UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
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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 THE CONTRIBUTION OF INHIBITORY CONTROL ON CHILDREN’S GESTURE USE IN AN EARLY MATHEMATICAL ENVIRONMENT(2023) Barkin, Raychel; Ramani, Geetha; Human Development; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Early academic scores are strong and robust predictors of children’s later school and career performance (Duncan et al., 2007; Rose, 2006). However, the USA ranks well below other countries on math scores (27th out of 34; OECD, 2013), and have been marked as particularly inadequate at “mathematics tasks with higher cognitive demand(s)”. Thus, it is important to focus on the mechanisms which may contribute to differences in early mathematics problem solving and find tools that are uniquely suited to addressing this issue. One advantageous strategy young children use during math problem solving are hand gestures. Gestures are one of several overtly observable strategies in math contexts(e.g., counting on fingers vs. counting out loud without gestures), but have been specifically recognized as useful given their ability to reduce the user's working memory load during math contexts (Goldin-Meadow & Wagner, 2005). As children get older, the type and frequency of strategies used are reported to shift from basic to more advanced and efficient (Siegler, 1987). This pattern is often seen as younger children using more overtly observable strategies (e.g., finger counting), whereas older children rely on more implicit strategies (e.g., memory retrieval of math facts, Geary et al., 1991). However, less is known about how differences in children’s concurrent domain-general abilities (e.g., working memory, inhibitory control) and domain-specific knowledge (e.g., math specific) contribute to strategic use of gesture during arithmetic problem solving. This line of research is vital given that gestures may be especially advantageous based on their capacity to bolster mental resources needed for problem solving. Using the Gestures in Math Environments model (GME model; Gordon & Ramani, 2021) as a framework, the current study provides a comprehensive assessment of the factors underlying children’s domain-general and specific abilities, and provides evidence as to their relation to children’s use of gesture as a strategy during arithmetic problem solving. Furthermore, it tests a newly proposed adaptation to the GME model where inhibitory control plays a moderating role on the relation between children’s working memory and use of gesture. One-hundred-thirty-seven 4- to 7-year-old children and their parents participated in this study. All children completed two sessions; an autonomous online-game based assessment and a video recorded zoom session regulated by a trained research assistant. At each session, children completed measures of inhibitory control, early mathematical knowledge, and working memory. Their gesture use was video recorded during one measure where children partake in arithmetic problem solving. Parents completed a standardized measure assessing their child’s inhibitory control and working memory abilities. Using structural equation modeling, the relations between all measures and a consideration of how each corresponded to a set of comprehensible latent factors (one factor each for inhibitory control, working memory, and math) were examined. Further examination of how each factor related to children’s use of gesture was investigated. In line with the original GME model, working memory ability was a unique predictor of children’s use of gesture above and beyond impacts of age, math knowledge, inhibitory control, and gender. While there is not any evidence from the current study to support the proposed moderation between inhibitory control and working memory on gesture use, a modification to the GME model with the addition of gender is subsequently recommended.Item What Can I Do? Preservice Elementary Teachers Developing Understandings of Self as Mathematics Teacher and Teaching in Context(2012) Neumayer DePiper, Jill; Edwards, Ann R; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In order to prepare preservice teachers (PSTs) to enact teaching practices that best support all students in learning mathematics, elementary mathematics teacher education must prepare PSTs to navigate the many social, political, and institutional dynamics in today's classrooms. In this research, I theorized that successful negotiation of these dynamics requires that teachers have an understanding of themselves as mathematics teachers, including an examined vision of their goals of mathematics teaching, the social and political contexts of schooling, and the realities of their school contexts. In this study, I explored how PSTs understood themselves as mathematics teachers and teaching through participation in a seminar designed to support critical examination of themselves as mathematics teachers, particularly as within complex realities of schooling and attention to equity and access. The theoretical perspective of performativity (Butler, 1999) was used to understand and support PST identity work and specifically guided the design of the seminar and the case analysis. Each of the four cases offers a unique perspective on how PSTs understood themselves as mathematics teachers and mathematics teaching and how these understandings shifted. The first of three findings across the cases was that PSTs understood themselves and their teaching differently. Specifically, as articulated in the second finding, they understood teaching for equity differently and in relation to their own self-understandings. The third finding is that PSTs' understandings of themselves as mathematics teachers and mathematics teaching shifted. Thus, understanding PSTs' mathematics teacher identities through a theoretical premise of performativity and supporting PSTs in deconstructing these contexts, expectations, and constraints supported some PSTs in repositioning themselves in relation to dominant discourses that framed their understandings of mathematics teaching and in problematizing mathematics teaching. These findings have implications for mathematics teacher education, offering new tools and specific concrete resources to support mathematics teacher critical self-examination. Findings also suggest the need for PSTs to engage in continued identity work and in facilitated opportunities to work at the intersections of mathematics teaching with issues of race, class, and institutional discourses of testing. Further research on operationalizing a critical pedagogy in mathematics teacher education is also needed.Item Pre-service Teachers' Mathematical Knowledge for Teaching: A Comparison of Two University Mathematics Courses(2009) Lueke, H. Michael; Chazan, Daniel; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)One enduring problem in the field of mathematics education is preparing teachers to present mathematics in sufficiently deep and meaningful ways to their students. A focus of this preparation is developing in practitioners sufficient knowledge of mathematics for teaching. Mathematical knowledge for teaching has been theorized widely and is currently the focus of many empirical investigations in the field. This study positions itself within this literature and seeks to connect the research to undergraduate, pre-service elementary school teachers (PSTs), and the content courses which comprise the bulk of their mathematical preparation within a typical university teacher education program. Little is known about the impact that these courses have on teacher knowledge and still less has been studied about the efficacy of different pedagogical--or mathematical--approaches in these courses among PSTs. In order to test claims made in situated learning theory and respond to prevalent political rhetoric about mathematics teacher education, this project compared mathematics courses designed for PSTs in two different universities along three dimensions: (1) Differences in pedagogical and mathematical approaches to developing content knowledge for teaching in PSTs; (2) Resulting differences in PST performance on mathematical knowledge for teaching instruments (3) Resulting differences among PSTs' attitudes about mathematics, teaching, and their perception of the course's relevance to their anticipated work as elementary school teachers. Data from multiple data sources reveals that, though differences were small, PSTs' mathematical knowledge for teaching was substantively different between the two campuses. In addition, the data indicate that PSTs developed different attitudes about mathematics and teaching. Finally, PSTs' evaluated their course's relevance for teaching practice differently. This study suggests that when designing content courses for pre-service teachers, teacher educators should pay close attention to the interaction between mathematical approaches and pedagogical perspectives.