Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Mathematical connection has received increasing attention and become one major goal in mathematics education. Two types of connections are distinguished: (a) between-concept connection, which cuts across two concepts; and (b) within-concept connection, which links two representations of one concept. For example, from the theoretical probability to experimental probability is a between-concept connection; generate a graph of a circle from its equation is a within-concept connection. Based on the directionality, unidirectional and bidirectional connections are discerned. Bidirectional connection portrays a pair of a typical and a reverse connection. The benefits of connections, especially bidirectional connections, are widely endorsed. However, researchers indicated that students and even teachers usually make unidirectional connections, and underlying reasons may be the curriculum and cognitive aspects. Previous studies have reported differences in learning opportunities for bidirectional connections in U.S. and Chinese textbook problems, but few have explored the high school level. This study addressed this issue by comparing the directionality of mathematical connections and textbook-problem features in popular U.S. (the UCSMP series) and Chinese (the PEP-A series) high school mathematics textbook problems. The results indicated that the between-concept condition and unidirectional connections dominated textbook problems. Mathematical topic, contextual feature, and visual feature were most likely to contribute to different conditions of connections. Overall, problems dealing with quadratic relations from Chinese textbooks presented a vigorous network of more unique and total between-concept connections with balanced typical and reverse directions than the U.S. counterparts. Problems from U.S. textbooks showed a denser network of (a) within-concept connections in two topics and (b) between-concept connections in probability and combinatorics than the Chinese counterparts, but still exhibited an emphasis on specific concepts, representations, and directionality. The study reached a generalized statement that the new-to-prior knowledge direction was largely overlooked in textbook problems. The results have implications for adopting graph theory and Social Network Analysis to visualize and evaluate mathematical connections and informing mathematics teachers and textbook authors to pay attention to the new-to-prior knowledge connection.

Although an increasing number of research studies in mathematics education have begun focusing their efforts on mathematical modeling as a need for change to convey mathematical ideas beyond schools, there is not enough information about the nature of the teacher knowledge for effective use of modeling in mathematics teaching and how this knowledge evolves. The goal of this study is to investigate teachers&rsquo / evolving knowledge when they engage in professional development activities based on lesson study cycle from modeling perspective. Professional development program of this study included a cyclical process. Lasting a month, each cycle consisted of meeting before the implementation of the model eliciting activity, implementation of the activity and meeting after the implementation. The study took five months and was conducted in two public schools. The participants were four in-service mathematics teachers where two teachers were selected from each school by purposive sampling. The study was designed as case study. Data analyses were conducted during and after data collection and with two approaches as with-in case and cross-case analysis. As the professional development activities created learning environments for the teachers to develop their models for teaching mathematics from a modeling perspective, the results of this study showed that the professional development program used in the study had a positive effect on teachers&rsquo / evolving pedagogical content knowledge and pedagogical knowledge based on the theoretical and empirical backgrounds in the literature. Besides, implications, suggestions for professional development, for teachers and for further research are provided.

<p>Local and international pundits concur that education systems play a pivotal role in fostering and developing values in learners. In some countries, like South Africa, the values and rights&nbsp / enshrined in the Constitution and the Bill of Rights resonate in the Schools Act. As one of the concerns of education is nationbuilding, my study investigates if the integration of the values does&nbsp / achieve tolerance and co-operation in the classroom by examining how learners make sense of values in the Mathematical Literacy curriculum. While I firmly believe that educational&nbsp / institutions have a responsibility to integrate positive values into all aspects of the school curriculum, it is my contention that learners cannot fully benefit from values specifically related to the&nbsp / Mathematical Literacy curriculum itself on their own. All stakeholders in education need to come together to establish an informed understanding of policy documents and reconcile the complexities and challenges that surround the transmission of values, so that educators will be able to assist learners in a meaningful way. The classroom life of a learner is intricately woven&nbsp / with that of the teacher. In order to unearth the views and practices of learners and teachers, I adopted a participatory approach. The qualitative study that ensued was conducted in three Mathematics Literacy classrooms at secondary schools in Cape Town, South Africa. The observation sessions afforded me the opportunity to experience and appreciate how the teachers&nbsp / integrate values into the Mathematical Literacy lessons while observing learners‟ behaviour in the classroom. The interactions and interviews with both learners and teachers aided in further unravelling their understanding and implementation of values in the Mathematical Literacy lessons. For learners to develop into responsible, caring and morally just citizens who arecapable of critical thought, they&nbsp / equire an education that provides them with the necessary opportunities and tools to develop. Mathematical Literacy is able to provide learners with the relevant opportunities and thinking&nbsp / tools to construct meaning around moral concepts. I strongly believe that for learners to accomplish this goal, educators need to be appropriately capacitated to facilitate opportunities for their&nbsp / learners.I did not find any evidence in the literature that suggests a fail-safe theoretical approach to success in values education. I am of the opinion that for any measure of success in values education, a combination of these theories of learning and moral development has to be employed.</p>

<p>Local and international pundits concur that education systems play a pivotal role in fostering and developing values in learners. In some countries, like South Africa, the values and rights&nbsp / enshrined in the Constitution and the Bill of Rights resonate in the Schools Act. As one of the concerns of education is nationbuilding, my study investigates if the integration of the values does&nbsp / achieve tolerance and co-operation in the classroom by examining how learners make sense of values in the Mathematical Literacy curriculum. While I firmly believe that educational&nbsp / institutions have a responsibility to integrate positive values into all aspects of the school curriculum, it is my contention that learners cannot fully benefit from values specifically related to the&nbsp / Mathematical Literacy curriculum itself on their own. All stakeholders in education need to come together to establish an informed understanding of policy documents and reconcile the complexities and challenges that surround the transmission of values, so that educators will be able to assist learners in a meaningful way. The classroom life of a learner is intricately woven&nbsp / with that of the teacher. In order to unearth the views and practices of learners and teachers, I adopted a participatory approach. The qualitative study that ensued was conducted in three Mathematics Literacy classrooms at secondary schools in Cape Town, South Africa. The observation sessions afforded me the opportunity to experience and appreciate how the teachers&nbsp / integrate values into the Mathematical Literacy lessons while observing learners‟ behaviour in the classroom. The interactions and interviews with both learners and teachers aided in further unravelling their understanding and implementation of values in the Mathematical Literacy lessons. For learners to develop into responsible, caring and morally just citizens who arecapable of critical thought, they&nbsp / equire an education that provides them with the necessary opportunities and tools to develop. Mathematical Literacy is able to provide learners with the relevant opportunities and thinking&nbsp / tools to construct meaning around moral concepts. I strongly believe that for learners to accomplish this goal, educators need to be appropriately capacitated to facilitate opportunities for their&nbsp / learners.I did not find any evidence in the literature that suggests a fail-safe theoretical approach to success in values education. I am of the opinion that for any measure of success in values education, a combination of these theories of learning and moral development has to be employed.</p>

Dissertation (Ph.D.)--Texas A&M University, 2004. / Title from PDF t.p. (viewed on Sept. 9, 2008). "Major subject: Educational Psychology." Includes bibliographical references (p. 119-136).

Made available in DSpace on 2014-12-17T14:36:09Z (GMT). No. of bitstreams: 1 AlexandreVCD.pdf: 600061 bytes, checksum: 8975f6c52572ab1b6b9b4aa66b8dcb02 (MD5) Previous issue date: 2004-12-17 / This research argues about the mathematical knowledge built in the tradition of the cassava flour production, seeking to analyse these mathematical knowledge in the perspective of the categories of time and measure, built and practiced in the flour production, located in Serra do Navio and Cal?oene, in Amap? - Brazil. The following work discuss the identification and the description of the mathematics during the production activities of the flour, where is presented elements related to generation and transmission of the traditional knowledge, which is the basis for maintenance of the tradition of the flour, characterizing the research as an Ethnomathematic study. The methodological procedures highlight ethnographical techniques and elements that characterize the participating observation. The results obtained showed us that the flour workers articulate some length, area and volume measure due to own and traditionally acquired systems, which is apprehended and countersigned by other kind of culturally established system; thus they relativism the measures systems and the official calendars. And it lifts as one of the main proposal that the academic mathematics and the tradition establish knowledge make conjunction of the both knowledge, that is important for a possible reflection and application in the construction of a pedagogical practice in mathematical education, trying to establish points of socio-economic and cultural mark / A presente pesquisa discute sobre os saberes matem?ticos constru?dos na tradi??o da produ??o da farinha de mandioca, buscando analisar esses saberes matem?ticos sobre a perspectiva das categorias do tempo e medida, constru?dos e praticados na produ??o de farinha, localizados nos Munic?pios da Serra do Navio e Cal?oene, no Estado do Amap?/Brasil. O seguinte trabalho faz um apanhado na identifica??o e na descri??o da matem?tica durante as atividades de produ??o da farinha e que nessas etapas est?o presentes elementos relacionados ? gera??o e a transmiss?o de um saber tradicional, condicionantes b?sico para manuten??o da tradi??o da farinha, caracterizando a pesquisa como um estudo de etnomatem?tica. Os procedimentos metodol?gicos destacam base das t?cnicas etnogr?ficas e de elementos que caracterizam a observa??o participante. Os resultados obtidos nos mostraram que os trabalhadores de farinha articulam algumas medidas de comprimento, de ?rea e de volume em decorr?ncia de sistemas pr?prios e tradicionalmente adquiridos, como tamb?m o tempo, apreendidos e referendados por outro tipo de sistema culturalmente estabelecido, deste modo relativizando os sistemas de medidas e calend?rios oficiais. Levantando como uma das principais propostas que a matem?tica acad?mica e os saberes da tradi??o estabelecem uma conjun??o desses conhecimentos, importantes para uma poss?vel reflex?o e aplica??o na constru??o de uma pr?tica pedag?gica em educa??o matem?tica, procurando estabelecer pontos de cunho s?cio-econ?mico e cultural

The thesis is the result of four years' work in mathematical education in Papua New Guinea. The first two years were spent in setting up a new Mathematics Education Centre at the University of Technology, Lae. A broad brief enabled the author to seek out the most crucial needs for the country and these appeared to lie in the area of basic number skills. Assessments of the situation and contributions to a changing attitude are described. This part of the thesis concludes with a critique of the role of a Mathematics Education Centre in a Third World country. The work had led to a conclusion that one of the priorities in mathematical education for the country lay in some form of adult numeracy campaign. At the same time the Department of Commerce had identified 'numeracy' as one of the prime needs for successful business development in Papua New Guinea. The author was therefore invited to spend a further two years in seeking to resolve this problem. The cheap long-life battery calculator became available at this point in time and provided the means for a possible solution. Its potential was appreciated and a grant was given from the Prime Minister's Nonformal Education Sectoral Fund to enable the author to research into ·the possibilities of adult numeracy teaching in the villages where 85% of the population lives. Detailed reports of the eighteen field tours undertaken are included in an appendix, together with some of the material specifically developed for the purpose. In this thesis the problems of organising an adult numeracy campaign in a country with poor communications and a limited budget are also considered. The thesis concludes with an attempt to identify the new style of teaching that will be required when a realistic use of the calculator is accepted as a normal part of the post-secondary and non-formal education system. This new style is seen to iriclude elements of the number skill teaching that was the prime concern of the first two years. References are made to the relatively few attempts to. teach adult numeracy in the Third World and also to some attempts in the developed world to meet the challenge presented by the incorporation of the calculator into the formal system of education.

No description available.

No description available.