Thesis (doctoral)--Universität Zürich. / Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Dept. of Psychology, Dec. 2003. / Includes bibliographical references. Also available on the Internet.

Solving proportion problems in schools is a very difficult task for most children. Too often children are taught to use techniques for solving fractions when working with ratio and proportion problems. Although these techniques may prove useful for obtaining a solution to a proportion problem, they do not provide rich learning opportunities for students to construct proportional relationships. Individual interviews, problem solving episodes, and personal journals were the primary tools used in collecting data for this study. The problem solving episodes became the key components in observing and interacting with the participants as they solved ratio and proportion problems. The researcher found that individuals must have many elaborated constructions to solve proportion tasks. Without these elaborated constructions the individual is unable to effectively coordinate the information needed to solve proportion tasks. That is, the individual is unable to reason proportionally. Another outcome of this study was the importance of finding meaningful and doable proportion tasks for the informants to complete. Unexpected outcomes of the study included the effect of engaging in problem solving on the identity of the child and the role of language in giving meaning to the tasks. / Typescript. / "Summer Semester, 1992." / "Submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: Grayson H. Wheatley, Professor Directing Dissertation. / Includes bibliographical references.

Thesis (M. Ed.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 70-75).

Thesis (M.Ed.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 70-75). Also available in print.

No description available.

No description available.

published_or_final_version / Education / Master / Master of Education

Proportionality is the content domain of mathematics that is rooted in ratio and proportion. It is believed to be vital for problem solving and reasoning, which are key cognitive domains of mathematics teaching and learning. Hence, ratio and proportion forms part of curricula for all countries. Studies carried out in different parts of the world found that while learners can do simple and routine manipulations of ratio and proportion, they struggle to solve problems that involve these concepts. Researchers apportion the blame for this to the strategies that learners use to solve the problems. Researchers found that learners use flawed strategies due to misconceptions that learners have on ratio and proportion. The purpose of the study is to explore learner errors and misconceptions on ratio and proportion. A test that comprised of questions that are appropriate to the National Curriculum Statement (NCS), for General Education and Training (GET) band, was used to collect data. Items in the instrument were selected and adapted from a tool used in Concepts in Secondary Mathematics and Science (CSMS) study. The participants in the study are 30 Grade 9 learners from a rural school in KwaZulu-Natal (KZN). The findings of the study are that learners have a limited knowledge and understanding of ratio and proportion, hence their performance in items on the topic is poor. A great proportion of the learners have serious misconceptions of ratio and proportion. They use incorrect strategies to solve problems on ratio and proportion that produce errors. The errors and misconceptions they exhibit are not different from those observed by similar studies conducted in other parts of the world. The study recommends a structured focus on ratio and proportion because the topic is fundamental to proportional reasoning. It recommends clarity for teacher trainers, textbook writers and teachers on what learners need to learn on ratio and proportion. It recommends serious exploration of errors and misconceptions on ratio and proportion, and a teaching approach that considers errors and misconceptions as opportunities for learning. / Thesis (M.Ed.)-University of KwaZulu-Natal, Edgewood, 2012.

Orientadores: Itala Loffredo D'Ottaviano, Jairo Jose da Silva / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-08-11T06:06:49Z (GMT). No. of bitstreams: 1 Bertato_FabioMaia_D.pdf: 35247388 bytes, checksum: fe87607b79cfaee008394ba92d66e341 (MD5) Previous issue date: 2008 / Resumo: Luca Pacioli (1445 - 1517), famoso matemático renascentista, escreveu "Summa di Arithmetica Geometria Proportione e Proportionalita" (1494), o que podemos considerar a obra que sintetiza todo o conhecimento matemático europeu acumulado ate 1500. Não obstante, sua outra obra,"De Divina Proportione" (1509), e a que contem, dentre as teorias das proporções, aqueles temas que mais lhe interessavam e que ele considerava "secretissima scientia": a "Divina Proporção", isto e, a "razão áurea". Os resultados contidos na obra, o papel que propunha para a Matemática ante as demais áreas do saber, bem como todas as suas concepções místicas, muito atraíram a atenção de artistas, nobres e intelectuais. Nosso trabalho consiste de uma tradução anotada e comentada da referida obra, a partir do manuscrito que se encontra na Biblioteca Ambrosiana de Milão / Abstract: Luca Pacioli (1445 - 1517), famous Renaissance mathematician, wrote "Summa de Arithmetica Geometria Proportione e Proportionalita" (1494). One can consider Summa a kind of encyclopedia in which Pacioli treats of almost all mathematical knowledge accumulated in Europe until the early 16th century. However, his other work "De Divina Proportione" (1509) contains, among the Theories of Proportions, the most important to him: the "Divine Proportion", i. e., the "Golden Ratio". The proposed role of Mathematics in respect of the others branches of knowledge, the mystical conceptions and the mathematical results presented in De Divina Proportione had attracted the attention of artists and intellectuals. This thesis consists of an Annoted and Commented translation into Portuguese of De Divina Proportione, based on the manuscript that belongs to Biblioteca Ambrosiana di Milano / Doutorado / Doutor em Filosofia