Theses and Dissertations from UMD

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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM

More information is available at Theses and Dissertations at University of Maryland Libraries.

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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.
Applying Mathematics to Physics and Engineering: Symbolic Forms of the Integral
(2010) Jones, Steven Robert; Campbell, Patricia F; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
A perception exists that physics and engineering students experience difficulty in applying mathematics to physics and engineering coursework. While some curricular projects aim to improve calculus instruction for these students, it is important to specify where calculus curriculum and instructional practice could be enhanced by examining the knowledge and understanding that students do or do not access after instruction. This qualitative study is intended to shed light on students' knowledge about the integral and how that knowledge is applied to physics and engineering. In this study, nine introductory-level physics and engineering students were interviewed about their understanding of the integral. They were interviewed twice, with one interview focused on and described as problems similar to those encountered in a mathematics class and the other focused on and described as problems similar to those found in a physics class. These students provided evidence for several "symbolic forms" that may exist in their cognition. Some of these symbolic forms resembled the typical interpretations of the integral: an area, an addition over several pieces, and an anti-derivative process. However, unique features of the students' interpretations help explain how this knowledge has been compiled. Furthermore, the way in which these symbolic forms were employed throughout the interviews shows a context-dependence on the activation of this knowledge. The symbolic forms related to area and anti-derivatives were more common and productive during the mathematics interview, while less common and less productive during the physics interview. By contrast, the symbolic form relating to an addition over several pieces was productive for both interview sessions, suggesting its general utility in understanding the integral in various contexts. This study suggests that mathematics instruction may need to provide physics and engineering students with more opportunities to understand the integral as an addition over several pieces. Also, it suggests that physics and engineering instruction may need to reiterate the importance, in physics and engineering contexts, of the integral as an addition over several pieces in order to assist students in applying their knowledge about the integral.
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.
SUBTLE CUES AND HIDDEN ASSUMPTIONS: AN ACTION RESEARCH STUDY OF TEACHER QUESTIONING PATTERNS IN 7TH AND 8TH GRADE MATHEMATICS CLASSROOMS
(2009) Callard, Andrew Henry; Chazan, Daniel; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
This action research project explores the link between a teacher's questioning patterns and the modes of thinking, analyzing, evaluating and communicating that are developed in his 7th and 8th grade math students. The highly qualitative analysis focuses on three videotaped lessons from his 7th and 8th grade classrooms, and evaluates the lessons according to four categories or "lenses": cognitive demand, task completion, self-efficacy, and metacognitive activity. It then seeks to identify and codify the predominant questioning pattern used in each lesson, and connect this pattern to the levels of success exhibited in each of the four categories. Four principal patterns are observed and discussed in the lessons: Unilateral Inquiry Response Evaluation, Multilateral Inquiry Response Evaluation, Inquiry Response Collection, and Inquiry Response Revoicing Controversy. The fourth pattern is proposed as a tool for managing classroom discourse that involves a variety of (sometimes competing) student opinions.
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.
UNDERSTANDING OPPORTUNITIES TO PRACTICE WHAT WE PREACH: MATHEMATICAL EXPERIENCES OF MATHEMATICS EDUCATION DOCTORAL STUDENTS
(2008-08-29) Marshall, Anne Marie; Chazan, Daniel; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Often times, there is a disconnect between the way in which mathematics education courses suggest the teaching and learning of mathematics should occur and the way mathematics education doctoral students actually experience mathematics teaching and learning. By asking mathematics education doctoral students to reflect on their mathematical experiences, I was able to further understand the nature of and impact of these experiences. In this study, I engaged in conversations with five other mathematics education doctoral students asking them to share their mathematics experiences in their doctoral preparation. Several factors influenced doctoral student mathematical experiences such as their perceptions of the nature of authority in the classroom, the level of interaction (between student and instructor, among students, and between the students and the mathematics), and nature and purpose of the mathematics in the course. The most typical experiences that doctoral students identified were consistent with traditional lecture courses where the instructor deposited knowledge upon students. Several participants reported on courses that broke the traditional mode and offered some authority to students in the decision-making in the classroom or encouraged a higher level of interaction by engaging students in group work. One particular set of courses deemed "influential", "transformational", and "empowering" embodied a classroom where inquiry reigned and the course environment allowed, required, and supported students to explore their own mathematical questions. This special set of courses featured a shared authority between instructors and students, engaged students in a high level of interaction, and explored mathematical questions and problems that came from the students' questions and ideas rather than from a textbook. The purpose of the course was a place where students could have an authentic opportunity to do mathematics. The importance of the mathematical inquiry in these courses, according to participants, was not only important for themselves as learners of mathematics but also necessary for their preparation of becoming mathematics educators.
An Investigation Into Student Understanding of Statistical Hypothesis Testing
(2008-08-03) Smith, Toni Michelle; Fey, James T.; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
In today's data driven world, the development of a statistically literate society is critical. As a result, many students are enrolling in university level introductory statistics courses and educators are promoting the development of strong understandings of the material taught in those courses. Statistical hypothesis testing, a powerful method of inferential statistics widely used in research, is taught in introductory courses. Though algorithmic in nature, statistical hypothesis testing is based on statistical theory. It is important that introductory students develop connected understandings of the algorithm, the concepts and logic that support it, and its uses. This study explored the degree to which undergraduate, introductory statistics students develop desired understandings of the overall "big picture" of statistical hypothesis testing. In order to investigate student understanding a mixed methods approach was employed--both large scale quantitative and small scale qualitative data were collected. In the quantitative phase, a framework for assessing understanding of the conceptual and logical foundations of statistical hypothesis testing and its uses was created, a multiple-choice instrument with items representative of the framework was constructed, and data on student performance on this instrument were collected. Scores from a course exam that assessed student ability to use the algorithm to solve traditional statistical hypothesis testing problems were collected and compared with those from the multiple-choice instrument. In the qualitative phase, in order to gain more insight into student thinking, follow-up interviews were conducted with students who represent a range of performance patterns on the two quantitative assessments. The data collected in this study indicated that introductory statistics students do not develop strong, connected understandings of the "big picture" of statistical hypothesis testing. Though they are able to perform the procedures, students do not have strong understandings of the concepts, logic, and uses of the method. A weak correlation between scores on the quantitative assessments indicated that procedural knowledge is not a predictor of overall understanding of statistical hypothesis testing. Analysis of quantitative and qualitative data indicated that students do not understand the role of indirect reasoning and inference in implementing and interpreting the results of a statistical hypothesis test.
Beyond PEMDAS: Teaching Students to Perceive Algebraic Structure
(2008-07-29) Merlin, Ethan Michael; Clark, Lawrence M.; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Evidence shows that transforming expressions is a major stumbling block for many algebra students. Using Sfard's (1991) theory of reification, I highlight the important roles that the process of parsing and the notions of subexpression and structural template play in competent expression transformation. Based on these observations, I argue that one reason students struggle with expression transformation is the inattentiveness of traditional curricula to parsing, subexpressions, and structural templates. However, simply refocusing attention on these ignored aspects of algebra will not alone ensure that students avoid common pitfalls. After examining evidence that students are very prone to overgeneralize, I argue for a connectionist view of how people's minds work when they are learning algebra. Utilizing these additional insights, the instructional strategies I ultimately recommend are strategies that focus on structure, but in ways that will make structure a winning competitor for student attention.
The Impact of Teacher Interaction on the Achievement and Self-Efficacy of Students Within a Computer-Based, Developmental Mathematics Course
(2008-07-31) Vernille Blocklin, Kristy M.; Graeber, Anna O.; Fey, James T.; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
A concern of our nation's universities and colleges is the number of students entering with what are considered to be sub-standard mathematics skills. According to the National Center for Education Statistics (NCES, 2001), in the fall of 2000, 24% of entering freshmen in 4-year institutions, and 53% of entering freshmen at 2-year institutions were enrolled in a developmental mathematics course. Since developmental educators are increasing their use of technology to "re-teach" this population of students, understanding the role of the instructor in such a setting can inform developmental educators about the needs of the students, thereby potentially increasing the success rate in such courses. Success in developmental mathematics courses could lead to an increase in college-level retention rates and increase students' learning and achievement in credit-bearing mathematics courses. The purpose of this study was to examine if teacher initiated interaction with developmental mathematics students studying in a computer-based classroom has an effect on their achievement or self-efficacy in mathematics. The study seeks to explore whether the role the instructor assumes is a factor in student success. Many theorists and researchers believe that teacher-student interaction and support/motivation provided by teachers are critical to students' mathematical achievement. Through the use of a quantitative, experimental design, the researcher attempted to gain insight into the role of a developmental mathematics teacher, the achievement of students enrolled in a computerized class, as well as their feelings of self-efficacy toward mathematics. Six sections of an existing computer-based developmental mathematics course was the setting at a four-year research university in the mid-Atlantic area. The treatment provided by the teacher included: conducting brief initial interviews to obtain background information; initiating interaction and encouragement in every session; monitoring student progress; setting intermediate goals; e-mailing about absences; and verbalizing feedback on tests. The repeated measure ANOVA results of this study indicated that there were significant improvements in student achievement, confidence, and attitude toward teacher when pre- and post- scores were compared in both the control and treatment group. However, no statistically significant difference occurred in achievement or self-efficacy when the classes were analyzed between groups; treatment group vs. control group.
Mathematics Teachers' Interpretations of Messages in Curricular Resources and the Relations of These Interpretations to Their Beliefs and Practices
(2008-07-28) Graybeal, Christy Danko; Fey, James T; Graeber, Anna O; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
The curricular materials that teachers use, the assessments that teachers are required to administer, and the professional development activities in which teachers engage all contain messages about mathematics and mathematics teaching. The recent emphasis on both reform-oriented teaching and high-stakes testing in mathematics has increased the number and intensity of competing and conflicting messages. This qualitative study used survey, observation, and interview research methods to explore the messages that five experienced, elementary certified, middle school mathematics teachers interpreted from a variety of resources and the ways that those interpretations related to their beliefs and practices. The teachers in this study interpreted messages in eleven themes. Four themes--Concepts and Procedures, Question types, Source of solution methods, and Technology--created the most tension for the teachers. In general, when the teachers agreed with messages from professional resources about mathematics curriculum and teaching, they attempted to reflect those messages in their practice. However, the resources often lacked supports necessary for the teachers to follow through with the messages in their practice. When the teachers disagreed with particular messages they sometimes consciously decided to not reflect those messages in their practice. But usually the messages were so pervasive that the teachers were not able to ignore them. At times they felt obliged to reflect all of the messages in their practice, regardless of their personal beliefs. The amount of support that the resources provided for teachers was a strong indicator of the degree to which the teachers were successful in reflecting the messages in their practice. Frequently the resources only superficially presented messages to the teachers. This phenomenon was especially apparent when the messages were reform-oriented messages. The study suggests that curriculum and policy writers need to consider the consistency of their messages, be more specific about their intentions, and provide more support to teachers as they try to translate recommendations into practice. Additionally, teacher educators and providers of professional development need to help teachers learn to critically examine curricular resources so that they can more consciously make decisions about to which messages they will attend.

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