Thesis (Ph.D.)--Indiana University, School of Education, 2005. / Source: Dissertation Abstracts International, Volume: 66-01, Section: A, page: 0123. Adviser: Peter W. Kloosterman. Title from dissertation home page (viewed Oct. 11, 2006)

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 162-176).

Resumo: Neste trabalho caracterizamos duas práticas educacionais. De um lado, o ensino de matemática como sendo toda prática que procura se justificar através da existência de uma única matemática de caráter universal e a priori, e que atribui para si, como missão, a transmissão dessa matemática da forma mais precisa possível. Diante desta concepção nós propomos que a história da matemática para o ensino de matemática tem como pano de fundo uma matemática a priori e que, neste caso, os "fatos históricos" acabam conectados por uma lógica imposta, de forma implícita, que em última análise está fundamentada em uma concepção de matemática. De outro lado, toda prática que considera determinar e ser determinada por uma concepção de matemática é educação matemática (EM). Assim, a EM considera suas práticas e a matemática como partes de uma dialética. Na EM os estudos de História da Matemática se justificam como um espaço que considera a existência de distintas concepções de matemática. Finalmente, apresentamos um contexto histórico para análise matemática (CHAM) como exemplo de considerações de história da matemática, do ponto de vista da EM caracterizada por nós. / Abstract: In this paper we understand two different educational practices. On one hand the mathematics teaching as all practice that justify itself because one believe there is a mathematics which is universal and a priori. This way of teaching consider that its mission is merely the transmission of the universal mathematics as accurately as possible. In this sense the history of mathematics as tied up to the concepts and to the logic of this priori science. On the other hand the Mathematics Education as a practice that consider that mathematics is engendered dialectically and because of this take into account different mathematical conceptions. In this sense the studies of mathematics history present several conceptions of mathematics. In this paper we also present a historical context for mathematical analysis (HCMA) as an example of how to understand the history of mathematics from the perspective of mathematics education. / Orientador: Rosa Lúcia Sverzut Baroni / Coorientador: Vanderlei Marcos do Nascimento / Banca: Romulo Campos Lins / Banca: Renata Cristina Geromel Meneghetti / Mestre

Thesis (Ed.D.)--Boston University.

Thesis (Ed.M.)--Boston University / The primary purpose of constructing a test on informal geometry is to provide the eighth-grade mathematics teacher with an objective means of measuring the achievement of his students in geometry. A secondary purpose is to explore the possibility that this test alone, or in conjunction with other criteria, might have value in predicting the degree of success of a student in demonstrative geometry.

Thesis (Ed.M.)--Boston University

Thesis (Ed.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The purpose of this study was to investigate how advanced mathematics students in the eighth, tenth and twelfth grades used inferential reasoning in the solution of problems that required knowledge of elementary number theory. Inferences were classified based on the level of ambiguity involved, simple or complex; the number of pieces of information used, single-item or combined-item; the type of inference, simple single-item, simple combined-item, complex single-item or complex combined-item; and the purpose of the inference (seventeen inference codes were identified). The use of inferences classified by type was of primary interest. Also investigated were the procedures subjects employed to obtain, maintain and control information. Each of the 18 subjects, 6 from each grade, solved ten different problems in two to three sessions. Each problem involved the identification of a "mystery" whole number in the range of 1 to 1000 on the basis of clues that were provided. As the subjects interacted with the computer program that presented the problems, they were asked to "think aloud." Using transcribed, typewritten protocols and all paper-pencil notations recorded by subjects, protocols were coded employing a coding scheme developed by the investigator [TRUNCATED] / 2031-01-02

Thesis (M.A.)--Boston University / This study proposed to determine by experiment the effect of the study of symbolic logic on the student's achievement in geometry. Its secondary purpose was to test the influence of the study of logic on the student's ability to solve non-mathematical problems. As a means of teaching the nature and value of proof, the study presented a unit on symbolic logic taught in conjunction with geometry. Current stress on concept as well as content, sustained interest in "the nature of proof," emphasis on the "foundations" in mathematics, and experiments with symbolic and Aristotelian logic all served to suggest the vitality of the problem and to set the direction for the experiment [TRUNCATED]

Through philosophical means, this thesis investigates the question: What mathematics can mean to students philosophically and psychologically? It is reasonable to assume that students may touch upon philosophical issues in trying to make sense of mathematics, since, in a sense, all individuals philosophise while searching for meaning in their own activities. Moreover, the existing literature indicates a substantial gap in our understanding of the meaning of mathematics and its philosophy in education. The thesis is based on a hermeneutical perspective. In this context, in-depth interviews were conducted with 17-year-old students in a Greek school. This method allowed me to obtain data which illuminated the objective meaning of students’ philosophical beliefs by way of the subjective, psychological meaning that they attributed to mathematics. The sample consisted of 28 students comprising both sexes and all levels of engagement with mathematics. The main issues that were examined were: whether mathematics exists; whether mathematical knowledge is certain, objective, true and immutable; whether mathematics consists of rules; and whether mathematical knowledge is based on logic or on experience. A thematic analysis helped me to move within the hermeneutical circle of understanding. As well as organising the objective meaning of students’ philosophical beliefs into themes and subthemes, analysis showed how for each student, there was an emergent a story which illustrating how they could combine such beliefs in order to find subjective meaning in mathematics. The most important finding of the study suggests that the students’ beliefs were influenced by common sense, and that students were able to find positive subjective meaning in mathematics when they were able to relate aspects of mathematical reasoning (e.g. certainty, subjectivity, rules, experience) to the operation of their everyday common sense. The study therefore shows that discussing philosophical issues, and in particular mathematical reasoning, could be of considerable benefit for students learning mathematics.

<p> In Florida, passing the Algebra I end-of-course examination (EOCE) is a graduation requirement. The test measures knowledge of basic algebra. In spring 2015, the Department of Education introduced a different version of the test. For the first two administrations of the new test, the failure rate for 9th-grade students in the state was almost 50%. In contrast, the failure rate for students in the school where this study was implemented exceeded 70%. The purpose of this study was to determine the outcome of small group intervention focusing on operations with rational numbers of high school students&rsquo; performance on the Algebra I EOCE. </p><p> After analyzing several potential methods of instruction, small group instruction with the incorporation of the use of manipulatives, visuals, and guided inquiry was selected. In addition, the focus of the study was chosen to be operations with rational numbers, an area many researchers have identified as critical for student understanding of algebraic concepts. Twenty students from the target population of 600 10th and 11th grade students volunteered to participate in the study. These participants received three to six small group instruction sessions before retaking the test. In Sept 2016, all the students in the target population were administered the Algebra I EOCE again. A t-test yielded no significant difference in the learning gains of those who participated in the study and the other students in the target population. The implications of the results were that the interventions had no significant impact on student achievement. A possible reason for the lack of success could have been that six intervention sessions were not enough to produce significant results. It is recommended that future research includes a substantially larger number of interventions.</p><p>