporting and creating liberatory mathematics education, particularly for Black doers and learners of mathematics. In the first study, “Common Denominators: QuantCrit as a means of contextualizing antiblackness in mathematics education,” I argue for including Black Critical Theory and Quantitive Critical Theory in mathematics education research. This conceptual paper foregrounds the contributions that QuantCrit and BlackCrit provide to larger critical conversations centering race and antiblack racism in mathematics education and provides a primer on how these frameworks could be applied to mathematics education research by scholars. The second study, “Black Mathematics Teachers and the Master’s House: A Black QuantCrit Analysis,” empirically explores BlackCrit and QuantCrit using secondary data on 74 Black mathematics teachers in an alternative certification program and their dispositions towards teaching racially and culturally diverse students. I partitioned the teachers into structurally similar and practically relevant clusters using K-means clustering. The findings reveal four clusters of Black mathematics teachers: Hegemonic Academics, Individual Actors, Disruptive Conductors, and Caring Custodians. The results of this study provide insights into the utility of intraracial comparisons. Additionally, this study complicates ongoing discourses in education about improving the lives of Black doers, learners, and teachers in mathematics by recruiting and retaining more Black teachers. The third study, “BlackQuantCrit as a North Star: Critical race research workshop for Black graduate students in Mathematics Education,” draws on critical ethnographic methods to explore the cultural practices of four Black graduate students whose research attends to mathematics education (BGMER) as they participate in a collaborative research workshop. The Black graduate students participated in six two-hour workshops as they learned about and applied BlackCrit and QuantCrit to their research. Data analysis (e.g., audio transcripts of the six two-hour workshops, field notes, the researchers' analytic memos, and other resources shared during the workshops) identified three salient themes: Antiblackness is Verb, CRT as North Star, and Care is a Verb. The findings in this study illuminated the types of support BGMERs need to become critical race researchers and how they take up BlackCrit and QuantCrit in their work.Item FEELING PREPARED TO TEACH: RETHINKING THEORY THROUGH EXPERIENCED MATHEMATICS TEACHERS’ PERSPECTIVES(2023) Viviani, William; Brantlinger, Andrew; Education Policy, and Leadership; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Researchers study teachers’ feelings of preparedness to teach for various purposes; it can serve as an indicator of the effectiveness of initial teacher preparation and is often equated to teacher self-efficacy. Despite being an object of study for several decades, the theory on teachers’ feelings of preparedness to teach is under-developed and the field lacks a shared understanding of what it should entail. This dissertation includes three stand-alone studies that highlight and address some gaps and assumptions in the literature on teachers’ feelings of preparedness to teach. The first article draws on interviews with ten experienced mathematics teachers to examine their descriptions of preparedness and build toward a definition of feelings of preparedness. These descriptions suggest two layers of preparedness: a static/provisioning layer and a dynamic/ambitious layer. The second article uses episodic interviews with six of the ten experienced teachers to investigate their feelings of (un)preparedness when they abruptly transitioned to online teaching. It shows that the online context, and not necessarily web-based technology, was the likely culprit for teachers feeling unprepared for online teaching. The third article builds a theoretical framework based on a review of 39 quantitative studies in the literature on teachers’ feelings of preparedness to teach. This framework is mapped visually with three columns, constructs that are theorized to predict feelings of preparedness, the preparedness constructs themselves, and constructs that feelings of preparedness may predict. These three studies come together to propose a reconceptualization of survey instruments and quantitative analysis for this topic. The static and dynamic layers of preparedness may help differentiate between the work and expectations of new teachers and experienced teachers and may have implications for both preparation programs and researchers. Contextual changes or disruptions, described in the second paper, can impact even experienced teachers, which may elevate the importance of school contexts in future analyses of teachers’ feelings of preparedness. The framework maps out where the field has been and proposes update considerations to survey items specific to teachers’ feelings of preparedness to teach.Item Noticing Teachers' Noticing: Understanding and Supporting Video Club Facilitation(2023) Walton, Margaret; Walkoe, Janet; Education Policy, and Leadership; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Facilitators of teacher professional development (PD) play an integral role in teacher learning. Facilitators often both plan and implement PD and it is important that they can make these experiences meaningful learning opportunities for teachers. Researchers have only recently delved more deeply into understanding the knowledge and skills facilitators need for their work, and how to support facilitators to learn such knowledge and skills. This qualitative three-article dissertation is a design-based research project that explores what facilitators do and how they learn to support teachers in developing a particular instructional skill- noticing student mathematical thinking. Noticing student thinking is how teachers center and build on student ideas in the classroom. I designed a facilitator PD (F-PD) that aimed to help six novice facilitators learn to lead video clubs, a type of teacher PD that has been shown to support teachers in learning to notice. I examined how the novice facilitators learned to lead video clubs and how characteristics of F-PD supported or constrained that learning. In the first study, “A Facilitator Noticing Framework: How Facilitators Notice Teacher Thinking,” I develop a framework for facilitators’ cognitive process as they support teachers to learn to notice in PD, like video clubs. I argue that, like teachers, facilitators also notice. However, facilitators primarily notice teacher, rather than student thinking. I explain the different aspects of teacher thinking that a facilitator might notice. I then use the framework as a lens to understand how three experienced facilitators’ interactions with teachers in video clubs support the teachers to notice student thinking. Study Two, “Novice Facilitators Learning to Lead Video Clubs: A Framing Perspective” is a close examination of how the participants in my F-PD learned to lead video clubs. The analysis included qualitative coding of the participants’ focus related to leading video clubs during discussions with each other and me as the F-PD leader. The findings indicate that participants’ understanding likely shifted. Early in the F-PD, participants appeared to think of leading video clubs as sustaining any general conversation between teachers. Later in the F-PD, the participants likely understood video club facilitation as paying attention and responding to aspects of teachers’ thinking related to noticing student thinking. The interactions between the participants and me, along with the F-PD design, appeared to contribute to this shift, which is also explained. In Study Three, “Designing to Support Facilitators to Learn to Notice Teacher Thinking,” I zoom out and look at the F-PD as an overall activity. I identify some of the problems that arose during the F-PD that constrained participants' learning. I explore how I changed the F-PD design in response or, how differences in the F-PD design from early to later session mitigated issues. I offer several design suggestions for future F-PDs, based on my findings.Item Rules of Engagement: The Role of Graduate Teaching Assistants as Agents of Mathematics Socialization for Undergraduate Students of Color(2023) Lue, Kristyn; Clark, Lawrence M; Education Policy, and Leadership; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The field of higher education has been concerned with the retention of underrepresented students of Color in the science, technology, engineering, and math (STEM) fields over the last few decades. STEM identity development has emerged as a useful analytic framework in this research, as students with stronger STEM identities—students who recognize themselves and are recognized by others as “STEM people”—are more likely to persist in the STEM fields. STEM identity develops through the process of socialization, in which agents of socialization set and maintain the norms, culture, and values that newcomers in the STEM fields should emulate. At institutions of higher education, instructors act as primary agents of socialization, signaling who “belongs”—and who doesn’t—in the STEM fields. Although prior research has identified the ways in which mathematics courses gatekeep underrepresented undergraduate students of Color out of the STEM fields, little research has focused specifically on undergraduate mathematics socialization. Furthermore, the role of graduate teaching assistants (GTAs) as agents of mathematics socialization remains unexamined, despite the large role they play in teaching lower-level undergraduate mathematics courses. This qualitative dissertation, which is grounded in Critical Race Theory and Critical Whiteness studies, utilizes critical ethnographic methods in order to examine the ways in which GTAs at a historically white [college and] university (HWCU) serve as agents of mathematics socialization for underrepresented undergraduate students of Color. Through fieldwork, individual interviews, and a series of focus groups with ten GTAs at a large, public, research-1 institution in the Mid-Atlantic region of the United States (MAU), this dissertation study explored: (1) GTAs’ perceptions of the dominant culture (e.g. values and practices) of the mathematics department at their institution, and whether they sought to align with or diverge from this culture, (2) the opportunities and constraints GTAs faced in breaking from these normative values and practices, and (3) whether the ways in which GTAs described trying to break from these practices reinforced the systematic exclusion of underrepresented undergraduate students of Color in their mathematics department. Key findings include four major themes: a culture of individualism and the hidden necessity of social ties in the mathematics department at MAU, the valuation of teaching as a means of doing research, attempts by GTAs to shift normative narratives of mathematical success, and identity tensions in supporting underrepresented undergraduate students of Color. These findings highlight the importance for agents of mathematics socialization to explicitly center race, racism, and power when trying to be inclusive of underrepresented undergraduate students of Color in university mathematics settings. Without doing so, racism and whiteness are reproduced and perpetuated in the mathematics socialization of underrepresented undergraduate students of Color, despite good intentions.Item EXPLORING EMBODIED MATHEMATICAL COGNITION THROUGH FROM HERE TO THERE!(2023) Katirci, Nihal; Williams-Pierce, Caroline; History/Library & Information Systems; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation seeks to investigate how digital gestures connect to students’ mathematical understanding when playing From Here to There! (FH2T). This investigation explores the intersection of three fields, game-based learning, embodied cognition, and mathematics education. I used three studies which break down the different aspects of the overall research: Study 1 (The Game Interaction Study) covers the interaction between the game and the researcher; Study 2 (The Quantitative Gesture Study) is based on an analysis of the quantitative data gathered by the developers; and Study 3 (The Student Observations Study) focuses on collecting qualitative data and analyzing it through embodied mathematical cognition and failure and feedback lenses. These three studies illuminate the understanding of digital gestures and mathematical learning.Item Exploring the Classroom Norms of an Undergraduate Precalculus Course and Their Relationship with Students' Self-Efficacy, Achievement, and STEM Intentions: A Convergent Mixed-Methods Study(2022) Gruber, Sean; Brantlinger, Andrew; Education Policy, and Leadership; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The number of students pursuing a science, technology, engineering, or mathematics (STEM) degree in the United States has continued to decline over the last two decades. These trends are alarming considering the national focus on providing accessible and quality STEM education to underrepresented students, as well as the fact that the number of STEM careers is projected to continue growing over the next decade. Following the nationwide push to retain students and workers in STEM fields within the United States, educational researchers have attempted to explain what goes on within undergraduate STEM classrooms to explain these trends. In so doing, researchers answer the call to analyze the teaching practices of college STEM instructors, particularly mathematics teachers, with the goal of improving instruction and student outcomes. Researchers generally agree that findings from research in K-12 classrooms on practices that engage students in the learning process, including student-centered learning, may be beneficial to students in undergraduate STEM classrooms. This study followed a convergent mixed-methods design that integrated quantitative and qualitative results in the analytic and results stages. The study utilized survey, interview, and observational data from the Precalculus course offered at Blackboard University (pseudonym) to describe the classroom norms of Precalculus and their predictive power of students’ achievement, self-efficacy, and STEM intentions. While evidence suggested some variation by dimensions of teaching considered and the Teaching Assistant (TA) for a discussion section, in general, instructors’ perceptions of classroom norms in the large lecture and discussion sections aligned with those of the students. Evidence from participants’ survey responses and interview comments suggested that both instructors and students perceived a hybrid of instructor- and student-centered norms in the large lecture and discussion sections, with more instructor-centered norms being perceived in the large lecture and more student-centered norms in the discussion sections. Hierarchical linear modeling was used to explain differences in students’ final exam grades, self-efficacy, and STEM intentions, controlling for the discussion sections students were in. Results suggested that students’ perceptions of the norms related to the teaching dimension of variation in instruction (e.g., having students explore different solution pathways and representations of problems) in the large lecture predicted an increase in students’ final exam grades and self-efficacy. However, norms related to the teaching dimension of instructor-to-student engagement (e.g., the instructor and students engaging with each other through asking and answering questions) in the large lecture predicted a decrease in students’ final exam grades. With respect to the discussion sections, norms related to the teaching dimension of instructor-to-student engagement predicted an increase in both students’ final exam grades and self-efficacy. None of the variables considered in this study predicted students’ STEM intentions.