College of Education
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The collections in this community comprise faculty research works, as well as graduate theses and dissertations..
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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 PLACE VALUE: A QUALITATIVE STUDY OF BEING A BLACK GIRL IN URBAN MATHEMATICS CLASSROOMS(2020) Fair, Camille; Clark, Lawrence M.; Education Policy, and Leadership; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This qualitative study documents and examines what it is like being in a Black girl body while learning math in urban schools. The ten participants in this study self- identified as Black and female, and they graduated from three high schools in an urban school district in the Northeast between 2017 and 2019. Despite demonstrating excellence in and out of school, participants’ stories were burdened by experiences of exclusion, marginalization and oppression in their K-12 math learning. Drawing on Critical Race Feminism (CRF), a framework used to theorize interlocking oppressional forces, I designed this qualitative study after conducting a pilot program to improve Black girls’ math experiences. Preliminary findings from the pilot study suggest that Black girls’ math experiences and performance outcomes are largely shaped by the extent to which they are given or denied social place and intellectual value in math classrooms. I appropriate the math concept of place value, and I use it as a metaphor in a framework I developed called Human Place Value. This study examines three questions to understand Black girls’ lived experiences in urban math classrooms: 1) How do Black girls face exclusion, marginalization, and other forms of oppression in math classes? 2) How do Black girls identify and recognize negative attitudes and beliefs about their identity in math classes? 3) How do Black girls respond to and navigate their experiences in math classes? I collected personal data about my participants through background questionnaires and one-on-one semi-structured interviews. I analyzed the data using tenets of CRF and classroom interaction frameworks to distill three themes across social place and intellectual value: visibility, positionality and knowledge production. Key findings from the study suggest that being in a Black girl body renders students particularly vulnerable to math marginalization in the form of hostility, maltreatment and instructional neglect. The data collected from the ten participants tell a collective story that warrant consideration for the role Human Place Value plays in teaching and learning that yields disparate mathematical outcomes. This study concludes with a presentation of counternarratives from two participants and cross-case insights that detail implications for theory and practice.Item Prospective Teachers' Noticing and Naming of Students' Mathematical Strengths and Support of Students' Participation(2019) Bowen, Diana Leigh; Walkoe, Janet; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation is a sequential qualitative case study that describes how prospective teachers begin to use strengths-based language and support students’ participation after participating in a digital learning experience on noticing and naming students’ mathematical strengths. The central research question guiding this work is: What feedback statements do prospective teachers (PTs) make before and after they receive explicit support for using strengths-based language and is there evidence of PTs’ sustained learning following this support? First, this study collected and analyzed prospective teachers’ feedback statements to students before and after a digital learning experience on noticing and naming students’ mathematical strengths (LessonSketch). The primary analysis used qualitative thematic coding to describe the type of language (strengths-based, mixed language, deficit-based, or uncommitted) used by six prospective teachers when making feedback statements and to qualify feedback statements. The secondary analysis followed two of the prospective teachers into field placements to determine if there was any evidence of sustained learning (as measured by PTs’ reflections on learning and moves in the classroom to support students’ participation). This study found that most (5 of 6) PTs moved from uncommitted or mixed language feedback statements to strengths-based feedback statements as a result of the digital learning experience. PTs went from mostly emerging strengths-based statements on the pre-assessment (20 of 28 statements) to primarily meaningful strengths-based statements on the post-assessment (22 of 28 statements). The overall finding from the secondary analysis is that while both PTs (Alicia and Marissa) showed positive shifts in their moves to support students’ participation only Marissa found the practice of noticing and naming students’ strengths as fundamental to her learning and teaching practice. On the other hand, both cases highlight examples of Marissa and Alicia, making specific and public feedback statements to position students' contributions positively and assign competence to students. Finally, tensions arise when PTs evaluate students’ responses for smartness while continuing to rank students’ responses and emphasize correctness.Item Teaching For Inclusion: The Effects Of A Professional Development Course For Secondary General And Special Education Mathematics Teachers For Increasing Teacher Knowledge And Self-Efficacy In Geometry(2015) Wright, Kenneth; Leone, Peter; Special Education; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The current study examined the effects of a co-teacher professional development course for increasing the knowledge and self-efficacy of special education and general education geometry teachers in an inclusion setting. The professional development course included instruction on Universal Design for Learning instructional strategies as well as similarity and congruence in geometry. The course was presented in a blended learning format and included in-person and online activities. The online activities used animated scripts of teacher instruction for collaborative discussion and decision-making. A multiple probe design across three sets of two teachers for a total of 6 participants was used in this study to demonstrate a functional relationship between the independent and dependent variables. The participants were six special education and general education geometry teachers from public charter schools in Washington, DC. Results of the study demonstrated that participants were able to improve their content and pedagogical content knowledge in geometry as well as their self-efficacy for teaching in an inclusion setting. Specifically, special education teachers demonstrated a greater increase in content knowledge while general education teachers demonstrated a greater increase in self-efficacy for teaching students with disabilities. The study suggests that providing professional development for co-teachers can enhance collaboration as well as increase content knowledge and teacher self-efficacy.Item Patterns in Curriculum Choices: Pre-Calculus Curricula in the Archdiocese of Washington(2015) Hurst, Christopher Bryan; Campbell, Patricia F; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This study aims to learn more about the choices made by mathematics teachers in the Archdiocese of Washington, given their unique independence from state or district curricular control. To study these choices, pre-calculus teachers completed a survey and submitted their course’s summative assessments. These responses were then compared to themselves, to each other, and to the Common Core to study the choices teachers made, both in the scope of their curricula and in the expectations they had for student performance. This study concludes that teachers choose pre-calculus curricula within two major archetypes, either advancing students’ algebraic skill or exploring new topics. Further, the study found that teachers’ assessments are well aligned to their stated curriculum, but that contrary to recent education trends, teachers have largely chosen to ignore statistics. Consequences of these choices are discussed, as well as implications for policy and future research.Item EXPLORING FUNDS OF KNOWLEDGE AND CAPITAL: CASE STUDIES OF LATINO IMMIGRANT FAMILIES SUPPORTING THEIR CHILDREN'S EDUCATION, WITH A FOCUS ON MATHEMATICS(2014) Napp-Avelli, Carolina A.; Chazan, Daniel; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Latino students are frequently positioned by widespread achievement gap discourse at the bottom of the attainment spectrum. Both students and families are portrayed as inadequate and deficient, and are blamed for their lack of success in mathematics. One recommendation to improve Latino students' educational performance is to increase parental involvement in mathematics among Latinos. However, life conditions of Latino immigrant families include factors that often make it difficult for parents to get involved in the education of their children in the ways that schools expect. This study explores the knowledge and resources two Latino immigrant families have acquired thorough their experiences and how they use them to support their children's education and mathematics education. In order to analyze families' resources, a theoretical framework composed by the concepts of educability, capital, and funds of knowledge and community cultural wealth was developed. The construct of educability, which analyzes the tensions between the limitations that poverty and other life conditions impose on families and the possibilities for students to succeed in school, provides the overarching structure of the framework. Bourdieu's theory of cultural capital and the cycle of reproduction of capital describe why social groups with more capital (middle and upper classes) acquire capital easily, whereas social groups with less capital (low socioeconomic working classes) have fewer opportunities to acquire capital. This piece of the framework explains why it is so difficult for students living in hard conditions to overcome them and succeed academically. The funds of knowledge and community cultural wealth perspectives made it possible to identify the resources and knowledge families have acquired through their experiences and understand their actions and hopes in connection to their life histories. In particular, the study analyzes how families use their resources along three dimensions that affect children's conditions of educability. First, the study looks at how parents influence students' dispositions towards education; second, how parents develop relationships with schools; and third, how parents influence what students do in their leisure time. The researcher's journey as a white middle-class highly educated woman working with Latino working-class families is also analyzed as part of the study.Item Embracing mathematics identity in an African-centered school: Construction and interaction of racial and mathematical student identities(2010) Nyamekye, Farhaana; Chazan, Daniel; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)ABSTRACT Title of Document: EMBRACING MATHEMATICS IDENTITY IN AN AFRICAN-CENTERED SCHOOL: CONSTRUCTION AND INTERACTION OF RACIAL AND MATHEMATICAL STUDENT IDENTITIES Farhaana Nyamekye, Ph.D, 2010 Directed By: Associate Professor of Mathematics Education, Daniel Chazan, Curriculum and Instruction This dissertation is a report of a multiple case study of eight seventh grade African American students attending an African-centered school. This African-centered school is attended solely by children of African descent and adheres to a system of African cultural values, focusing on culture, relationships, and academic excellence. The report provides in depth case analyses of two of these students as they navigate their multiple identities. The foci of the analyses are on the students' construction of their math learner identities and racial identities and on their construction of both of these identities taken together. Phenomenological variant of ecological systems theory illuminates the challenges and supports that these students encounter in constructing their identities. The mathematics and racial socialization practices within the school and within the students' home environments are documented within this report as support mechanisms that provide opportunities for the students to construct identities as African American mathematics learners. The findings suggest that academic spaces that reduce the stress of racism and help students to value their racial identity may be particularly important spaces for other African American mathematics learners. The findings also have positive implications for the implementation of African and African American cultural practices and programs that can help other African American learners to positively construct identities as both African Americans and math learners. The documented findings raise critical questions about whether other African American learners that share the historical legacy of enslavement with the students in this study would benefit from African-centered schooling, despite the heterogeneity within this population.Item UNDERSTANDING THE CHALLENGES OF IMPLEMENTING A MULTIPLE SOLUTION NORM(2009) Hollenbeck, Richard; Chazan, Daniel; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Most mathematics educators endorse the idea that important concepts and procedures should be taught by asking students to solve problems whose solutions can be derived by multiple solution methods. This vision for classroom activity involves the teacher routinely soliciting multiple ideas for solving a single problem; students communicating what they are thinking; students respectfully listening to what others say; and students discussing their solution methods and comparing the advantages or each. This dissertation explores some of the practical challenges that teachers face when using multiple solutions in the mathematics classrooms, and considers how teachers might address these challenges. In addition, this dissertation puts forth a theoretical framework for analyzing how classrooms make use of students' multiple solutions. These issues were examined by utilizing a first-person research methodology in an eighth grade classroom with students who had a history of behavioral concerns and low academic performance.Item Finite Mixture Model Specifications Accommodating Treatment Nonresponse in Experimental Research(2009) Wasko, John A.; Hancock, Gregory R; Measurement, Statistics and Evaluation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)For researchers exploring causal inferences with simple two group experimental designs, results are confounded when using common statistical methods and further are unsuitable in cases of treatment nonresponse. In signal processing, researchers have successfully extracted multiple signals from data streams with Gaussian mixture models, where their use is well matched to accommodate researchers in this predicament. While the mathematics underpinning models in either application remains unchanged, there are stark differences. In signal processing, results are definitively evaluated assessing whether extracted signals are interpretable. Such obvious feedback is unavailable to researchers seeking causal inference who instead rely on empirical evidence from inferential statements regarding mean differences, as done in analysis of variance (ANOVA). Two group experimental designs do provide added benefit by anchoring treatment nonrespondents' distributional response properties from the control group. Obtaining empirical evidence supporting treatment nonresponse, however, can be extremely challenging. First, if indeed nonresponse exists, then basic population means, ANOVA or repeated measures tests cannot be used because of a violation of the identical distribution property required for each method. Secondly, the mixing parameter or proportion of nonresponse is bounded between 0 and 1, so does not subscribe to normal distribution theory to enable inference by common methods. This dissertation introduces and evaluates the performance of an information-based methodology as a more extensible and informative alternative to statistical tests of population means while addressing treatment nonresponse. Gaussian distributions are not required under this methodology which simultaneously provides empirical evidence through model selection regarding treatment nonresponse, equality of population means, and equality of variance hypotheses. The use of information criteria measures as an omnibus assessment of a set of mixture and non-mixture models within a maximum likelihood framework eliminates the need for a Newton-Pearson framework of probabilistic inferences on individual parameter estimates. This dissertation assesses performance in recapturing population conditions for hypotheses' conclusions, parameter accuracy, and class membership. More complex extensions addressing multiple treatments, multiple responses within a treatment, a priori consideration of covariates, and multivariate responses within a latent framework are also introduced.Item UNDERSTANDING AND TEACHING RATIONAL NUMBERS: A CRITICAL CASE STUDY OF MIDDLE SCHOOL PROFESSIONAL DEVELOPMENT(2009) Walters, Jonathan Kirk; Croninger, Robert; Education Policy, and Leadership; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A lot of money is spent each year on teacher professional development, but researchers and policymakers are still trying to determine what that investment yields in terms of improvements in teacher knowledge and practice. This study focuses on the extent to which middle school mathematics teachers comprehended and made use of the core content, pedagogical content and pedagogical components of a well designed professional development model. At the time of data collection, the teachers were participating in a large, federally funded randomized field trial on professional development that focused on rational numbers. Compared with many other teachers participating in the randomized study, these three teachers were highly receptive to the intensive, content-focused model and thus represent a critical case study of professional development. Using interview and classroom observation data from the 2007-08 school year, the study indicates that teachers understood and implemented many of the pedagogical components emphasized in the model, but they had difficulty comprehending and articulating the core rational number content. Within the domain of rational numbers, the study shows that teachers had more difficulty understanding ratio and proportion concepts as compared with fraction and decimal concepts. The study also describes sources of variation in teachers' understanding of the professional development material and the extent to which they utilized the professional development material while teaching. Teachers' understanding of math content is a critical link in the theory of action driving current educational policies that call for increased rigor and coherence in K-12 mathematics. This case study illustrates that even well designed and well implemented professional development models may be incapable of improving teachers' content knowledge to levels that positively affect their instructional practices.