Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 135-139).

This was an investigation of students’ mathematics confidence and how it is shaped by their accumulated experiences in mathematics education, and informs their view of the purpose of mathematics in their current and envisioned lives. There is no shortage of studies on black students’ poor performance in mathematics education and its seeming persistence in spite of reform initiatives and policy changes. Conversely, there is a dearth of studies in the field on high achieving black students and the construction of their mathematics identities. Some scholars have argued that the plenitude of data on the failure of black students in mathematics education has contributed to mainstream beliefs of a racial hierarchy of mathematics ability in America. This perception has not only shaped attitudes and behaviors of educational scholars, policymakers, practitioners, but it has contributed to the alienation of many students from the community of “doers of mathematics.” In an effort to combat the pervasiveness of race-based beliefs of math ability, some researchers in the field of mathematics have advocated for the need to refocus research on better understanding students’ mathematics identity and its relationship to their performance. In light of this, this study, using ethnographic methods, examined the mathematics confidence—a subset of mathematics identity—of a group of seniors enrolled in honor’s pre-calculus at an under resourced urban comprehensive high school. Data collected and analyzed for this study showed that participants, in spite of a history of mostly success in math and despite being socialized to view the classroom as opportunity to challenge disparaging views of African Americans, refused to seek or claim membership to the community of math people. This study provides new insights into black students’ perception of and sense of belongingness to mathematics, and its potential impact on their academic and economic prospects. / Urban Education

Empowerment through proficiency in mathematics could better not only one’s life, but also one’s chances in study and work. The current study is an exploration of what reflection and mathematics confidence entail during mathematics problem solving. Reflections on experiences with mathematics create awareness of the individual’s level of confidence in the social, psychological and intellectual domains. Personal, strategic and task knowledge enhances meaning and promotes the understanding of mathematics tasks during problem solving. The level of mathematics confidence can be described as either fearful or fearless when solving mathematics problems. Reflecting on achievement, with or without fear, is regarded as vital for higher-order reasoning by means of metacognitive processes, moderates mathematic confidence and fosters achievement. Although research in metacognition is increasing, literature involving mathematics confidence and reflection is scarce. The current study explores this link between reflection and mathematics confidence by focusing on metacognitive reflective skills. A mixed-method design consisting of positivist and interpretivist paradigms is employed. Merging of the quantitative and qualitative findings indicates that metacognitive strategies include reflecting on task, personal and strategic awareness. Regulating understanding, planning, monitoring and evaluating during problem solving occurs in accordance with these active internal processes. Mathematics confidence during problem-solving emerges from experiences relating to a variety of contexts involving mathematics. The findings confirm the dimensionality of mathematics confidence and present sources of participants’ mathematics confidence and metacognitive skills as reflected upon. The schools in the sample represent single-gender (all-boys and all-girls) and co-ed schools and findings should not be generalised to all schools. Reflection on metacognitive knowledge and regulation deepens the awareness of the level of confidence and promotes, to some extent, a knowing of knowledge. The study therefore evaluates the role reflection and mathematics confidence play during problem solving in senior phase mathematics. / Thesis (MEd (Mathematics Education))--North-West University, Potchefstroom Campus, 2013.

Empowerment through proficiency in mathematics could better not only one’s life, but also one’s chances in study and work. The current study is an exploration of what reflection and mathematics confidence entail during mathematics problem solving. Reflections on experiences with mathematics create awareness of the individual’s level of confidence in the social, psychological and intellectual domains. Personal, strategic and task knowledge enhances meaning and promotes the understanding of mathematics tasks during problem solving. The level of mathematics confidence can be described as either fearful or fearless when solving mathematics problems. Reflecting on achievement, with or without fear, is regarded as vital for higher-order reasoning by means of metacognitive processes, moderates mathematic confidence and fosters achievement. Although research in metacognition is increasing, literature involving mathematics confidence and reflection is scarce. The current study explores this link between reflection and mathematics confidence by focusing on metacognitive reflective skills. A mixed-method design consisting of positivist and interpretivist paradigms is employed. Merging of the quantitative and qualitative findings indicates that metacognitive strategies include reflecting on task, personal and strategic awareness. Regulating understanding, planning, monitoring and evaluating during problem solving occurs in accordance with these active internal processes. Mathematics confidence during problem-solving emerges from experiences relating to a variety of contexts involving mathematics. The findings confirm the dimensionality of mathematics confidence and present sources of participants’ mathematics confidence and metacognitive skills as reflected upon. The schools in the sample represent single-gender (all-boys and all-girls) and co-ed schools and findings should not be generalised to all schools. Reflection on metacognitive knowledge and regulation deepens the awareness of the level of confidence and promotes, to some extent, a knowing of knowledge. The study therefore evaluates the role reflection and mathematics confidence play during problem solving in senior phase mathematics. / Thesis (MEd (Mathematics Education))--North-West University, Potchefstroom Campus, 2013.

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