Thesis (Ph. D.)--Michigan State University. Dept. of Curriculum, Teaching, and Educational Policy, 2008. / Title from PDF t.p. (viewed Aug. 4, 2009). Includes bibliographical references (p. 287-297). Also issued in print.

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Education." Includes bibliographical references (p. 402-406).

Thesis (M.S.) -- Central Connecticut State University, 2009. / Title from electronic title page. Project advisor: S. Louise Gould. "A special project submitted in partial fulfillment of the requirements for the degree of Master of Science in Secondary Mathematics."

Thesis (Ph. D.)--Drexel University, 2007. / Includes abstract and vita. Includes bibliographical references (leaves 88-94).

<p> Mathematics, in general, and algebra courses, in particular, have been categorized as "gatekeepers" for higher education, better jobs, and even citizenship. For many low-income and working adults, community college is the institution where they choose to develop their mathematics understanding so they can pursue their dreams. Unfortunately many fail in their attempts. In an effort to better understand their plight so that the community colleges can better meet their needs, I studied community college students' foundational fraction understanding. Specifically, I examined students' procedural skills and problem-solving strategies to determine evidence of fragmented knowledge and fragile learning. I investigated a sample of 373 adult students in four tiers of community college developmental education mathematics courses: Computational Arithmetic, Pre-Algebra, Beginning Algebra, and Intermediate Algebra. In Phase 1, I quantitatively examined students' performance on a written assessment of foundational fraction problems. I compared groups of students to determine if differences might be due to factors of course level, age, and number of years out of school. In Phase 2, I interviewed 33 of the lowest performing students and examined their explanations and categorized students' problem-solving strategies and levels of procedures and explanations while using the strategies. My analysis revealed five major findings. 1. Students' average score on an 11-item foundational fraction assessment was 74%, below what I considered mastery level on the assessment. 2. The assessment scores differed based on course level rather than other demographic factors. 3. On specific NAEP items, Algebra and Intermediate Algebra students scored similarly to United States eighth-graders, whereas Arithmetic and Pre-Algebra students scored higher than 4th graders yet lower than eighth-graders. 4. The foundational fraction items related to magnitude tended to be the most difficult for the students. 5. The major characteristics of students' conceptual understanding were fragmented, fragile, non-fluent and only rarely, sophisticated. While community college developmental education students know something about fractions, my research indicated that their knowledge was held as multiple unconnected knowledge chunks, bits and pieces of prior knowledge mixed with inaccurate, imprecise and partial notions and procedures making students' resulting "fraction sense" tenuous. Although they sometimes successfully solved problems, occasionally with sophisticated self-generated strategies, students were not fluent in their fraction knowledge. The dissertation ends with some recommendations for instructors to address students' limited fraction understanding along with some suggestions for the system as a whole to make fraction instruction a greater priority in developmental courses so that more students can achieve their goals.</p>

This thesis investigates how adult learners continuously negotiate their relationship with schoolroom mathematics through discourses akin to being ‘more’ or ‘less’ able to ‘do’ and ‘be’ mathematical. It argues that mathematical identities are politically and socially constructed, and that available forms of knowledge inscribe particular mathematical practices on the individual in the classroom. By paying attention to the precarious and contradictory productions of the self, and investigating the allure of undergoing a transformation of the self, I contribute to critical understandings of the psychic costs of re-engaging with learning mathematics as an adult learner. This analysis is a critical narrative inquiry of stories of adults (not)taming mathematics. As an iterative study into identity formation it puts theory to work in unusual ways. In bringing together internal and external processes (and the intersection of biography, aspiration and discursive practice), I unmask how participants underwent what Mendick (2005) calls “identity work”. Working with a Lacanian psychoanalytical through a Foucauldian tradition, I navigate the construction of selfhood during processes of reinvention as (non)mathematical subjects, experiencing ‘success’ (and alienation) through models of collaborative learning, in the contemporary mathematical classroom. The study examines the lived experiences of 11 adult learners using a range of qualitative methods. I actively seek the complexities within various types of provision (including adult education, further education, work-based learning, and community outreach programs) and the multiple forms of knowledge available (or not) through authoritarian discourses of education. Engaging a mobile epistemology, this thesis connects subject positions, techniques of power, psychic costs of reinventing the self, and how the processes of visceral embodiment of mathematics affects learning in the classroom. It argues that mathematical identities are discursively constructed, and the relationship between selfhood and ‘being’ and ‘doing’ mathematical-ness is told as much through narratives characterised by affection as by fear. Rather than provide answers or ‘best practice’ for the collaborative classroom, I conclude with an explanation of why I question common sense assumptions, such as that adult learners want to be placed in a hierarchical positions and judged as independent mathematical thinkers in class, and the practical implications for this in the classroom.

This research uses a case study approach to examine the learning experiences of mature non-specialist first year undergraduate university students studying mathematics as an ancillary subject. The challenges faced by such students taking mathematics as a subsidiary subject within their main degree have not been adequately addressed in the literature: this study seeks to address this gap. The research took place in a UK inner-city post-1992 university which has a very diverse student intake. A qualitative data set was generated from in-depth and focus group interviews of 22 mature students, the majority of whom were non-specialists taking mathematics as a required ancillary subject. An additional quantitative data set was derived from a questionnaire distributed to 250 students taking first year mathematics modules, either as an ancillary or as a specialism subject. A small number of mature students specialising in mathematics in both the interviews and the survey were included in order to compare the experiences and views of the both specialist and non-specialist groups. The Mixed Methods Research Design adopted combined results from the qualitative and quantitative analyses, and was accompanied by a post-structuralist theoretical framework which examines the discursive practices students were exposed to in relation to their construction of mathematics as a subject and their experiences of learning mathematics. The study shows that the major perceived factors that affect mature non-specialist students learning of mathematics include the pedagogical model that is used; the attitudes and beliefs of the learners; the support available to aid learning; and the prevalent discourses about the learning and perceptions of mathematics. These findings have a number of important implications for policy and practice for teaching mathematics to such students, for our understanding of student identities and for widening participation. The evidence from this study suggest that there should be a shift of government policy on access and financing for mature students; a review of mechanism of financial support for mature students; changes in the organisation and resourcing of small classes; a review of curriculum and pedagogy to fit the diverse background of learners; and the development of mathematics support provisions that are embedded in courses that require mathematical skills.

Thesis (M.Ed.)--University of Hong Kong, 1984. / Includes bibliographical references (leaf 126-128). Also available in print.

<p> The parallel research traditions of explicit-objective and tacit-emergent vary greatly in how they define, assess, and enable development of teacher mathematical knowledge. Despite these diversities, widespread agreement exists in mathematics education research that a teacher's mathematical knowledge is a key competency of an effective teacher. This research report investigates the nature and development of teacher mathematical knowledge of fraction multiplication defined from a tacit-emergent perspective. Questions about the nature and development of teacher mathematical knowledge for fraction multiplication were investigated in this report at the individual and collective levels. In addition, this research report also investigated the developmental links between these levels. The concept study design and the framework for teacher knowledge used in this report derived from the work of Davis and colleagues (Davis &amp; Simmt, 2006; Davis &amp; Renert, 2014). </p><p> The results from this report were multifaceted for both the individual and collective levels of mathematical knowledge. Teachers' individual mathematics-for-teaching (M4T) knowledge of fraction multiplication developed throughout their participation in the mathematical environments of the concept study. Furthermore, two types of collective action emerged as proposed links between the collective and individual development of teachers' M4T knowledge of fraction multiplication. These proposed links, titled <i>synergistic realizations</i> and <i> recursive elaborations</i> emerged in this report as patterns of mathematical action existent in moments of coaction. Recursive elaboration defines the decision-making mechanism where the collective expands the realm of what is possible for a single mathematical realization. Synergistic realization defines the collective decision action in which all previous realizations are abandoned for one innovation in the mathematical realization of a mathematical concept. A discussion of the implications for defining teachers' mathematical knowledge of fraction multiplication as nested systems of individual and collective knowledge is included in the conclusion of this report.</p>

Thesis (Ph. D.)--Drexel University, 2006. / Includes abstract and vita. Includes bibliographical references (leaves 224-237).